TEAS 7 study guide
Learn the methods, work through examples and use short drills to find what needs another look.
Lessons and worked examples
Open a lesson for the method, an example and mistakes to watch for. Use the drill after studying, then return to the explanation for anything you missed.
Key ideas and details
Practice this topicFind the main idea and summarize
A useful summary preserves the passage’s central point and its most important support. It leaves out minor examples, repetition and your own opinion.
Method
- Name the topic, then ask what the author says about that topic. “Community gardens” is a topic; “community gardens need shared maintenance plans to last” is a main idea.
- Give each paragraph a short label. Look for the idea that explains why those paragraphs belong together.
- A summary should cover the whole selection. Reject a choice that accurately describes only one example or introduces a claim the author never makes.
Common mistakes
- Choosing a true detail instead of a summary.
- Turning a cautious conclusion into an absolute claim.
- Adding an explanation based on personal experience rather than the passage.
Remember: Topic + main point + essential support; no new information.
Worked example
A library added evening hours after a survey. Evening visits increased, but daytime visits fell slightly. Staff will review the total visits and staffing costs before deciding whether to keep the hours. Which summary best fits?
- Identify the change: the library tested longer hours.
- Include the mixed result: evening visits increased while daytime visits fell slightly; the passage does not establish whether the same visitors changed their visiting times.
- Preserve the open decision: the library will evaluate use and cost, rather than declaring the trial a success or failure.
Answer: The library is evaluating whether the benefits of its evening-hours trial justify its costs.
Infer meaning without inventing facts
An inference connects clues the author provides. It can go beyond a sentence’s literal wording, but it cannot depend on facts that the passage never establishes.
Method
- Separate what is stated from what is strongly implied. A person checking the clock repeatedly may be concerned about time; the text has not necessarily shown that the person will miss a train.
- Use several clues together when possible. Actions, contrast, repeated details and the ending can reveal an unstated concern or message.
- Match the strength of the answer to the evidence. “May” or “likely” often fits limited evidence better than “must,” “always” or “only.”
Common mistakes
- Picking a possible event that is not supported.
- Assuming a character’s private feelings without behavioral or verbal evidence.
- Importing outside knowledge when the passage supplies the rules.
Worked example
Before the community meeting, Noor moved the chairs into a circle and put the microphone away. “Everyone should be able to respond to everyone else,” she said. What does this suggest about her goal?
- The circle makes participants face one another.
- Removing the microphone reduces the emphasis on one speaker.
- Her statement directly favors exchange among participants.
Answer: Noor wants a discussion in which participants interact, rather than a presentation by one speaker.
Follow conditions and written directions
Directions often combine a normal sequence with exceptions. Identify which conditions apply before deciding the next step.
Method
- Read words such as before, after, unless, only if and except carefully. They change which action is allowed.
- Convert the instructions into a short ordered list. If a condition branches the process, keep the branches separate.
- Check whether the question asks for the first step, the next step or the final outcome. An action can be required eventually but still be wrong as the next action.
Common mistakes
- Following the standard sequence while ignoring an applicable exception.
- Treating a recommendation as a requirement.
- Doing a later valid step before its prerequisite.
Remember: Identify the condition, then follow that branch.
Worked example
To borrow a tool, show your membership card, then sign the loan form. If the tool has a battery, ask a staff member to test it before signing. Ari has shown a card and is borrowing a cordless drill. What must Ari do next?
- The membership-card step is complete.
- The drill meets the battery condition.
- The battery test must happen before signing, so the normal sequence has an extra step.
Answer: Ask a staff member to test the battery.
Locate the detail the question asks for
Detail questions reward precise retrieval. Find the relevant passage, then check the answer’s people, dates, quantities and qualifiers against it.
Method
- Use a distinctive word from the question to find the relevant sentence, but expect the correct answer to paraphrase it.
- Read the surrounding sentence too. A qualifier or exception may be separated from the main statement.
- Distinguish similar categories: registered versus attended, available versus reserved, proposed versus approved, and some versus all.
Common mistakes
- Selecting a number found nearby but attached to a different category.
- Confusing an initial rule with a later exception.
- Choosing an inference when the question asks what is explicitly stated.
Worked example
A notice says: “The tour admits 24 visitors. Online registration closes Thursday. Six places are reserved for walk-in visitors on Saturday; unused reserved places open to the waiting list at 9:15.” How many places are initially reserved for walk-ins?
- Find the sentence containing “reserved for walk-in visitors.”
- It assigns six places, not the tour’s total capacity of 24.
- The later release rule does not change the initial reservation.
Answer: Six places.
Read charts, tables and visual information
A visual is a source with its own title, labels, units and limits. Read those before interpreting a trend or comparing values.
Method
- Identify what each axis, row, column, symbol or shaded region represents. Check the unit and time period.
- Compare like with like. Counts and percentages answer different questions, and a larger group can have more events but a smaller rate.
- Use the caption and footnotes. A missing observation is not automatically zero, and a chart alone rarely establishes a cause.
Common mistakes
- Reading the largest count as the largest rate.
- Ignoring a scale break or a nonzero graph baseline.
- Claiming one variable caused another because they changed together.
Worked example
Which workshop has the highest attendance rate?
| Workshop | Registered | Attended |
|---|---|---|
| A | 20 | 18 |
| B | 40 | 30 |
| C | 30 | 24 |
- The question asks for a rate, so divide attended by registered.
- A: 18/20 = 90%; B: 30/40 = 75%; C: 24/30 = 80%.
- Compare the percentages rather than the attendance counts.
Answer: Workshop A, at 90%, despite workshop B having more attendees.
Reconstruct a sequence of events
The order in which events are narrated is not always the order in which they happened. Build a timeline using explicit time markers and dependencies.
Method
- Notice earlier, later, meanwhile, the following week and had already. These signals may shift the timeline.
- An event can be described first because it is important, even if it happened last.
- For procedures, use prerequisites as well as dates. For stories, distinguish a character’s recollection from present action.
Common mistakes
- Using paragraph order as chronological order.
- Confusing a decision with its later implementation.
- Assuming two events were simultaneous because they appear in one sentence.
Worked example
The article opens with the new bridge’s June opening. It then explains that the design was approved in January and that a February inspection led to a revised railing, which was installed in April. What happened immediately after the inspection?
- Arrange the dated events: January approval, February inspection, April railing installation, June opening.
- The inspection led to the railing revision.
- The opening appears first in the article, but it happened last.
Answer: The railing design was revised; the revised railing was later installed in April.
Craft and structure
Practice this topicSeparate fact, opinion and bias
A factual claim can be checked against evidence. An opinion expresses a judgment or preference. Bias appears when wording or evidence selection systematically favors one view.
Method
- A claim can be factual in form and still be false; “factual” does not mean the passage has proved it.
- Evaluative words such as best, ugly, sensible and wasteful often express opinion unless a measurable standard is defined.
- Look for loaded labels, stereotypes, one-sided examples and omitted counterevidence. A disclosed viewpoint is not by itself proof that every statement is unreliable.
Common mistakes
- Treating a confident tone as evidence.
- Calling every statement by a biased writer false.
- Assuming a prediction is a verified fact because it includes a number.
Worked example
An editorial says, “The council allocated $40,000 to the plaza. This foolish project will appeal only to people who have nothing useful to do.” Which part is a checkable factual claim?
- A budget record could verify the $40,000 allocation.
- “Foolish” is an evaluation without a specified standard.
- The description of visitors is a dismissive generalization rather than established evidence.
Answer: The council allocated $40,000 to the plaza.
Use context to interpret words and phrases
Choose the meaning that fits this passage, not simply the most familiar dictionary meaning. Nearby contrasts, examples and consequences supply clues.
Method
- Try replacing the word with each proposed meaning. The sentence and its surrounding paragraph should still make sense.
- Contrast signals such as although, but and unlike often reveal what a word does not mean.
- A phrase may be figurative. “A narrow window” can refer to a short opportunity rather than a physical opening.
Common mistakes
- Choosing a familiar meaning that contradicts the sentence.
- Ignoring contrast words.
- Interpreting a figurative phrase literally.
Worked example
“The committee’s initial enthusiasm was tempered by the repair estimate; members still supported the project, but agreed to reduce its size.” What does tempered mean here?
- The members did not abandon the project.
- Their enthusiasm became more restrained after they saw the cost.
- The next clause confirms a moderated response: a smaller project.
Answer: Moderated or reduced in intensity.
Identify why the author wrote the text
Author purpose is the effect the writer aims to have on the reader: explain, instruct, persuade, describe or entertain. Many texts have more than one feature, so choose the main purpose.
Method
- Consider the text’s overall structure and ending, not just its topic. Two texts about recycling can serve different purposes.
- A call to action and supporting reasons suggest persuasion. Ordered steps suggest instruction. An explanation of how something works suggests information.
- Ask whether an anecdote supports a larger argument. An entertaining example does not necessarily make entertainment the main purpose.
Common mistakes
- Choosing a purpose based only on the subject.
- Confusing the author’s purpose with a character’s goal.
- Allowing one descriptive sentence to outweigh the rest of the text.
Worked example
A brochure explains that evening classes are available, lists three benefits of enrolling and ends with “Reserve a place by Friday.” What is its primary purpose?
- The class facts provide background.
- The benefits support a favorable evaluation.
- The closing request identifies the action the writer wants readers to take.
Answer: To persuade readers to enroll in the classes.
Recognize perspective and tone
Perspective concerns the writer’s position or way of seeing an issue. Tone is the attitude conveyed by word choice. Use both stated judgments and subtle qualifiers as evidence.
Method
- Separate who is speaking from whose view is being quoted. Reporting another person’s opinion does not establish agreement.
- A writer can support an idea while acknowledging limits. Words such as promising, provided that and cautiously often signal conditional approval.
- Choose a tone of the right strength. Concerned is not necessarily hostile; appreciative is not necessarily uncritical.
Common mistakes
- Attributing a quoted opponent’s position to the author.
- Ignoring a qualifying clause.
- Choosing an extreme emotional label for restrained wording.
Worked example
“The trial offers a promising way to reduce waiting, although two busy days are too little evidence for a permanent schedule change.” How would you describe the writer’s perspective?
- “Promising” expresses a favorable response.
- The qualification limits what the evidence justifies.
- The writer supports further consideration, not an immediate permanent change.
Answer: Cautiously supportive of the trial.
Integration of knowledge and ideas
Practice this topicSupport predictions with textual evidence
A justified prediction follows from the passage’s conditions, patterns or causes. Identify the evidence first, then choose the conclusion it supports most directly.
Method
- Connect the evidence to the claim explicitly: “Because these conditions remain in place, this outcome is likely.”
- Distinguish a pattern from a guarantee. Repeated past events may support a prediction without proving it will happen every time.
- For select-all-that-apply questions, evaluate each statement independently. Do not select an unsupported claim just because it sounds compatible with the passage.
Common mistakes
- Making a prediction unrelated to the stated change.
- Turning a repeated pattern into certainty.
- Selecting an answer that requires an additional unstated cause.
Worked example
At the last three plant exchanges, the tables nearest the entrance ran out first. Next month the organizers will put duplicate displays at both entrances and direct visitors to each. If visitors follow those directions, which outcome is most reasonable to predict?
- The repeated problem is concentrated demand at one entrance.
- The new plan spreads equivalent displays and visitors between two entrances.
- The directly supported prediction concerns a more even distribution of visitors, not a guaranteed increase in total attendance.
Answer: Demand is likely to be spread more evenly across the displays.
Compare themes and ideas across texts
Compare what each text says about a topic, rather than merely noting that both mention it. A shared theme may appear in different settings, examples or genres.
Method
- Write a short statement of each text’s main idea or theme. A theme is a broader message, not just a subject such as friendship.
- Identify the exact relationship: agreement, contrast, different emphasis, or an exception that qualifies a general claim.
- Support both halves of a comparison. A choice can accurately describe the first text but misrepresent the second.
Common mistakes
- Naming a shared topic without a shared message.
- Assuming both authors reach the same conclusion because they discuss the same issue.
- Applying a detail from one text to the other.
Worked example
Text A describes an apprentice who improves after accepting a colleague’s corrections. Text B describes a gardener who changes a failing planting plan after listening to neighbors. What theme is shared?
- The settings and tasks differ.
- In both accounts, a person revises an approach after receiving useful input.
- The shared message concerns willingness to learn from others, not the superiority of either occupation.
Answer: Being open to other people’s feedback can help someone improve.
Test an argument’s evidence and reasoning
An argument links a claim to reasons and evidence. Evaluate whether the evidence is relevant, sufficient and fairly interpreted, and whether another explanation remains possible.
Method
- Identify the conclusion before evaluating support. An example can illustrate a claim without showing how common it is.
- Look for missing comparisons, selective samples and alternative causes. A change that happened after a policy is not automatically caused by that policy.
- Distinguish weakening an argument from proving it false. A limitation may reduce confidence without establishing the opposite conclusion.
Common mistakes
- Assuming correlation proves causation.
- Rejecting an argument merely because you dislike its conclusion.
- Saying limited evidence proves the opposite claim.
Worked example
A shop says its new display caused sales to rise because sales were higher the following weekend. That weekend was also the town’s annual festival. What is the main weakness in the claim?
- The claim assigns the increase specifically to the display.
- The festival could independently bring more shoppers.
- Without a suitable comparison, the evidence cannot separate the effects of the display and the festival.
Answer: The argument overlooks another plausible cause of the sales increase.
Combine sources without losing their limits
When a question uses a passage plus a table, notice or second account, gather the relevant evidence from each. A correct synthesis respects differences in dates, populations, definitions and reliability.
Method
- Identify each source’s role. A schedule shows planned hours; a log shows what happened; an advertisement may emphasize benefits.
- Check that quantities use the same definitions before comparing or combining them. “Booked” and “attended” are not interchangeable.
- When sources conflict, ask whether timing, scope or a later correction explains the difference. Favor direct, relevant evidence over unsupported authority.
Common mistakes
- Using only one source when the question requires both.
- Comparing incompatible time periods or populations.
- Treating a later update and an earlier notice as equally current.
Remember: Match the source, scope and date before combining evidence.
Worked example
A notice says a grant requires workshops to have at least 80% attendance. Use the table to identify the workshop that meets this attendance requirement.
| Workshop | Registered | Attended |
|---|---|---|
| First aid | 25 | 20 |
| Map reading | 20 | 15 |
| Bike repair | 30 | 21 |
- The notice supplies the threshold: at least 80%.
- The table supplies registered and attended counts.
- First aid: 20/25 = 80%; map reading: 75%; bike repair: 70%. “At least” includes exactly 80%.
Answer: First aid meets the attendance requirement. The other two workshops fall below the stated threshold.
Numbers and algebra
Practice this topicFractions, decimals and percentages
The same quantity can be written in different forms. Convert to the form that makes the calculation easiest.
Method
- A fraction means numerator divided by denominator.
- Multiply a decimal by 100 to express it as a percentage; divide a percentage by 100 to get a decimal.
- Simplify fractions by dividing numerator and denominator by the same nonzero number.
Common mistakes
- Writing 0.4375% instead of multiplying by 100.
- Rounding a decimal too early when an exact value is available.
Remember: Percent means per hundred.
Worked example
Write 7/16 as a decimal and a percentage.
- Divide 7 by 16 to obtain 0.4375.
- Multiply 0.4375 by 100 to obtain 43.75.
Answer: 0.4375 and 43.75%.
Calculate with rational numbers
Use operation order and sign rules with integers, fractions and decimals.
Method
- Work inside parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.
- Add fractions using a common denominator. Dividing by a nonzero fraction means multiplying by its reciprocal.
- Multiplying or dividing two negative numbers gives a positive result; unlike signs give a negative result.
Common mistakes
- Adding numerators and denominators separately.
- Completing addition before multiplication.
- Dropping a negative sign when using the calculator.
Worked example
Evaluate −3/4 + 2 × (5/8).
- Multiply first: 2 × 5/8 = 10/8.
- Rewrite −3/4 as −6/8.
- Add: −6/8 + 10/8 = 4/8 = 1/2.
Answer: 1/2, or 0.5.
Compare and order numbers
Translate mixed representations into comparable values and place them on a number line.
Method
- A number farther right on the number line is greater.
- For negative numbers, the value closer to zero is greater.
- Convert fractions and percentages to decimals, or use a common denominator when exact comparisons are easier.
Common mistakes
- Treating a larger negative magnitude as a larger value.
- Comparing digits without first matching fractions, decimals and percentages.
Worked example
Order −0.35, −2/5, 3/8 and 36% from least to greatest.
- Convert −2/5 = −0.4, 3/8 = 0.375 and 36% = 0.36.
- The negative values come first: −0.4 < −0.35.
- Then 0.36 < 0.375.
Answer: −2/5, −0.35, 36%, 3/8.
Solve one-variable equations
Keep an equation balanced while isolating the unknown.
Method
- Distribute multiplication and combine like terms before isolating the variable.
- Apply the same operation to both sides.
- Substitute your answer into the original equation to check it.
Common mistakes
- Distributing to only the first term in parentheses.
- Changing one side without making the same change on the other side.
Worked example
Solve 3(2x − 5) = 4x + 7.
- Distribute: 6x − 15 = 4x + 7.
- Subtract 4x from both sides: 2x − 15 = 7.
- Add 15, then divide by 2: 2x = 22, so x = 11.
- Check: 3(22 − 5) = 51 and 44 + 7 = 51.
Answer: x = 11.
Set up multistep word problems
Identify what is being asked, keep the units visible, and choose operations in a logical order.
Method
- List the known quantities and name the unknown.
- Calculate intermediate quantities before combining them.
- When buying or packing whole items, decide whether the situation requires rounding up or down.
Common mistakes
- Buying packs for all 95 worksheets instead of only the shortage.
- Rounding 6.5 down when it would leave too few copies.
Worked example
A class needs 95 worksheets. There are already 17 copies, and new copies come in packs of 12. How many packs are needed?
- Find additional copies needed: 95 − 17 = 78.
- 78 ÷ 12 = 6.5 packs.
- Six packs supply only 72 copies, so round up to 7 whole packs.
Answer: 7 packs.
Percentage changes and original amounts
Always identify the base quantity: a percentage describes a fraction of something.
Method
- Percent change = change ÷ original amount × 100.
- An increase of p% multiplies by 1 + p/100; a decrease multiplies by 1 − p/100.
- To recover an original amount, divide the final amount by the percentage multiplier. Apply consecutive changes in sequence.
Common mistakes
- Adding 30% of the discounted price back to it.
- Adding consecutive discount rates instead of multiplying their remaining fractions.
Worked example
A jacket costs $63 after a 30% discount. What was its original price?
- After a 30% discount, 70% of the original price remains.
- Let the original price be x: 0.70x = 63.
- Divide: x = 63 ÷ 0.70 = 90.
Answer: $90.
Estimate and check reasonableness
Use nearby convenient values to predict the size of a result, then round the final calculation as requested.
Method
- Choose rounding that keeps the estimate useful for the decision.
- Identify whether you need an approximate result, an upper bound or a lower bound.
- Keep extra digits during calculations and round at the end unless instructed otherwise.
Common mistakes
- Presenting an estimate as the exact answer.
- Rounding repeatedly at intermediate stages and accumulating error.
Worked example
Estimate the cost of 19 items at $4.85 each by rounding the quantity to the nearest ten and the price to the nearest dollar.
- Round 19 to 20 and $4.85 to $5.
- Multiply 20 × $5 = $100.
- Both values were rounded upward, so this estimate is above the exact $92.15.
Answer: About $100.
Use proportions
A proportion states that two ratios are equal. Match corresponding quantities before solving.
Method
- Keep units in the same relative positions in both ratios.
- Scale both quantities by the same factor when the relationship is direct.
- Use inverse reasoning when a fixed job takes less time with more equal-rate workers; the number of workers times time stays constant.
Common mistakes
- Putting blue/white on one side and white/blue on the other.
- Assuming every relationship is direct, even when increasing workers reduces time.
Worked example
A paint mixture uses 3 cups of blue paint for every 8 cups of white. How much blue is needed for 28 cups of white?
- Match blue to white: 3/8 = x/28.
- The white quantity is multiplied by 28/8 = 3.5.
- Multiply blue by the same factor: 3 × 3.5 = 10.5.
Answer: 10.5 cups of blue paint.
Ratios and rates
A ratio compares quantities; a rate compares quantities with different units. Unit rates make alternatives easy to compare.
Method
- For a part-to-part ratio, add the ratio parts before dividing a total.
- Divide by the relevant quantity to obtain a rate per one unit.
- Track compound units such as miles per hour and dollars per kilogram.
Common mistakes
- Dividing the total by 8 instead of by 9.
- Reversing a unit rate, such as hours per mile versus miles per hour.
Worked example
A 63-person group has a student-to-tutor ratio of 8:1. How many tutors are there?
- The ratio has 8 + 1 = 9 total parts.
- Each part represents 63 ÷ 9 = 7 people.
- Tutors occupy one part.
Answer: 7 tutors.
Model constraints with algebra
Translate a scenario into an expression, equation or inequality, solve it, and interpret the result in context.
Method
- Name the variable and include fixed and per-unit quantities separately.
- At most means ≤; at least means ≥; fewer than means <.
- Reverse the inequality sign when multiplying or dividing by a negative number. Apply whole-number restrictions after solving.
Common mistakes
- Leaving the fixed fee out of the model.
- Rounding a spending limit upward to an unaffordable whole number.
Worked example
A rental costs $18 plus $7 per hour. With a $60 budget, what is the greatest whole number of hours affordable?
- Let h be rental hours: 18 + 7h ≤ 60.
- Subtract 18: 7h ≤ 42.
- Divide by 7: h ≤ 6.
- Six hours costs exactly $60 and is allowed.
Answer: 6 hours.
Measurement and data
Practice this topicRead tables, charts and graphs
Check labels, scales and denominators before interpreting a display.
Method
- Read the title, axis units, legend and any scale multiplier.
- Distinguish a count from a percentage, and a cumulative total from the change during an interval.
- Use the correct subgroup denominator; avoid unsupported conclusions between or beyond measured values.
Common mistakes
- Adding cumulative totals, which double-counts earlier observations.
- Comparing bar height when the axis does not start at zero.
- Confusing thousands of dollars with dollars.
Worked example
A cumulative delivery chart records 18 parcels at 9 am, 31 at 10 am and 47 at 11 am. How many were delivered between 10 and 11 am?
- Cumulative values include all earlier deliveries.
- Subtract the starting total for the requested interval from its ending total.
- 47 − 31 = 16.
Answer: 16 parcels.
Summarize a data set
Choose and calculate measures of center and spread that answer the question.
Method
- Mean = total divided by number of observations. Weight group means by their group sizes.
- Sort values before finding the median; for an even count, average the two middle values.
- Mode is the most frequent value, and range is maximum minus minimum. Extreme values can pull the mean away from the median.
Common mistakes
- Taking the middle listed value before sorting.
- Averaging group means without accounting for unequal group sizes.
- Confusing the range with the maximum value.
Worked example
Find the mean and median of 6, 8, 9, 9 and 23.
- The total is 55 and there are 5 values, so the mean is 11.
- The values are already ordered; the middle, third value is 9.
- The large value 23 raises the mean above the median.
Answer: Mean 11; median 9.
Describe relationships between variables
Look for the direction and form of a relationship while separating association from causation.
Method
- The independent or explanatory variable is used to explain or predict changes in the dependent or response variable.
- A positive association means the variables tend to increase together; a negative association means one tends to decrease as the other increases.
- A constant change in output for equal input changes indicates a linear pattern. An observed association alone does not establish cause.
Common mistakes
- Assuming any increasing pattern is linear.
- Claiming that one variable causes another from an observational scatterplot alone.
- Extrapolating far outside the measured range without evidence.
Worked example
A table lists hours worked as 2, 4, 6 and pay as $34, $68, $102. Describe the relationship.
- Every extra 2 hours adds $34.
- The constant rate is $34 ÷ 2 = $17 per hour.
- Pay is proportional to hours in this table: pay = 17 × hours.
Answer: A positive, linear, proportional relationship at $17 per hour.
Calculate geometric quantities
Choose the quantity needed—length, area or volume—and match the formula and units to it.
Method
- Perimeter measures a boundary; area measures a surface; volume measures space occupied.
- Rectangle area is length × width; triangle area is base × perpendicular height ÷ 2; circle area is πr² and circumference is 2πr.
- Split a composite figure into known shapes or subtract a missing region. Square or cube scale factors for area or volume.
Common mistakes
- Using perimeter when the task requires area.
- Using a slanted triangle side as its perpendicular height.
- Doubling area when all lengths double; area actually multiplies by 4.
Worked example
A rectangular floor measures 8 m by 5 m. A 2 m by 1.5 m rectangular area will not be tiled. How much area will be tiled?
- Find the full area: 8 × 5 = 40 m².
- Find the excluded area: 2 × 1.5 = 3 m².
- Subtract: 40 − 3 = 37 m².
Answer: 37 m².
Convert measurements
Multiply by conversion factors so unwanted units cancel, and preserve the type of measurement.
Method
- Write conversion factors as equal quantities in different units, such as 1 m/100 cm.
- Area conversions require squared factors; volume conversions require cubed factors.
- Use 60 minutes per hour, not 100. For temperature, apply the stated conversion formula rather than a simple scale factor.
Common mistakes
- Moving a decimal in the wrong direction.
- Using a length conversion factor only once for square or cubic units.
- Mixing US and imperial capacity units when the problem specifies a system.
Worked example
A tank contains 0.045 m³ of water. Using 1 m³ = 1,000 L, express this in milliliters.
- 0.045 m³ × 1,000 L/m³ = 45 L.
- 45 L × 1,000 mL/L = 45,000 mL.
- The volume stays the same while the unit size changes.
Answer: 45,000 mL.
Human anatomy and physiology
Practice this topicDescribe position, planes and body compartments
Use one fixed reference position to describe where structures lie, then distinguish tissue organization from the compartments that protect organs.
Method
- Anatomical directions are referenced to a person standing upright with palms forward, even if the person is currently lying down or turning a limb. Right and left belong to the person being described.
- Medial/lateral compare distance from the midline; superior/inferior compare height; anterior/posterior compare front and back; superficial/deep compare depth. Proximal/distal compare distance from a limb’s attachment to the trunk.
- Sagittal sections separate right and left; midsagittal specifies equal halves. Frontal sections separate front and back. Transverse sections separate upper and lower portions.
- The dorsal cavity includes the cranial and vertebral cavities. The ventral cavity includes the thoracic and abdominopelvic regions; the diaphragm separates chest from abdomen.
- Cells form tissues; several tissue types combine into organs; cooperating organs form organ systems. A serous membrane has a parietal layer along the cavity wall and a visceral layer at the organ surface. Its fluid reduces friction.
Common mistakes
- Changing the meaning of medial/lateral when a hand rotates; use anatomical position as the reference.
- Calling every right–left section midsagittal; only the midline section gives equal halves.
- Treating overlapping cavity names as mutually exclusive: a pleural region is in the thorax, which is part of the ventral cavity.
Remember: First choose the reference: midline, head-to-foot, front-to-back, surface, or limb attachment.
Worked example
A line travels from a person’s wrist to the elbow. A second line goes from the skin of the forearm inward toward the radius bone. How should the two directions be described?
- Identify the reference for each comparison: the first follows a limb toward its attachment; the second changes distance from the body surface.
- The elbow is closer than the wrist to the arm’s attachment, so the first line travels proximally.
- The bone is farther inside the body than skin, so the second line travels deeper. Do not use proximal as a synonym for deep.
Answer: First line: proximal. Second line: deep.
Connect breathing mechanics with gas exchange
Trace how a pressure difference moves air, then explain why a thin, well-perfused alveolar surface transfers oxygen and carbon dioxide.
Method
- Quiet inhalation begins when the diaphragm contracts and thoracic volume increases. Alveolar pressure briefly falls below atmospheric pressure, so air flows inward. Quiet exhalation relies mainly on elastic recoil as inspiratory muscles relax.
- Air travels through conducting passages to alveoli. Mucus traps particles and cilia move the mucus toward the throat; these defenses differ from alveolar gas exchange.
- Each gas diffuses down its own partial-pressure gradient. At healthy lung surfaces, oxygen enters the blood while carbon dioxide leaves it. Diffusion itself does not require an ATP-driven gas pump.
- Gas exchange improves with larger surface area and a shorter diffusion path. Surfactant lowers alveolar surface tension, helping air sacs remain open.
- Ventilation supplies alveolar air; perfusion supplies pulmonary blood. An alveolus cannot contribute normally to oxygen delivery when either air supply or blood flow is missing.
Common mistakes
- Saying all expiration requires active contraction; distinguish quiet expiration from forced expiration.
- Assuming oxygen always moves toward a place with greater total pressure; compare oxygen partial pressures.
- Treating ventilation and perfusion as interchangeable. Air does not replace the blood needed to carry oxygen onward.
Remember: Volume up → pressure down → air in. Exchange additionally needs a thin surface and flowing blood.
Worked example
An alveolus receives fresh air normally. The membrane becomes thicker, while surface area, gas gradients and blood flow remain unchanged. What happens to oxygen transfer, and why?
- Separate air movement from diffusion: normal ventilation means air still reaches the alveolus.
- Compare the diffusion pathway before and after the change. Oxygen must cross a longer distance through the thicker membrane.
- With the other stated factors held constant, the longer diffusion path lowers the rate of transfer into blood. The gradient’s direction does not reverse.
Answer: Oxygen transfer slows despite preserved ventilation.
Trace circulation and explain pressure-driven flow
Follow blood through the two circuits, use valve direction to reason about backflow, and relate vessel structure to transport and exchange.
Method
- Systemic veins return blood to the right atrium. Blood passes to the right ventricle, pulmonary arteries, lung capillaries, pulmonary veins, left atrium and left ventricle before returning to systemic arteries.
- Arteries carry blood away from the heart; veins return it. Oxygen content does not define vessel type: adult pulmonary arteries carry relatively oxygen-poor blood.
- Atrioventricular valves limit backflow into atria during ventricular contraction. Semilunar valves limit arterial backflow into ventricles. They open and close in response to pressure differences.
- The left ventricle generates higher pressure for the systemic circuit. In a stable normal circulation, both ventricles pump the same average volume over time.
- Cardiac output = heart rate × stroke volume. Narrowing an arteriole increases resistance; thin capillary walls support exchange with tissue fluid.
Common mistakes
- Defining an artery as an oxygen-rich vessel rather than a vessel carrying blood away from the heart.
- Assuming the thicker left ventricle must pump more blood per minute than the right in a normal steady state.
- Confusing mitral-valve backflow into the left atrium with aortic-valve backflow into the left ventricle.
Remember: Right heart → lungs; left heart → body. Atria receive, ventricles eject.
Worked example
Heart rate rises from 60 to 90 beats/min while stroke volume remains 70 mL/beat. How much does cardiac output increase?
- Calculate the starting output: 60 × 70 = 4,200 mL/min.
- Calculate the later output: 90 × 70 = 6,300 mL/min.
- Subtract to find the increase: 6,300 − 4,200 = 2,100 mL/min. The proportional increase is 2,100 ÷ 4,200 = 50%.
Answer: Cardiac output increases by 2.1 L/min, from 4.2 to 6.3 L/min.
Separate digestion, propulsion and absorption
Track food through the digestive tract and distinguish enzymes that break molecules from structures that mix, move and absorb them.
Method
- Food passes through the esophagus, stomach, small intestine and large intestine. Accessory organs supply secretions; food does not normally pass through the liver, gallbladder or pancreas.
- Mechanical digestion includes chewing and mixing. Chemical digestion breaks molecular bonds. Peristalsis propels contents through coordinated muscular activity and can work without gravity as the main force.
- Salivary amylase starts starch digestion; stomach proteases begin protein digestion. Pancreatic and intestinal enzymes continue digestion in the small intestine, yielding molecules small enough to absorb.
- The liver makes bile and the gallbladder stores it. Bile emulsifies fat, improving lipase access; it is not a fat-digesting enzyme. Pancreatic bicarbonate helps neutralize acidic chyme.
- Small-intestinal folds, villi and microvilli increase the surface for nutrient absorption. The small intestine also absorbs most water; the large intestine recovers much of the remainder and helps form feces.
Common mistakes
- Calling bile an enzyme or saying the gallbladder manufactures it.
- Equating absorption with digestion: digestion makes smaller molecules; absorption moves them across the intestinal lining.
- Saying the colon absorbs most dietary water; the small intestine normally absorbs most, and the colon recovers much of what remains.
Remember: Move, break down, absorb: these are different steps, often occurring together.
Worked example
A learner has normal pancreatic lipase delivery but greatly reduced bile delivery to the small intestine. Explain why fat digestion may be slower without claiming that lipase has disappeared.
- Identify each secretion’s job: lipase hydrolyzes fat molecules, while bile disperses large droplets into smaller droplets.
- Reduced emulsification leaves a smaller total fat surface exposed to the enzyme.
- Lipase can still be present and active, but reduced access to the substrate can lower the overall rate of digestion.
Answer: Less bile reduces fat emulsification and the surface available to lipase.
Follow neural signals from stimulus to response
Distinguish sensory input from motor output, explain chemical synapses, and connect neural structure with rapid coordination.
Method
- The brain and spinal cord form the central nervous system. Peripheral nerves connect the CNS with receptors and effectors. Afferent pathways carry input inward; efferent pathways carry output outward.
- In a withdrawal reflex, sensory input can be processed through spinal interneurons to produce motor output before conscious awareness. Not all reflexes have the same circuit; a simple stretch reflex includes a direct sensory-to-motor connection.
- Myelin supports efficient signal conduction. Action potentials are all-or-none events; information about stimulus strength can be carried by firing frequency and the number of recruited neurons.
- At a chemical synapse, transmitter released from a presynaptic terminal binds receptors on the next cell. The resulting effect can be excitatory or inhibitory. Electrical synapses use a different mechanism.
- Sympathetic activity commonly increases heart rate and reduces digestive activity during action. Parasympathetic activity generally supports rest and digestion. The cerebellum helps coordinate smooth movement and balance.
Common mistakes
- Treating afferent as a synonym for motor; afferent carries input toward the CNS.
- Assuming every reflex must wait for conscious recognition or contains exactly the same number of neurons.
- Saying a stronger stimulus necessarily produces a taller action potential in the same neuron.
Remember: Afferent arrives; efferent exits. Then ask whether the question concerns an individual impulse or the rate of impulses.
Worked example
A stronger stimulus produces 40 action potentials each second instead of 20, but recorded action-potential amplitudes remain similar. Does the unchanged amplitude mean that stimulus strength was not communicated?
- Recognize that individual action potentials are all-or-none once threshold is reached.
- Compare the event rate rather than requiring the height of each event to change: 40 per second is twice 20 per second.
- The change in firing frequency can carry information about stimulus intensity even when each impulse has a similar amplitude.
Answer: No. The higher firing frequency can communicate the stronger stimulus.
Explain muscle force, movement and relaxation
Identify the three muscle types and use sliding-filament mechanics to explain how stimulation, calcium and ATP produce controlled force.
Method
- Skeletal muscle is striated and supports many voluntary movements; cardiac muscle is striated, involuntary and connected through intercalated discs; smooth muscle is nonstriated and moves contents or changes the diameter of hollow organs.
- During skeletal-muscle shortening, thin actin filaments slide past thick myosin filaments. The sarcomere shortens while the filaments themselves retain their lengths.
- Calcium binds troponin in skeletal muscle, changing regulatory positioning so myosin can interact with actin. This specific regulatory description should not be assumed to apply unchanged to smooth muscle.
- ATP binding lets myosin detach from actin; ATP hydrolysis helps prepare another cycle. ATP also supports calcium reuptake, so normal relaxation requires energy.
- Recruiting more motor units increases the number of active fibers. Tendons transmit muscle pull to bone; antagonistic muscles enable opposing movements. Isometric contraction creates tension with little length change.
Common mistakes
- Saying actin and myosin filaments shrink during normal contraction instead of sliding past one another.
- Assuming relaxation is simply a state in which no energy is used.
- Using tendon and ligament interchangeably: tendons generally join muscle to bone; ligaments generally join bone to bone.
Remember: Calcium permits access; ATP permits cycling and reset.
Worked example
During an experiment, calcium remains available but ATP supply is exhausted after many myosin heads have attached to actin. Why is this not the same as normal relaxation?
- Normal cross-bridge detachment requires ATP binding to myosin.
- Without new ATP, attached heads cannot detach through the usual cycle. Calcium reuptake is also energy-dependent.
- Relaxation therefore requires restoration of the normal energy-dependent processes, not simply removal of energy.
Answer: ATP depletion can leave cross-bridges attached and impair calcium handling; normal relaxation needs ATP.
Reproductive structures and hormone cycles
Keep gamete production, transport, fertilization, and implantation separate. Then connect each cycle event to the hormone that regulates it.
Method
- Testes and ovaries produce gametes and reproductive hormones. Normal human gametes have 23 chromosomes; fertilization restores the diploid number of 46.
- Sperm develop in seminiferous tubules, mature in the epididymis, and travel through the ductus deferens and connecting ducts to the urethra. Accessory glands add much of the fluid in semen.
- Fertilization usually occurs in a uterine tube. The developing blastocyst normally implants in the endometrium of the uterus.
- FSH supports follicle development. The midcycle LH surge triggers ovulation. The corpus luteum then supplies progesterone and estrogen; their decline in a cycle without pregnancy leads to shedding of the functional endometrium.
Common mistakes
- Treating the ovary, uterine tube, and uterus as interchangeable sites.
- Confusing sperm with semen or assuming sperm ducts are the pathway that carries hormones to the blood.
Remember: Production, maturation, transport, fertilization, implantation: identify the event before naming the structure.
Worked example
An ovarian follicle develops normally, but no midcycle LH surge occurs. Which later event is most directly affected?
- Follicle development is already established in the scenario.
- LH provides the immediate trigger for the mature follicle to release its oocyte.
- Therefore, the missing surge most directly interferes with ovulation, even though a follicle has developed.
Answer: Ovulation is most directly affected.
Skin layers, protection, and temperature control
Use the location of a skin structure to predict its function. The surface barrier, deeper connective tissue, and subcutaneous fat have different jobs.
Method
- The epidermis is avascular epithelium. Living basal cells divide, while their descendants move outward and help form the protective keratinized surface.
- The dermis contains vessels, nerves, and many glands within strong connective tissue. Subcutaneous tissue beneath the skin contains much insulating and cushioning fat.
- The surface barrier limits water loss and microbial entry. Melanin helps protect cell DNA from ultraviolet radiation; sebaceous glands supply lubricating sebum.
- Sweat cools mainly through evaporation. Skin vasodilation brings more heat to the surface. Ultraviolet exposure also initiates an early step in vitamin D production.
Common mistakes
- Putting blood vessels in the epidermis because its deepest cells are alive; those cells receive nutrients by diffusion from the dermis.
- Assuming liquid sweat cools equally well whether it evaporates or remains on the skin.
Worked example
Why can a person sweat heavily in humid air yet cool less effectively than in dry air?
- Separate sweat secretion from sweat evaporation.
- Evaporation removes heat from skin.
- Humid air reduces evaporation, so equal sweat production need not produce equal cooling.
Answer: Less of the sweat evaporates, so less heat is removed by evaporation.
Endocrine signaling and negative feedback
A hormone is a signal, its receptor identifies a responsive target, and feedback adjusts further release. Follow these links to predict changes.
Method
- Endocrine secretions enter blood; exocrine secretions travel through ducts. The pancreas does both: insulin and glucagon are hormones, while digestive enzymes are duct-delivered secretions.
- A cell responds to a hormone only through an appropriate receptor and signaling machinery. Water-soluble peptide hormones usually act through surface receptors; steroid hormones commonly bind intracellular receptors.
- Negative feedback opposes a change or reduces upstream stimulation. Thyroid hormone inhibits TRH and TSH release; loss of downstream hormone can therefore increase upstream signals.
- Insulin favors glucose uptake and storage; glucagon supports glucose availability during fasting. ADH is made in hypothalamic neurons and released from the posterior pituitary.
Common mistakes
- Assuming a low downstream hormone always means a low upstream stimulating hormone.
- Treating a hormone’s release site as necessarily the place where it was synthesized.
Worked example
A target gland stops making its hormone, but the pituitary and feedback pathways remain functional. Predict the pituitary stimulating hormone.
- The target hormone normally inhibits further pituitary stimulation.
- Lower target hormone means less inhibitory feedback.
- The intact pituitary therefore tends to release more stimulating hormone.
Answer: The stimulating pituitary hormone tends to rise.
Urine formation and kidney regulation
Track the direction of each substance: filtration puts fluid into the nephron, reabsorption returns useful material to blood, and secretion adds selected material to tubular fluid.
Method
- Glomerular filtration moves water and small solutes from capillary blood into the capsular space. Cells and nearly all large plasma proteins remain in blood.
- Reabsorption moves substances from tubule to blood; secretion moves them from blood to tubule. A filtered substance need not appear in final urine: glucose is normally recovered.
- ADH promotes collecting-duct water reabsorption, reducing urine volume. Aldosterone promotes sodium recovery and potassium secretion in responsive distal-nephron cells.
- Kidneys regulate acid–base balance through hydrogen-ion and bicarbonate handling. Urine flows from renal pelvis to ureter to bladder to urethra.
Common mistakes
- Using reabsorption and secretion interchangeably; their directions are opposite.
- Confusing ureters, which enter the bladder, with the urethra, which leaves it.
Remember: Reabsorption returns; secretion sends into the tubule.
Worked example
Glucose enters initial filtrate but is absent from final urine. Which transport process explains this?
- The observation rules out “glucose was never filtered.”
- Removing glucose from tubular fluid requires movement out of the tubule.
- Returning glucose to blood is reabsorption, not secretion.
Answer: Tubular reabsorption recovers the filtered glucose.
Immune defenses and memory
Distinguish rapid innate defenses from antigen-specific adaptive responses. Within adaptive immunity, separate antibody production from direct killing of infected cells.
Method
- Innate defenses include barriers, phagocytes, and inflammation. Local inflammation commonly increases blood flow, vessel permeability, and immune-cell recruitment.
- B cells can become antibody-secreting plasma cells. Cytotoxic T cells directly attack selected infected or abnormal body cells; helper T cells coordinate other responses.
- Memory lymphocytes allow a faster response after re-exposure to a recognized antigen. Passive transfer of preformed antibodies can protect promptly but does not by itself create recipient immune memory.
- Lymph nodes monitor lymph; the spleen monitors blood. Immature T cells undergo important maturation in the thymus, whereas B-cell development occurs primarily in bone marrow.
Common mistakes
- Assuming antibodies against one antigen bind all unrelated antigens equally well.
- Calling transferred antibodies active immunity just because they are protective; active immunity requires the recipient’s own response.
Worked example
Antibody responses are measured after exposure to a familiar antigen X and a new antigen Y. What result supports antigen-specific memory?
- Prior exposure occurred only for X.
- Look for a response advantage tied to that antigen, rather than a general response to every injection.
- A faster response to X than Y fits persistent, antigen-specific memory cells.
Answer: The matching antibody response develops more rapidly for X.
Bone tissue, joints, and skeletal functions
Bone is living tissue, a mineral reservoir, and part of a mechanical system. Its cells, matrix, marrow, and connections contribute different functions.
Method
- Osteoblasts form bone matrix; osteoclasts resorb bone. Mineral provides hardness and compressive strength, while collagen contributes flexibility and tensile strength.
- The axial skeleton includes skull, vertebral column, and thoracic cage. Limbs and their girdles form the appendicular skeleton.
- Ligaments connect bone to bone; tendons connect muscle to bone. Articular cartilage covers joint surfaces and helps distribute loads with low friction.
- Red marrow produces blood cells. Growth plates support lengthening of long bones. Fracture repair progresses from hematoma through soft and bony calluses to remodeling.
Common mistakes
- Reversing osteoblast and osteoclast functions or treating adult bone as inactive.
- Confusing tendon with ligament, or growth-plate cartilage with articular cartilage.
Worked example
Bone resorption exceeds formation for several months. Predict the net change in bone material.
- Osteoclasts remove bone; osteoblasts deposit new matrix.
- Compare removal with replacement rather than asking whether either process is present.
- More removal than replacement produces a net loss.
Answer: The amount of bone material decreases.
Biology
Practice this topicCells: structure, transport and organization
Use a structure’s function to predict what happens when it changes. Then distinguish movement of water from movement of solutes and cells from larger levels of organization.
Method
- A typical bacterial cell has DNA, ribosomes, cytoplasm and a plasma membrane, but no membrane-bound nucleus. A typical nucleated animal or plant cell is eukaryotic and contains membrane-bound organelles.
- Ribosomes build proteins. The rough ER receives many proteins destined for secretion or membranes; the Golgi modifies and sorts them. Lysosomes digest material, while mitochondria supply much of the ATP in aerobically active cells.
- The plasma membrane regulates exchange. A plant cell wall provides support but does not replace the membrane’s selective barrier. Microvilli increase the membrane area available for exchange.
- Simple diffusion and facilitated diffusion move substances down their gradients without direct ATP expenditure. Facilitated diffusion uses a membrane protein. Active transport requires an energy source to drive transport against an electrochemical gradient.
- For osmosis, first compare nonpenetrating solutes across a water-permeable membrane. A hypertonic external solution draws water out of a cell; a hypotonic one drives net water entry. Water molecules still move both ways at equilibrium, but there is no net movement.
- Cells form tissues; tissues contribute to organs; organs cooperate in organ systems. Different cell types can specialize for absorption, secretion or contraction.
- Normal mitosis preserves chromosome number in each daughter cell. Meiosis reduces the chromosome number in gametes. Copying DNA before division does not mean each final daughter retains twice the original chromosome number.
Common mistakes
- Calling every protein-mediated transport process active: a channel can support passive movement down a gradient.
- Using “hypertonic” without saying relative to what, or ignoring whether the solute can cross the membrane.
- Assuming every human cell has a nucleus or mitochondria. Mature red blood cells are important exceptions to the typical nucleated-cell model.
- Confusing DNA replication with a permanent doubling of chromosome number after normal mitosis.
Remember: Match the failed job to the structure: sorting → Golgi; digestion → lysosome; most aerobic ATP → mitochondria; selective exchange → membrane.
Worked example
A model cell has 0.2 mol/L of a solute inside and is placed in a large 0.5 mol/L solution of the same solute. Water crosses its membrane; the solute does not. Predict the initial direction of water movement and the change in cell volume.
- Check permeability: water crosses, but the solute is nonpenetrating.
- Compare concentrations: the outside has more nonpenetrating solute and is hypertonic relative to the cell.
- Water moves outward overall, toward the higher solute concentration.
- Losing water reduces the cell’s volume. The rigid wall of a plant cell and the absence of a wall in an animal cell affect the visible response, but not the initial direction of water movement.
Answer: Net water movement is out of the cell, so the cell’s water-filled volume decreases.
DNA, RNA and protein synthesis
Trace genetic information without confusing the DNA template, the RNA message and the amino acid chain. Read sequence labels and strand directions before using base-pair rules.
Method
- DNA and RNA are nucleotide chains. DNA normally contains deoxyribose and thymine; RNA contains ribose and uracil. Both contain adenine, guanine and cytosine.
- During DNA replication, each original strand guides a new complementary strand. Each completed DNA molecule contains one original and one new strand: semiconservative replication.
- Transcription makes RNA from a DNA template. Complementary DNA bases pair A–T and G–C; in an RNA copy, U pairs with template A. The new RNA is complementary and antiparallel to the template strand.
- A typical nuclear protein-coding gene in a eukaryote is transcribed and its RNA processed in the nucleus. The mature mRNA then reaches a cytoplasmic ribosome for translation. RNA processing can remove introns and join retained exons.
- The ribosome reads mRNA in codons of three bases. tRNA brings amino acids; rRNA helps form the ribosome and catalyze peptide-bond formation. A stop codon signals termination rather than adding an amino acid.
- The coding DNA strand and mRNA have corresponding sequences when both are written 5′ to 3′, except that mRNA has U instead of T. Do not use that shortcut for the template strand.
- A base substitution can preserve an amino acid, replace it or create a stop signal, depending on the codon. An insertion or deletion that is not a multiple of three can change the reading frame. A sequence change alone does not establish how severe a functional effect will be.
Common mistakes
- Copying a template sequence directly or ignoring its 5′/3′ direction.
- Putting thymine into an mRNA answer.
- Counting a stop codon as an amino acid, or treating each nucleotide as a whole codon.
- Claiming every mutation changes a protein or causes disease; several codons can encode the same amino acid.
Remember: DNA stores; mRNA carries the message; tRNA carries the amino acid; the ribosome assembles the chain.
Worked example
The DNA template is 3′-TAC TTT CCG ATT-5′. A supplied codon key gives AUG = methionine, AAA = lysine, GGC = glycine and UAA = stop. What mRNA and short amino acid chain result?
- The strand is explicitly the template, read 3′ to 5′; make its complementary RNA 5′ to 3′.
- Apply RNA pairing: TAC → AUG, TTT → AAA, CCG → GGC and ATT → UAA.
- Read from AUG in groups of three: methionine, lysine and glycine.
- Stop at UAA. The stop signal is not a fourth amino acid.
Answer: mRNA: 5′-AUG AAA GGC UAA-3′. Chain: methionine–lysine–glycine, with three amino acids.
Mendelian inheritance and probability
Write the parental genotypes, list their possible gametes and calculate only the outcome requested. Use stated assumptions instead of treating every trait as a simple dominant–recessive trait.
Method
- A genotype is an allele combination; a phenotype is an observable characteristic. Under complete dominance, AA and Aa share the dominant phenotype while aa shows the recessive phenotype.
- During normal gamete formation, the two alleles of a gene segregate. An Aa parent supplies A or a with equal probability. Offspring receive one allele from each parent.
- Aa × Aa gives genotype probabilities 1/4 AA, 1/2 Aa and 1/4 aa. With complete dominance, the phenotype probabilities are 3/4 dominant and 1/4 recessive.
- A recessive-phenotype offspring can reveal a dominant-phenotype parent’s hidden allele. In a test cross with aa, an aa offspring means the other parent supplied a.
- For unlinked genes that assort independently, multiply probabilities for combined outcomes. Complete dominance, no masking interaction between genes and equal survival are also needed for the familiar 9:3:3:1 observed-phenotype expectation.
- Independent offspring do not use up an expected quota. A 25% chance for each offspring does not guarantee exactly one affected offspring in a family of four.
- Dominant does not mean common, stronger or beneficial. Phenotype can also be influenced by environment, incomplete dominance, codominance, multiple genes and other effects outside a simple Mendelian model.
Common mistakes
- Adding independent probabilities when both events must occur; multiply them instead.
- Treating a recessive phenotype and a carrier genotype as the same outcome.
- Applying independent-assortment ratios to linked genes without checking the assumptions.
- Reporting an unconditional probability after the question has supplied new information, such as an observed phenotype.
Remember: First genotype, then gametes, then offspring; apply phenotype rules last.
Worked example
At an autosomal gene with complete dominance, two Aa parents have an offspring known to show the dominant phenotype. What is the chance that the offspring is a carrier of a?
- List the equally likely combinations: AA, Aa, aA and aa. Aa and aA are the same genotype reached by different parental contributions.
- Use the known phenotype to exclude aa.
- Among the three remaining combinations, two contain a.
- Divide two carrier combinations by three compatible combinations.
Answer: 2/3. The unconditional carrier probability is 1/2, but knowing the phenotype changes the relevant group.
Biological macromolecules
Connect a molecule’s building blocks and structure to its function. Similar ingredients can produce different properties when their bonds or three-dimensional arrangements differ.
Method
- Carbohydrates include simple sugars and polysaccharides. Starch and glycogen store glucose; cellulose provides structural support in plant walls. Sharing glucose subunits does not make these polymers identical.
- Proteins consist of amino acids connected by peptide bonds. Their sequence and folding support roles such as catalysis, signaling, transport and structural support.
- Nucleic acids are nucleotide polymers. A nucleotide contains a sugar, phosphate and nitrogenous base. DNA stores hereditary sequence information and several forms of RNA help use it.
- Lipids include triglycerides, phospholipids and steroids. A triglyceride contains glycerol and three fatty acids. Lipids are not all polymers made by repeating one type of monomer.
- A phospholipid has a hydrophilic head and hydrophobic tails. In a bilayer, heads face the watery compartments and tails face inward. Cis double bonds bend fatty acid chains and reduce their ability to pack tightly.
- Hydrolysis uses water to break a bond; dehydration synthesis joins units with water released. Denaturation is different: a protein can lose its functional folding without its amino acid chain being completely digested.
- Enzymes depend on their active-site structure and suitable conditions. Temperature or pH changes can affect activity; an experiment must separate temporary changes in reaction conditions from lasting structural damage.
- At a fixed enzyme concentration, adding substrate increases the rate until the active sites are mostly occupied. The rate then approaches a maximum because the available enzyme is working near capacity.
Common mistakes
- Calling every large biological molecule a protein or every lipid a repeating polymer.
- Confusing denaturation, which changes folding, with complete hydrolysis, which breaks the chain into smaller products.
- Assuming all carbohydrates are only energy stores; some are structural.
- Assuming one amino acid substitution always destroys a protein. The effect depends on the site and chemical change.
Remember: Sequence, bonds and shape all matter: knowing the building block alone does not determine the whole molecule’s behavior.
Worked example
Two enzyme samples are tested with equal substrate at 30°C. One had previously been heated to 90°C and cooled; it now has very little activity. Its amino acid sequence is intact. What best explains the result?
- Testing temperature and substrate are now equal, so they do not explain the current difference.
- The intact sequence argues against complete hydrolysis into amino acids.
- Earlier high heat may have altered the enzyme’s folding.
- An altered active site can prevent normal binding or catalysis even after cooling.
Answer: Persistent denaturation of the enzyme is the best explanation; preserved sequence does not guarantee preserved function.
Microorganisms, transmission and disease
Distinguish an organism’s structure, how it spreads and whether it causes harm. A microbe can be present without causing disease, and a treatment works only if its biological target is relevant.
Method
- Bacteria are prokaryotic cells. Fungi, including yeasts, are eukaryotes. Many protozoa are single eukaryotic cells; some are parasites. Microscopic size does not make all organisms bacteria.
- Viruses are acellular particles with a DNA or RNA genome inside a protein-containing structure; some also have an envelope. They use suitable host cells to produce new particles rather than carrying out independent cellular reproduction.
- Microorganisms can be harmless, helpful or pathogenic depending on the organism and setting. Normal microbiota can compete with potential pathogens. Some residents can cause opportunistic infection when they enter a different site or host defenses are weakened.
- Transmission routes differ. Contaminated hands, water, shared needles, respiratory material and animal vectors can each matter for particular pathogens. Interrupt the relevant route rather than assuming one rule applies to every infection.
- An antibacterial drug may target bacterial cell walls or ribosomes. A virus lacks those bacterial targets, so an antibiotic is not automatically an antiviral treatment.
- Resistant bacteria may exist before treatment. An antibiotic can select for them by suppressing susceptible competitors. Bacteria do not deliberately acquire a needed trait; mutation and gene transfer generate variation that selection can act on.
- Vaccination can establish immune memory. Refrigeration can slow growth without sterilizing material. Detecting a microbe in an ill person establishes presence, but additional evidence is needed to show it caused the illness.
Common mistakes
- Treating viruses as small bacterial cells or assuming antibiotics treat every infectious agent.
- Equating the presence of a microorganism with proof that it causes disease.
- Saying bacteria change purposefully because they need to survive.
- Confusing slow growth, disinfection and complete sterilization.
Remember: Ask four separate questions: What is it? Where is it? How does it spread? What target does the intervention affect?
Worked example
A culture begins with 900 antibiotic-susceptible bacteria and 100 resistant bacteria. A treatment kills 90% of the susceptible bacteria and none of the resistant bacteria. Before any further reproduction, why are resistant cells now a much larger share of the survivors?
- The population already contained resistance before treatment.
- Ten percent of the 900 susceptible bacteria survive: 90 cells.
- All 100 resistant bacteria survive, leaving 90 + 100 = 190 survivors.
- The resistant share rises from 10% to 100/190, or about 53%, because susceptible cells were removed preferentially.
Answer: Differential survival selected for pre-existing resistance. The drug did not need to create a new resistant trait to change the population’s composition.
Chemistry
Practice this topicAtoms, ions and the periodic table
Use proton count to identify an element, neutron count to distinguish isotopes, and electron count to determine charge. Connect outer electrons with bonding and periodic-table groups.
Method
- Atomic number is the number of protons. Mass number is protons plus neutrons, so neutrons = mass number − atomic number.
- A neutral atom has equal proton and electron counts. Charge = protons − electrons: gaining electrons makes an anion; losing electrons makes a cation.
- Isotopes share an atomic number but have different neutron counts. The periodic-table atomic mass is an abundance-weighted average, not the mass number of every atom.
- Main-group elements in the same column usually share a valence-electron pattern. Ionic compounds use ion ratios whose charges sum to zero; covalent bonds involve shared electrons.
Common mistakes
- Subtracting an electron for a negative charge: a negative ion has gained electrons.
- Treating the decimal atomic mass on a periodic table as an exact neutron or mass-number count.
- Changing formula subscripts to balance a reaction: subscripts identify the substance.
Remember: Protons identify; neutrons distinguish isotopes; electrons set charge.
Worked example
A potassium-41 ion has atomic number 19 and charge 1+. How many protons, neutrons and electrons does it contain?
- Atomic number 19 gives 19 protons.
- Neutrons = 41 − 19 = 22.
- A 1+ charge means one electron fewer than protons: 19 − 1 = 18.
Answer: 19 protons, 22 neutrons and 18 electrons.
Properties, states and physical changes
Determine whether identity changes, distinguish amount from material properties, and select a separation method using the properties that differ.
Method
- A physical change preserves chemical identity. Melting, freezing, crushing and evaporation do not themselves produce new substances. A chemical change produces different substances.
- Mass and volume depend on sample size. Density is mass divided by volume and is independent of sample size for a uniform material at the same conditions.
- A solution is a homogeneous mixture. Ordinary filtration removes suspended solids, not dissolved ions; distillation can collect a volatile solvent separately from a nonvolatile solute.
- During a pure substance’s phase change at constant pressure, added energy can change the state without raising temperature. Boiling temperature depends on external pressure.
Common mistakes
- Using the final cylinder level rather than the displaced volume.
- Assuming a change in appearance proves a chemical reaction.
- Assuming a clear, uniform liquid must be a pure substance.
Worked example
An insoluble 72 g object raises a cylinder’s water level from 18 mL to 42 mL. Find its density and predict whether a smaller piece of the same uniform material has a different density.
- The displaced volume is 42 − 18 = 24 mL.
- Density = 72 g ÷ 24 mL = 3 g/mL.
- A smaller piece has proportionally less mass and volume, leaving the same density at the same conditions.
Answer: 3 g/mL; a smaller piece has the same density.
Chemical reactions and conservation
Account for every atom, use coefficients as ratios, and separate what a reaction changes from what it conserves.
Method
- Chemical reactions rearrange atoms. Balance an equation by changing coefficients, never by changing a compound’s formula subscripts.
- A coefficient multiplies the entire formula. In 3 H2O, there are six hydrogen atoms and three oxygen atoms.
- Balanced coefficients give particle or mole ratios. The limiting reactant runs out first and limits the amount of product; another reactant can remain.
- A gas escaping from an open vessel can reduce the measured mass without violating conservation. Include everything that leaves or enters when comparing total mass.
- Bond breaking requires energy; bond formation releases it. The net balance determines whether the reaction releases or absorbs energy.
Common mistakes
- Comparing reactant molecule counts without applying the balanced ratio.
- Counting 2 CO2 as two oxygen atoms rather than four.
- Assuming a closed system gains mass because a visible solid forms.
Worked example
For N2 + 3 H2 → 2 NH3, a model starts with 3 N2 molecules and 6 H2 molecules. How much ammonia forms and what remains?
- Each N2 molecule needs three H2 molecules.
- Six H2 molecules can react with only two N2 molecules, so H2 limits the reaction.
- Two complete reaction groups form four NH3 molecules and leave one N2 molecule.
Answer: 4 NH3 molecules form; 1 N2 molecule remains, with no H2 left.
Conditions that change reaction rates
Explain rate changes through effective collisions, and keep rate separate from the total amount of product.
Method
- Increasing a reacting solute’s concentration generally increases collision frequency. Increasing a solid’s exposed surface area allows more simultaneous contact with another reactant.
- A moderate temperature increase generally speeds a reaction because particles move faster and more collisions overcome the activation-energy barrier.
- A catalyst supplies an alternative pathway with a lower activation-energy barrier and is regenerated overall. It does not supply additional reactant atoms.
- Protein enzymes can lose their functional shape at excessive temperatures. Faster collisions do not compensate for a catalyst that no longer functions.
- Average rate compares a measured change with elapsed time. Equal final product amounts can be reached at very different rates. Change only one variable to isolate a cause.
Common mistakes
- Treating faster reaction as proof of more final product.
- Changing temperature and concentration together, then attributing the difference to only one.
- Saying heating lowers activation energy rather than increasing the fraction of particles able to overcome it.
Worked example
Identical reactions generate 18 mL and 30 mL of gas during their first 15 seconds. Find their average rates during that interval and say what can be concluded about final gas yield.
- First reaction: 18 ÷ 15 = 1.2 mL/s.
- Second reaction: 30 ÷ 15 = 2.0 mL/s.
- The second is faster in the measured interval, but the initial rates alone do not establish either final yield.
Answer: 1.2 mL/s and 2.0 mL/s; the final yields cannot be determined from these interval measurements alone.
Solutions, concentration and solubility
Track the amounts of solute and solvent separately. Distinguish how quickly a substance dissolves from the maximum amount that can remain dissolved.
Method
- The solute is dissolved in the solvent. Mass percent is solute mass divided by total solution mass, multiplied by 100.
- Dilution adds solvent while keeping the amount of solute fixed. For molar concentrations, C1V1 = C2V2 when the solute neither reacts nor is lost.
- Solubility is an equilibrium limit at specified conditions. Stirring can speed dissolving without changing that limit. Cooling some saturated solutions causes excess solute to crystallize.
- A saturated solution can exchange particles with excess solid at equal dissolving and crystallizing rates. Equilibrium does not mean particles stop moving.
- Dissolved ions can carry current. Molecular solutes need not form ions. Gas solubility generally rises with gas partial pressure at fixed temperature.
Common mistakes
- Dividing solute mass by solvent mass when asked for mass percent of the solution.
- Using added water volume instead of final solution volume in a dilution calculation.
- Equating faster dissolving with greater solubility.
Worked example
A solution contains 18 g of salt in 282 g of water. Find its mass percent. Then predict its mass percent after adding 150 g of water without losing salt.
- Initial total mass is 18 + 282 = 300 g; mass percent = 18/300 × 100 = 6%.
- After adding water, total mass is 450 g but the salt mass is still 18 g.
- New mass percent = 18/450 × 100 = 4%.
Answer: The solution changes from 6% salt by mass to 4% salt by mass.
Acids, bases and pH
Use proton transfer to identify acids and bases. Read pH as a logarithmic concentration measure, and distinguish acid strength from concentration.
Method
- A Brønsted–Lowry acid donates a proton; a base accepts one. Strong acids ionize essentially completely in dilute water, while weak acids ionize only partially.
- Lower pH means greater hydrogen-ion concentration. A one-unit difference means a tenfold concentration ratio; a two-unit difference means a hundredfold ratio.
- At 25°C, pH + pOH = 14 and neutral water has pH approximately 7. Neutrality always means equal hydrogen-ion and hydroxide-ion concentrations; its numerical pH can vary with temperature.
- Strong acid and strong base neutralize according to their reaction ratio. Compare reacting amounts, not volume alone, to determine whether one remains in excess.
- Buffers reduce the effect of small additions of acid or base. Their capacity is limited, and a buffer need not have pH 7.
Common mistakes
- Treating pH as a linear scale or assigning more hydrogen ions to a higher pH.
- Using “strong” and “concentrated” interchangeably.
- Assuming any equal-volume acid–base mixture must be neutral without checking concentration and reaction ratio.
Worked example
At 25°C, a solution has pH 4. It is diluted to 100 times its original volume. Assume a fully ionized acid and negligible water ionization. Estimate the new pH.
- Initial hydrogen-ion concentration is 10⁻⁴ mol/L.
- A hundredfold dilution reduces it to 10⁻⁶ mol/L.
- The pH is therefore approximately 6: a two-unit rise for a hundredfold concentration reduction.
Answer: Approximately pH 6 under the stated assumptions.
Scientific reasoning
Practice this topicMeasurements and tools
Choose a suitable instrument, keep track of units and decide how much a measurement actually tells you.
Method
- Match the tool to the quantity, expected range and required resolution. A balance measures mass, a graduated cylinder measures liquid volume and a stopwatch measures elapsed time.
- Precision describes agreement among repeated readings. Accuracy describes agreement with a trustworthy reference. Closely grouped readings can all be wrong by the same offset.
- For an analog scale, read from the correct viewing position and estimate a digit between the smallest marked divisions when the scale permits it. Do not add unsupported decimal places.
- Keep units attached throughout a calculation. Use subtraction to remove a container’s mass or find displaced volume; divide mass by volume to calculate density.
- Repeated readings can reveal random variation, but averaging does not automatically remove a calibration bias. Matching rounded displays also do not prove exact equality.
Common mistakes
- Calling a set accurate merely because repeated readings agree.
- Using a final cylinder reading instead of the change in volume for displacement.
- Multiplying when converting to a larger metric unit, or reporting more precision than the instrument supports.
Remember: Tool → unit → reading → calculation → reasonable precision.
Worked example
In an original hypothetical measurement, a 42 g object raises a water level from 25 mL to 39 mL. It is fully submerged, does not dissolve and traps no air. Find its density.
- The object’s volume is the increase in water reading: 39 − 25 = 14 mL.
- Density = mass ÷ volume = 42 g ÷ 14 mL = 3 g/mL.
- Using the final 39 mL reading would incorrectly include the water already present before adding the object.
Answer: 3 g/mL
Reason from evidence
Separate what was observed from what might explain it, then choose the conclusion the evidence can support.
Method
- An observation records something seen or measured. An explanation proposes why it happened. A testable hypothesis must allow a possible result that would count against it.
- Induction develops a generalization from particular observations. Deduction uses a general premise to predict a particular result.
- An association in an observational study does not isolate a cause. Randomized, well-controlled experiments provide stronger causal evidence, but still have limits.
- Check the denominators when comparing counts, the baseline when reading a graph and the sampled population when interpreting a broad claim.
- Averages alone do not show how individuals vary. A failed positive control can make an unknown sample’s result inconclusive. Rejecting one explanation does not prove another.
Common mistakes
- Treating a larger number of cases as a larger risk without checking group sizes.
- Changing “is associated with” into “is caused by.”
- Generalizing one species, sample or short experiment to every situation.
Remember: Ask: What was measured? What was controlled? What remains possible?
Worked example
In a hypothetical survey, 24 of 120 people in group A and 18 of 60 in group B report headaches. Groups chose their own beverage habits. Which group has the higher reported proportion, and can the beverage be identified as the cause?
- Group A: 24 ÷ 120 = 0.20, or 20%.
- Group B: 18 ÷ 60 = 0.30, or 30%. B has fewer cases but a higher proportion.
- Because beverage choice was not assigned and other factors may differ, the survey alone cannot isolate a beverage effect.
Answer: Group B has the higher reported proportion: 30% versus 20%. The survey does not establish the cause.
Further reading
Predict relationships in data
Use patterns, rates and supplied models to make predictions without extending them further than the evidence allows.
Method
- Read axis labels and units first. A graph’s slope is change in the vertical quantity divided by change in the horizontal quantity.
- Increasing does not necessarily mean directly proportional. A constant nonzero baseline, a plateau or a changing rate can make a simple ratio model inappropriate.
- Interpolation predicts between measured values using an explicit or supported pattern. Extrapolation extends beyond the measured range and needs additional caution.
- Compare rates using consistent time intervals and units. Combine counts before calculating an overall proportion when groups have different sizes.
- A peak in the measured data suggests where to collect more observations; it does not automatically locate an exact optimum. Use a supplied mechanism only under its stated assumptions.
Common mistakes
- Comparing total amounts when the collection times differ.
- Assuming a rising trend continues at the same rate indefinitely.
- Averaging group percentages without accounting for unequal group sizes.
Remember: Read the range before trusting the prediction.
Worked example
The original hypothetical data below show a constant increase over the measured interval. Estimate the product amount at 5 minutes, then explain whether 100 mg at 50 minutes is established.
| Time (min) | Product (mg) |
|---|---|
| 2 | 4 |
| 4 | 8 |
| 6 | 12 |
- The increase is 4 mg every 2 minutes, equivalent to 2 mg/min.
- Five minutes is halfway between 4 and 6 minutes. Interpolation gives (8 + 12) ÷ 2 = 10 mg.
- Fifty minutes is far outside the measured interval. A prediction of 100 mg assumes the rate continues despite possible reactant limits or changed conditions.
Answer: About 10 mg at 5 minutes under the linear pattern. The data do not establish 100 mg at 50 minutes.
Design and evaluate investigations
Build a comparison that tests the intended question, measures outcomes consistently and preserves an honest record of the results.
Method
- The independent variable is deliberately manipulated; the dependent variable is the measured response. An operational definition specifies exactly how that response is measured.
- Match important conditions except the treatment being tested. A vehicle control contains the treatment’s carrier without its active component. A positive control checks whether a method can detect a known positive sample.
- Random assignment reduces systematic differences between treatment groups. Representative sampling concerns which population the findings can describe. These solve different problems.
- Blinding can reduce expectation bias in subjective scoring. Independent replication requires independent experimental units; ten readings from one sample are not ten independently treated samples.
- Plan methods before seeing results. Investigate unusual values and document any correction or exclusion. Human studies require voluntary informed participation and protection of identifiable data.
Common mistakes
- Changing light, water or species at the same time as the factor supposedly being tested.
- Counting multiple measurements from one treatment container as independent treatment replications.
- Deleting an unexpected value solely because it conflicts with the preferred explanation.
Remember: Change deliberately, compare fairly, measure consistently, report completely.
Worked example
A hypothetical investigator compares a fertilizer in one bright room with no fertilizer in one dim room. Plants in the bright room grow more. Redesign the comparison to test the fertilizer effect.
- Identify the confound: room light changes together with fertilizer exposure.
- Use replicated independent pots and randomly assign similar numbers to fertilizer and comparison conditions within each room.
- Match water, soil and observation period; define growth as a measured change in height or dry mass using the same method.
- Compare fertilizer and comparison plants within the room conditions, documenting the full results.
Answer: Put both randomized treatment groups in each room and standardize the other conditions and outcome method.
Conventions of standard English
Practice this topicSpelling and commonly confused words
Check both the letters and the meaning of a word. A correctly spelled word can still be the wrong word for its sentence.
Method
- Read the whole sentence before choosing a homophone: a principle is a rule, while principal can mean main or a school leader.
- Separate its, the possessive form, from it’s, which expands to it is or it has. The same meaning check distinguishes your/you’re and their/there/they’re.
- For common inflections, consonant + y usually becomes ies or ied: policies, studied. A vowel before y usually keeps the y: essays, played.
- Many words drop a final silent e before a vowel-initial suffix: making, usable. Do not treat a spelling pattern as exception-free; noticeable and courageous retain the e.
- Use standard American spellings in this practice. Reread the completed sentence rather than accepting a word just because it looks familiar.
Common mistakes
- Adding an apostrophe to a possessive pronoun.
- Choosing a correctly spelled homophone without checking its meaning.
- Applying an informal “always” spelling rule despite a familiar exception.
Remember: For a contraction, expand it. If neither “it is” nor “it has” fits, it’s does not fit.
Worked example
Complete the sentence: “The council adopted a new ___ to protect residents’ ___.” Choose between principle/principal and privacy/privacey.
- The first blank names a guiding rule, not a leader or something that is main.
- That meaning requires principle.
- Privacy is the standard spelling of the noun; the alternative adds an unnecessary e.
Answer: The council adopted a new principle to protect residents’ privacy.
Punctuation that makes relationships clear
Identify clauses and intended meaning before choosing punctuation. Several marks can be valid in English, so the required relationship matters.
Method
- A comma alone cannot join two independent clauses. Use a period, a semicolon, or a comma with a coordinating conjunction when the meaning fits.
- A conjunctive adverb such as however does not act like and or but. Between independent clauses, a common pattern is “clause; however, clause.”
- Use a colon after a complete clause to introduce an explanation or list. Do not place it directly between a verb and its object.
- Set off a nonessential interruption with a matched pair of commas. An identifying, restrictive phrase stays attached to the noun without those commas.
- Possessive singular nouns generally take ’s; regular plurals ending in s take a final apostrophe. Distinguish the coach’s schedule from the coaches’ schedules.
Common mistakes
- Using a comma alone between complete sentences.
- Separating a subject from its verb with a lone comma.
- Adding an apostrophe merely because a noun is plural.
Remember: When a semicolon joins clauses, check that both are complete. Before a colon introducing a list or explanation, check that the preceding clause is complete.
Worked example
Repair the comma splice while preserving the contrast: “The application was complete, however, the signature was missing.”
- “The application was complete” and “the signature was missing” are each independent clauses.
- However signals contrast but cannot join those clauses using commas alone.
- Use a semicolon before however and a comma after it.
Answer: The application was complete; however, the signature was missing.
Complete and well-built sentences
Find the subject and finite verb, then check whether a dependent clause has been left standing alone.
Method
- An independent clause expresses a complete thought. A clause beginning with because, although, or when generally needs a main clause to complete the sentence.
- A phrase with an -ing form is not automatically a complete sentence: “The technician checking the meter” lacks a finite main verb.
- A compound sentence joins independent clauses; a complex sentence combines an independent clause with a dependent clause.
- Repair a fragment by adding what is missing or attaching it to the sentence it modifies. Preserve the original time, cause, or contrast relationship.
- Parallel elements use matching grammatical structures: “to inspect, to label, and to store” or “inspecting, labeling, and storing.”
Common mistakes
- Mistaking a long phrase for a complete sentence.
- Dropping a connecting word and unintentionally changing the meaning.
- Repairing one fragment by creating a run-on sentence.
Remember: Length does not make a sentence complete. Find the subject, finite verb, and completed thought.
Worked example
Combine these words into a complete sentence without changing the intended cause: “Because the delivery arrived after closing. The clerk stored it the next morning.”
- Because makes the first clause dependent.
- The second clause can stand alone and provides the main action.
- Attach the dependent clause to the main clause with a comma.
Answer: Because the delivery arrived after closing, the clerk stored it the next morning.
Knowledge of language
Practice this topicGrammar for clear meaning
Make each verb, pronoun, and modifier point clearly to the word or idea it belongs to.
Method
- Match a verb with the head of its subject, not a nearby noun in a prepositional phrase: “The box of supplies is ready.”
- Keep tense consistent unless the timing actually changes. Use past perfect when necessary to distinguish an earlier past event.
- A pronoun should have an identifiable referent. If two people could be meant by she, he, or they, use a name or noun to clarify.
- Place a modifier near what it describes. After “Walking into the room,” the following subject should be the person who walked in.
- Choose the grammatical case required by the pronoun’s role. Remove an accompanying name to check a compound object: “for Maya and me” becomes “for me.”
Common mistakes
- Making a verb agree with the closest noun rather than the subject.
- Leaving a pronoun’s referent ambiguous.
- Changing the intended meaning while fixing the grammar.
Remember: For an introductory action phrase, ask: who did this? Put that person or thing next.
Worked example
Revise this sentence so it clearly says that the inspector found the leak while checking the valve: “While checking the valve, a leak was found by the inspector.”
- The introductory phrase describes the person performing the check.
- The current subject is a leak, which cannot check a valve.
- Make the inspector the subject immediately after the introductory phrase.
Answer: While checking the valve, the inspector found a leak.
Language for the audience and purpose
A good revision suits the reader’s knowledge, the document’s purpose, and the action the reader needs to take.
Method
- Identify the audience and purpose before selecting tone. A notice to first-time visitors needs direct instructions, while a technical report may appropriately use defined specialist terms.
- Use familiar words and explain necessary jargon for a general audience. Plain language can remain accurate and professional.
- Replace vague references with specific actions, dates, or locations when the prompt provides them. Do not invent details to make a sentence sound helpful.
- For an objective report, describe observations and evidence rather than insults, speculation, or unsupported certainty.
- Preserve important conditions and limits when simplifying. “Some applications” and “all applications” do not make the same claim.
Common mistakes
- Choosing the longest or most formal wording automatically.
- Replacing useful specific information with a vague phrase.
- Adding promises or facts the original message does not support.
Remember: Ask what this particular reader needs to understand or do next.
Worked example
A library notice for new visitors says, “Patrons must utilize the self-service circulation apparatus prior to egress.” Rewrite it in clear language without changing the instruction.
- The readers are ordinary visitors, not staff learning technical terminology.
- The required action is checking out materials before leaving.
- Use familiar terms and address the reader directly.
Answer: Use the self-checkout machine to check out your items before you leave.
Paragraph unity and organization
A paragraph should develop one central point in an order the reader can follow.
Method
- A topic sentence states the central point; supporting sentences explain, illustrate, or provide evidence for it.
- Choose an order that fits the purpose: steps in sequence, causes before effects, a claim followed by support, or a comparison organized by consistent criteria.
- Track references such as this change or these results. The idea they refer to normally must appear first.
- Use transitions that match the logical relationship. However signals contrast; therefore signals a conclusion or result.
- A true or interesting sentence can still be irrelevant. Keep details that help develop the paragraph’s stated focus.
Common mistakes
- Placing this or these before the reader knows the referent.
- Using a transition because it sounds formal even though its meaning is wrong.
- Keeping an unrelated detail merely because it is accurate.
Remember: Main point → relevant support → explanation or result.
Worked example
Order these sentences: A. “This change reduced the time spent searching for tools.” B. “The workshop reorganized its storage area.” C. “Frequently used tools were placed beside the workbenches.”
- B introduces the reorganization.
- C explains the concrete change.
- A refers back to that change and gives its result.
Answer: B, C, A.
Language and vocabulary in writing
Practice this topicPlanning, revising, and editing
Match the writing task to the problem. Rearranging an argument is revision; fixing a misspelling is editing.
Method
- Before drafting, define the audience, purpose, and scope. Gather relevant evidence and outline a logical route through the main ideas.
- A focused thesis or central claim should be specific enough to guide the document and supportable with the evidence available.
- Revise the substance first: missing support, irrelevant material, unclear organization, or an argument that does not answer the assigned question.
- Edit sentence-level clarity, grammar, and word choice after the overall message works. Proofread the final version for remaining mechanical errors.
- Writing is iterative. New evidence may require returning to an outline or revising a thesis; the stages are useful tools rather than an inflexible one-way sequence.
Common mistakes
- Proofreading a paragraph whose main point still needs to change.
- Treating a strong opinion as sufficient evidence.
- Assuming every draft must follow the same rigid sequence without revisiting earlier decisions.
Remember: Fix the message before polishing its surface.
Worked example
A student has a correctly spelled, grammatical draft arguing for longer weekend library hours. It lists costs but contains no evidence that anyone would use the extra hours. What should the student do next?
- The main problem concerns support for the argument, not spelling or punctuation.
- The writer needs relevant evidence of demand, such as documented requests or attendance data.
- Use the evidence to revise the argument, including any limits it reveals, before final proofreading.
Answer: Gather credible evidence about demand for the extra hours and revise the argument to reflect it.
Inferring meaning from roots and affixes
Break an unfamiliar word into meaningful parts, build a tentative meaning, and check it against the sentence.
Method
- A prefix often changes direction, number, time, or negation: pre- means before, inter- means between, and sub- often means under or below.
- Roots carry a central meaning: chron relates to time, bio to life, and aud to hearing.
- A suffix may signal meaning or word class: -less means without, -able suggests capable of being, and -tion commonly forms a noun naming an action or result.
- Use context to select the sense that fits. A word part supplies a clue, not permission to ignore the sentence.
- Limit the inference to what the parts support: portable describes a capability, not a completed action; biodegradable does not mean something disappears immediately.
- Avoid assuming that every matching sequence of letters is a meaningful affix or that a literal parts-based translation is the word’s only modern meaning.
Common mistakes
- Choosing a definition that matches one prefix but contradicts the context.
- Confusing a word’s grammatical role with its full meaning.
- Inventing a root meaning from a similar-looking but unrelated word.
Remember: Parts suggest; context confirms.
Worked example
“The two sensors were synchronized so that each recorded a measurement at exactly the same moment.” What does synchronized mean in this sentence?
- The root chron relates to time.
- The opening element syn- suggests together.
- The sentence confirms that the sensors record at the same moment.
Answer: Coordinated to operate at the same time.
Five question formats
Most TEAS 7 questions are multiple choice; roughly one fifth use another response format. Read the response instructions before answering. All formats are scored right or wrong, without partial credit.
Multiple choice
Select one answer from four choices.
Solve the question first when possible, then compare the options.
Multiple select
Select every answer that applies.
Check each option independently. A complete correct selection is required; there is no partial credit.
Fill in the blank
Enter the requested answer. Our practice uses numerical entries.
Follow the requested units and rounding. Do not round intermediate calculations unnecessarily.
Ordered response
Place all the options in the required order.
Identify what must come first or last, then check every adjacent step. The whole order must be correct.
Hotspot
Select the requested area on a diagram.
Use the labels and orientation to locate the region. Our practice also provides keyboard-selectable regions.
Format, timing and calculator
| Section | Questions | Minutes |
|---|---|---|
| Reading | 45 | 55 |
| Mathematics | 38 | 57 |
| Science | 50 | 60 |
| English and Language Usage | 37 | 37 |
| Total | 170 | 209 |
3 hours 29 minutes of answering time. An optional 10-minute break follows Mathematics.
Take the sections in the order shown. You can revisit questions within the current section, but you cannot return to a section once you leave it. Unused time does not carry over.
The basic calculator is available in every section. Check units, estimate the expected size of an answer and enter operations carefully; the calculator cannot choose the calculation for you.
In our full practice, the optional 10-minute break follows Mathematics. Question feedback remains hidden until the sitting ends. Standard or 1.5× timing can be selected before starting.
Extra-time practice does not establish eligibility for official accommodations. Arrange those with your testing organization before registration.
Build a study plan around your weak areas
Use these schedules as starting points. Give unfamiliar topics more time, keep all four subjects in rotation and review mistakes before taking another test.
Two-week study plan
Days 1–2
Take the diagnostic. Review every missed question, separate unfamiliar concepts from timing or reading mistakes, and choose two priority domains.
Days 3–7
Work through the matching lessons and short drills. Rotate in the other subjects daily; do not leave English or reading until the end.
Days 8–10
Take timed sections and review them before starting another. Practice skipping and flagging questions that consume too much time.
Days 11–14
Complete a full timed rehearsal, review the weak areas it reveals, then use brief focused practice. Leave time to check your official exam arrangements.
Six-week study plan
Week 1
Take the diagnostic and establish a repeatable study schedule. Review core arithmetic, passage evidence and sentence structure.
Weeks 2–3
Rotate through all four subjects. Spread anatomy and physiology across sessions, and include biology, chemistry and scientific reasoning.
Week 4
Use mixed practice and alternate response types. Explain each missed answer in your own words before replaying the drill.
Week 5
Move to timed sections. Use accuracy, unanswered questions and pacing together to choose the next lesson or drill.
Week 6
Take a full rehearsal with fresh questions where available, review it carefully and finish with targeted practice rather than repeated tests without review.
A missed answer can mean missing knowledge, a misread instruction or a rushed calculation. Note which one applies and choose a lesson, careful drill or timed section accordingly. Repeating the same answers from memory is less useful than solving a fresh problem.
Use your practice results
Start with your subject and topic breakdowns. Read the explanations for incorrect and unanswered questions, then choose a drill that targets the cause. Compare later attempts using the same mode and time setting.
Practice accuracy and official ATI scores
Our percentage is raw accuracy on original practice questions. All 170 questions count toward a full practice result. The real exam contains 150 scored questions and 20 unidentified pretest questions.
ATI equates its overall and section scores to account for differences between test forms. We cannot convert our raw results into those official scores or apply ATI’s preparedness bands to them. Our demanding practice goals are study targets, not admissions predictions.
Programs set their own score requirements and may consider other application information. Check your school’s minimums and how it uses the TEAS result.
Check these before exam day
- Confirm that your program requires TEAS and accepts your selected testing format and score date.
- Check its application deadline, score-report delivery requirements and retake rules.
- Read the current identification, arrival and permitted-material instructions from your testing organization.
- For a remote sitting, complete the required equipment and environment checks in advance.
- Arrange any accommodations before registering and follow the instructions supplied for your approved setup.
- Use official ATI examples as well as this independent practice so the official question formats feel familiar.
Official TEAS guidance
Original independent preparation, not affiliated with or endorsed by ATI. This guide covers TEAS 7 admissions testing, not HESI A2, NCLEX or ATI nursing-course exams.