Content category II of the Elementary Education: Mathematics Subtest (5003): about 15 of the 50 questions (30%). The topics ETS lists, how they are tested and practice questions with explanations.
50 questions on the real 65-minute clock, weighted like the ETS test, with a score by content category and an explanation for every answer.
Or start the free Algebraic Thinking drillFrom the ETS Elementary Education: Mathematics Subtest (5003) Study Companion, content category II.
Algebraic thinking at the elementary level: writing and evaluating expressions, solving one- and two-step equations and inequalities, interpreting what a solution means in a word problem, and extending number and shape patterns. Know the properties of equality and how a pattern’s rule is written.
Answer each question, then open the explanation.
Question 1
The perimeter of a rectangle is given by P = 2l + 2w. If P = 46 centimeters and l = 15 centimeters, what is w? Enter the number of centimeters.
Numeric entry: answer in centimeters.
Answer: 8 centimeters
Substitute the known values to get 46 = 30 + 2w. Then 16 = 2w, so w = 8 centimeters; 16 is twice the width.
Question 2
The formula A = bh/2 gives the area of a triangle. Which formula gives h in terms of A and b, where b is positive?
Answer: B: h = 2A/b
Multiplying A = bh/2 by 2 gives 2A = bh, and dividing by b gives h = 2A/b. The expression A/(2b) divides by 2 instead of undoing division by 2.
Question 3
Three students each buy a notebook costing x dollars and a folder costing $2. Their group also pays one $5 delivery fee. Which expression gives the total cost in dollars?
Answer: A: 3(x + 2) + 5
Each student spends x + 2, so the three students spend 3(x + 2). Adding one delivery fee gives 3(x + 2) + 5; placing 5 inside the parentheses would charge the fee three times.
Question 4
In the expression 6p + 11, what is the coefficient of p?
Answer: B: 6
The coefficient is the numerical factor multiplying the variable, which is 6. The number 11 is the constant term, while 6p is the entire variable term.
Take the full test under the real clock
50 questions on the real 65-minute clock, weighted like the ETS test, with a score by content category and an explanation for every answer.
Or start the free Algebraic Thinking drillETS lists about 15 of the 50 questions in Algebraic Thinking, about 30% of the test.
Knows how to evaluate and manipulate algebraic expressions, equations and formulas; Understands the meanings of the solutions to linear equations and inequalities; Knows how to recognize and represent patterns (number and shape).
Algebraic thinking at the elementary level: writing and evaluating expressions, solving one- and two-step equations and inequalities, interpreting what a solution means in a word problem, and extending number and shape patterns. Know the properties of equality and how a pattern’s rule is written.
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