Content category III of the Core Academic Skills for Educators: Mathematics (5733): about 18 of the 56 questions (32%). The topics ETS lists, how they are tested and practice questions with explanations.
56 questions on the real 90-minute clock, weighted like the ETS test, with a score by content category and an explanation for every answer.
Or start the free Algebra and Geometry drillFrom the ETS Core Academic Skills for Educators: Mathematics (5733) Study Companion, content category III.
Translating words into expressions and equations, solving linear equations and inequalities, working with simple functions and graphs, and core geometry: angle facts, similar triangles, the Pythagorean theorem, and perimeter, area and volume formulas.
Answer each question, then open the explanation.
Question 1
How many lines of reflection symmetry does a rectangle with unequal adjacent side lengths have?
Answer: C: 2
The horizontal and vertical midlines each divide the rectangle into mirror-image halves. Its diagonals are not symmetry lines because adjacent sides have unequal lengths.
Question 2
Two triangles are similar. A side of the smaller triangle is 8 centimeters and its corresponding side in the larger triangle is 12 centimeters. Another side of the smaller triangle is 10 centimeters. How long is its corresponding side in the larger triangle, in centimeters?
Answer: C: 15
The scale factor from smaller to larger is 12/8 = 1.5. Multiplying the other side by 1.5 gives 15 centimeters.
Question 3
A number y is one third of the quantity obtained by subtracting 7 from twice a number x. Which equation expresses x in terms of y?
Answer: D: x = (3y + 7)/2
The stated relationship is y = (2x − 7)/3. Multiplying by 3, adding 7, and dividing by 2 gives x = (3y + 7)/2.
Question 4
Which expression is equal to x + y for all real numbers x and y?
Answer: B: y + x
Changing the order of the addends leaves their sum unchanged. Products, quotients, and differences do not equal the sum for all real values.
Take the full test under the real clock
56 questions on the real 90-minute clock, weighted like the ETS test, with a score by content category and an explanation for every answer.
Or start the free Algebra and Geometry drillETS lists about 18 of the 56 questions in Algebra and Geometry, about 32% of the test.
Algebra: properties of operations, equivalent expressions, writing equations that model problems, solving linear equations and simple quadratic equations, linear inequalities, functions and their graphs; Geometry: angles, parallel and perpendicular lines, properties of triangles and polygons, congruence and similarity, the Pythagorean theorem, perimeter, circumference, area and volume, and the coordinate plane.
Translating words into expressions and equations, solving linear equations and inequalities, working with simple functions and graphs, and core geometry: angle facts, similar triangles, the Pythagorean theorem, and perimeter, area and volume formulas.
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