Praxis Core Math Practice Test: Geometry and Measurement
- Geometry and Measurement
- 10 questions
- 14 minutes
Ten geometry and measurement questions like those on the Praxis Core Mathematics test. Tip: write the units next to every number; a unit that does not match is often the clue to a mistake.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
A rectangular rug is 12 feet long and 7.5 feet wide. What is its area?
Correct answer: B
Area = length × width = 12 × 7.5 = 90 square feet. Adding all four sides gives the perimeter, 39 feet, not the area.
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Question 2
A circle has a radius of 5 centimeters. What is its area?
Correct answer: C
Area = πr2 = π × 52 = 25π. The value 10π is the circumference, and 100π uses the diameter in place of the radius.
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Question 3
The two legs of a right triangle are 9 inches and 12 inches long. How long is the hypotenuse?
Correct answer: A
92 + 122 = 81 + 144 = 225, and the square root of 225 is 15. Adding the legs (21) ignores the Pythagorean theorem.
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Question 4
A box is 30 cm long, 20 cm wide and 10 cm high. How many liters does it hold? (1 liter = 1,000 cubic centimeters)
Correct answer: B
Volume = 30 × 20 × 10 = 6,000 cm3, and 6,000 ÷ 1,000 = 6 liters. Moving the decimal point the wrong way gives 60 or 600.
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Question 5
A shelf is 2.5 feet long. How many inches long is it?
Correct answer: C
There are 12 inches in a foot, so 2.5 × 12 = 30 inches. Treating a foot as 10 inches gives 25.
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Question 6
Two angles of a triangle measure 48° and 67°. What is the measure of the third angle?
Correct answer: D
The angles of a triangle add up to 180°: 180 − 48 − 67 = 65°. The value 115° is the sum of the two given angles.
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Question 7
A 6-foot-tall person casts a shadow 4 feet long. At the same time, a tree casts a shadow 18 feet long. How tall is the tree?
Correct answer: B
The ratio of height to shadow is 6 : 4 = 1.5, so the tree is 18 × 1.5 = 27 feet tall. Flipping the ratio to 4 : 6 gives the wrong answer of 12 feet.
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Question 8
Two angles are supplementary. One of them measures 112°. What is the measure of the other angle?
Correct answer: A
Supplementary angles add up to 180°, so 180 − 112 = 68°. The answer 248° uses 360° as the total, and 112° would fit only if the angles had to be equal.
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Question 9
A rectangular garden is 10 meters by 6 meters. A triangular pond with a base of 4 meters and a height of 3 meters is built inside it. How many square meters of the garden are left for planting?
Correct answer: D
Garden: 10 × 6 = 60 m2. Pond: 12 × 4 × 3 = 6 m2. Left: 60 − 6 = 54 m2. Forgetting the 12 in the triangle formula gives 48.
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Question 10
What is the distance between the points (1, 2) and (4, 6) on the coordinate plane?
Correct answer: C
The horizontal change is 3 and the vertical change is 4, so the distance is the square root of 32 + 42 = 25, which is 5. Adding 3 + 4 = 7 skips the Pythagorean theorem.
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