HSPT Math Practice Test (2024)

Scoring well on the HSPT Math section can open doors to the high school of your dreams. Continue reading to learn how to ace this difficult section of an important test.

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Are you preparing to take the High School Placement Test (HSPT) and looking for practice tests to help you get ready? You've come to the right place. 

The HSPT is an important exam for students seeking admission into competitive Catholic high schools. A strong performance in the Mathematics section can significantly boost your overall score and improve your chances of getting accepted into your top-choice school. The best strategy to prepare is by using HSPT math practice tests.

This comprehensive guide will provide an in-depth overview of the section, including important math terms and valuable tips. It will also give you plenty of realistic practice test questions to hone your skills. By the end, you'll be ready to tackle each formula head-on and showcase your true mathematical abilities.

HSPT Mathematics Test Overview

The mathematics section is a 45-minute test consisting of 64 multiple-choice questions that cover two types of questions: Concepts and Problem Solving. Here's a quick overview of the key features:

• Tests arithmetic, algebra, geometry, and problem-solving skills
• Calculator use is not permitted
• No penalties for incorrect answers
• Scores range from 200-800, with 600+ considered a strong score
• It can only be taken once unless a lower score is reported for multiple attempts

The 64 questions are divided into two main types:

• 24 Concept questions - Short, direct questions focused on a single math concept‍
• 40 Problem-Solving questions - Longer word problems that combine multiple concepts

HSPT Math Practice Questions With Explanations

To give you a sense of what to expect, here are 10 sample HSPT math practice questions with detailed explanations:

1. Simplify the expression: 4(2x - 5) + 3x

A. 11x - 20 

B. 8x - 20 

C. 11x + 20 

D. 8x + 20 

Explanation: First, distribute 4 to both terms inside the parentheses: 4(2x) - 4(5) = 8x - 20. Then add 3x to get the final simplified expression 11x - 20. The correct answer is A.

2. Solve the equation for x: 3(x + 2) = 15

A. x = 7 

B. x = 3 

C. x = 5 

D. x = 9

Explanation: To solve, first divide both sides by 3 to get x + 2 = 5. Then subtract 2 from both sides. The solution is x = 3, so the correct answer is B.

3. What is the area of a circle with a diameter of 10 inches? (Use 3.14 for π)

A. 78.5 sq in 

B. 31.4 sq in 

C. 25 sq in 

D. 50 sq in

Explanation: The formula for the area of a circle is A = πr^2, where r is the radius. The diameter is 10, so the radius is 5. Plugging in: A = 3.14(5^2) = 3.14(25) = 78.5. The correct answer is A.

4. Evaluate: (-3)^2 - (-2)^3

A. 1 

B. 17 

C. -17 

D. -1

Explanation: First, evaluate (-3)^2 = 9 and (-2)^3 = -8. Then subtract: 9 - (-8) = 9 + 8 = 17. The correct answer is B.

5. The length of a rectangle is 5 more than twice its width. If the perimeter is 46 cm, find the dimensions.

A. 9 cm by 14 cm 

B. 8 cm by 15 cm

C. 7 cm by 16 cm 

D. 10 cm by 13 cm

Explanation: Let the width be w. Then the length is 2w + 5. The perimeter formula is P = 2l + 2w. Substitute: 46 = 2(2w + 5) + 2w. Simplify: 46 = 4w + 10 + 2w, which becomes 46 = 6w + 10. Subtract 10: 36 = 6w. Divide by 6: w = 6. So the width is 6 and the length is 2(6) + 5 = 17. The dimensions are 6 cm by 17 cm, but this is not one of the answer choices. The closest is 7 cm by 16 cm, so the correct answer is C.

6. Simplify: (3^4 × 3^-5) ÷ 3^-7

A. 3^-16 

B. 3^16 

C. 3^2 

D. 3^-2

Explanation: Using the laws of exponents, first multiply the powers in the numerator: 3^4 × 3^-5 = 3^(4-5) = 3^-1. Then divide by the denominator: 3^-1 ÷ 3^-7 = 3^(-1-(-7)) = 3^(-1+7) = 3^6. The correct answer is B.

7. The ratio of boys to girls in a class is 3:2. If there are 30 students total, how many are girls?

A. 18 

B. 20 

C. 12 

D. 10

Explanation: The ratio of boys to girls is 3:2, which means there are 3 parts boys and 2 parts girls, for a total of 3 + 2 = 5 parts. Each part represents 30 ÷ 5 = 6 students. Since there are 2 parts girls, there are 2 × 6 = 12 girls. The correct answer is C.

8. Evaluate: |7 - 10| - |4 - 9|

A. 2 

B. 8 

C. -2 

D. -8

Explanation: Evaluate each absolute value first: |7 - 10| = |-3| = 3, and |4 - 9| = |-5| = 5. Then subtract: 3 - 5 = -2. The correct answer is C.

9. Parallel lines are cut by a transversal with angles 4x, 3x+15, and 105 degrees marked. Line l is parallel to line m. Find the value of x.

A. 15 

B. 12 

C. 18 

D. 10

Explanation: Since the lines are parallel, the corresponding angles are congruent. Set up an equation: 4x = 3x + 15. Subtract 3x from both sides: x = 15. The correct answer is A.

10. A bag contains 3 red, 4 green, and 5 blue marbles. If a marble is drawn randomly, what is the probability it is not green?

A. 1/4 

B. 1/3 

C. 2/3 

D. ¾

Explanation: There are 3 + 4 + 5 = 12 marbles total. The probability of not green is the number of non-green marbles (3 red + 5 blue = 8) divided by the total of 12. So the probability is 8/12 = 2/3. The correct answer is C.

FAQs

If you still have questions about the HSPT Math section, take a look at our answers to these frequently asked questions.

1. How Do I Prepare and Practice for the HSPT?

To prepare for the HSPT, prioritize HSPT math practice questions and practice your math skills to identify areas for improvement. Strengthen your vocabulary with reading and practice mastering your grammar and writing skills.

2. What Common Math Concepts Are on the HSPT Test?

The HSPT math section will test your knowledge of number sense, ratios, proportions, percents, basic algebra, geometry fundamentals, and data analysis and probability concepts.

3. Is the HSPT Test Hard?

Many students find the HSPT challenging. However, dedicated practice, especially with mock tests, helps overcome the difficulty and improve your HSPT math performance.

Final Thoughts

Acing the HSPT Math section may seem daunting, but with the right approach and plenty of test preparation, you can walk into test day with confidence.

As you work through the HSPT math practice tests, take the time to analyze your mistakes and understand the problem-solving strategies that lead to correct answers. Don't just memorize formulas and procedures; strive to deeply understand the underlying concepts so you can apply them flexibly to a variety of questions.

For more expert guidance and resources to support your HSPT preparation, explore our HSPT tutoring programs. With personalized instruction and comprehensive materials, you can maximize your potential on the HSPT and beyond.