## 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.