Mathematical Reasoning Practice Questions

1. What is the probability of rolling a sum of 7 with two fair six-sided dice?

1/6

1/9

1/12

1/36

2. What is the sum of the interior angles of a nonagon (9-sided polygon)?

1080°

1260°

1440°

1620°

3. What is the solution to the equation |2x + 1| = 7?

x = -4 or x = 3

x = -4 or x = 4

x = -3 or x = 3

x = -3 or x = 4

4. If f(x) = 3x + 2 and g(x) = x² - 1, what is (g ∘ f)(2)?

49

56

63

64

5. What is the area of a regular hexagon with side length 4?

24√3

32√3

36√3

48√3

6. If a regular octagon has a side length of 5 units, what is its area?

60.36 square units

70.71 square units

80.82 square units

90.93 square units

7. If f(x) = x³ - 2x + 1, what is f'(x) (the derivative of f(x))?

3x² - 2

3x² + 2

x² - 2

x² + 2

8. If f(x) = x² - 4x + 4, what are the x-intercepts of f(x)?

x = 0 and x = 4

x = 2 only

x = -2 and x = 6

No x-intercepts

9. If the diameter of a circle is increased by 20%, by what percentage does the area increase?

20%

36%

40%

44%

10. If the sum of two numbers is 15 and their product is 56, what is the sum of their squares?

113

117

121

125