Mathematical Reasoning Practice Questions

1. If the half-life of a radioactive substance is 10 days, what percentage of the substance remains after 30 days?

12.5%

25%

33.3%

37.5%

2. What is the value of cos 60°?

1/4

1/3

1/2

√3/2

3. What is the value of ∑ⁿᵢ₌₁ i², where n = 5?

30

45

55

65

4. 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

5. If the probability of an event A is 0.3 and the probability of event B is 0.4, what is the probability of either A or B occurring if they are mutually exclusive?

0.12

0.5

0.7

0.8

6. What is the area of a triangle with sides of length 3, 4, and 5 units?

6 square units

7.5 square units

9 square units

10 square units

7. If f(x) = x³ - 2x² + x - 3, what is f'(x)?

3x² - 4x + 1

3x² - 4x - 3

3x² - 2x + 1

x² - 4x + 1

8. If 4ˣ = 64, what is the value of x?

2

3

4

6

9. What is the slope of a line parallel to y = -3x + 2?

-3

-1/3

1/3

3

10. What is the value of cos(60°)?

1/4

1/3

1/2

√3/2