Mathematical Reasoning Practice Questions

1. If 2ˣ = 32, what is the value of x?

3

4

5

6

2. If sin(θ) = 4/5, what is cos(θ)?

3/5

4/5

5/13

12/13

3. What is the sum of the solutions to the equation x² - 5x + 6 = 0?

3

4

5

6

4. If a cube has a volume of 27 cubic units, what is the length of its diagonal?

3√3 units

9 units

3√2 units

6 units

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

25

30

35

40

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

1/6

1/9

1/12

1/36

7. What is the value of (3 + 4i)(3 - 4i), where i is the imaginary unit?

9

16

25

41

8. If a² + b² = c² and a = 3, b = 4, what is c?

5

6

7

8

9. If sin(θ) = 3/5 and θ is in the second quadrant, what is cos(θ)?

-4/5

-3/5

3/5

4/5

10. If log₃(x) = 4, what is the value of log₉(x)?

1

2

3

4