Mathematical Reasoning Practice Questions

1. If log₃(x) = 4 and log₃(y) = 2, what is log₃(x/y)?

1

2

3

4

2. What is the value of cos(arcsin(3/5))?

3/5

4/5

5/3

5/4

3. If f(x) = e^x and g(x) = ln(x), what is (f ∘ g)(e)?

e

e²

ln(e)

e^e

4. If log₅(x) = 2 and log₅(y) = 3, what is log₅(x²y)?

5

6

7

8

5. What is the sum of the geometric sequence 1, 2, 4, 8, ..., 128?

127

255

256

511

6. In a right triangle, if one angle is 30°, what is the ratio of the shorter leg to the hypotenuse?

1:3

1:2

√3:2

1:√2

7. If a triangle has sides of length 5, 12, and 13 units, what is its area?

30 square units

60 square units

90 square units

120 square units

8. If the radius of a sphere is tripled, by what factor does its volume increase?

9

18

27

81

9. If the radius of a circle is doubled, by what factor does its area increase?

2

3

4

8

10. 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