BLEPT Reviewer 1 MATH

BLEPT MATH Reviewer

Instructions:

Please answer each question to the best of your ability. Each question is multiple choice, and only one answer per question is correct. Select the most appropriate answer from the options provided.

When you have completed all questions, click the "Submit" button at the bottom of the page to see your score. Good luck!

1. What is the derivative of f(x) = 3x² + 2x + 7?

A) 6x + 2
B) 6x + 7
C) 3x + 2
D) 3x² + 2

2. Evaluate: lim_x→0 (sin x)/x

A) 0
B) 1
C) ∞
D) -1

3. Find the integral of f(x) = 6x.

A) 3x² + C
B) 6x² + C
C) 3x² + C
D) x³ + C

4. Solve: If log₂(x) = 5, then x = ?

A) 10
B) 32
C) 25
D) 16

5. Find the sum of the infinite geometric series: 3 + 1 + 1/3 + 1/9 + ...

A) 9/2
B) 3/2
C) 6
D) 5

6. What is the determinant of the matrix |2 3| |1 4|?

A) 10
B) 5
C) 7
D) 2

7. Solve for x: e^x = 5

A) ln(1/5)
B) ln(5)
C) 5
D) -ln(5)

8. Find the second derivative of f(x) = x³ - 2x² + x.

A) 6x - 2
B) 6x - 4
C) 3x² - 4x + 1
D) 6x + 2

9. Find the value of cos(60°).

A) √3/2
B) 1/2
C) 1
D) 0

10. Solve for x: 2x + 3 = 5x - 9

A) 4
B) 3
C) -4
D) -3

11. What is the solution set of x² - 5x + 6 = 0?

A) {1, 5}
B) {2, 3}
C) {-2, -3}
D) {3, 5}

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

A) 9
B) 8
C) 9
D) 6

13. Find the area under y = 2x from x = 0 to x = 3.

A) 12
B) 10
C) 9
D) 8

14. Solve for x: ln(x) = 2

A) e²
B) 2e
C) e
D) 2

15. What is the binomial coefficient "5 choose 2"?

A) 20
B) 10
C) 15
D) 5

16. Simplify: (x³y²)(x²y³)

A) x⁵y⁵
B) x⁶y⁶
C) x⁵y⁵
D) x⁶y⁵

17. What is the slope of the line 3x - 2y = 6?

A) 2/3
B) 3/2
C) -2/3
D) -3/2

18. Find the magnitude of the vector v = (3, 4).

A) 4
B) 7
C) 5
D) 6

19. Find the domain of f(x) = 1/(x² - 4).

A) All real numbers
B) All real numbers except x = 2, -2
C) x > 0
D) x ≠ 0

20. Solve: |x - 4| = 5

A) x = -1 only
B) x = 9 only
C) x = -1 or x = 9
D) x = 1 or 9

21. Simplify: (2x - 3)²

A) 4x² - 12x + 9
B) 4x² + 9
C) 4x² - 6x + 9
D) 2x² - 6x + 9

22. Find the angle between two vectors a and b where a · b = 0.

A) 90°
B) 45°
C) 180°
D) 0°

23. Which of the following represents an even function?

A) y = x³
B) y = x²
C) y = x³ + 2
D) y = x + 1

24. Find the range of f(x) = x² + 2x + 5.

A) All real numbers
B) [4, ∞)
C) (-∞, 5]
D) [0, ∞)

25. If sin θ = 3/5, what is cos θ in the first quadrant?

A) 4/5
B) 3/5
C) 5/3
D) √2/2

26. What is the polar form of the point (0, -2)?

A) (2, 90°)
B) (2, 0°)
C) (2, 270°)
D) (2, 180°)

27. Find the number of permutations of the word "BOOK".

A) 12
B) 12
C) 24
D) 6

28. Solve for x: 4^(x-1) = 64

A) 4
B) 4.5
C) 5
D) 6

29. Find the volume of a sphere with radius 2.

A) (32/3)π
B) (16/3)π
C) 8π
D) 4π

30. Find the value of tan(45°).

A) 1
B) 0
C) √3
D) 1/√3

Result