[ LET 47 ] Board Licensure Examination for Professional Teachers REVIEWER - Mathematics

Professional Education.

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. There are 50 questions in total.

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

1. Solve for \( x \): \( \frac{x + 2}{x - 3} = \frac{2}{x + 1} \)

A) 4
B) 5
C) 3
D) 1

2. Simplify: \( \frac{x^2 - 4}{x^2 - 2x - 8} \)

A) \( \frac{x + 2}{x - 4} \)
B) \( \frac{x - 2}{x + 4} \)
C) \( \frac{x - 4}{x + 2} \)
D) \( x + 2 \)

3. If \( \frac{1}{x - 2} + \frac{2}{x + 3} = 0 \), find \( x \).

A) 5
B) -3
C) -2
D) 2

4. Solve for \( x \): \( \frac{x^2 - 1}{x^2 - 4} = \frac{2}{3} \)

A) -1
B) 1
C) 2
D) -2

5. Simplify: \( \frac{4x^2 - 16}{2x^2 - 8} \)

A) 2
B) \( \frac{2(x + 2)}{x - 4} \)
C) \( \frac{4(x + 2)}{x - 4} \)
D) \( \frac{x + 4}{x - 2} \)

6. If \( \frac{3}{x + 1} - \frac{5}{x - 2} = 1 \), find \( x \).

A) 3
B) 0
C) -1
D) -2

7. Simplify: \( \frac{x^3 - 8}{x - 2} \)

A) \( x^2 + 2x + 4 \)
B) \( x^2 - 2x + 4 \)
C) \( x^2 + 2x - 4 \)
D) \( x^2 - 2x - 4 \)

8. Find \( x \) if \( \frac{2x}{x - 3} = \frac{4}{x + 1} \).

A) 5
B) 3
C) 2
D) 1

9. Solve for \( x \): \( \frac{x + 5}{x - 1} + \frac{x - 1}{x + 5} = 2 \).

A) 0
B) 4
C) -4
D) 3

10. Simplify: \( \frac{x^2 + 3x + 2}{x^2 - 1} \)

A) \( \frac{x + 2}{x - 1} \)
B) \( \frac{x + 1}{x + 1} \)
C) \( x + 1 \)
D) \( x + 2 \)

11. If \( \frac{4}{x - 2} + \frac{3}{x + 1} = 1 \), find \( x \).

A) 5
B) 2
C) 1
D) 0

12. Solve for \( x \): \( \frac{x^2 - 9}{x^2 - 4} = \frac{1}{2} \)

A) 1
B) -1
C) 3
D) -3

13. If \( \frac{x + 1}{x - 1} - \frac{x - 1}{x + 1} = 0 \), find \( x \).

A) 0
B) 1
C) -1
D) 2

14. Simplify: \( \frac{x^2 + 4x + 4}{x^2 - 1} \)

A) \( \frac{(x + 2)^2}{(x - 1)(x + 1)} \)
B) \( x + 3 \)
C) \( x + 2 \)
D) \( x + 1 \)

15. Solve for \( x \): \( \frac{x - 2}{x + 3} = \frac{3}{4} \)

A) 6
B) 5
C) 4
D) 3

16. If \( \frac{2x + 1}{x - 3} = 5 \), find \( x \).

A) 4
B) 7
C) 6
D) 3

17. Simplify: \( \frac{5x^2 - 15}{10x - 30} \)

A) \( \frac{x}{2} \)
B) \( \frac{3}{2} \)
C) \( \frac{x - 3}{2} \)
D) \( \frac{5}{3} \)

18. If \( \frac{3}{x + 2} - \frac{2}{x - 3} = 1 \), find \( x \).

A) 1
B) 4
C) -4
D) -1

19. Solve for \( x \): \( \frac{x - 1}{x + 2} + \frac{x + 2}{x - 1} = 5 \).

A) 3
B) 4
C) -1
D) 1

20. Simplify: \( \frac{3x^3 + 6x^2}{3x^2} \)

A) \( x + 2 \)
B) \( x^2 + 2x \)
C) \( 2x + 3 \)
D) \( 2x + 1 \)

21. If \( \frac{x + 4}{x - 1} = 3 \), find \( x \).

A) -3
B) 5
C) 7
D) 1

22. Solve for \( x \): \( \frac{2x + 1}{x - 3} = \frac{5}{3} \)

A) 4
B) 5
C) 1
D) -1

23. Simplify: \( \frac{x^2 - 1}{x^2 + 2x + 1} \)

A) \( \frac{(x - 1)(x + 1)}{(x + 1)^2} \)
B) \( \frac{x - 1}{x + 1} \)
C) \( x - 1 \)
D) \( x + 1 \)

24. If \( \frac{1}{x - 1} + \frac{1}{x + 1} = 0 \), find \( x \).

A) 1
B) -1
C) 0
D) 2

25. Solve for \( x \): \( \frac{x + 2}{x - 1} = \frac{4}{x + 3} \)

A) 5
B) -5
C) -2
D) 4

26. Simplify: \( \frac{2x^2 - 8}{x^2 - 4} \)

A) \( 2 \)
B) \( 2 \cdot \frac{x + 2}{x - 2} \)
C) \( x + 4 \)
D) \( 2 \cdot \frac{x - 2}{x + 2} \)

27. If \( \frac{3x - 1}{x + 2} = 2 \), find \( x \).

A) -5
B) 4
C) 3
D) 2

28. Solve for \( x \): \( \frac{x^2 - 4}{x - 2} = 0 \)

A) 2
B) 4
C) 0
D) -2

29. Simplify: \( \frac{6x^2 + 9x}{3x} \)

A) \( 3x + 2 \)
B) \( 2x + 3 \)
C) \( 2x + 6 \)
D) \( 2x + 9 \)

30. If \( \frac{x^2 - 1}{x^2 - x - 2} = 0 \), find \( x \).

A) 1
B) -1
C) 2
D) -2

31. Solve for \( x \): \( \frac{2x + 5}{x - 3} = \frac{3}{2} \)

A) 1
B) 4
C) 7
D) 2

32. Simplify: \( \frac{4x^3 - 8x^2}{4x^2} \)

A) \( x - 2 \)
B) \( x + 2 \)
C) \( 2x - 4 \)
D) \( 2x + 4 \)

33. If \( \frac{x - 3}{x + 1} + \frac{x + 1}{x - 3} = 4 \), find \( x \).

A) 5
B) -2
C) 4
D) 3

34. Solve for \( x \): \( \frac{x^2 + 3x}{x + 2} = 3 \)

A) -1
B) 1
C) 2
D) 0

35. Simplify: \( \frac{5x^3 + 10x^2}{5x^2} \)

A) \( 2x + 5 \)
B) \( x + 2 \)
C) \( x + 5 \)
D) \( 2x + 3 \)

36. If \( \frac{x + 5}{x - 2} = 4 \), find \( x \).

A) 6
B) 2
C) 5
D) 4

37. Solve for \( x \): \( \frac{x^2 - 5x}{x - 4} = 2 \)

A) 5
B) 3
C) 1
D) 0

38. If \( \frac{4x + 1}{x + 3} = \frac{1}{2} \), find \( x \).

A) 2
B) -2
C) -5
D) -1

39. Solve for \( x \): \( \frac{3x - 2}{2} = 4 \)

A) 5/6
B) 10/3
C) 2/3
D) 4/7

40. Simplify: \( \frac{8x^2 - 4x}{4x} \)

A) \( 2x - 1 \)
B) \( 2x + 1 \)
C) \( 4x - 1 \)
D) \( 2x + 4 \)

41. Solve for \( x \): \( \frac{x^2 - 9}{x - 3} = 0 \)

A) 3
B) -3
C) 0
D) 9

42. If \( \frac{2x + 3}{x - 1} = 5 \), find \( x \).

A) 4
B) 1
C) -1
D) 2

43. Simplify: \( \frac{x^2 - 16}{x^2 - 4} \)

A) \( \frac{x + 4}{x + 2} \)
B) \( \frac{x - 4}{x - 2} \)
C) \( 4 \)
D) \( x + 2 \)

44. If \( \frac{x + 2}{x - 3} = \frac{2}{5} \), find \( x \).

A) -1
B) -5
C) 2
D) 1

45. Solve for \( x \): \( \frac{3x + 1}{2x - 5} = 2 \)

A) 4
B) 3
C) 5
D) 2

46. Simplify: \( \frac{x^2 + 5x + 6}{x + 2} \)

A) \( x + 3 \)
B) \( x + 2 \)
C) \( 2x + 3 \)
D) \( 2x + 1 \)

47. If \( \frac{5x - 3}{x + 4} = 1 \), find \( x \).

A) 1
B) 5
C) 3
D) 2

48. Solve for \( x \): \( \frac{2x - 1}{x + 3} = 3 \)

A) 1
B) 9
C) 4
D) 3

49. Simplify: \( \frac{9x^2 - 1}{3x + 1} \)

A) \( 3x - 1 \)
B) \( 3x + 1 \)
C) \( 2x + 1 \)
D) \( x - 1 \)

50. If \( \frac{x^2 - 4}{x^2 - x - 6} = 0 \), find \( x \).

A) -2
B) 2
C) 0
D) 1

Result

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