College Entrance Examination Reviewer 9

College Entrance Exam 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 solution to the equation \( 3x - 7 = 11 \)?

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

2. Simplify: \( (2x^2y)(3xy^2) \)

A) \( 5x^3y^3 \)
B) \( 6x^2y^2 \)
C) \( 6x^3y^3 \)
D) \( 5x^2y^2 \)

3. What is the domain of the function \( f(x) = \frac{1}{x - 3} \)?

A) All real numbers
B) \( x \neq 0 \)
C) \( x > 3 \)
D) \( x \neq 3 \)

4. Solve for x: \( x^2 - 4x - 5 = 0 \)

A) \( x = 5, x = -1 \)
B) \( x = 4, x = -2 \)
C) \( x = 3, x = -3 \)
D) \( x = 2, x = -5 \)

5. Factor: \( x^2 + 6x + 9 \)

A) \( (x + 3)^2 \)
B) \( (x - 3)^2 \)
C) \( (x + 2)(x + 4) \)
D) \( (x + 1)(x + 9) \)

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

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

7. What is the solution to the inequality \( 2x - 5 > 3 \)?

A) \( x < 4 \)
B) \( x > 4 \)
C) \( x > -4 \)
D) \( x < -4 \)

8. What is the vertex of the parabola \( y = x^2 - 6x + 8 \)?

A) (2, 0)
B) (3, 8)
C) (3, -1)
D) (1, 2)

9. Find the inverse of \( f(x) = 2x + 1 \)

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

10. Evaluate: \( \log_2(8) \)

A) 2
B) 3
C) 4
D) 1

11. Solve for x: \( 5^{x} = 125 \)

A) 3
B) 5
C) 25
D) 4

12. What is the sum of the roots of \( x^2 - 7x + 12 = 0 \)?

A) 7
B) 12
C) -7
D) 5

13. Rationalize: \( \frac{1}{\sqrt{5}} \)

A) \( \sqrt{5} \)
B) \( \frac{\sqrt{5}}{5} \)
C) \( \frac{5}{\sqrt{5}} \)
D) \( \frac{1}{5} \)

14. What is the discriminant of \( x^2 + 4x + 4 = 0 \)?

A) 8
B) 0
C) -4
D) 16

15. Which of the following is a solution to \( |x - 2| = 5 \)?

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

16. What is the horizontal asymptote of the function \( f(x) = \frac{2x + 3}{x + 1} \)?

A) y = 0
B) y = 2
C) y = 1
D) y = 3

17. What is the degree of the polynomial \( 3x^4 - 5x^2 + 2x - 1 \)?

A) 2
B) 4
C) 1
D) 3

18. Which of the following is equivalent to \( (x + 2)^2 \)?

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

19. Solve for x: \( x^2 = 49 \)

A) \( x = \pm 7 \)
B) \( x = 7 \)
C) \( x = 49 \)
D) \( x = \pm 14 \)

20. What is the value of the expression \( \sqrt{16} + \sqrt{9} \)?

A) 6
B) 7
C) 5
D) 8

21. What is the slope of the line \( y = -3x + 7 \)?

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

22. Simplify: \( (x^3)^2 \)

A) \( x^5 \)
B) \( x^3 \)
C) \( x^6 \)
D) \( x^9 \)

23. Find the value of \( f(2) \) for \( f(x) = 3x^2 + 1 \)

A) 7
B) 12
C) 13
D) 11

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

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

25. What is the standard form of the equation of a circle with center at (0, 0) and radius 4?

A) \( x^2 + y^2 = 8 \)
B) \( x + y = 4 \)
C) \( x^2 + y^2 = 16 \)
D) \( x^2 + y^2 = 4 \)

26. What are the x-intercepts of the graph of \( y = (x - 2)(x + 5) \)?

A) x = 2 and x = -5
B) x = -2 and x = 5
C) x = 0 and x = 5
D) x = -2 and x = -5

27. If \( f(x) = x^2 \) and \( g(x) = 2x \), what is \( (f \circ g)(x) \)?

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

28. Solve: \( \frac{3}{x} + \frac{2}{x} = \frac{10}{x} \)

A) x = 1
B) x = 5
C) x = 10
D) No solution

29. If \( a^2 = 9 \), what are the possible values of \( a \)?

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

30. What is the range of the function \( f(x) = x^2 \)?

A) All real numbers
B) \( [0, \infty) \)
C) \( (-\infty, 0] \)
D) \( (-\infty, \infty) \)

Result

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