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MATH 40 SAMPLE QUESTIONS

The following questions are a small sample of the material covered in Math 40. You will find the answers at the bottom of the page. If you wish to print this sheet, click on the pdf icon to view a printable version.

For a sample of Math 15 questions click here or for Math 20 click here.



1. In the completely factored form of \( 8x^{2} - 24x \), one of the factors is:

A. \( x - 16 \) B. \( x - 27 \) C. \( x - 3 \) D. \( 2x - 6 \)



2. In the completely factored form of \( 12x^{2} - 17x - 5 \), one of the factors is:

A. \( 3x + 5 \) B. \( 3x - 5 \) C. \( 4x - 5 \) D. \( 6x - 5 \)



3. In the completely factored form of \( 64m^{2} - 25n^{2} \), one of the factors is:

A. \( 4m - 5 \) B. \( 4m + 5n \) C. \( 8m + 5 \) D. \( 8m + 5n \)



4. In the completely factored form of \( 6w^{2} + 5w - 4 \), one of the factors is:

A. \( 6w - 1 \) B. \( 3w - 1 \) C. \( 3w + 4 \) D. \( 3w - 4 \)



5. The completely factored form of \( 2ab^{2} + a - 8b^{2} - 4 \)

A. \( (a - 4)(2b^{2} + 1) \) B. \( (a + 4)(2b^{2} - 1) \) C. \( (a - 1)(2b^{2} + 41) \) D. cannot be factored



6. The completely factored form of \( 36x^{2} - 4y^{2} \)

A. \( (6x + 2y)(6x - 2y) \) B. \( 4(3x + y)(3x - y) \) C. \( (3x + y)(3x - y) \) D. cannot be factored



7. Find \( f(-2) \) when \( f(x) = 3x^{2} + 4x - 9 \)

A. \( 11 \) B. \( -13 \) C. \( -5 \) D. \( -29 \)



8. Find \( f(3.5) \) when \( f(x) = -x^{2} + 8x \)

A. \( 40.25 \) B. \( 24.5 \) C. \( -4.25 \) D. \( 15.75 \)



9. Find \( g(z + h) \) when \( f(x) = -3x + 1 \)

A. \( -3z - 3h + 1 \) B. \( -3z + 3h + 1 \) C. \( -3z + h + 1 \) D. \( (-3x + 1)(z + h) \)



10. Choose the answer below that best describes the type of equation: \( \dfrac{2}{x - 6} + \dfrac{x}{x - 4} = \dfrac{1}{3} \)

A. Exponential B. Logarithmic C. Quadtratic D. Rational



11. Choose the answer below that best describes the type of equation: \( 5^{x - 2} = 7^{x} \)

A. Exponential B. Logarithmic C. Quadtratic D. Rational



12. Solve the equation: \( 3 - \dfrac{2}{y} = \dfrac{5}{6} \)

A. \( \left\{ -\dfrac{9}{5} \right\} \) B. \( \left\{ -\dfrac{5}{9} \right\} \) C. \( \left\{ \dfrac{13}{12} \right\} \) D. \( \left\{ \dfrac{12}{13} \right\} \)



13. Solve the equation: \( 2y^{2} - 2y = 3 \)

A. \( \left\{ \dfrac{2 + \sqrt{3}}{4}, \dfrac{2 - \sqrt{3}}{4} \right\} \) B. \( \left\{ \dfrac{1 + \sqrt{7}}{2}, \dfrac{1 - \sqrt{7}}{2} \right\} \) C. \( \left\{ \dfrac{1 + \sqrt{5}}{2}, \dfrac{1 - \sqrt{5}}{2} \right\} \) D. \( \left\{ \dfrac{1 + 3\sqrt{3}}{2}, \dfrac{1 - 3\sqrt{3}}{2} \right\} \)



14. To identify the graph of the function \( f(x) = x^{2} - 4 \), make a table of values. Choose the graph that best represents the function.

A. B. C. D.
graph 20 graph 21 graph 22 graph 23



15. To identify the graph of the function \( f(x) = \sqrt{x} + 3 \), make a table of values. Choose the graph that best represents the function.

A. B. C. D.
graph 24 graph 25 graph 27 graph 26



16. To identify the graph of the function \( f(x) = 3|x| - 4 \), make a table of values. Choose the graph that best represents the function.

A. B. C. D.
graph 28 graph 29 graph 30 graph 31



17. To identify the graph of the function \( f(x) = \frac{2}{3}x - 4 \), make a table of values. Choose the graph that best represents the function.

A. B. C. D.
graph 32 graph 33 graph 34 graph 35



18. Choose the graph that best represents \( y \leq x^2 + 4 \).

A. B. C. D.
graph 36 graph 37 graph 38 graph 39



19. Choose the graph that best represents \( x^2 + y^2 > 16 \).

A. B. C. D.
graph 40 graph 41 graph 42 graph 43




Click here to see the answers
1. C   2. B   3. D   4. C   5. A   6. B   7. C   8. D   9. A   10. D   11. A   12. D   13. B   14. C   15. D   16. B   17. A   18. C   19. D  

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