## 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.

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.

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.

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.

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.

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

 A. B. C. D.

19. Choose the graph that best represents $$x^2 + y^2 > 16$$.

 A. B. C. D.