## Precalculus Test

1.
If $5x - \dfrac{1}{2} (x+4) = 1$, then $x =$
(A)
$\dfrac{5}{9}$
(B)
$- \dfrac{2}{9}$
(C)
$\dfrac{2}{3}$
(D)
$\dfrac{1}{3}$
2.
$\left(\dfrac{-16a^2}{39b}\right)\left(\dfrac{13b^4}{8a^3}\right) \div (4b^3) =$
(A)
$- \dfrac{1}{6a}$
(B)
$- 6a$
(C)
$- \dfrac{8b^6}{3a}$
(D)
$- \dfrac{8b^{11}}{3a}$
3.
In the system of equations$\left\{ \begin{array}{l l} 5x-y=1\\ x+3y=13 \end{array} \right.\ , y =$
(A)
$- \dfrac{7}{8}$
(B)
$1$
(C)
$4$
(D)
No Solution
4.
If $f(x) = 2 x^2 - 1$ and $g(x) = 5x + 2$, then $f(g(-1))=$
(A)
$-19$
(B)
$-13$
(C)
$17$
(D)
$7$
5.
If $x = -7$, then $2 | x + 5 | - | 1 - 2x | =$
(A)
$-19$
(B)
$-11$
(C)
$19$
(D)
$-9$
6.
One of the roots of $20x^2 + 3x -2 = 0$ is
(A)
$\dfrac{1}{4}$
(B)
$\dfrac{2}{5}$
(C)
$-\dfrac{1}{4}$
(D)
$4$
7.
When $3x^2 - 5x + 8$ is divided by $x + 2$, the remainder is
(A)
$3x - 11$
(B)
$-14$
(C)
$0$
(D)
$30$
8.
$m^{-2}(m^{-3} + m^{-1})=$
(A)
$m^6 + m^2$
(B)
$\dfrac{1}{m^5} + \dfrac{1}{m^3}$
(C)
$\dfrac{1}{m^5 + m^3}$
(D)
$m^8$
9.
The inequality $3x - 6 > 5x$ is equivalent to
(A)
$x < 3$
(B)
$x > 3$
(C)
$x > -3$
(D)
$x < -3$
10.
The inequality $|x+1| < 7$ is equivalent to
(A)
$0 < x < 6$
(B)
$-8 < x < 6$
(C)
$-6 < x < 6$
(D)
$-1 < x < 6$
11.
For how many values of $\theta$ between $0$ and $2 \pi$ radians is $sin \theta = - cos \theta$?
(A)
$1$
(B)
$2$
(C)
$3$
(D)
$4$
12.
$\dfrac{\dfrac{x^2 + x}{5x - 20}}{\dfrac{x + 1}{4 - x}}=$
(A)
$\dfrac{x(x+1)^2}{(5x - 20)(4 - x)}$
(B)
$- \dfrac{x}{5}$
(C)
$\dfrac{x(4 - x)}{5(x - 4)}$
(D)
$\dfrac{x}{5}$
13.
One of the roots of $x^2 = x + 5$ is
(A)
$\dfrac{-1 + \sqrt{21}}{2}$
(B)
$\dfrac{-1 - \sqrt{6}}{2}$
(C)
$\dfrac{1 - \sqrt{21}}{2}$
(D)
$\dfrac{1 + \sqrt{6}}{2}$
14.
$-2^4+3^{-1}+4^0=$
(A)
$\dfrac{61}{48}$
(B)
$- \dfrac{44}{3}$
(C)
$\dfrac{52}{3}$
(D)
$- \dfrac{47}{3}$
15.
The inequality $x^2 - x > 6$ is equivalent to
(A)
$x < -2$ or $x > 3$
(B)
$-2 < x < 3$
(C)
$x < -2$
(D)
$x > 3$
16.
Which of the following could be the graph of $y = (x - 2)^2 - 1$?
(A)
(B)
(C)
(D)
17.
If $4^x = 5$, then $x =$
(A)
$\dfrac{4}{\sqrt{5}}$
(B)
$\dfrac{5}{\sqrt{4}}$
(C)
$\dfrac{log 5}{log 4}$
(D)
$\dfrac{log 4}{log 5}$
18.
$\dfrac{5}{x^2 - 5x + 6} - \dfrac{5}{x - 3} =$
(A)
$\dfrac{5}{x - 2}$
(B)
$\dfrac{5}{2 - x}$
(C)
$\dfrac{-5 - 5x}{x^2 - 5x + 6}$
(D)
$0$
19.
Which of the following could be a portion of the graph of $y = \left(\dfrac{1}{2}\right)^x$?
(A)
(B)
(C)
(D)
20.
The number of moles of an ideal gas $n$ is directly proportional to its volume $V$ and inversely proportional to its temperature $T$. Which of the following could be the variation equation?
(A)
$n = \dfrac{kT}{V}$
(B)
$n = \dfrac{kV^3}{T}$
(C)
$n = \dfrac{kV}{T}$
(D)
$n = kVT$
21.
If $f(x) = \sqrt{4x - 16}$, for what value of $x$ does $f(x) = 8$?
(A)
$\pm t$
(B)
$4$
(C)
$20$
(D)
$\{-16, 20\}$
22.
The length of a rectangle is 1 less than twice the width. The perimeter of the rectangle is 200 feet. If $x$ represents the width of the rectangle, then an equation that can be used to find the length and the width of the rectangle is
(A)
$(2x - 1) x = 200$
(B)
$(1 - 2x) x = 200$
(C)
$2 (1 - 2x) + 2x = 200$
(D)
$2 (2x - 1) + 2x = 200$
23.
If $y = \dfrac{x + 2}{x - 3}$, then $x =$
(A)
$\dfrac{y + 2}{y - 3}$
(B)
$\dfrac{3y + 2}{y - 1}$
(C)
$\dfrac{x + 5}{y}$
(D)
$xy - 3y + 2$
24.
An equation of the line in the figure shown is
(A)
$2x - 3y = 12$
(B)
$3x - 2y = 8$
(C)
$2x - 3y = 18$
(D)
$\dfrac{2}{3} x + y = -4$
25.
Which of the following could be a portion of the graph of $y = -cos2x$?
(A)
(B)
(C)
(D)
26.
If $f(x) = x^2 - x + 4$, then $f(a+h) =$
(A)
$a^2 - a + 4 + h$
(B)
$a^2 + 2ah + h^2 - a - h + 4$
(C)
$a^2 + h^2 - a - h + 4$
(D)
$(a + h)^2 - a + 4 + h$
27.
$log_{3} \dfrac{1}{9}=$
(A)
$2$
(B)
$-2$
(C)
$3$
(D)
$\sqrt{2}$
28.
In the figure shown below, $x =$
(A)
$8$
(B)
$24$
(C)
$\dfrac{27}{8}$
(D)
$\dfrac{96}{9}$
29.
$tan(\theta + \pi) =$
(A)
$- cot \theta$
(B)
$- tan \theta$
(C)
$tan \theta$
(D)
$cot \theta$
30.
The graph of $y = f(x)$ is shown in the figure below. Which of the following could be the graph of $y = f(-x)$?
(A)
(B)
(C)
(D)
31.
$(3m^{x-1})(2m^{2x})=$
(A)
$6m^{2x^2-2x}$
(B)
$5m^{2x^2-2x}$
(C)
$6m^{3x-1}$
(D)
$6(2m)^{3x-1}$
32.
The number of books in a school library is 180 after a 25% increase. Find the number of books before the increase.
(A)
$45$
(B)
$72$
(C)
$144$
(D)
$135$
33.
If $3 log_{b} x - log_{b} y = log_{b} z$, then $z =$
(A)
$x^3 - y$
(B)
$\dfrac{3x}{y}$
(C)
$3x - y$
(D)
$\dfrac{x^3}{y}$
34.
$\sqrt{36x^6 y^2 - 64x^4}$
(A)
$6x^3 y - 8x^2$
(B)
$2x^2 \sqrt{9x^2y^2 - 16}$
(C)
$2x^2y \sqrt{9x^2 - 16}$
(D)
$6x^3 y - 8x$
35.
$\dfrac{1 + \dfrac{4}{x} - \dfrac{45}{x^2}}{1+ \dfrac{2}{x} - \dfrac{35}{x^2}} =$
(A)
$-8$
(B)
$\dfrac{x + 9}{x + 7}$
(C)
$\dfrac{5}{4}$
(D)
$\dfrac{x - 41}{x - 33}$
36.
$\dfrac{x}{\sqrt[3]{4x}}=$
(A)
$\dfrac{x^2 \sqrt[3]{2}}{2}$
(B)
$\dfrac{x \sqrt[3]{2}}{2x}$
(C)
$\dfrac{\sqrt[3]{2x}}{8x}$
(D)
$\dfrac{\sqrt[3]{2x^2}}{2}$
37.
In the figure shown below, $tan \theta =$

(A)
$\dfrac{\sqrt{x^2 - a^2}}{a}$
(B)
$\dfrac{\sqrt{x^2 + a^2}}{a}$
(C)
$\dfrac{\sqrt{x^2 - a^2}}{x}$
(D)
$\dfrac{\sqrt{x^2 + a^2}}{x}$
38.
If $3^{x-12} = 9^{2x}$, then $x =$
(A)
$-12$
(B)
$-4$
(C)
No Solution
(D)
$4$
39.
If $log_{2} x + log_{2} (x - 2) = 3$,
(A)
$4$
(B)
$2$
(C)
$-2$
(D)
$\dfrac{5}{2}$
40.
The domain of the function below is:
(A)
$(-\infty, \infty)$
(B)
$[-2,2)$
(C)
$[-2,1]$
(D)
$[-4,-1]$
41.
The graph of the piecewise function$f(x) = \left\{ \begin{array}{l l} -2x + 4 & \quad \textrm{if x > 0} \\ 3 & \quad \textrm{if x \leq 0} \end{array} \right.\$ is
(A)
(B)
(C)
(D)
42.
If $sin \theta = \dfrac{3}{5}$ and $tan \theta < 0$, then $cos \theta =$
(A)
$-\dfrac{5}{3}$
(B)
$-\dfrac{2}{5}$
(C)
$-\dfrac{4}{5}$
(D)
$-\dfrac{3}{4}$
43.
An equation of the circle with center $(-3, 0)$ and radius $5$ is
(A)
$(x+3)^2 + y^2 = \sqrt{5}$
(B)
$(x-3)^2 + y^2 = 10$
(C)
$(x+3)^2 + y^2 = 25$
(D)
$(y+3)^2 + x^2 = 25$
44.
If $\left(x + \dfrac{1}{2}\right)^3 = \dfrac{1}{64}$, then $x =$
(A)
$-\dfrac{1}{4}$
(B)
$\dfrac{1}{8}$
(C)
$\dfrac{1}{2}$
(D)
$\dfrac{\sqrt[3]{-7}}{4}$
45.
$\sqrt{\sqrt{2}}$
(A)
$2$
(B)
$16$
(C)
$\sqrt[4]{2}$
(D)
$\sqrt[4]{4}$