Intermediate Algebra Test

1.
If \(x =-2\) and \(y = 4\), then \(3xy+ \left(\dfrac{y}{x}\right)^2=\)
(A)
\(-28\)
(B)
\(-20\)
(C)
\(28\)
(D)
\(20\)
2.
If \(\dfrac{2}{3} - \dfrac{1}{6} x = 2\), then \(x =\)
(A)
\(\dfrac{3}{2}\)
(B)
\(-8\)
(C)
\(8\)
(D)
\(2\)
3.
\(\sqrt{25} + \sqrt{-9} =\)
(A)
\(5 + 3i\)
(B)
\(2\)
(C)
\(8i\)
(D)
\(4\)
4.
\(4 (x - y) - 2 [ y - 3(4x)] =\)
(A)
\(20x-6y\)
(B)
\(6y-28x\)
(C)
\(22xy\)
(D)
\(28x-6y\)
5.
The width of a rectangle is 15 less than the length. Its area is 54. Find the length
(A)
\(9\)
(B)
\(18\)
(C)
\(21\)
(D)
\(27\)
6.
\(\left(\dfrac{x^{-2}}{y}\right)^2 = \)
(A)
\(\dfrac{-x^4}{y^2}\)
(B)
\(\dfrac{1}{x^4y^2}\)
(C)
\(x^4y^2\)
(D)
\(\dfrac{x^0}{y}\)
7.
If \(3x + 2y = -1\), then \(x = \)
(A)
\(- \dfrac{1}{3} - 2y\)
(B)
\(- \dfrac{2}{3} y - 1\)
(C)
\(\dfrac{-2y+1}{3}\)
(D)
\(\dfrac{-2y-1}{3}\)
8.
\(\dfrac{10^x}{2^x} = \)
(A)
\(5^0\)
(B)
\(5^x\)
(C)
\(5\)
(D)
\(5x\)
9.
The sum of two numbers is 64. One number is five less than the twice the other. Find the larger number.
(A)
\(23\)
(B)
\(31\)
(C)
\(41\)
(D)
\(59\)
10.
\(a^{1 \over 3} a^{1 \over 2} = \)
(A)
\(\sqrt[6]{2a^5}\)
(B)
\(\dfrac{1}{\sqrt[6]{a}}\)
(C)
\(\sqrt[6]{a}\)
(D)
\(\sqrt[6]{a^5}\)
11.
\(2 | -5 -4 | + (-2)^3 =\)
(A)
\(10\)
(B)
\(-26\)
(C)
\(26\)
(D)
\(-10\)
12.
\(\sqrt{48} - 5 \sqrt{27} = \)
(A)
\(-11\)
(B)
\(-29\sqrt{3}\)
(C)
\(\sqrt{3}\)
(D)
\(-11\sqrt{3}\)
13.
If \( log _{x} 81 = 4\), then \(x = \)
(A)
\(324\)
(B)
\(3\)
(C)
\(-3\)
(D)
\(\dfrac{1}{3}\)
14.
If \(f(x) = x^2 - 3x\), then \(f(a - 2)= \)
(A)
\(a^2-3a-2\)
(B)
\(a^2-3a+2\)
(C)
\(a^2-7a+10\)
(D)
\(a^2-7a-2\)
15.
Which of the following is an equation of the line with slope \(-3\) and y-intercept \(-2\)?
(A)
\(y = 2x - 3\)
(B)
\(y = -2x -3\)
(C)
\(y = -3x +2\)
(D)
\(y = -3x -2\)
16.
Write an equation of the line passing through the point \((-1,2)\) and parallel to the line \(y = 2x - 5\).
(A)
\(y = - \dfrac{1}{2} x + \dfrac{3}{2}\)
(B)
\(y = -2x -4\)
(C)
\(y = 2x + 2\)
(D)
\(y = 2x + 4\)
17.
What are the values of \(x\) for which \((x - 2)(x + 5) \leq 0\)?
(A)
\(-5 \leq x \leq 2\)
(B)
\(x \leq -5\)
(C)
\(x \leq 2\)
(D)
\(x \leq -5\) or \(x \geq 2\)
18.
\(\dfrac{8.1 \times 10^2}{0.9 \times 10^{-5}} = \)
(A)
\(0.9 \times 10^{-7}\)
(B)
\(-9.0 \times 10^7\)
(C)
\(9.0 \times 10^7\)
(D)
\(9.0 \times 10^{-7}\)
19.
The inequality \(2x > 2 + 7 x\) is equivalent to
(A)
\(x < \dfrac{2}{5}\)
(B)
\(x < - \dfrac{2}{5}\)
(C)
\(x > \dfrac{2}{5}\)
(D)
\(x > - \dfrac{2}{5}\)
20.
\((-xy^5)(2xy^2)^4=\)
(A)
\(-2x^5 y^{13}\)
(B)
\(-2x^4 y^{40}\)
(C)
\(-2x^5 y^{11}\)
(D)
\(-16 x^5 y^{13}\)
21.
In the system of equations\( \left\{ \begin{array}{l l} 2x+y=2\\ x-y=7 \end{array} \right.\ , y =\)
(A)
\(-4\)
(B)
\(0\)
(C)
\(2\)
(D)
\(4\)
22.
If the triangles \(ABC\) and \(DEF\) are similar, then \(x =\)
(A)
\(2\)
(B)
\(5\)
(C)
\(18\)
(D)
\(21\)
23.
\(\dfrac{3}{\sqrt{x} - 2} = \)
(A)
\(\dfrac{3\sqrt{x}}{x-2}\)
(B)
\(\dfrac{3}{x - 4}\)
(C)
\(\dfrac{3 \sqrt{x} + 6}{x - 4}\)
(D)
\(\dfrac{3 \sqrt{x} - 6}{x - 4}\)
24.
If \(f(x) = x^2 + 5x + 3\), then \(f(-4) =\)
(A)
\(-33\)
(B)
\(-1\)
(C)
\(7\)
(D)
\(20\)
25.
Find the slope of the line passing through the points \((-9,2)\) and \((-1,6)\) .
(A)
\(2\)
(B)
\(\dfrac{2}{5}\)
(C)
\(\dfrac{1}{2}\)
(D)
\(-\dfrac{4}{5}\)
26.
\(2^{3x+1} = \dfrac{1}{16}\), then \(x =\)
(A)
\(\dfrac{7}{3}\)
(B)
\(1\)
(C)
\(- \dfrac{5}{3}\)
(D)
\(- \dfrac{4}{3}\)
27.
Divide using long division \(\dfrac{x^2 + 3x - 8}{x - 2}\)
(A)
\(x^2 + 4 + \dfrac{3}{x - 2}\)
(B)
\(x + 5 + \dfrac{2}{x - 2}\)
(C)
\(x + 4 + \dfrac{3}{x - 2}\)
(D)
\(x + 5 - \dfrac{18}{x - 2}\)
28.
Which of the following could be an equation for the graph shown in the figure?
(A)
\(3x - 2y = 4\)
(B)
\(2x - 3y = 6\)
(C)
\(3x - 2y = -2\)
(D)
\(\dfrac{3}{2} x - 2y = 4\)
29.
One of the solutions of \(x^2 - 5x = 6\) is
(A)
\(-1\)
(B)
\(-2\)
(C)
\(2\)
(D)
\(-6\)
30.
Write an equation of the line passing through the point \((2,3)\) which is perpendicular to the \(x\) axis.
(A)
\(x = 2\)
(B)
\(x = -2\)
(C)
\(y = -3\)
(D)
\(y = 3\)
31.
One factor of \(x^4 + 5x^2 - 36\) is
(A)
\(x + 4\)
(B)
\(x^2 - 9\)
(C)
\(x + 2\)
(D)
\(x^2 + 4\)
32.
\(\dfrac{x^2y}{15} . \dfrac{1}{y^3} \div \dfrac{3x}{5} =\)
(A)
\(\dfrac{x}{9y^2}\)
(B)
\(\dfrac{x^3}{25y^2}\)
(C)
\(\dfrac{x}{y^2}\)
(D)
\(\dfrac{x^3}{y^2}\)
33.
\(\dfrac{\dfrac{1}{2x} + \dfrac{y}{2x^2}}{\dfrac{1}{4} + \dfrac{y}{4x}} =\)
(A)
\(1\)
(B)
\(2\)
(C)
\(\dfrac{x}{2}\)
(D)
\(\dfrac{2}{x}\)
34.
One factor of \(8x^2 + 2x - 15\) is
(A)
\(8x - 5\)
(B)
\(2x - 3\)
(C)
\(4x - 5\)
(D)
\(x + 3\)
35.
If you paid 32 dollars for a pair of shoes that was listed for 40 dollars, what rate of discount did you receive?
(A)
\(80 \%\)
(B)
\(20 \%\)
(C)
\(8 \%\)
(D)
\(0.2 \%\)
36.
\(\dfrac{x}{x^2 - 1} . \dfrac{x^2 - 2x -3}{x^2 - 3x} = \)
(A)
\(x - 1\)
(B)
\(- \dfrac{2}{x}\)
(C)
\(- \dfrac{2}{x^4 - 3}\)
(D)
\(\dfrac{1}{x - 1}\)
37.
If \(\dfrac{2x}{x-1} + \dfrac{1}{2x} = 2\), then \(x =\)
(A)
\(\dfrac{1}{5}\)
(B)
\(-1, \dfrac{3}{4}\)
(C)
\(\pm 1\)
(D)
\(\dfrac{3}{2}\)
38.
\(\dfrac{x^2 - 7}{x - 3} + \dfrac{2}{3-x} =\)
(A)
\(x + 3\)
(B)
\(x^2 - 5\)
(C)
\(\dfrac{x^2 - 5}{x - 3}\)
(D)
\(\dfrac{x^2 - 5}{(x - 3)(3 - x)}\)
39.
\(\dfrac{1}{3} log _{b} x - 4 log _{b} y\) is equivalent to
(A)
\(log _{b} \dfrac{y^4}{x^3}\)
(B)
\(log _{b} \dfrac{\sqrt[3]{x}}{y^4}\)
(C)
\(log _{b} \dfrac{x^3}{y^4}\)
(D)
\(log _{b} \dfrac{1}{x^3y^4}\)
40.
If \(x^2 + 3x - 7 = 0\), then \(x=\)
(A)
\(\dfrac{3 \pm \sqrt{19}}{2}\)
(B)
\(-1, 7\)
(C)
\(- \dfrac{7}{2}, \dfrac{1}{2}\)
(D)
\(\dfrac{-3 \pm \sqrt{37}}{2}\)