Elementary Algebra Test

1.
Simplify \(\dfrac{20x^6}{5x^2}\)
(A)
\(4x^4\)
(B)
\(4x^8\)
(C)
\(15x^4\)
(D)
\(4x^3\)
2.
Solve \(\dfrac{2}{3} x = 6\)
(A)
\(x = 1\)
(B)
\(x = 9\)
(C)
\(x = 4\)
(D)
\(x = 12\)
3.
If the sum of three consecutive even numbers is \(114\), what is the largest of these even numbers?
(A)
\(36\)
(B)
\(38\)
(C)
\(40\)
(D)
\(42\)
4.
On the number line shown below, which letter best locates the number \(\dfrac{4}{3}\)?
(A)
\(P\)
(B)
\(Q\)
(C)
\(R\)
(D)
\(S\)
5.
Find the area of the square whose perimeter is 20 inches.
(A)
\(25 in^2\)
(B)
\(10 in^2\)
(C)
\(16 in^2\)
(D)
\(625 in^2\)
6.
Multiply \((3x+5y)(x-2y)\)
(A)
\(3x^2+11xy-10y^2\)
(B)
\(3x^2-10y^2\)
(C)
\(3x^2-xy-10y^2\)
(D)
\(3x^2-xy+10y^2\)
7.
Evaluate \(3.12 \div 0.2\)
(A)
\(1.56\)
(B)
\(15.6\)
(C)
\(0.156\)
(D)
\(156\)
8.
Simplify \((-2xy^2)^3\)
(A)
\(-8x^3y^6\)
(B)
\(-6x^3y^6\)
(C)
\(-2xy^6\)
(D)
\(-8x^3y^5\)
9.
One of the solutions of the equation \(x^2 = 8x\) is
(A)
\(64\)
(B)
\(8\)
(C)
\(2 \sqrt{2}\)
(D)
\(-2 \sqrt{2}\)
10.
Add \({\dfrac{7}{10}} + {\dfrac{2}{3}}\)
(A)
\(\dfrac{9}{30}\)
(B)
\(\dfrac{41}{30}\)
(C)
\(\dfrac{9}{13}\)
(D)
\(\dfrac{3}{10}\)
11.
Simplify \(6^{-2}\)
(A)
\(-12\)
(B)
\(-36\)
(C)
\(\dfrac{1}{36}\)
(D)
\(3\)
12.
Perform the operation \((-2x^2-3)-(7x^2-2)\)
(A)
\(-9x^2-5\)
(B)
\(-9x^2-1\)
(C)
\(5x^2-5\)
(D)
\(5x^2-1\)
13.
Multiply \(2^3 . 2^4\)
(A)
\(4^{12}\)
(B)
\(4^7\)
(C)
\(2^7\)
(D)
\(2^{12}\)
14.
In the right triangle ABC shown below, the length of AC is
(A)
\(12\)
(B)
\(6\)
(C)
\(2 \sqrt{41}\)
(D)
\(2\)
15.
Evaluate \(8 - (3) ( 2)\)
(A)
\(10\)
(B)
\(7\)
(C)
\(2\)
(D)
\(12\)
16.
One of the factors of \(x^2 + 4x - 12\) is
(A)
\(x + 2\)
(B)
\(x - 6\)
(C)
\(x - 3\)
(D)
\(x - 2\)
17.
Find the measure of angle x in the given figure.
(A)
\(100°\)
(B)
\(10°\)
(C)
\(200°\)
(D)
\(40°\)
18.
Find the slope of the line determined by the points \((2,5)\) and \((-2,3)\).
(A)
\(- \dfrac{1}{2}\)
(B)
\(2\)
(C)
Undefined
(D)
\(\dfrac{1}{2}\)
19.
Divide \(\dfrac{3x^2+x-5}{x-1}\)
(A)
\(3x+4-\dfrac{1}{x-1}\)
(B)
\(3x^2+5\)
(C)
\(4x+5\)
(D)
\(3x+4-\dfrac{9}{x-1}\)
20.
Find the graph of \(y = 2x + 1\)
(A)
(B)
(C)
(D)
21.
Subtract \(\sqrt{4} - 1.3\)
(A)
\(2.7\)
(B)
\(0.7\)
(C)
\(-2.6\)
(D)
\(1.3\)
22.
The coordinates of point P, shown in the figure below, are
(A)
\((-5,-4)\)
(B)
\((-5,4)\)
(C)
\((5,-4)\)
(D)
\((5,4)\)
23.
Find y for \( \left\{ \begin{array}{l l} 2x+y=16\\ x=y-4 \end{array} \right.\ \)
(A)
\(8\)
(B)
\(4\)
(C)
\(\dfrac{8}{3}\)
(D)
\(16\)
24.
Subtract \(\dfrac{1}{2} - \sqrt{0.81}\)
(A)
\(-0.45\)
(B)
\(-0.31\)
(C)
\(0.41\)
(D)
\(-0.4\)
25.
If \(y = mx + b\) and \(m \ne 0\), then \(x =\)
(A)
\(\dfrac{y}{m}-b\)
(B)
\(\dfrac{y-b}{m}\)
(C)
\(y-\dfrac{b}{m}\)
(D)
\(\dfrac{m}{y-b}\)
26.
The sum of two numbers is 56. Six times the smaller number equals the larger number. Find the larger number.
(A)
\(8\)
(B)
\(28\)
(C)
\(48\)
(D)
\(44.8\)
27.
Simplify \(20a - 12b - a + 3b\)
(A)
\(19a-15b\)
(B)
\(21a-9b\)
(C)
\(21a-15b\)
(D)
\(19a-9b\)
28.
Multiply \((\sqrt{3}-\sqrt{2})(\sqrt{3}+6\sqrt{2})\)
(A)
\(-9\)
(B)
\(-15\)
(C)
\(-9 + 5 \sqrt{6}\)
(D)
\(-4 \sqrt{6}\)
29.
Find the shaded area of the triangle if the radius of the given circle is 4 cm.
(A)
\(8π cm^2\)
(B)
\(16π cm^2\)
(C)
\(16 cm^2\)
(D)
\(8 cm^2\)
30.
Factor completely \(6x^3y - 9x^2 z + 3x^2\)
(A)
\(3x(2x^2y-3xz+x)\)
(B)
\(3(x^3y-3x^2z+x^2)\)
(C)
\(3x^2(2xy-3z+1)\)
(D)
\(3x^2(2xy-3z)\)
31.
Evaluate \((\dfrac{2}{3})^2 - \dfrac{2}{9}\)
(A)
\(2\)
(B)
\(\dfrac{2}{9}\)
(C)
\(\dfrac{1}{3}\)
(D)
\(0\)
32.
Evaluate \(xy - 3y\) when \(x = 2\) and \(y = -6\)
(A)
\(6\)
(B)
\(-13\)
(C)
\(-30\)
(D)
\(-6\)
33.
Solve \(x^2 - 8x = 48\)
(A)
\(x = 12,-4\)
(B)
\(x = 48,56\)
(C)
\(x = 4,-12\)
(D)
\(z = 16,-3\)
34.
Multiply and simplify \(\dfrac{xy}{x^2-4} . \dfrac{x+2}{6x}\)
(A)
\(\dfrac{y(x+1)}{6(x-2)}\)
(B)
\(\dfrac{y}{6(x-2)}\)
(C)
\(\dfrac{y}{3(x-4)}\)
(D)
\(\dfrac{y}{6(x+2)}\)
35.
Simplify \(3 \sqrt{18}- \sqrt{2}\)
(A)
\(9 \sqrt{2}\)
(B)
\(12\)
(C)
\(5 \sqrt{2}\)
(D)
\(8 \sqrt{2}\)
36.
Simplify \(\dfrac{3x^2y^3-24x^4y^5}{3xy^2}\)
(A)
\(xy-24x^4y^5\)
(B)
\(xy-21x^3y^3\)
(C)
\(x^2y-8x^4y^3\)
(D)
\(xy-8x^3y^3\)
37.
Solve \(30n^2 - n - 1 = 0\)
(A)
\(n=\dfrac{1}{6},- \dfrac{1}{5}\)
(B)
\(n=\dfrac{1}{10},- \dfrac{1}{3}\)
(C)
\(n=\dfrac{1}{3},- \dfrac{1}{10}\)
(D)
\(n=\dfrac{1}{5},- \dfrac{1}{6}\)
38.
Subtract \(\dfrac{3}{y-2} - \dfrac{1}{y+3}\)
(A)
\(\dfrac{2}{(y-2)(y+3)}\)
(B)
\(\dfrac{2y+7}{(y-2)(y+3)}\)
(C)
\(\dfrac{2y+11}{(y-2)(y+3)}\)
(D)
\(- \dfrac{2}{5}\)
39.
If \(x = 3\) and \(y = -1\) then \(\dfrac{x+11}{2x-y}\)
(A)
\(2\)
(B)
\(\dfrac{11}{3}\)
(C)
\(\dfrac{14}{5}\)
(D)
\(-2\)
40.
Three-fourths of a number equals 24. Find the number.
(A)
\(18\)
(B)
\(13.5\)
(C)
\(32\)
(D)
\(72\)
41.
Find the graph of the solution set for \(x + 2 < 3x - 10\).
(A)
(B)
(C)
(D)
42.
Solve \(\sqrt{x}+6=11\)
(A)
\(x = 5\)
(B)
\(x = \sqrt{5}\)
(C)
\(x = 25\)
(D)
\(x = 115\)
43.
If the width of a rectangle is one-third of its length and its length is 15, what is the area of the rectangle?
(A)
\(40\)
(B)
\(75\)
(C)
\(20\)
(D)
\(225\)
44.
\(15\) is what percent of \(120\)?
(A)
\(12.5 \% \)
(B)
\(0.08 \% \)
(C)
\(18 \% \)
(D)
\(8 \% \)
45.
On a map, 1 inch corresponds to 4 miles. If two cities are 8 inches apart on the map, how far apart are they in miles?
(A)
\(12\)
(B)
\(64\)
(C)
\(2\)
(D)
\(32\)