## 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)
$32$