# Algebra multiple choice questions

(See attached file for full problem description with PROPER EQUATIONS AND SYMBOLS)

---

The average of the numbers 5, 9, 10, 13, and a equals 11. Find the

value of a.

a. 16

b. 17

c. 18

d. 20

A shirt is on sale for $34.40, which is 20% off the original price.

Find the original price of the shirt.

a. $36.40

b. $41.28

c. $43.00

d. $54.40

How many quarts of water does one add to 6 quarts of a 60% alcohol

solution to create a 40% alcohol solution?

a. 2 qt.

b. 3 qt.

c. 6 qt.

d. 9 qt.

Express (7 + 3i) - (2 - 3i) in the form a + bi where a and b are real

numbers.

a. 5 - 6i

b. 5 + 6i

c. 9

d. 9 + 5i

Find the value of k that completes the square for x2 + 10x + k.

a. 5

b. 10

c. 25

d. 100

Find the solutions to the equation: |2x - 14| = 6.

a. x = -4, 10

b. x = 4, 10

c. x = 11, 17

d. x = 12, 14

Solve the inequality 7 < 4x + 3 ≤ 21, and express the solution as an

interval.

a. (1, 4.5]

b . [1.75, 7)

c . (7/3, 17)

d. [4.5, 5.25]

Solve the inequality -18 >0, and express the solution as an interval

6x-42

a. (-3, ∞)

b. (7, ∞)

c. (-∞,-3)

d. (-∞, 7)

Solve the inequality 2|x - 10| < 3, and express the solution as an

interval.

a. (7, 8.5)

b. (8.5, 10)

c. (8.5, 11.5)

d. (11.5, 13)

An object is shot upward with an initial velocity of 240 feet per

second so that its height s (in feet) above the ground after t seconds

is given by s = -16t2 + 240t. For what values of t will the object be at

least 416 feet above the ground?

a. [2, 5]

b. [2, 13]

c. [3, 5]

d. [3, 13]

Find the distance d(A, B) between the points A(−1, 0) and B(4, 3).

a. 3√ 2

b. 5

c. √34

d. 8

Determine the point A(x, y) so that the points A(x, y), B(0, 3), C(1, 0),

D(7, 2) will be the vertices of a parallelogram.

a. A(−6, 1)

b. A((3, 7)

c. A(5, 6)

d. A(6, 5)

Find the midpoint of the line segment from A(−2, 9) to B(4, 5).

a. C(1, 7)

b. D(3, 7)

c. P(4, 9)

d. Q(5, 9)

Find the point on the positive y-axis that is a distance 5 from the

point P(3, 4).

a. A(0, 6)

b. B(0,8)

c. C(6,0)

d. D(8,0)

Find the x-intercept and y-intercept of the equation 5x − 3y = 30.

a. 6 and 10 respectively

b. 10 and 6 respectively

c. 6 and −10 respectively

d. 6 and 2 respectively

Give the equation for the circle with center C(3, −2) and radius 4.

a. x2 + y 2 = 52

b. (x − 3)2 + ( y − 2)2 = 16

c. (x + 3)2 + ( y − 2)2 = 42

d. (x − 3)2 + ( y + 2)2 = 16

Give the center of the circle with equation x 2 + 2x + y 2 −10y + 22 = 0.

a. A(2, 4)

b. B(1, 5)

c. C(−1, 5)

d. D(−2, 4)

Find an equation for the line with slope 1/2 and y-intercept 3.

a. x/2 − y = 3

b. −x + 2y = 6

c. x + 2y = 6

d. 2x − y = 3

Find the slope of the line through the points A(−1, 6) and B(5, 2)

a. −1

b. −2/3

c. 2/3

d. 1

11. Find an equation for the line with y-intercept 3 that is perpendicular

to the line 4

3

y = 2 x − .

a. 2y = 6 − 3x

b. 2y = 3x + 6

c. 3y = 9 − 2x

d. 3y = 2x + 9

Fahrenheit and Celsius temperatures are related by the equation

F = 9 C + 32, where F is the temperature in degrees Fahrenheit and C

is the temperature on the Celsius scale. If the temperature is a

balmy 77° Fahrenheit, what is the temperature on the Celsius scale?

a. 25°

b. 33.8°

c. 43°

d. 45°

If f(x) = x2 + 5, find f(a + h) − f(a)

a. 2ah + h2 + 10

b. 2ah + h2 + 5

c. 2ah + h2

d. h2

From a square piece of cardboard with width x inches, a square of

width x − 3 inches is removed from the center. Write the area of

the remaining piece as a function of x.

a. f(x) = 6x − 9

b. f(x) = 6x + 9

c. f(x) = 2x2 − 9

d. f(x) = 2x2 − 6x − 9

If P(4, −5) is a point on the graph of the function y = f(x), find the

corresponding point on the graph of y = 2f(x − 6).

a. A(1, 8)

b. B(2, −5)

c. C(6, 8)

d. D(10,−10)

Explain how the graph of y − 5 = (x − 3)2 can be obtained from the

graph of y = x2.

a. Shift the graph of y = x2 left 3 units and down 5 units

b . Shift the graph of y = x2 left 3 units and up 5 units

c . Shift the graph of y = x2 right 3 units and down 5 units

d. Shift the graph of y = x2 right 3 units and up 5 units

Determine e the vertex of y = x 2 − 8x + 22.

a. A(−4, 11)

b . B(−4, 18)

c . C(4, 6)

d . D(4, 8)

An object is projected upward from the top of a tower. Its distance

in feet above the ground after t seconds is given by

s(t) = −16t 2 + 64t + 80 . How many seconds will it take to reach ground

level?

a. 1 second

b . 4 seconds

c . 5 seconds

d . 8 seconds

Find the maximum value of y = −x 2 + 6x.

a. 8

b . 9

c . 10

d . 11

Several values of the two function f and g are listed in the following

tables:

x 4 5 6 7

f(x) 7 6 5 4

x 4 5 6 7

g(x) 6 7 4 5

Find ( f o g)(6).

a. 4

b . 5

c . 6

d . 7

Given f(x) = 5x + 7 and g(x) = x2 + 7, find (g o f )(x).

a. (g o f )(x) = 5x2 + 7

b . (g o f )(x) = 5x2 + 42

c . (g o f )(x) = (5x)2 + 14

d . (g o f )(x) = 25x2 + 70x + 56