Download DMAT 0305 Final Exam Review

1
DMAT 0305
Final Exam Review
Write the following as an algebraic expression. Simplify if possible.
1) Subtract 9x + 10 from 2x - 14.
A) -7x - 24
B) 11x - 4
C) -7x + 4
Write the phrase as an algebraic expression. Let x represent the unknown number.
2) The product of a number and 9
x
A) x + 9
B) 9x
C)
9
D) 7x + 24
D) x - 9
Write the following phrase as an algebraic expression and simplify if possible. Let x represent the unknown number.
3) Two times a number, increased by eight
A) 2x - 8
B) 2x + 8
C) 2 + 8x
D) 2x + 16
Use an associative property to complete the statement.
4) (7x + 9y) + 3z =
A) (9y + 7x) + 3z
B) 7x + (9y + 3z)
C) (7x + 9y + 3z)
D) 7x + 9y + 3z
Use the distributive property to write the expression without parentheses. Then simplify, if necessary.
5) -3(x + 6)
A) -3x + 18
B) -3x - 18
C) x - 18
D) -3x + 6
Simplify the expression. First use the distributive property to remove any parentheses.
6) -4(2x - 9) - 4x + 6
A) 4x + 42
B) -12x + 42
C) -12x - 30
D) 12x + 42
7) Solve the equation. Don't forget to first simplify each side of the equation, if possible.
-8(x + 7) - (-9x - 6) =4
A) 54
8) Solve the equation.
B) - 46
D) 9
C) 18
D) 54
B) -1
C) {3}
D) -12
B) all real numbers
C) 59
D) 77
C) no solution
D) all real numbers2
9(n - 9) = 81
A) 58
9) Solve the equation.
C) - 54
B) 15
1
1
(x + 6) = (x + 8)
5
7
A) 1
Solve the equation.
10) -7(x + 7) + 68 = 2x - 9(x + 1)
A) no solution
11) Solve the equation. -4(x + 4) = 4x - 8(x +2)
A) 48
1
B) -96
V1
Solve the formula for the specified variable.
12) A = P + PRT
for R
P-A
A
A) R =
B) R =
PT
T
13) A =
1
h(B + b)
2
A) B =
2A + bh
h
2
C) R =
PT
A-P
D) R =
A-P
PT
C) B =
A - bh
h
D) B =
2A - bh
h
for B
B) B = 2A - bh
Write the sentence as an equation or inequality. Use x to represent any unknown number.
14) The sum of 8 and twice a number is 24. Find the number
A) 36
B) 8
C) 24
D) 12
Solve. Round all amounts to one decimal place.
15) 40% of what number is 80?
A) 2000
B) 32
D) 200
Solve.
C) 20
16) In a recent International Gymnastics competition, the U.S., China, and Romania were the big winners. If the
total number of medals won by each team are three consecutive integers whose sum is 99 and the U.S. won
more than China who won more than Romania, how many medals did each team win?
A) U.S.: 101 medals; China: 100 medals; Romania: 99 medals
B) U.S.: 35 medals; China: 34 medals; Romania: 33 medals
C) U.S.: 32 medals; China: 31 medals; Romania: 30 medals
D) U.S.: 34 medals; China: 33 medals; Romania: 32 medals
17) A 12-ft. board is cut into 2 pieces so that one piece is 8 feet longer than 3 times the shorter piece. If the shorter
piece is x feet long, find the lengths of both pieces.
A) shorter piece: 28 ft; longer piece: 36 ft
B) shorter piece: 24 ft; longer piece: 44 ft
C) shorter piece: 6 ft; longer piece: 36 ft
D) shorter piece: 1 ft; longer piece: 11 ft
Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
18) Jeans are on sale at the local department store for 25% off. If the jeans originally cost $43, find the sale price.
A) $53.75
B) $32.25
C) $41.93
D) $10.75
19) A company increased the number of its employees from 540 to 575. What was the percent increase in
employees?
A) 6.1%
B) 93.9%
C) 6.5%
D) 51.6%
Solve. Round all amounts to one decimal place.
20) 93 is 10% of what number?
A) 9.3
B) 93
C) 930
D) 9300
Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
21) A chemist needs 110 milliliters of a 80% solution but has only 76% and 98% solutions available. Find how many
milliliters of each that should be mixed to get the desired solution.
A) 20 ml of 76%; 90 ml of 98%
B) 10 ml of 76%; 100 ml of 98%
C) 100 ml of 76%; 10 ml of 98%
D) 90 ml of 76%; 20 ml of 98%
V1
3
22) How much pure acid should be mixed with 5 gallons of a 50% acid solution in order to get an 80% acid
solution?
A) 20 gal
B) 12.5 gal
C) 2.5 gal
D) 7.5 gal
23) Because of budget cutbacks, MaryAnn was required to take a 11% pay cut. If she earned $58,000 before the pay
cut, find her salary after the pay cut.
A) $57,362
B) $57,936.20
C) $51,620
D) $5162
Graph the set of numbers given in interval notation. Then write an inequality statement in x describing the numbers
graphed.
24) (- , -5]
A) x > -5
B) x
-5
C) x
-5
D) x < -5
Solve the inequality. Graph the solution set and write it in interval notation.
25) x + 9 < 19
A) (10, )
B) (- , 10]
C) [10, )
D) (- , 10)
V1
4
26) -30x + 6 -6(4x - 6)
A) (- , -5)
B) [-5, )
C) (- , -5]
D) (-5, )
Graph the inequality on a number line. Then write the solution in interval notation.
27) -5 x < -1
A) [-5, -1]
B) [-5, -1)
C) (-5, -1]
D) (-5, -1)
Solve the inequality. Graph the solution set and write it in interval notation.
28) 3 3x - 3 18
A) (-7, -2)
B) [-7, -2]
C) [2, 7]
D) (2, 7)
V1
5
29) -4x + 6 - 5x < 10 - 11x + 10
A) (7, )
B) (- , 7)
C) (- , 13]
D) (13, )
Find the unknown complementary or supplementary angle.
30) Two angles are supplemental. One angle is 30 ° more than twice the other angle. What is the measure of the
smaller angle?
A) 50°
B) 70°
C) 20°
D) 40°
Solve.
31) Two angles are complementary if their sum is 90°. If the measure of the first angle is x°, and the measure of the
second angle is (3x - 2)°, find the measure of each angle.
A) 1st angle = 31°; 2nd angle = 59°
B) 1st angle = 22°; 2nd angle = 64°
C) 1st angle = 23°; 2nd angle = 67°
D) 1st angle = 22°; 2nd angle = 68°
Substitute the given values into the formula and solve for the unknown variable.
32) d = rt; t = 4, d = 36
A) 32
B) 40
C) 9
D) 0.1
Solve. Round all amounts to one decimal place.
33) What number is 80% of 100?
A) 800
B) 80
D) 8000
C) 8
34) Solve. If needed, round to one decimal place.
How much pure acid should be mixed with 7 gallons of a 50% acid solution in order to get an 80% acid
solution?
A) 10.5 gal
B) 3.5 gal
C) 17.5 gal
D) 28 gal
35) State in which quadrant or on which axis the point lies. (-4, 0)
A) quadrant III
B) quadrant IV
C) x-axis
D) y-axis
V1
6
Find the x- and y-coordinates of the following labeled points.
36)
A) A(4, 24); B(1, -3)
B) A(4, 4); B(-3, 1)
C) A(4, 1); B (4, 1)
D) A(4, 4); B(1, -3)
Plot the ordered pair. State in which quadrant or on which axis the point lies.
37) (0, 5)
A) y-axis
B) quadrant I
C) y-axis
D) x-axis
V1
38) (-1, 2)
A) quadrant IV
C) quadrant I
7
B) quadrant III
D) quadrant II
39) Complete the ordered pair so that it is a solution of the given linear equation.
9x + y = -67
(-8, ), (0, ), (1, )
A) (-8, 5), (0, -67), (1, -76)
B) (-8, 5), (0, -77), (1, -76)
C) (-8, -8), (0, -67), (1, -76)
D) (-8, 5), (0, 0), (1, -76)
Complete the ordered pair so that it is a solution of the given linear equation.
40) y = -x + 5;
(2, ), (5, ), (0, )
A) (2, 2) (5, 5) (0, 0)
B) (2, 6) (5, 0) (0, 5)
C) (2, 3) (5, 0) (0, 5)
D) (2, 3) (5, -1) (0, 5)
V1
8
Identify the intercepts.
41)
A) (2, 0), (0, 8)
B) (-2, 0), (0, 8)
Find the slope of the line that passes through the given points.
42) (-8, 10) and (-8, 4)
7
3
A) B) 8
8
C) (-2, 0), (0, -8)
D) (-8, 0), (0, 8)
C) 0
D) undefined
43) (9, -5) and (-7, -5)
A) undefined
B) - 5
C) -
B) -2
C) 1
5
8
D) 0
Find the slope of the line if it exists.
44)
A) 2
45) Find the slope of the line that passes through the given points.
A) -
1
2
B) - 2
D) -1
(-4, 0) and (-3, 8)
C) 8
D)
7
8
46) Find the slope of the line. y - 1x = 2
A) m = -3
B) m = - 1
C) m =
21
8
D) m= 1
V1
9
47) Graph the linear equation by finding and plotting its intercepts.-x + 2y = -2
A)
B)
C)
D)
V1
10
Use the slope-intercept form to graph the equation.
1
48) y = - x + 2
4
A)
B)
C)
D)
V1
49) Graph the linear equation.
11
y = -9
A)
B)
C)
D)
V1
12
Complete the table of ordered pairs for the given linear equation; then plot the solution.
50) 5x + 2y = 10
x y
0
0
1
-5
A)
B)
x
y
0
5
2
0
1 -2.5
4
-5
x y
3 5
2
0
1 2.5
2 -5
C)
D)
x y
0 -5
2
0
1 2.5
4
5
x y
0 5
2
0
1 2.5
4 -5
Solve the system of equations by graphing.
51) 3x + y = -3
2x + y = -4
A) (-1, 6)
B) no solution
C) (1, -6)
D) (-6, 1)
V1
13
52) Solve the system of equations by the substitution method. The y value is
-5x + y = 34
-6x + 7y = 93
A) no solution
B) 1
C) 9
D) 2
Write an equation of the line with the given slope, m, and y-intercept (0, b).
53) m = 6, b = -2
A) y = 2x - 6
B) y = -2x + 6
C) y = -6x + 2
D) y = 6x - 2
Find an equation of the line with the given slope that passes through the given point. Write the equation in the form
Ax + By = C.
54) m = 6; (4, 9)
A) 6x - y = -9
B) 6x - y = 15
C) 6x - y = 50
D) 6x - y = -33
Find an equation of the line through the pair of points. Write the equation in the form Ax + By = C.
55) (8, 2) and (3, 5)
A) -6x + 2y = -28
B) 3x + 5y = 34
C) 6x - 2y = -28
D) -3x + 5y = 34
Find an equation of the line.
56) Vertical line through (2, -10)
A) y = -10
B) y = 2
Solve the system of equations by the addition method.
57) 2x + 3y = 6
-4x - 6y = -12
A) (2, 3)
C) no solution
C) x = 2
D) x = -10
B) (0, 0)
D) infinite number of solutions
Without actually solving the problem, choose the correct solution by deciding which choice satisfies the given conditions.
58) At the local convenience store, 7 bags of chips and 4 containers of dip cost $29. However, 6 bags of chips and 5
containers of dip cost $28. What is the cost of one bag of chips and one container of dip?
A) chips = $3; dip = $2
B) chips = $3.50; dip = $1.50
C) chips = $5; dip = $3
D) chips = $4; dip = $1
Solve the system of equations by the addition method.
59) x + y = -9
x+y=5
A) (0, -4)
B) (-9, 5)
C) no solution
D) (0, 0)
C) 7x2 + 36x - 18
D) 7x2 - 36x
60) Perform the indicated operation.
(24x + 9) - (-7x2 - 12x + 9)
A) -7x2 + 12x + 18
B) 7x2 + 36x
Find an equation of the line.
61) Perpendicular to y = -10, through (-4, 1)
4
27
x+
A) x = -4
B) y =
11
11
C) x =
1
4
D) y = 1
V1
Find an equation of the line described. Write the equation in slope-intercept form if possible.
62) Through (5, -24) and (-8, 15)
1
77
A) y = -3x - 9
B) y = 3x - 39
C) y = x 3
3
14
D) y = -
1
67
x3
3
63) Multiply. 3x6 (-8x4 )
A) -24x24
B) 24x24
C) -24x10
D) 24x-10
B) 5z 2 + 120z + 144
C) 5z 2 + 144
D) 25z 2 + 144
B) 2y2 + 20
C) y2 - 8y + 20
D) y2 + 8y - 20
B) 2
C) z + 15
D) 0
B) 423.43
C) 60,490,000
D) 6,049,000
C) 2.29 × 10-5
D) 2.29 × 10-4
C) 7.1 × 10-4
D) 7.1 × 10-5
64) Multiply. (5z + 12)2
A) 25z 2 + 120z + 144
65) Multiply using the FOIL method.
(y - 2)(y + 10)
A) 2y - 20
Simplify the expression.
66) z 0 + 150
A) 16
Write the number in standard notation.
67) 6.049 × 107
A) 604,900,000
68) Write the number in scientific notation.
0.000229
A) 2.29 × 104
B) 2.29 × 10-3
Write the number in scientific notation.
69) 71,000
A) 7.1 × 105
B) 7.1 × 104
70) Simplify the expression. Write the result using positive exponents only.
A) z 12x12
B)
1
27
z x27
71) Find the quotient using long division.
A) x + 2 -
9
x+7
B) x + 3
C)
1
(zx)54
-3
(z9 x9 )
D) z 6 x6
x2 + 9x + 5
x+7
C)
x+2
x+7
D) x - 2 +
9
x+7
V1
15
Find the quotient using long division.
6m 2 + 5m - 14
72)
m+2
A) 6m + 7
B) 6m - 7
73) Factor out the GCF from the polynomial.
A) 5x(7x5 y + 9y3 )
C) m - 7
7
m-7
35x6 y + 45xy3
B) xy(35x5 + 45y2 )
74) Factor the four-term polynomial by grouping.
A) (y - 8)(3x + y)
D) 6m - 7 +
B) (y - 8)(x + 3)
C) 5y(7x6 + 9xy2 )
D) 5xy(7x5 + 9y2 )
3x - 24 + xy - 8y
C) (x - 8)(3 + y)
D) (x - 8y)(3 + y)
75) Factor the trinomial completely. If the polynomial cannot be factored, write "prime." What is one of the
factors?
x2 - 6x - 55
A) (x - 55)
B) (x + 11)
C) (x - 11)
D) prime
76) Factor the trinomial completely. If the polynomial cannot be factored, write "prime." What is one of the
factors?
x2 + 21x + 22
A) prime
B) (x + 22)
C) (x + 1)
D) (x + 11)
C) (2x + 5)
D) (2x - 3)
C) prime
D) (3y + 4)
B) (8x - 3)2
C) (8x + 3)(8x - 3)
D) prime
B) prime
C) (z - 6)2
D) (z + 6)(z - 6)
77) When factored completely, one of the factors is:
2x2 - 7x - 15
A) (x - 5)
B) (x + 5)
78) When factored completely, one of the factors is:
6y2 - 17y + 12
A) (2y - 3)
B) (6y + 3)
79) Factor the binomial completely.
64x2 - 9
A) (8x + 3)2
Factor the binomial completely.
80) z 2 - 36
A) (z + 6)2
V1
Answer Key
Testname: DMAT 0305 FINAL EXAM REVIEW
1) A
2) B
3) B
4) B
5) B
6) B
7) A
8) C
9) B
10) A
11) D
12) D
13) D
14) B
15) D
16) D
17) D
18) B
19) C
20) C
21) D
22) D
23) C
24) C
25) D
26) B
27) B
28) C
29) B
30) A
31) C
32) C
33) B
34) A
35) C
36) B
37) A
38) D
39) A
40) C
41) B
42) D
43) D
44) D
45) C
46) D
47) B
48) C
49) B
50) D
51) C
52) C
53) D
54) B
55) B
56) C
57) D
58) A
59) C
60) B
61) A
62) A
63) C
64) A
65) D
66) B
67) C
68) D
69) B
70) B
71) A
72) B
73) D
74) C
75) C
76) A
77) A
78) A
79) C
80) D
V1