Download Math 094 Final Exam Review.tst

Math 094 Final Exam Review
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the expression.
1) 12 ÷ 3 ∙ 4 - 6 ∙ 8
A) -47
2)
1)
B) -40
C) -32
D) 80
∣6(-3)∣ - ∣1 - 8∣
∣10(2)∣
A)
11
20
2)
B) -
11
20
C)
5
4
D) -
5
4
If x = -4 and y = -2, evaluate the expression.
3) x4 + 4y
A) 240
3)
B) 248
C) -24
Identify the property illustrated by the expression.
4) 13 + (5 + 18) = (13 + 5) + 18
A) identity element for addition
C) distributive property
D) -16
4)
B) associative property of addition
D) commutative property of addition
Find the reciprocal or multiplicative inverse.
7
5)
9
A) - 9
7
5)
B) - 7
9
C) 9
Simplify the expression.
6) [20 - (4 + 6) ÷ 2] - [1 + 18 ÷ 3]
A) 5
B) 15
7) (11z + 11) - (2z - 9)
A) 9z + 2
Solve the equation.
8) 7x + 9 + 8x + 3 = 2
2
A)
3
9)
D)
9
7
6)
C) 3
D) 8
B) 9z + 20
C) 9z - 20
D) 13z + 20
8
B)
15
2
C) 3
7)
8)
D) 10
2
2
k=
15
5
A) 3
9)
B) 7
C) 17
10) 2(x + 5) + 105 = 7x - 5(x - 9)
A) 150
C) no solution
D) 16
10)
B) 60
D) all real numbers
1
11)
5(y - 5) = 2y - 5
3
A) 10
11)
B) -40
C) 40
D) -10
Write the following as an equation, using x for the unknown number. Then solve.
12) The sum of four times a number and 3 is equal to the difference of twice the number and 8. Find
the number.
11
A) 4(x + 3) = 2x - 8; - 10
B) 4x + 3 = 2x - 8;
2
11
C) 4x + 3 = 2x - 8; 2
D) 4x + 3 = 2x + 8;
12)
5
2
Solve.
13) The length of a rectangular room is 3 feet longer than twice the width. If the room's perimeter is
198 feet, what are the room's dimensions?
A) Width = 64 ft; length = 134 ft
B) Width = 37 ft; length = 77 ft
C) Width = 48 ft; length = 51 ft
D) Width = 32 ft; length = 67 ft
13)
14) A 9-ft. board is cut into 2 pieces so that one piece is 5 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: 15 ft; longer piece: 32 ft
B) shorter piece: 1 ft; longer piece: 8 ft
C) shorter piece: 4.5 ft; longer piece: 27 ft
D) shorter piece: 22 ft; longer piece: 27 ft
14)
15) 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 = 22°; 2nd angle = 68°
B) 1st angle = 23°; 2nd angle = 67°
C) 1st angle = 31°; 2nd angle = 59°
D) 1st angle = 22°; 2nd angle = 64°
15)
Solve the formula for the specified variable.
16) P = 2L + 2W
for W
A) W = P - L
B) W = P - L
2
16)
C) W = P - 2L
D) W = P - 2L
2
Solve the inequality. Graph the solution set and write it in interval notation.
17) 1 < 2x + 3 < 6
A) - 3 , 1
2
3
B) -∞,
2
3
C) -1,
2
17)
D) (-1, ∞)
18) x - 6 > 5x + 6
A) (-3, ∞)
Find the slope of the line.
19) 11x - 6y = 66
11
A) m = 6
Revised Fall 2012
18)
B) (-∞, -3)
C) (3, ∞)
D) (-∞, 3)
19)
B) m =
11
6
C) m =
6
11
D) m = 11
2
Find the slopes of the lines that are (a) parallel to and (b) perpendicular to the line passing through the pair of points.
20) (-6, -10) and (1, 4)
20)
1
1
A) (a) 2; (b) B) (a) ; (b) - 2
C) (a) 2; (b) - 2
2
2
Determine whether the pair of lines is parallel, perpendicular, or neither.
21) 4x - 9y = 4
18x + 9y = -8
A) parallel
B) perpendicular
21)
C) neither
Find an equation of the line through the pair of points. Write the equation in the form Ax + By = C.
22) (-5, -1) and (3, 6)
A) 7x - 8y = -27
B) 4x + 3y = -6
C) -7x - 8y = -27
D) -4x - 3y = -6
Find an equation of the line.
23) Perpendicular to y = -4, through (8, 12)
A) y = 12
B) x = 8
24) Parallel to y = -10, through (-5, 2)
12
A) y = x - 10
B) y = -5
5
Find the slope of the line.
25) x = -5
A) 0
Revised Fall 2012
22)
23)
1
C) x = 8
1
D) y = - x + 16
2
24)
C) x = -5
D) y = 2
C) 5
D) undefined
25)
B) -5
3
Graph.
26) 3x + 4y = -24
26)
y
10
10
5
-10
5
-5
10 x
5
-10
-5
-5
y
5
10 x
y
10
5
5
-5
10 x
5
-10
-5
-5
-5
-10
C)
10 x
-10
B)
10
-10
5
-5
-10
A)
y
-10
D)
27) x - 3 = 0
27)
y
y
-10
10
10
5
5
-5
5
10
-10
x
-5
-5
-5
-10
-10
A)
5
10
5
10
x
B)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-10
-10
Revised Fall 2012
x
-5
-5
C)
-5
D)
4
Graph the inequality.
28) 2x + 5y ≤ 10
28)
y
10
5
5
-5
x
5
-5
-5
5
x
-5
-10
A)
y
-10
B)
y
10
5
5
-5
y
5
-5
x
5
x
-5
-5
C)
-10
D)
Answer true or false.
29) If the two equations in a system of linear equations are added and the result is 3 = 0, the system
has no solution.
A) False
B) True
Solve the system of equations.
30) x = -6y + 24
-6x + 5y = 61
A) (-7, 6)
31)
2x + 5y = 4
-5x + 3y = 21
A) (3, 2)
30)
B) no solution
C) (-6, 5)
D) (6, 6)
31)
B) (-3, -2)
C) (3, -2)
D) (-3, 2)
Write a system of equations in x and y describing the situation. Do not solve the system.
32) An order of 3 orders of fries, 5 hamburgers, and 4 drinks costs $17. An order of 4 orders of fries, 4
hamburgers, and 5 drinks costs $17. All drinks are $1.
A) 3x + 5y + 4 = 13
B) 3x + 5y + 1 = 17
4x + 4y + 5 = 12
4x + 4y + 1 = 17
C)
3x + 5y + 4 = 17
4x + 4y + 5 = 17
Revised Fall 2012
29)
D)
32)
(3x)(5y) + 4 = 17
(4x)(4y) + 5 = 17
5
Solve.
33) The three angles in a triangle always add up to 180°. If one angle in a triangle is 78° and the
second is 5 times the third, what are the three angles?
A) 78°, 83°, 19°
B) 78°, 84°, 18°
C) 78°, 86°, 16°
D) 78°, 85°, 17°
33)
34) A chemist needs 130 milliliters of a 46% solution but has only 26% and 91% solutions available.
Find how many milliliters of each that should be mixed to get the desired solution.
A) 95 ml of 26%; 35 ml of 91%
B) 40 ml of 26%; 90 ml of 91%
C) 90 ml of 26%; 40 ml of 91%
D) 95 ml of 26%; 40 ml of 91%
34)
35) A certain aircraft can fly 1120 miles with the wind in 4 hours and travel the same distance against
the wind in 7 hours. What is the speed of the wind?
A) 80 mph
B) 60 mph
C) 100 mph
D) 40 mph
35)
Solve the system.
36)
x + y + z = -1
x - y + 3z = -11
3x + y + z = -9
A) (-4, 4, -1)
37)
36)
B) (-1, 4, -4)
C) (-1, -4, 4)
D) ∅
y9
y4
37)
A)
1
y5
B) y 5
C) y 7
D) y 13
B) -16x40
C) 16x13
D) 16x40
38) (8x8)(-2x5)
A) -16x13
38)
Simplify the expression. Write the result using positive exponents only.
-2
xy 3
39)
x3y
A)
40)
1
8
x y8
B)
x4
y4
C)
1
5
x y7
39)
D)
y4
x4
44x-6y 2
47x-9y 4
A)
x3
64y 2
40)
B)
1
64x9y 2
C)
64
x3y 2
41) Subtract (6x + 3) from the sum of (9x2 + 8x + 1) and (x3 - 3).
A) -x3 - 9x2 - 2x + 5
B) x3 + 9x2 + 2x - 5
C) x3 - 9x2 - 2x + 5
Revised Fall 2012
D)
3x3
y2
41)
D) x3 - 9x2 - 2x - 5
6
Multiply.
42) (x + 1)(5x + 11)
A) 5x2 + 16x + 11
42)
B) 5x2 + 16x + 16
C) 5x2 + 14x + 11
D) 5x2 + 11x + 16
43) (8x - 9)2
43)
A) 64x2 - 144x + 81
C) 64x2 + 81
B) 8x2 - 144x + 81
D) 8x2 + 81
44) (8x - 1)(x2 - 4x + 1)
A) 8x3 - 32x2 + 8x + 1
44)
B) 8x3 - 33x2 + 12x - 1
D) 8x3 - 31x2 + 4x - 1
C) 8x3 + 33x2 - 12x + 1
45) (x2 - 12b)(x2 + 12b)
A) x2 - 144b 2
45)
B) x4 - 24x2b + 144b 2
D) x4 + 24x2b + 144b 2
C) x4 - 144b 2
46) (9x - 1)(x2 - 7x + 1)
A) 9x3 + 64x2 - 16x + 1
46)
B) 9x3 - 63x2 + 9x + 1
D) 9x3 - 62x2 + 2x - 1
C) 9x3 - 64x2 + 16x - 1
Divide.
47)
8x3 - 8
2x + 2
47)
A) 4x2 - 4x + 4
B) 4x2 - 4x + 4 -
16
2x + 2
C) 4x2 + 4x + 4
D) 4x2 - 4x + 4 -
8
2x + 2
Factor out the GCF from the polynomial.
48) 128m9 - 32m7 + 48m3
A) 16m3(8m6 - 2m4 + 3)
C) m3(128m6 - 32m4 + 48)
B) -m3(-128m6 - 32m4 - 48)
D) 16(8m9 - 2m7 + 3m3)
Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
49) x2 + 11x + 28
A) prime
50) 4a2 + 4ab - 7a - 7b
A) (4a + 7)(a + b)
Revised Fall 2012
B) (x + 4)(x + 7)
C) (x - 4)(x + 1)
48)
49)
D) (x - 4)(x + 7)
50)
B) (4a - 7)(a - b)
C) (4a + 7)(a - b)
D) (4a - 7)(a + b)
7
Answer Key
Testname: MATH 094 FINAL EXAM REVIEW
1) C
2) A
3) B
4) B
5) D
6) D
7) B
8) C
9) A
10) C
11) D
12) C
13) D
14) B
15) B
16) D
17) C
18) B
19) B
20) A
21) C
22) A
23) B
24) D
25) D
26) D
27) D
28) B
29) B
30) C
31) D
32) C
33) D
34) C
35) B
36) A
37) B
38) A
39) B
40) A
41) B
42) A
43) A
44) B
45) C
46) C
47) B
48) A
49) B
50) D
Revised Fall 2012
8