Sample Departmental Final - Math 46
Perform the indicated operation. Simplify if possible.
7 - x - 2x + 3
1)
x-2
2-x
A)
x + 10
x-2
B) - x + 4
x-2
C)
x+4
x-2
D) - x + 10
x-2
Solve the problem.
2) The sum of a number and its square is 72. Find the number.
A) 8 or 9
B) 8 or -9
C) -8 or 9
D) -8 or -9
Find the following product.
3) (x + 1)(x2 - x + 1)
A) x3 + 1
C) x3 - 2x2 - 2x - 1
D) x3 + 2x2 + 2x + 1
C) 40 sq. m
D) 364 sq. m
B) x3 - 1
Find the area of the figure.
4)
14 m
26 m
1m
14 m
26 m
A) 260 sq. m
B) 26 sq. m
Use the point-slope form of the linear equation to find an equation of the line with the given slope and passing
through the given point. Then write the equation in standard form.
5) Slope- 7 ; through (5, 3)
8
A) 7x + 8y = -59
Solve the equation.
6) -8x + 1 = -39
A) -32
7) x + 20 + 5x - (6x + 24) = -4
A) 0
Simplify the expression.
8) [29 - (4 + 6) ÷ 2] - [1 + 18 ÷ 3]
A) 12
B) 7x + 8y = 59
C) 7x - 8y = 59
D) 8x + 7y = -59
B) -5
C) 5
D) 32
B) all real numbers
C) 4
D) no solution
B) 14
C) 24
D) 17
1
Solve the system of equations.
9) -5x - 15y = 9
x + 3y = 0
A) (9, 0)
C) infinite number of solutions
B) (0, 9)
D) no solution
Use the vertical line test to determine which graph is NOT a graph of a function.
10)
A)
B)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
C)
5
10 x
5
10 x
D)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
Perform the indicated operation. Simplify if possible.
2
7
+
11)
2
2
x - 3x + 2
x -1
A)
9x - 12
(x - 1)(x + 1)(x - 2)
B)
12x - 9
(x - 1)(x + 1)(x - 2)
C)
28x - 12
(x - 1)(x + 1)(x - 2)
D)
9x - 12
(x - 1)(x - 2)
2
Use formulas to find the area of the figure.
12)
13 in.
5 in.
20 in.
A) 130 in. 2
B) 50 in. 2
C) 100 in. 2
Find the following product.
13) 8x2(-4x2 + 3x - 6)
A) -32x4 + 24x2 - 48
C) -32x4 + 24x3 - 48x2
D) 32.5 in. 2
B) 4x4 + 11x + 2
D) -32x4 + 24x - 48
Factor the polynomial completely. If the polynomial cannot be factored, write prime.
14) 5x3 + 5x2y - 30xy2
A) (x - 2y)(5x2 + 15xy)
B) 5x(x + 2y)(x - 3y)
C) 5x(x - 2y)(x + 3y)
D) prime
Find the measures of angles 1, 2, and 3.
15)
60°
A) ∠ 1 = 120°; ∠ 2 = 60°; ∠ 3 = 120°
C) ∠ 1 = 30°; ∠ 2 = 90°; ∠ 3 = 60°
B) ∠ 1 = 30°; ∠ 2 = 120°; ∠ 3 = 30°
D) ∠ 1 = 30°; ∠ 2 = 90°; ∠ 3 = 30°
Find the domain and the range of the relation.
16) {(8, 1), (-8, 0), (-5, -5), (13, -8)}
A) domain: {-8, -5, 8, 13} ; range: {0, 1}
C) domain: {-8, -5, 8, 13} ; range: {-8, -5, 0, 1}
B) domain: {-5, 0, 8, 13} ; range: {-8, -5, 1, 13}
D) domain: {-8, 0, 1, 8} ; range: {-8, -5, 13}
Write in standard notation.
17) 7.951 x 10-5
A) -795,100
Solve the equation.
18) 6x - 9 + 9x + 4 = 5x + 10x - 8
A) 288
B) 0.000007951
C) 0.0007951
D) 0.00007951
B) 0
C) all real numbers
D) no solution
3
Factor out the GCF (greatest common factor) from the polynomial.
19) 4m9 + 6m4 + 8m2
A) 2m2(2m7 + 3m2 + 4)
C) 2(2m9 + 3m4 + 4m2)
B) m2(4m7 + 6m2 + 8)
D) -2m2(2m7 - 3m2 - 4)
Solve the inequality. Graph the solution set and write it in interval notation.
20) -7 ≤ -2x + 3 < -3
A) [3, 5]
-2
-1
0
1
2
3
4
5
6
7
8
9
10
-1
0
1
2
3
4
5
6
7
8
9
10
-10 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
B) (3, 5]
-2
C) [-5, -3)
D) (-5, -3]
-10 -9
Simplify the expression. Write the result using positive exponents only.
21) -4z-3
-64
A) - 4
B) 3
C) - 1
3
z
z
64z3
D)
1
64z3
Factor the polynomial completely. If the polynomial cannot be factored, write prime.
22) x4 - 81
A) (x2 + 9)(x2 + 9)
B) (x2 + 9)(x + 3)(x - 3)
C) (x2 - 9)(x2 - 9)
D) prime
Solve the equation.
23) -2x + 2(-2x - 4) = -10 - 4x
A) 9
5
B) - 1
C) 9
4
D) 1
Solve the compound inequality. Graph the solution set.
24) 6x - 4 < 2x or -4x ≤ -12
A) (1, 3)
1
2
3
4
5
6
7
8
2
3
4
5
6
7
8
3
4
5
6
7
8
B) [1, 3]
1
C) (-∞, 1) ∪ [3, ∞)
1
2
D) ∅
-3
-2
-1
0
1
2
3
Factor the polynomial completely. If the polynomial cannot be factored, write prime.
25) 25x2 - 16
A) (5x - 4)2
B) (5x + 4)2
C) (5x + 4)(5x - 4)
D) prime
List the elements of the set.
26) If A = {17, 18, 19, 22} and B = {15, 17, 18, 20}, list the elements of A ∩ B.
A) {17, 18}
B) { }
C) {15, 17, 18, 19, 20, 22}
D) {15, 19, 20, 22}
Find the slope of the line that is perpendicular to the equation of the given line.
27) 3x - 4y = 9
A) - 4
3
Multiply.
28) (-8)(-7)(-3)
A) 168
B) 3
4
C) 4
3
D) - 3
4
B) -68
C) -168
D) -178
5
Graph the linear equation.
29) x + 8y = -8
A)
B)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
C)
5
10 x
5
10 x
D)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
Factor the polynomial completely. If the polynomial cannot be factored, write prime.
30) z2 - 6z + 9
A) (z - 6)(z + 6)
B) (z - 3)2
C) (z - 3)(z + 3)
Solve the system of equations.
31)
y = 2x - 4
4y + 20x = -72
A) (-2, -8)
C) infinite number of solutions
D) (z + 3)2
B) (-8, -2)
D) no solution
Factor the polynomial completely. If the polynomial cannot be factored, write prime.
32) x2 - x - 35
A) (x + 5)(x - 7)
B) (x - 35)(x + 1)
C) (x - 5)(x + 7)
6
D) prime
Divide. Simplify if possible.
z2 + 11z + 24 ÷
z2 + 3z
33)
z2 + 16z + 64
z2 + 14z + 48
A)
z+6
z
B)
z+6
z2 + 8z
C) z + 6
D)
z
z2 + 16z + 64
Solve.
34) A 6-ft. board is cut into 2 pieces so that one piece is 2 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: 3 ft; longer piece: 18 ft
B) shorter piece: 6 ft; longer piece: 20 ft
C) shorter piece: 16 ft; longer piece: 18 ft
D) shorter piece: 1 ft; longer piece: 5 ft
Factor the polynomial completely. If the polynomial cannot be factored, write prime.
35) x2 - 8x - 33
A) (x - 11)(x + 3)
B) (x + 11)(x - 3)
C) (x - 33)(x + 1)
D) prime
Solve the inequality. Graph the solution set and write it in interval notation.
36) x - 9 < -4
A) [5, ∞)
2
3
4
5
6
7
8
3
4
5
6
7
8
3
4
5
6
7
8
3
4
5
6
7
8
B) (-∞, 5]
2
C) (-∞, 5)
2
D) (5, ∞)
2
Simplify the expression. Write the result using positive exponents only.
4 -2
37) xy
5
xy
8
A) x 6
y
B)
1
C)
x7y 9
1
x12y 10
6
D) y8
x
Divide. Simplify if possible.
7
38) 7x2 ÷ 56x3
4x
32x
A) x7
7
B) 7x
4
3
C) 392x
128
7
3
D) 49x
16
Solve the problem.
39) The area of a circle is 49π square meters. Find its radius.
A) 14 m
B) 24.5 m
C) 49 m
D) 7 m
Write the sentence as an equation. Use x to represent any unknown number.
40) The difference of twice a number and three is nine.
A) 2x - 3 = 9
B) 3 - 2x = 9
C) 2(x - 3) = 9
D) 2x + 3 = 9
Solve the equation.
41) b(b + 13) = 0
A) b = 1, b = -13
D) b = 13, b = 0
B) b = -13, b = 0
C) b = -1, b = -13
Factor the polynomial completely. If the polynomial cannot be factored, write prime.
42) 9z2 + 6z - 8
A) (3z - 4)(3z + 2)
B) (9z + 4)(z - 2)
C) (3z + 4)(3z - 2)
D) prime
Solve the equation.
43) x2 - 2x - 63 = 0
A) x = - 7, x = 9
B) x = 7, x = -9
C) x = 7, x = 9
D) x = -63, x = 0
7 28
B) p m
q 35
28
C) pm
q 35
11
D) pm
q 12
B) 5 , - 13
3
3
C) 5 , - 13
4
4
D) ∅
Simplify the expression.
44)
pm4
7
q5
7 11
A) p m
q 12
Solve the absolute value equation.
45) |3x + 4| + 17 = 8
A) - 5 , 13
3 3
Factor.
46) 64p3 - 1
A) (4p - 1)(16p2 + 1)
C) (4p - 1)(16p2 + 4p + 1)
B) (64p - 1)(p 2 + 4p + 1)
D) (4p + 1)(16p2 - 4p + 1)
Solve the system of equations.
47)
-2x + 7y = 6
5x + 3y = 26
A) (4, -2)
B) (-4, 2)
C) (4, 2)
D) (-4, -2)
Perform the indicated operations.
48) (6x2 + 4) - (-x3 + 9x2 - 10)
A) 7x3 + 13x2 + 10
B) x3 - 3x2 + 14
C) 7x3 + 9x2 + 14
D) x3 + 15x2 - 6
8
Factor by grouping.
49) 18x2 - 15x + 24x - 20
A) (18x - 4)(x + 5)
B) (3x - 4)(6x + 5)
C) (18x + 4)(x - 5)
D) (3x + 4)(6x - 5)
Solve.
50) Five times some number added to 4 amounts to -2 added to the product of 3 and the number.
A) 6
B) -3
C) -6
D) 3
51) Linda and Dave leave simultaneously from the same starting point biking in opposite directions. Linda bikes
at 7 miles per hour and Dave bikes at 8 miles per hour. How long will it be until they are 25 miles apart
from each other?
A) 25 hrs
B) 25 hrs
C) 3 hrs
D) 1 2 hrs
56
5
3
Find the perimeter of the figure named and shown.
52) Equilateral triangle
19 mi
A) 180.5 mi
B) 56 mi
C) 57 mi
Solve the system of equations.
53)
-3x + 2y = 5
6x - 4y = -10
A) (0, 0)
C) infinite number of solutions
B) (-3, 2)
D) no solution
9
D) 38 mi
Graph the function.
54) f(x) = - 3 x - 3
5
A)
B)
y
-10
y
10
10
5
5
-5
10 x
5
-10
-5
-5
-5
-10
-10
C)
5
10 x
5
10 x
D)
y
-10
y
10
10
5
5
-5
10 x
5
-10
-5
-5
-5
-10
-10
Add or subtract as indicated. Write the answer in lowest terms.
55) 2 1 + 5 7
3
8
A) 1 4
11
Find the product.
56) (p + 7q)(p - 7q)
A) p2 - 14q 2
B) 5 1
24
C) 8 5
24
D) 2 1
2
B) p2 - 14pq - 49q 2
C) p2 + 14pq - 49q 2
D) p2 - 49q 2
B) 3
C) -7
D) no solution
B) 22
C) -12
D) 12
Solve the equation.
-4
57) 1 + 2 =
x+7
x+3
x2 + 10x + 21
A) 0
Solve the equation.
58) -3x - 17 + 4x = 5
A) -22
10
Multiply. Simplify if possible.
5p - 5 · 9p2
59)
p
8p - 8
A)
45p3 - 45p2
8p2 - 8p
B) 8
45p
C) 45p
8
D)
40p2 + 80p + 40
9p3
Write the algebraic expression described. Simplify if possible.
60) If x represents the first of four consecutive odd integers, express the sum of the first integer and the fourth
integer in terms of x.
A) 2x + 3
B) 4x + 12
C) 2x + 8
D) 2x + 6
Find the slope of the line that goes through the given points.
61) (9, 2) and (5, -4)
A) - 1
B) 3
7
2
C) 2
3
D) - 3
2
C) 16
D) 16
x
C) s12t5
D) s12t4
C) 49
D) 13
Simplify.
62)
4+ 2
x
x + 1
4
8
A) 1
B) x
16
Use the quotient rule to simplify the expression.
14 5
63) s 2t
st
A) s12t3
B) s16t6
Evaluate the expression for the given replacement values.
64) (x + 3y)2 x = 4, y = 3
A) 26
B) 169
Multiply.
65) (3x - 5y)2
A) 3x2 - 30xy + 25y 2
C) 3x2 + 25y 2
B) 9x2 - 30xy + 25y 2
D) 9x2 + 25y 2
11
Graph the inequality.
66) 3x + y < 4
A)
B)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
C)
5
10 x
5
10 x
D)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
Add.
67) ∣2 + (-4)∣
A) 2
B) -2
C) -8
D) 6
B) -2x + 3
C) -16x + 24
D) -40x
Simplify.
68) - 8 (10x + 15)
5
A) -16x - 24
Use the Pythagorean Theorem to find the missing length in the right triangle.
69)
6 km
8 km
A) 10 km
c
B) 9 km
C) 8 km
12
D) 7 km
The figure shows two parallel lines intersected by a transversal. One of the angle measures is given. Find the measure
of the indicated angle.
70)
25°
Find the measure of ∠3.
A) 115°
B) 155°
C) 25°
D) 65°
B) 5x - 48x5 + 6
x
C) 11x + 6
D) 5x + 6
Perform the division.
-40x6 - 48x5 - 48x4
71)
-8x5
A) 5x + 6 + 6
x
Solve the inequality. Graph the solution set.
72) |x + 17| + 11 < 13
A) (-19, -15)
-20
-15
-10
-5
0
5
10
15
20
B) (-∞, -19)
-35
-30
-25
-20
-15
-10
-5
0
C) (15, 19)
15
20
25
30
35
40
45
50
D) (-∞, -15)
-35
-30
-25
-20
-15
-10
-5
Find the product using the FOIL method.
73) (5x - 3)(6x - 1)
A) 30x2 + 13x + 3
B) 11x2 - 4
0
5
C) 30x2 + 3
13
D) 30x2 - 23x + 3
Solve the equation.
74) x(3x + 16) = 12
A) 2 , -6
3
B) 0, - 16
3
C) 0, 16
3
D) 3 , 6
2
B) 1
40
C) 40x2
2
D) x
40
C) 2, - 10
3
D) ∅
C) (0, 1), (4, 0)
D) (0, 1), (-4, 0)
Simplify.
75)
16
7x
2
35x
A) 40
Solve the inequality. Graph the solution set.
76) |6k + 9| > -4
A) (-∞, - 13 ) ∪ (- 5 , ∞)
6
6
-2
-1
0
1
2
3
4
5
6
7
8
9
10 11
0
1
2
3
4
5
6
7
8
9
10 11
B) (- 5 , ∞)
6
-2
-1
C) (- 13 , - 5 )
6
6
-2
-1
0
1
2
3
4
5
6
7
8
9
10 11
-1
0
1
2
3
4
5
6
7
8
9
10 11
D) (-∞, ∞)
-2
Solve the absolute value equation.
77) |3x + 2| - 5 = 3
A) - 2, 10
3
B) 3, - 5
Find the x- and y- intercepts of the following linear equation.
78) -6x - 24y = 24
A) (0, -1), (4, 0)
B) (0, -1), (-4, 0)
14
Simplify the expression.
79) 7 + (-13) - (-8)
A) -14
B) -2
Simplify the expression by combining any like terms.
80) -9y + 2 - 7 + 6 + y - 1
A) -10y + 1
B) -8y - 1
C) 12
D) 2
C) -10y
D) -8y
C) -5
D) 13
Evaluate the function.
81) Find f(-2) when f(x) = x 2 + 2x - 5.
A) 5
B) 3
Find an equation of the line through the given points. Write the equation in standard form.
82) Through (4, 0) and (2, 5)
A) -5x + 2y = 20
B) 4x - 3y = -23
C) 5x + 2y = 20
D) -4x + 3y = -23
Solve the system of equations by graphing the equations on the same set of axes.
83) y = x - 5
y = -2x - 8
y
10
5
-10
-5
5
10 x
-5
-10
A) (6, -1)
Find the slope of the line.
84) x = 2
A) m = 0
B) (-1, 6)
C) (-1, -6)
D) no solution
B) m = 1
C) m = -1
D) undefined slope
Find the equation of the line. Write the equation using function notation.
85) Through (2, 3); perpendicular to x + 3y = -3
A) f(x) = - 1 x + 7
B) f(x) = 1 x + 7
C) f(x) = 3x - 9
3
3
3
3
15
D) f(x) = 3x - 3
Use similar triangles and the fact that corresponding sides are proportional to find the length of the segment marked
with an x.
86)
6 in.
5 in.
6 in.
B) 1 1 in.
5
A) 1 in.
C) 1 6 in.
25
D) 7 1 in.
5
Simplify the rational expression.
2x + 2
87)
2
10x + 16x + 6
A)
1
5x + 3
Simplify the following.
88) z0 + 150
A) 2
B)
2x
5x + 3
C)
B) 0
2x + 5
5x + 16
D)
2x + 2
10x2 + 16x + 6
C) z + 15
D) 16
C) 48°
D) 12°
Find the measure of angle A for the triangle shown.
89)
30°
102°
A) 228°
B) 60°
16
Match the linear equation with its graph.
90) y = 2x - 4
A)
8
-8
-6
-4
B)
y
8
6
6
4
4
2
2
-2
2
4
6
8 x
-8
-6
-4
-2
-2
-2
-4
-4
-6
-6
-8
-8
C)
y
2
4
6
8 x
2
4
6
8 x
D)
8
-8
-6
-4
y
8
6
6
4
4
2
2
-2
2
4
6
8 x
-8
-6
-4
-2
-2
-2
-4
-4
-6
-6
-8
-8
17
y
Answer Key
Testname: MATH 46
1) A
2) B
3) A
4) B
5) B
6) C
7) B
8) D
9) D
10) D
11) A
12) B
13) C
14) C
15) D
16) C
17) D
18) D
19) A
20) B
21) A
22) B
23) D
24) C
25) C
26) A
27) A
28) C
29) D
30) B
31) A
32) D
33) A
34) D
35) A
36) C
37) A
38) A
39) D
40) A
41) B
42) C
43) A
44) B
45) D
46) C
47) C
48) B
49) D
18
Answer Key
Testname: MATH 46
50) B
51) D
52) C
53) C
54) D
55) C
56) D
57) D
58) B
59) C
60) D
61) B
62) D
63) D
64) B
65) B
66) A
67) A
68) A
69) A
70) B
71) A
72) A
73) D
74) A
75) A
76) D
77) C
78) B
79) D
80) D
81) C
82) C
83) C
84) D
85) D
86) B
87) A
88) A
89) C
90) A
19