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Intermediate Algebra Practice Final A
Find the slope of the line through the pair of points.
1) (1, -3) and (-2, -5)
2
A) - 3
1)
3
B)
2
2
C)
3
3
D) - 2
Solve the problem.
2) Mardi received an inheritance of $50,000. She invested part at 10% and deposited the remainder in
tax-free bonds at 11%. Her total annual income from the investments was $5100. Find the amount
invested at 10%.
A) $40,000
B) $20,000
C) $39,000
2)
D) $44,900
Decide whether the pair of lines is parallel, perpendicular, or neither.
3) 3x - 2y = 1 and 2x + 3y = -5
A) Parallel
3)
B) Neither
C) Perpendicular
Find the slope of the line through the pair of points.
4)
4) (-2, -8) and (-2, -6)
A) Undefined
B) -2
C) 0
D) 2
Find an equation of the line satisfying the conditions. Write the equation in slope -intercept form.
5) Through (1, 9); perpendicular to x = 5
A) y = -9
5)
C) y = -1
B) y = 1
D) y = 9
Solve the problem.
6) Find f(-4) when f(x) = 3x2 + 5x - 2.
A) 66
6)
B) 26
C) 30
D) -6
Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.
7)
7) 5x + 3y = -4
-30x - 18y = 24
A) Inconsistent: no solutions
B) {(-12, -20)}
C) {(-20, -12)}
D) Dependent: {(x, y) 5x + 3y = -4}
Solve.
8) A plane flies 420 miles with the wind and 310 miles against the wind in the same length of time. If
the speed of the wind is 22 mph, what is the speed of the plane in still air?
A) 151 mph
B) 136 mph
C) 146 mph
8)
D) 171 mph
Evaluate the expression. Assume all variables represent nonzero numbers.
9) -100 + (-2)0
A) -2
9)
B) 0
C) 2
1
D) -12
Evaluate the expression.
1
10)
-7 -2
A) 49
10)
B) -7
C) 7
D) -49
Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero
real numbers.
11) (-3x4 )5
11)
A) -243x20
B) -243x9
C) 243x20
D) 243x9
Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero
numbers.
2x3 y-3 -4
12)
12) x-2 y3
A)
13) - y24
2x20
B)
y24
2x5
C)
y24
16x20
D)
2x20
y24
2x3 y-3 -4
x-5 y2
A)
2x32
y20
13)
B)
y20
16x32
C)
y20
2x8
D)
y20
2x32
For the given polynomial function, find the requested value.
14) f(x) = 3x5 + 3x4 + 3x3 - x2 ; find f(-2)
A) -80
14)
B) -76
C) -47
D) -81
For the given pair of functions, find the requested item.
15) Given f(x) = 4x - 3 and g(x) = -8x + 7, find (f - g)(x).
A) -4x - 4
B) -4x2 + 10
15)
C) 12x + 10
D) 12x - 10
For the pair of functions, find the product function or functional value indicated.
16) Find (fg)(3).
f(x) = x2 - 7
16)
g(x) = 3x
A) (fg)(3) = 9x2 - 7
B) (fg)(3) = 6
C) (fg)(3) = 18
D) (fg)(3) = 9x3 - 63x
Find the product.
17) (r - 8)2
A) r + 64
17)
B) r2 + 64
C) 64r2 - 16r + 64
2
D) r2 - 16r + 64
Divide.
18) ( 8 r3 - 14 r2 + 5 r - 18 ) ÷ (r - 2 )
19)
18)
A) 8 r2 - 2 r - 9
9
B) 8 r2 + 2 r + r - 2
C) 8 r2 + 2 r + 9
D) r2 + 9 r + 2
6x7 -18x3
6x7
A) 1 - 3x 4
19)
B) 1 - 3
x4
C) 1 - 18x3
D) - 3
x4
Perform the indicated operation and express in lowest terms.
3x2 + 9x - 12
2x2 - 9x + 10
· 20)
2 - x
2
2x + 3x - 12
A) -(3x - 3)
21)
B) -(3x - 3)(x + 4)
20)
C)
3x - 3
2 - x
D) 3x + 3
16y2 - 4z 2
4y2 - 7yz - 2z 2
÷ 4y2 + 6yz - 4z 2
y2 - 4z 2
A)
4y + 2z
4y + z
B)
21)
4y + 2z
4y - z
C) 1
D)
4y - 2z
4y + z
Write the rational expression in lowest terms.
7k - 28
22)
24 - 6k
A) 1
B) - 22)
7
6
C)
7
6
D) -1
Perform the indicated operation and express in lowest terms.
2x + 3
x + 1
23)
- 2
2
x + 7x + 10
x + 7x + 10
A)
24)
1
x + 5
B) x + 2
23)
C)
x + 4
x2 + 7x + 10
D)
4
x2 + 7x + 10
6
8
- x - 4
4 - x
A)
16
x - 4
24)
B)
-2
x + 4
C)
3
14
x - 4
D) -1
25)
9x
x2 - 5x + 6
- 36
25)
x2 - 6x + 8
A)
9(x - 6)
(x - 3)(x - 4)
B)
9x - 36
(x - 2)(x - 3)(x - 4)
C)
9
(x - 2)(x - 3)
D)
x - 6
(x - 3)(x - 4)
Solve the problem.
26) A contractor finds that it takes Sam Tockett 9 hours to construct a wall of a certain size. It takes Jim
Lowell 6 hours to construct the same wall. How long would it take if they worked together?
5
3
C) 15 hr
D)
hr
A) 1 hr
B) 3 hr
18
5
26)
27) Martha can rake the leaves in her yard in 3 hours. Her younger brother can do the job in 7 hours.
How long will it take them to do the job if they work together?
21
10
21
hr
B)
hr
C)
hr
D) 7 hr
A)
10
21
4
27)
Solve the formula for the specified variable.
28) A = P(1 + nr) for r
P - A
A) r = Pn
29)
28)
A - P
B) r = Pn
A
C) r = n
Pn
D) r = A - P
1
1
1
+ = for c
a
b
c
A) c = a + b
29)
B) c = ab(a + b)
C) c = a + b
ab
D) c = ab
a + b
Solve the problem.
30) The cost of manufacturing clocks is given by c = 25 n + 144, where c is the total cost and n is the
number produced. What is the cost when no clocks are produced?
A) 60
B) 3600
C) 25
30)
D) 300
Simplify the expression involving rational exponents.
31) (-27)2/3
32) - 31)
A) -9
B) -3
C) Not a real number
D) 9
49 1/2
16
32)
A) Not a real number
C) - B) - 7
4
D)
4
4
7
49
32
33) - 64 - 2/3
125
A) - C)
33)
16
25
B) Not a real number
25
16
D)
16
25
Find the missing length in the right triangle. Simplify the answer if necessary.
34)
34)
36
c
15
A) c = 39
B) c = 3 119
C) c = 27
D) c = 33
Express in simplified form. Assume that all variables represent positive real numbers.
4
35) - 625x5 y11
4
4
4
A) -5xy2 xy3
B) 5xy2 xy3
C) 5xy2 xy3
D) -5xy2 + xy3
35)
Perform the indicated operations and simplify. Assume that all variables represent positive real numbers.
36)
3x + 6 48x + 7 27x
A) 46 3x
36)
B) 45 3x
C) 13 78x
D) 14 78x
Multiply, then simplify the product. Assume that all variables represent positive real numbers.
37) (5 + 2)2
A) 27 + 5 2
B) 25 + 10 2
C) 7 + 10 2
D) 27 + 10 2
Rationalize the denominator. Assume that all variables represent positive real numbers.
50
38)
x
A)
5x
x
B)
5 2x
x
C) 5 2x
37)
38)
D) 5
2
x
Add or subtract as indicated. Write your answers in standard form.
39) (7 + 8i) - (-5 + i)
A) 12 + 7i
39)
C) 2 + 9i
B) 12 - 7i
D) -12 - 7i
Multiply.
40) (8 - 4i)2
A) 80 - 64i
40)
B) 48 - 64i
C) 48 + 64i
5
D) 80 + 64i
41) (6 - 3i)2
A) 45 + 36i
41)
B) 45 - 36i
C) 27 + 36i
D) 27 - 36i
Solve the given problem using Galileoʹs formula, d = 16t2 . Round answer to the nearest tenth.
42) A young boy is delighted to drop various objects from a hotel balcony to the ground below. If he
is 225 ft above the ground, how long does it take for one of the objects to fall to the ground?
A) 14.1 sec
B) 225.0 sec
C) 15 sec
42)
D) 3.8 sec
Find the imaginary solutions of the given equation.
43) x2 + x + 6 = 0
-1 + -23 -1 - -23
A)
, 2
2
C)
43)
-1 + i 23 -1 - i 23
, 2
2
B)
1 + i 23 1 - i 23
, 2
2
D)
1 + -23 1 - -23
, 2
2
Solve the given equation by completing the square.
44) z 2 + 18z + 63 = 0
44)
A) - 9 + 3 2, - 9 - 3 2
B) - 18 + 3 7
C) 9 + 3 2
D) 9 + 3 7, 9 - 3 7
Solve the problem. Round to the nearest tenth, if necessary.
45) A jet plane traveling at a constant speed goes 1200 mi with the wind, then turns around and travels
for 1000 mi against the wind. If the speed of the wind is a constant 50 mph, and the total flight took
4 hours, find the speed of the plane.
A) 550 mph
B) 435 mph
C) 525 mph
45)
D) 605 mph
Solve the problem.
46) Find f(-1) when f(x) = x2 + 5x + 6.
A) 0
46)
B) 12
C) 2
D) -10
Write the equation in standard form of the line satisfying the given conditions.
47) Through (-6, -9); horizontal
A) x = -6
47)
B) x = 9
C) y = 6
6
D) y = -9
Graph the equation.
48) y = 1
48)
y
10
5
-10
-5
5
10
x
-5
-10
49) x = 1
49)
y
10
5
-10
-5
5
10
x
-5
-10
State the intercepts and Graph the equation.
50)
50) y - x = -1
y
10
5
-10
-5
5
10
x
-5
-10
x-intercept: ________________
y -intercept: ________________
7
Graph the line.
51) Through (0, 5); m = - 3
51)
y
10
5
-5
-10
5
10
x
-5
-10
Find an equation of the line satisfying the conditions. Write the equation in slope -intercept form.
52) Through (-6, 5); parallel to -7x + 5y = 57
52)
Write the equation in standard form of the line satisfying the given conditions.
53)
53) Through (-8, 6); undefined slope
54) Through (3, 5); m = - 8
9
54)
Write the equation in standard form of the line through the given points.
55) (-7, -5) and (7, -2)
55)
Graph the compound inequality.
56) 2x - y > 4 and x ≤ 4
56)
y
4
2
-4
-2
2
4
6x
-2
-4
-6
8
Decide whether the relation is a function, and give the domain.
57)
57)
y
10
5
-10
-5
5
10
x
-5
-10
function Yes No
Domain:_______________
Decide whether the relation is a function, and give the domain and range.
58)
58)
y
10
5
-10
-5
5
10
x
-5
-10
function Yes No
Domain:_______________
Decide whether the relation is a function, and give the domain.
y
10
5
-10
-5
5
10
x
-5
-10
59)
function Yes No
Domain:_______________
9
59)
Factor by grouping.
60) x3 + 4x2 - 5x - 20
60)
Factor the polynomial completely.
61) 49x2 - 4
61)
Solve the equation.
62) 3x3 + 23x2 + 40x = 0
62)
63) 3x2 + 28x
63)
+ 49 = 0
Solve.
64) (x - 4)(x - 9) = -4
64)
65) (x + 4)(x + 1) = 18
65)
Solve the equation.
2
t
66) = t
5t - 12
67)
5
3
2
- = y + 4
y - 4
y2 - 16
68) 1 - 69)
66)
67)
3
7
= 2x
4
68)
1
2
-3
+ = x + 6
x + 3
2
x + 9x + 18
69)
70)
4x - 5 - 9 = 0
70)
71)
x + 3 = x - 3
71)
72) 1 - 73)
4
x
- 32
= 0
x2
72)
3
5
= 1 + x - 4
x + 4
73)
74) 16y = 1 - 24y
74)
75) 32y = 1 - 48y
75)
10
Answer Key
Testname: IAPFAFALL2009
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
C
A
C
A
D
B
D
C
B
D
A
C
B
B
D
C
D
C
B
A
A
B
A
C
A
B
B
B
D
D
D
C
C
A
A
A
D
B
A
B
D
D
C
A
A
C
D
11
Answer Key
Testname: IAPFAFALL2009
48) None; (0, 1)
y
10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
49) (1, 0); none
y
10
5
-10
-5
-5
-10
50)
y
10
5
-10
-5
-5
-10
12
Answer Key
Testname: IAPFAFALL2009
51)
y
10
5
-5
-10
5
10
x
-5
-10
7
67
52) y = x + 5
5
53) x = -8
54) 8x + 9y = 69
55) 3x - 14y = 49
56)
y
4
2
-4
-2
2
4
6x
-2
-4
-6
57) Not a function; domain: [1, 5]; range: [-5, -3]
58) Not a function; domain: (-∞, 1] ; range: (-∞, ∞)
59) Not a function; domain: [-9, 1]; range: [3, 5]
60) (x + 4)(x2 - 5)
61) (7x + 2)(7x - 2)
8
62) -5, - , 0
3
63) -7, - 7
3
64) {5, 8}
65) {2, -7}
66)
67)
68)
69)
{4, 6}
{17}
{-2}
No solution
13
Answer Key
Testname: IAPFAFALL2009
70)
43
2
71) {6}
72) 8, -4
73) {6, -8}
1
74)
32
75)
1
64
14