Download Practice 116 Exit Exam

Practice 116 Exit Exam
Name___________________________________
The Exit Exam will be 20 multiple-choice questions. You must get 14 correct to pass the course. These problems are similar
in format and difficulty to those on the exam. The answers are given on the last page.
MULTIPLE CHOICE. Write the letter of the answer in the blank provided. If your instructor provides an optical answer
sheet, record your answers there as well. There is one answer per question. You may use your calculator. Good luck.
Use the power rule and the power of a product or quotient rule to simplify the expression.
1) (mn)7
A) mn 7
2)
C) m 8 n 8
B) 7mn
1)
D) m 7 n 7
2x2 y4 4
z2
A)
2x8 y16
z8
2)
B)
16x6 y8
z6
C)
16x8 y16
z8
D)
2x8 y16
z6
Use the quotient rule to simplify the expression.
s 7 t10
3)
s2t
A) s 5 t8
3)
B) s 5 t9
C) s 9 t11
D) s 5 t10
Use the product rule to simplify the expression. Write the result using exponents.
4) t5 · t9 · t4
A) t49
4)
B) t13
C) t14
D) t18
B) x2
C) x6
D) x8
5) x2 · x6
A) x9
5)
Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of
these.
6)
6) -12s 5 - 1s + 9
A) 5; trinomial
B) 6; trinomial
C) 6; binomial
D) 7; trinomial
Perform the indicated operation.
7) (3x8 + 3x7 - 3x3 + 9) - (13x8 - 4x5 + 9x3 - 10)
7)
B) -10x8 + 3x7 - 4x5 - 12x3 + 19
D) 10x8 + 3x7 + 4x5 - 12x3 + 19
A) 10x8 + 3x7 - 4x5 - 12x3 + 19
C) -10x8 + 3x7 + 4x5 - 12x3 + 19
8) (-8y + 7) + (-2y2 + 3y - 3)
A) -2y2 + 5y + 4
B) -2y2 - 5y + 4
C) -2y2 - 5y + 10
D) -11y2 - 2y + 4
9) 7z - (11 - 2z)
A) 5z + 11
B) 9z - 11
C) 5z - 11
D) 9z + 11
8)
9)
1
10) [(1.3x3 + 7.3x2 + 4.2) + (6.6x - 2.1)] - (3.2x2 -x - 9.4)
A) 1.3x3 + 4.1x2 + 7.6x + 11.5
10)
B) 13x6 + 11.5
C) 1.3x3 + 4.1x2 + 6.6x + 11.5
D) 1.3x3 + 10.5x2 + 5.6x - 7.3
Multiply.
11)
1 8 1 6
x x
3
2
1
A) - x14
6
11)
B)
1 48
x
6
1
C) - x48
6
12) (x + 1)(x2 - x + 1)
A) x3 + 1
B) x3 - 2x2 - 2x - 1
C) x3 - 1
D) x3 + 2x2 + 2x + 1
13) (y + 6)(y + 7)
A) y2 + 13y + 13
D)
1 14
x
6
12)
13)
C) 2y + 42
B) y2 + 13y + 42
14) (5z + 12)2
A) 5z 2 + 144
D) 2y2 + 42
14)
B) 25z 2 + 144
C) 25z 2 + 120z + 144
D) 5z 2 + 120z + 144
Multiply using the FOIL method.
15) (b - 2)(b + 5)
A) 2b2 + 10
B) b2 - 3b + 10
C) b2 + 3b - 10
D) 2b - 10
Multiply.
16) (5p + 2)(5p - 2)
A) p2 - 4
B) 25p2 + 20p - 4
C) 25p2 - 20p - 4
D) 25p2 - 4
B) 4a 2 + 9
C) 2a 2 + 9
D) 2a 2 - 12a + 9
B) 2x + 36
C) x2 + 12x + 12
D) 2x2 + 36
C) 0.0000002122
D) 0.00002122
17) (2a - 3)2
A) 4a 2 - 12a + 9
Multiply using the FOIL method.
18) (x + 6)(x + 6)
A) x2 + 12x + 36
15)
16)
17)
18)
Write the number in standard notation.
19) 2.122 × 10-6
A) 0.000002122
19)
B) -2,122,000
Write the number in scientific notation.
20) A light-year is a measure of length defined as the distance that light travels in one year, which is
about 9,500,000,000,000 kilometers. Write this number in scientific notation.
A) 95 × 1011
B) 9.5 × 1012
C) 9.5 × 10-12
D) 0.95 × 10-11
2
20)
21) 0.000000080604
A) 8.0604 × 108
21)
B) 8.0604 × 10-7
C) 8.0604 × 10-8
D) 8.0604 × 10-9
Evaluate the expression using exponential rules. Write the result in standard notation.
22) (7.6 × 103 ) × (8.0 × 103 )
A) 6,080,000
B) 60.8 × 106
C) 60,800,000
22)
D) 60.8 × 109
Perform the division.
18x6 - 24x3
23)
-6x6
A) 18x6 + 23)
4
x3
4
B) -3 - 24x3
C) -3 + B) prime
C) (15z + 4)(z - 3)
D) (3z - 4)(5z + 3)
B) 8, -8
C) 0, -8
D) 0, -8, 8
C) - 1, 0
D) - 1, 0 , (0, 0)
x3
D) -3 + 4x3
Factor the trinomial by grouping.
24) 15z 2 + 11z - 12
A) (3z + 4)(5z - 3)
24)
Solve the equation.
25) y3 + 16y2 + 64y = 0
A) 0, 8
25)
Find the x-intercepts of the graph of each equation.
26) y = 4x2 + 4x
A) (0, 0)
26)
B) - 1, 0 , (4, 0)
Simplify the rational expression.
x3 - 27
27)
3 - x
A)
28)
x3 - 27
3 - x
27)
B) x2 - 9
C)
1
3 - x
D) -x2 - 3x - 9
3x + 3
2
15x + 24x + 9
A)
1
5x + 3
28)
B)
3x + 3
C)
15x2 + 24x + 9
3x
5x + 3
D)
3x + 5
5x + 24
Solve the problem.
29) A drug is injected into a patient and the concentration of the drug is monitored. The drugʹs
7t
. Estimate the drugʹs
concentration, C(t), in milligrams after t hours is modeled by C(t) = 3t2 + 3
concentration after 4 hours. (Round to the nearest hundredth.)
A) 2.01 mg
B) 0.69 mg
C) 1.87 mg
3
D) 0.55 mg
29)
Find the domain of the rational expression.
x2 - 30x
30) f(x) = 5x
A) x|x is a real number and x ≠ 30)
1
5
B) {x|x is a real number and x ≠ 5}
C) {x|x is a real number and x ≠ 0}
D) {x|x is a real number and x ≠ 0 and x ≠ 30}
Find the quotient and simplify.
x2 - 6x + 9 5x - 15
31)
÷ 2x - 6
10
A) 10
31)
B)
x2 - 6x + 9
(x - 3)2
C) 1
D)
(x - 3)2
4
Find the product and simplify.
4
z3
· 32)
8z 3z 2
A)
z
6
32)
B)
1
6
C)
z3
6z 2
D)
1
6z
Multiply or divide as indicated.
4
x2 + 4x
· 33)
2x + 8
7
A)
34)
2x
7
33)
B)
x2 + 9x + 8
28
C)
4x2 + 16x
14x + 56
D)
x + 4
x + 2
(x + 3)2 x2 - 9
÷ x - 3
3x - 9
A)
3(x + 3)
x - 3
34)
B)
6(x2 + 9)
x2 - 9
C)
(x + 3)3
3(x - 3)
D)
(x + 3)2
(x - 3)2
Find the least common denominator (LCD).
9
3
35)
, x2 + 4x x2 + 9x + 20
A) x(x - 1)2
35)
B) x(x - 1)(x + 5)
C) x(x + 4)(x + 5)
D) (x - 1)2
Perform the indicated operation. Simplify if possible.
x
4
36)
- 2
2
x + 7x - 44 x + 7x - 44
A) x - 4
36)
B) x + 11
C)
4
1
2(x + 11)
D)
1
x + 11
Find the least common denominator (LCD).
1
1
37)
, 2
2
x + 14x + 49 x + 7x
A) (x + 7)2
37)
C) x(x + 7)2
B) x(x + 1)(x + 7)
D) x(x + 7)
Perform the indicated operation. Simplify if possible.
30
x2 - 11x
+ 38)
x - 5
x - 5
A) x - 5
38)
B) x - 6
C) x + 6
D) x + 5
Rewrite the rational expression as an equivalent rational expression with the given denominator.
4
39)
= 5x 20x2
A)
16x
20x2
B)
16
20x2
C)
4x2
20x2
D)
4
20x2
Perform the indicated operation. Simplify if possible.
x - 2
3x + 7
40)
+ x2 + 9x + 20 x2 + 5x + 4
41)
42)
40)
A)
4x2 + 21x + 33
(x - 4)(x - 5)(x - 1)
B)
C)
4x + 5
2
2x + 14x + 24
D) 4x + 5
4x2 + 21x + 33
(x + 4)(x + 5)(x + 1)
2
7
+ 5x 10x
A)
3
5x
41)
B)
11
10x
C)
8
5x
D)
11
10x2
4
- 7x
x5
A)
7x6 - 4
x5
42)
B)
4 - 7x
x5
C)
4 - 7x6
x5
D)
4 - 7x4
x5
Solve the equation.
7x
1
43)
+ 4 = 5
4
A)
44)
5
7
43)
B) - 79
28
C) - 75
28
D)
107
28
2
t
= t
5t - 12
A) 4, 6
39)
44)
B) 0, 24
9
C) 0, 36
5
D) 0
Solve the equation for the indicated variable.
nE
45) I = for r
nr + R
A) r = -R
In - E
B) r = 45)
nE-IR
In
C) r = IR
In + E
D) r = IR(In - E)
Solve the proportion.
x + 6 12
46)
= x
7
A)
42
5
46)
B)
6
5
C) - 72
5
D)
42
19
Solve.
47) Five divided by the difference of a number and 6 equals the quotient of 10 and the sum of the
number and 8. Find the number.
14
20
B)
C) -4
D) 20
A)
5
3
Solve the proportion.
1 x
48) = 2 5
A)
1
10
47)
48)
B)
5
2
C) 5
D) 10
Solve.
49) On an architectʹs blueprint, 1 inch corresponds to 9 feet. Find the length of a wall represented by a
1
line 2 inches long on the blueprint. Round to the nearest tenth if necessary.
3
A) 25.9 ft
B) 38.6 ft
C) 3.3 ft
D) 21 ft
Solve the absolute value equation.
50) |x| + 3 = 13
A) 10
B) -10, 10
C) -10
D) 16
51)
50)
3x + 6
= 3
2
A) -4, 0
51)
B) 4, 0
C) -4, 4
D) ∅
C) -9x
D) 9 x
Simplify. Assume that all variables represent any real number.
52) 81x2
A) 9x
49)
B) -9 x
52)
Find the square root. Assume that all variables represent positive real numbers.
53) 0.0081
A) 0.0009
B) 0.9
C) 0.09
6
53)
D) 0.009
Evaluate.
54) If f(x) = 2x - 5, find the value of f(15).
A) 5
B) 30
54)
C) 25
D)
30
Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable.
55)
55) 7
A) 7.000
B) 2.646
C) 2.643
D) 2.651
Use rational exponents to write as a single radical expression.
3
6
56) x · x2
A) x15
57)
6
x · x
3
A) x2
B)
6
x5
56)
C)
6
x3
D)
x5
57)
B)
x2
C)
6
x2
D) x8
Write with positive exponents. Simplify if possible.
58) 81-5/4
58)
1
A) - 243
1
B)
243
C) 243
D) not a real number
Use rational exponents to simplify the following.
12
59)
(x + 5)4
A) (x + 5)1/3
B) x1/3 + 5 1/3
59)
C) x3 + 5 3
D) (x + 5)3
Simplify the radical expression. Assume that all variables represent positive real numbers.
120
60)
6
A) 2 5
B)
120
6
C) 6
D)
60)
720
6
Use the quotient rule to divide and simplify.
200
61)
2500
A)
8
100
B)
61)
2
5
C)
Find the distance between the pair of points.
62) (-5, -7) and (7, 7)
A) 52 13 units
B) 2 85 units
200
2500
D)
5 8
50
62)
C) 52 units
7
D) 2 units
Simplify the radical expression. Assume that all variables represent positive real numbers.
63) 50x2 y
B) 5x2 2y
A) 5xy 2
C) 5xy2 2
63)
D) 5x 2y
Use the quotient rule to divide and simplify.
64)
18x11
64)
2x
A) x5 2
B) 3x5 x
C) 3x5
D) x5 3
Add or subtract. Assume all variables represent positive real numbers.
65) 36 + 500 + 4 + 45
A) 109 5 + 8
B) 13 5 + 36 + 4
C) 500 + 45 + 8
D) 13 5 + 8
66)
63 + 567
A) 12 7
65)
66)
B) 12 14
C) 84
D) -6 7
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
t
67)
t + y
A)
68)
B)
t + ty
t + y
C)
t - t y
t - y
D)
t + t y
t + y
35
5x
A)
69)
t - ty
t - y
68)
7 5x
5x
B)
35 x
x
C)
7 5x
x
D)
35 5x
5x
4
8 - 3
A)
67)
69)
4
4
- 8
3
B)
32 + 4 3
-5
C)
32 - 4 3
61
D)
32 + 4 3
61
Use the Pythagorean theorem to find the unknown side of the right triangle.
70)
70)
15
20
A) 56
B) 18
C) 25
8
D) 24
71)
71)
13
A)
458
17
2
289
2
B) 17
C)
B) -1
C) -1, 2
D) 289
Solve.
72)
73)
3 - x = x - 1
A) 2
x + 2 = 6
A) 38
72)
D) ∅
73)
B) 36
C) 64
D) 34
Use the square root property to solve the equation.
74) (11 - 14x)2 = 42
74)
A)
14 - 42 14 + 42
, 11
11
B)
C)
11 - 42 11 + 42
, 14
14
D)
42 - 11
, 14
42 + 11
14
53
31
, - 14
14
Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
2
75) x2 + x + _______
75)
5
4
2 2
2
1
1 2
2
B) x2 + x + = x + A) x2 + x + = x + 25
5
5
5
25
5
2
1
1 2
2
2
1 2
C) x2 + x + = x + D) x2 + x + = x + 5
25
5
5
25
5
Solve the equation by completing the square.
76) x2 + 3x - 9 = 0
76)
A)
-3 - 3 5
2
B)
C)
-3 - 3 5 -3 + 3 5
, 2
2
D) -3 - 3 5, -3 + 3 5
3 + 3 5
2
Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
1
77) x2 + x + _______
77)
6
1
1
1 2
1
B) x2 + x + = x + A) x2 + x + 144 = (x +12)2
6
12
6
6
2
1
1
1
1
1
1 2
C) x2 + x + = x + D) x2 + x + = x + 6
144
12
6
36
6
9
Solve.
78) Because of the increase in traffic between Springfield and Orangeville, a new road was built to
connect the two towns. The old road goes south x miles from Springfield to Freeport and then goes
east x + 3 miles from Freeport to Orangeville. The new road is 7 miles long and goes straight from
Springfield to Orangeville. Find the number of miles that a person saves by driving the new road
over the old one.
78)
Springfield
Freeport
A)
Orangeville
89 + 7 miles
3
89
C) - + miles
2
2
B)
89 - 7 miles
D)
3
89
+ miles
2
2
Use the quadratic formula to solve the equation.
79) 2x2 + 10x = - 7
79)
A)
-10 - 11 -10 + 11
, 2
2
B)
-5 - 39 -5 + 39
, 2
2
C)
-5 - 11 -5 + 11
, 4
4
D)
-5 - 11 -5 + 11
, 2
2
Solve.
80)
2
x2 - 11x + 18
= 2x
x
- x - 9 x - 2
80)
A)
5 - 17 5 + 17
, 2
2
B)
5 - 33 5 + 33
, 2
2
C)
-5 - 33 -5 + 33
, 2
2
D)
-5 - 17 -5 + 17
, 2
2
81) Two pipes can be used to fill a pool. Working together, the two pipes can fill the pool in 6 hours.
The larger pipe can fill the pool in 3 hours less time than the smaller pipe can alone. Find the time
to the nearest tenth of an hour it takes for the smaller pipe working alone to fill the pool.
A) 13.7 hours
B) 10.7 hours
C) 10.8 hours
D) 13.8 hours
10
81)
Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
82) f(x) = (x - 2)2
82)
y
10
5
-10
-5
5
10
x
-5
-10
A) vertex (0, -2); axis x = 0
B) vertex (2, 0); axis x = 2
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C) vertex (-2, 0); axis x = -2
x
5
10
x
y
10
10
5
5
-5
10
D) vertex (0, 2); axis x = 0
y
-10
5
5
10
x
-10
-5
-5
-5
-10
-10
11
Sketch the graph of the quadratic function by finding the vertex, intercepts, and determining if the graph opens upward
or downward.
83)
83) f(x) = -x2 - 1
y
10
5
-10
-5
5
10
x
-5
-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
12
Match the function with its graph.
84) f(x) = x2 + 2x - 3
84)
B)
A)
y
10
5
5
(-1, 4)
-10
y
10
-5
5
10
x
-10
-5
5
-5
-5
-10
-10
C)
10
x
10
x
(1, -4)
D)
y
y
10
5
-10
-5
10
5
(1, 4)
5
10
x
-10
-5
5
-5
(-1, -4)-5
-10
-10
13
VOCABULARY. You should know the following vocabulary terms.
85) Exponents and Polynomials Chapter: exponent, base, coefficient, constant term, polynomial, binomial,
trinomial, monomial, degree of a term, degree of a polynomial, distributive property, FOIL, scientific notation,
dividend, quotient, divisor
Factoring Polynomials Chapter: factored form, factors, terms, GCF (greatest common factor), integers, sum,
difference, perfect square trinomial, quadratic equation, Pythagorean Theorem, hypotenuse and leg of right
triangle
Rational Expressions Chapter: undefined, domain, reciprocal, denominator, LCD (least common denominator),
proportion
Absolute value Chapter: absolute value
Rational Exponents and Radicals Chapter: square root, irrational number, perfect square, cube root, index, nth
root, radical sign, rational number, midpoint of a line, distance between two points, like radicals, rationalizing
the denominator, conjugate, rationalizing the numerator
Quadratic Equations, Functions, and Graphs Chapter: quadratic or second -degree equation, completing the
square, simple interest, compound interest, quadratic formula, discriminant, solving an equation by quadratic
methods, quadratic function, parabola, vertex, axis of symmetry, x and y intercepts, orientation (opens up or
down), minimum and maximum of quadratic function
14
Answer Key
Testname: PRAC_EXIT_EXAM_116
1) D
2) C
3) B
4) D
5) D
6) A
7) C
8) B
9) B
10) A
11) D
12) A
13) B
14) C
15) C
16) D
17) A
18) A
19) A
20) B
21) C
22) C
23) C
24) A
25) C
26) D
27) D
28) A
29) D
30) C
31) C
32) B
33) A
34) A
35) C
36) D
37) C
38) B
39) A
40) B
41) B
42) C
43) C
44) A
45) B
46) A
47) D
48) B
49) D
50) B
15
Answer Key
Testname: PRAC_EXIT_EXAM_116
51) A
52) D
53) C
54) A
55) B
56) B
57) A
58) B
59) A
60) A
61) B
62) B
63) D
64) C
65) D
66) A
67) A
68) C
69) D
70) C
71) B
72) A
73) D
74) C
75) C
76) C
77) C
78) B
79) D
80) C
81) A
82) B
83) D
84) D
85)
16