KYOTE College Algebra Practice Exam 3
1. Simplify.
x2(
x3
− 7
x)
− (7
x − 9
x3)
A)
x5 + 2
x3
− 7
x
B)
x6 + 2
x3
− 7
x
C)
x5
− 9
x3
− 14
x
D)
x5
− 16
x3
− 7
x
E)
x6 + 9
x3
− 14
x
2. A man invests 10,000 dollars in two accounts, the first yielding 4 percent annual interest and the
second, 5 percent. If
x dollars is invested in the first account, how much annual interest does the man
earn on his investement?
A) 900
.0
B) 0
.09
x
C) 9
x
D)
−x + 50000
E)
−0
.01
x + 500
.0
3. What is the set of all values of
x for which the expression
x + 6
x2
− 2
x − 8
is not defined?
A)
{−6
,−4
,2
}
B)
{−6
,−2
,4
}
C)
{−4
,2
}
D)
{−2
,4
}
E)
{−6
}
4. If
x and
y satisfy both 9
x + 2
y = 14 and 7
x + 2
y = 2, then
y =?.
A) 44
B)
−40
C) 6
D)
−20
E) 22
5. Simplify.
2
x − 8
−
3
x
A)
−6
x + 24
x(
x − 8)
B)
−x − 16
x(
x − 8)
C)
−x − 24
x(
x − 8)
D)
−6
x(
x − 8)
E)
−x + 24
x(
x − 8)
6. The line with equation 5
x − 4
y = 3 is perpendicular to
A)
y =5
4
x
B)
y =
−4
5
x
C)
y =
−5
4
x
D)
y =4
5
x
E)
y =4
3
x
1
7. Expand and simplify. (7
x − 6
y)2
A) 49
x2 + 36
y2
B) 49
x2
− 84
xy − 36
y2
C) 49
x2
− 36
y2
D) 49
x2
− 84
xy + 36
y2
E) 49
x2
− 42
xy + 36
y2
8. Simplify.
(
x15
y12)2
z
x5(
y4
z2)2
A)
x6
y3
z2
B)
x6
y3
z3
C)
x25
y16
z3
D)
x25
y16
z2
E)
x6
y6
z3
9. Simplify.
x2 +
x − 6
x2
− 4
x + 4
A)
x + 3
x − 2
B)
x + 6
x − 2
C)
x + 2
x − 2
D)
x − 3
x − 2
E)
x − 6
x − 2
10. Solve
1
x − 1
−
4
7
= 5 for
x.
A)46
39
B)39
46
C)39
38
D)
−8
13
E)38
39
11. A rectangle has length 21 inches and width 16 inches. What is the length of a diagonal from one
corner to the opposite corner, rounded to the nearest inch?
A) 28
B) 24
C) 26
D) 27
E) 25
12. If a line has slope
−2 and passes through the point (3
,2), what is the
y-coordinate of the point on
the line whose
x-coordinate is 5?
A)
−2
B)
−5
C)
−6
D)
−3
E)
−4
2
13. Simplify. (
7
x
x
-4
)
-2
A)1
49
x6
B) 7
x6
C)1
49
x6
D)7
x10
E)1
49
x10
14. A rectangular field is enclosed by 320 feet of fencing. If the length of the field is 6 feet more than its
width, what is its length, in feet?
A) 80
B) 83
C) 77
D) 157
E) 163
15. What is
F in the formula
L =3
5
F − 5 when
L = 8?
A)55
3
B) 5
C)9
5
D)39
5
E)65
3
16. Which of the following is the equation of the parabola whose graph is shown below?
A)
y = (
x − 5) (
x + 1)
B)
y = (
x + 5) (
x − 1)
− 10
C)
y =2(
x − 5) (
x + 1)
D)
y =2(
x + 5) (
x − 1)
E)
y = (
x − 5) (
x + 1)
− 10
–5
5
–1
17. Find
√
x3
y2
when
x = 2 and
y =
−7
.
A)2
√
2
7
B)4
49
C)2
√
2
49
D)
−2
√
2
7
E)
±2
√
2
7
3
18. Simplify. 3
√
8
x27 +
x12
A) 2
x4 3
√
x15 + 1
B) 8
x9 +
x4
C) 2
x24 +
x4
D) 2
x9 +
x4
E)
x4 3
√
8
x15 + 1
19. If
f (
x)=2
x + 9, and
f(
a) = 7, then
a =?
A) 9
B) 23
C)
−1
D) 7
E) 8
20. One solution of 2
x2 =
−x + 6 is
A) 2
B)2
3
C)3
2
D)
−1
E)
−3
2
21. One of the factors of 3
x2 + 18
x + 24 is
A) 3
x + 2
B)
x + 4
C)
x + 8
D)
x + 24
E) 3
x + 4
22. Solve
x − s
7=
y − t
5for
x.
A)7
5
y +
−7
5
t − s
B)5
7
y +
−1
7
t +
−1
7
s
C)7
5
y +
−1
5
t +1
5
s
D)5
7
y +
−5
7
t +
s
E)7
5
y +
−7
5
t +
s
4
23. Solve
−4
x +4=
−6+3
x for
x.
A)
−2
7
B)
−10
C)
−5
D)7
10
E)10
7
24. Find
x2
x − y
when
x =
−3 and
y =
−4
A)
−9
B)
−9
7
C)9
7
D) 9
E)
−3
4
25. Solve
−7
x<x + 5 and express the solution in interval notation.
A) (
−∞,
−6
5)
B) (
−5
8
,∞)
C) (
−8
5
,∞)
D) (
−5
6
,∞)
E) (
−∞,
−5
8)
5
Key: KYOTE12CART3
1)
⋄ A
2)
⋄ E
3)
⋄ D
4)
⋄ D
5)
⋄ E
6)
⋄ B
7)
⋄ D
8)
⋄ C
9)
⋄ A
10)
⋄ A
11)
⋄ C
12)
⋄ A
13)
⋄ E
14)
⋄ B
15)
⋄ E
16)
⋄ A
17)
⋄ A
18)
⋄ E
19)
⋄ C
20)
⋄ C
21)
⋄ B
22)
⋄ E
23)
⋄ E
24)
⋄ D
25)
⋄ B
Standards Table
Standard
Problems Max Score
KYOTECA.01.3: 17,24
2
KYOTECA.02.3: 1,7
2
KYOTECA.03.3: 8,13
2
KYOTECA.04.3: 18
1
KYOTECA.05.3: 21
1
KYOTECA.06.3: 5
1
KYOTECA.07.3: 9
1
KYOTECA.08.3: 15,23
2
KYOTECA.09.3: 22
1
KYOTECA.10.3: 25
1
KYOTECA.11.3: 20
1
KYOTECA.12.3: 10
1
KYOTECA.13.3: 4
1
KYOTECA.14.3: 2,14
2
KYOTECA.15.3: 11
1
KYOTECA.16.3: 6,12
2
KYOTECA.17.3: 16
1
KYOTECA.18.3: 3,19
2
Description of Standards
1. KYOTECA.01.3: Evaluate algebraic expressions at specified values of their variables using signed
numbers, rational exponents, order of operations and parentheses.
2. KYOTECA.02.3: Add, subtract and multiply polynomials.
3. KYOTECA.03.3: Simplify algebraic expressions involving integer exponents.
4. KYOTECA.04.3: Simplify algebraic expressions involving square roots and cube roots.
5. KYOTECA.05.3: Factor a polynomial in one or more variables by factoring out its greatest
common factor. Factor a trinomial. Factor the difference of squares.
6. KYOTECA.06.3: Add, subtract, multiply and divide simple rational expressions.
7. KYOTECA.07.3: Simplify a rational expression.
8. KYOTECA.08.3: Solve a linear equation.
9. KYOTECA.09.3: Solve a multivariable equation for one of its variables.
10. KYOTECA.10.3: Solve a linear inequality in one variable.
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11. KYOTECA.11.3: Solve a quadratic equation.
12. KYOTECA.12.3: Solve an equation involving a radical, a rational or an absolute value expression.
13. KYOTECA.13.3: Solve a system of two linear equations in two variables.
14. KYOTECA.14.3: Solve problems that can be modeled using a linear or quadratic equation or
expression.
15. KYOTECA.15.3: Solve geometry problems using the Pythagorean theorem and the properties of
similar triangles.
16. KYOTECA.16.3: Understand and apply the relationship between the properties of a graph of a line
and its equation.
17. KYOTECA.17.3: Find the intercepts and the graph of a parabola given its equation. Find an
equation of a parabola given its graph.
18. KYOTECA.18.3: Evaluate a function at a number in its domain. Find the domain of a rational
function or the square root of a linear function.
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