Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1)
2)
f (x) = -3x, g(x) =
1)
29
5
A)
(f - g)(-2) =
C)
(f - g)(-2) = -
Find
1
, (f - g)(-2) = ?
x-3
B) (f
31
5
D)
- g)(-2) =
31
5
(f - g)(-2) = -
29
5
f
(x).
g
2)
f (x) = x2 + 4 and g(x) = x - 9
3)
A)
x-9
f
(x) =
g
x2 + 4
C)
x2 + 4
f
(x) =
,x
g
x-9
9
B)
x-9
f
(x) =
,x
g
x2 + 4
D)
x2 + 4
f
(x) =
g
x-9
9
The graphs of h and k are shown. Find the values for the given values of x, if possible.
k
a. (h k)(0); b.
(-2); c. (k - h)(0)
h
A)
B) a.
a. -5; b. -4; c. -4
C) a. undefined; b. -4; c. -4
-4; b. undefined; c. -4
D) a. -4; b. undefined; c. 4
1
3)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
4)
Consider the function g(y) = {(-5, 22), (-2, 1), (1, -2), (4, 13), (9, 78)}. Find the
function value g(1).
4)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
5)
5)
Find the x- and y-intercepts of the function.
B(x) = 2x + 5
2
A) x-intercept: - , 0 ; y-intercept: (5, 0)
5
B) x-intercept:
-
5
, 0 ; y-intercept: (0, -5)
2
C)
x- and y-intercept: (0, 0)
5
D) x-intercept: - , 0 ; y-intercept: (0, 5)
2
6)
A)
B) [-
(- , -9) (-9, )
C) (- , -9] [-9, )
7)
6)
Find the domain. Write the answer in interval notation.
x-3
m(x) =
x2 + 9
, -9) (-9, ]
D) (- , )
7)
Find the domain. Write the answer in interval notation.
17 + a
r(a) =
a
A)
B) (-17,
(- , 0) (0, )
C) (- , -17) (-17, )
0)
D) (- , )
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
8)
8)
If K(x) = x - 9 + x, find K(1).
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
9)
9)
Find ( f + g)(3) for the given functions.
f (x) = -1 +
A)
48
x2
g(x) = 2x + 1
C) x2
B) 15
2
+ 2x
D)
4x2 + 4x + 0
10)
Find the domain and range of the relation. Use interval notation where appropriate.
A)
B) Domain:
Domain: [-2, 2]; Range: [-6, 6]
C) Domain: [0, 6]; Range: [0, 2]
[-6, -2]; Range: [2, 6]
D) Domain: [-6, 6]; Range: [-2, 2]
3
10)
11)
C)
12)
11)
Find the x- and y-intercepts of the function.
h(x) = -1
A) x-intercept: (0, -1); y-intercept: none
B) x-intercept:
D)
x-intercept: (-1, 0); y-intercept: none
f (x) = x2 - 3x, g(x) = 5x - 2, (g f )(-2) = ?
A) (g f )(-2) = 48
C) (g f )(-2) = 180
none; y-intercept: (0, -1)
x-intercept: none; y-intercept: (-1, 0)
12)
B) (g
f )(-2) = 30
D) (g f )(-2) = -120
4
13)
13)
Find the domain of the relation. Use interval notation where appropriate.
A)
B) [–40,
{–20, –10, 0, 10, 15}
C) [–20, 15]
20]
D) {0, –20, –40, 20}
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
14)
14)
Identify the domain and range of the function.
g(x) = {(7, 7), (8, -20), (9, -16), (-7, -3)}
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
15)
15)
Determine if the relation defines y as a function of x.
x
y
A)
B) Not
Function
a function
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
16)
If g(y) = 2y2 + 5y + 7, find g(m).
16)
5
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
17)
A)
18)
17)
Is the graph below the graph of a function?
B) No
Yes
n(x) = x - 1, p(x) = x2 - 5x, (p n)(x) = ?
x2
A)
(p n)(x) =
C)
(p n)(x) = x2 - 5x - 1
18)
B) (p
- 7x + 6
D)
n)(x) =
x2
- 5x + 6
(p n)(x) = x2 - 7x - 1
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
19)
Find the domain and range of the relation. Use interval notation where
appropriate.
6
19)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
20)
Determine if the function is constant, linear, quadratic, or none of these.
f (x) = -11x - 1
A) Quadratic
B) Constant
C) Linear
D) None of these
20)
21)
Write a system of linear equations represented by the augmented matrix.
1 0 0 -11
0 1 0 10
0 0 1 -10
21)
A)
B) x =
x + y + z = -11
x + y + z = 10
x + y + z = -10
C) (x - 1) + y + z = -11
x + (y - 1) + z = 10
x + y + (z - 1) = -10
11
y = -10
z = 10
D) x = -11
y = 10
z = -10
22)
A triangle has one angle that measures 4° more than 2 times the smallest angle, and the
largest angle measures 4° less than 3 times the measure of the smallest angle. Find the
measures of the three angles.
A) 30°, 64°, 86°
B) 29°, 63°, 88°
C) 30°, 63°, 87°
D) 29°, 64°, 87°
22)
23)
Solve the system. If there is no unique solution, label the system as either dependent or
inconsistent.
-2x + y = -4(z - 4)
-2x + 2(-4y + 4z) = -9
4(-2x + 4z) = 64 - 4y
A) (-2, -8, 5)
B) (-1, 26, -3)
C) Dependent system (infinitely many solutions)
D) Inconsistent system (no solution)
23)
24)
Solve the system of equations.
10x
+ 20z = 82
y + 2z = 2
x - 5y
= 11
24)
A)
(0, -4, 6)
B)
5, -
6 8
,
5 5
C)
7
5, 3,
8
5
D)
41
, 3, 0
5
25)
Nail polish remover is essentially a mixture of water and a chemical called acetone. How
much pure acetone must be combined with a solution that is 40% acetone to make 30 oz
of a 58% solution?
A) 13 oz
B) 15 oz
C) 21 oz
D) 9 oz
25)
26)
Paula invested into two accounts; one pays 4% simple interest and the other pays 5%
simple interest. She invested $1000 more in the account paying 5% than in the account
paying 4%. At the end of the first year, Paula's total return was $950. How much did she
invest in each account?
A) $10,000 at 4%; $11,000 at 5%
B) $9000 at 4%; $12,000 at 5%
C) $11,000 at 4%; $10,000 at 5%
D) $12,000 at 4%; $9000 at 5%
26)
27)
An isosceles triangle has two angles of the same measure (see figure). If the angle
represented by y measures 45° more than the angle x, find the measures of all angles of
the triangle.
27)
[Figure is not necessarily drawn to scale.]
A) 42°; 42°; 87°
C) 50°; 50°; 80°
28)
40°; 100°
D) 45°; 45°; 90°
28)
Solve the system.
-4x + 8y = 4
x = 2y - 1
1
A) 0,
2
B) (9,
29)
B) 40°;
5)
C)
Infinitely many solutions; (x, y) y =
D)
No solution; { }; inconsistent system
1
1
x + ; dependent system
2
2
There are 16 coins consisting of nickels, dimes, and quarters which are collected from a
newspaper vending machine. The total value of the coins is $1.75 and there are 4 more
dimes than quarters. Find the number of each type of coin.
A) 6 nickels; 7 dimes; 3 quarters
B) 7 nickels; 5 dimes; 9 quarters
C) 9 nickels; 8 dimes; 2 quarters
D) 7 nickels; 9 dimes; 2 quarters
8
29)
30)
31)
Graph the solution set of the compound inequality.
4x – 3y 60 or y > x
A)
B)
C)
D)
Consider the matrix below.
(a) Determine the order of the matrix.
(b) Determine if the matrix is a row matrix or a column matrix.
[ -7 -5.7 -2 ]
A) (a) 3 × 1
B) (a) 1 × 3
(b) row matrix
(b) row matrix
C) (a) 1 × 3
D) (a) 3 × 1
(b) column matrix
(b) column matrix
9
30)
31)
32)
The graph of a system of linear equations is given. Identify whether the system is
consistent or inconsistent.
2x - 5y = 4
4y = 3x + 1
A)
32)
B) consistent
inconsistent
33)
Solve the system by using the substitution method.
3(x - 2y) = -18
9x = -8y - 2
A) (-4, 1)
B) (0, 3)
C) (-2, 2)
D) No solution; { }; inconsistent system
33)
34)
The graph of a system of linear equations is given. Identify whether the system is
dependent or independent.
2x - 5y = 4
4y = 3x + 1
34)
A)
B) independent
dependent
10
35)
35)
Solve the system.
1
y=- x-3
9
x + 9y = 5
A) (5, 0)
B) (-4, 1)
C)
1
Infinitely many solutions; (x, y) y = - x - 3 ; dependent system
9
D)
No solution; { }; inconsistent system
36)
A rectangle has the perimeter of 30 inches. The length is 3 in longer than the width. Find
the dimensions of the rectangle.
A) 7 inches by 10 inches
B) 6 inches by 9 inches
C) 9 inches by 12 inches
D) 3 inches by 6 inches
36)
37)
The small zoo at Nichols Park charges $11 for adult admission, $9 for child admission
(18 years old and under), and $6 for senior admission (60 years old and over). For one
day, the zoo collected $727 and admitted 82 visitors. If the adult admission is 8 more
than the senior admission, how many persons of each category were admitted on this
particular day?
A) 35 adults; 20 children; 27 seniors
B) 35 adults; 15 children; 32 seniors
C) 32 adults; 21 children; 29 seniors
D) 32 adults; 23 children; 27 seniors
37)
38)
Solve the system by the addition method.
-4x + 14y = 58
-0.2x = 2.3 - 0.7y
A) (17, 9)
B) (3, 5)
38)
39)
C)
Infinitely many solutions; (x, y) y =
D)
No solution; { }; inconsistent system
2
29
x+
; dependent system
7
7
One angle measures 39° more than 2 times another. If the two angles are complementary,
find the measures of the angles.
A) 17°; 73°
B) 19°; 71°
C) 27°; 63°
D) 22°; 68°
11
39)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
40)
40)
Solve the system of equations by graphing.
2x - 3y = 2
y=2
12
Answer Key
Testname: TEST2-REV1
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
B
C
B
g(1) = -2
D
D
A
9
B
D
B
A
A
Domain = {7, 8, 9, -7}; Range = {7, -20, -16, -3}
A
16) g(m) = 2m 2
17) B
18) A
19) Domain: (-
+ 5m + 7
, )
Range: [0, )
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
C
D
A
C
B
D
A
D
C
A
B
B
B
C
B
D
B
A
D
A
13
Answer Key
Testname: TEST2-REV1
40)
14