Download Exam 2 Review (Ch 3

Math 100
Exam 2 Review
Name___________________________________
The problems inluded in this review will give you a good idea of the types of problems you will see on your exam. Just
be sure you understand the underlying concepts. Memorizing how to do problems is not nearly as good as
understanding why they are done that way.
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Decide whether the equation defines y as a function of x. (Remember that to be a function, every value of x must give
one and only one value of y.)
1) y = x2 - 5
1)
A) No
B) Yes
2) x = y 2 + 5
A) Yes
2)
B) No
Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither.
3) 3x - 4y = -5
8x + 6y = -5
A) Parallel
B) Perpendicular
C) Neither
4) 6x + 2y = 8
9x + 3y = 15
A) Parallel
5) y = 2x - 4
6x + 3y = 7
A) Neither
4)
B) Neither
C) Perpendicular
5)
B) Perpendicular
C) Parallel
Does the system have one solution, no solution, or an infinite number of solutions?
6) x + y = 4
x + y = 5
A) One
B) Infinite number
C) No Solution
7) 6x - y = 22
x + 6y = 16
A) Infinite number
6)
7)
B) No Solution
C) One
8) x + 2y = 0
1
y = - x
2
A) No Solution
3)
8)
B) One
C) Infinite number
Find an equation in slope -intercept form of the line satisfying the specified conditions.
9) Through (2, 2), perpendicular to -3x - 4y = 2
4
2
4
2
1
1
3
3
A) y = x - B) y = - x - C) y = - x + D) y = x + 3
3
3
3
2
2
4
4
9)
Find the domain and range of the function.
10) y = x - 6
A) Domain: (-∞, ∞), range: (-∞, ∞)
C) Domain: (-∞, ∞), range: [0, ∞)
B) Domain: [6, ∞), range: (-∞, ∞)
D) Domain: [6, ∞), range: [0, ∞)
Find the intercepts for the graph of the equation.
11) 2x + y = -6
B) (-6, -2) (-2, -6)
A) (-3, 0) (0, -6)
C) (-2, 0) (-2, 0)
10)
11)
Find the slope of the line going through the given pair of points.
12) (6, 4) and (-9, -3)
1
7
B) - C) - 3
A)
3
15
13) (5, -7) and (5, 3)
3
A)
10
14) (-9, 7) and (4, 7)
A) 3
D) (0, -2) (0, -2)
12)
D)
15
7
13)
B) 10
C) Undefined
10
D)
3
B) 0
C) 1
D) 16
14)
Solve by graphing. Label the axes and show where the solution is located on the graph.
15) The cost, c, in dollars of car rental is 6 + 0.25m, where m is the number of miles driven.
Graph the equation and use the graph to estimate the cost of car rental if the number
of miles driven is 34.
15)
40
35
30
25
20
15
10
5
5 10 15 20 25 30 35 40 45 50 m
A) About 15 dollars
C) About 11 dollars
Solve by the substitution method.
16) 3x + 3y = 5
9x = 10 + 9y
1 5
, A)
18 18
C) {(x, y)| 3x + 3y = 5}
B) About 20 dollars
D) About 35.5 dollars
16)
B)
D) ∅
25 5
, 18 18
Solve the problem.
17) An electrician charges a fee of $45 plus $30 per hour. Let y be the cost in dollars of using the
electrician for x hours. Find the slope-intercept form of the equation.
A) y = 30x - 45
B) y = 45x + 30
C) y = 30x + 45
D) y = 45x - 30
Solve the system by elimination.
18) -3x + 2y = -6
6x - 4y = -12
A) {(-18, 12)}
C) {(x, y)|-3x + 2y = -6}
17)
18)
B) {(18, -12)}
D) ∅
Solve the system by the elimination method.
19) 2x - 6y = 5
-8x + 24y = -20
A) {(10, -30)}
C) {(x, y)|2x - 6y = 5}
19)
B) {(-30, 10)}
D) ∅
State whether the graph is or is not that of a function.
20)
20)
y
10
5
-10
-5
5
10
x
-5
-10
A) Function
B) Not a function
21)
21)
y
10
5
-10
-5
5
10
x
-5
-10
A) Not a function
Tell whether or not the relation is a function.
22) {(-9, 1), (-9, -2), (1, -5), (3, -2), (7, -7)}
A) No
B) Function
22)
B) Yes
23) {(-5, -2), (-2, 5), (2, -3), (6, 5)}
A) Yes
23)
B) No
The table of values gives two points that lie on a line. Use the points to find the slope and y -intercept of the line. Then
use these values to write an equation of the line in slope -intercept form.
24)
24)
x y
-9 1
6 -3
4
7
10
11
10
11
4
7
A) y = x - B) y = - x + C) y = x + D) y = - x - 15
5
9
3
9
3
15
5
Use the geometric interpretation of slope (rise divided by run) to find the slope of the line. Then, by identifying the
y-intercept from the graph, write the slope-intercept form of the equation of the line.
25)
25)
y
10
5
-10
-5
5
10
x
-5
-10
A) y = - 3x - 6
B) y = -6x - 2
1
C) y = - x - 2
3
D) y = 6x - 2
Write a system of equations for the problem, and then solve the system.
26) There were 42,000 people at a ballgame in Los Angeles. The dayʹs receipts from $13 reserved seats
and $6 general-admission seats were $343,000. How many of each type of seat were sold?
B) $13 seats: 22,750; $6 seats: 19,250
A) $13 seats: 29,000; $6 seats: 13,000
C) $13 seats: 13,000; $6 seats: 29,000
D) $13 seats: 19,250; $6 seats: 22,750
27) A boat travels 36 miles downstream in 4 hours and returns upstream in 12 hours. Find the rate of
the speed of the current and the speed of the boat in still water if x = the speed of the boat in still
water and y = speed of the current.
Downstream
Upstream
r
x + y
x - y
A) Boat: 9 mph; current: 3 mph
C) Boat: 15 mph; current: 9 mph
t
4
12
26)
27)
d
4(x + y)
B) Boat: 6 mph; current: 3 mph
D) Boat: 3 mph; current: 6 mph
Write an equation of the line through the given point with the given slope. Write the equation in slope -intercept form.
28)
28) (4, 5); m = - 3
1
1
B) y = -3x + 17
C) y = - x + 17
D) y = -3x - 17
A) y = -3x + 3
17
Write the slope-intercept form of the equation for the line passing through the given pair of points.
29) (1, -2) and (4, -2)
A) 1x + 4y = 0
B) 4x + 1y = 0
C) x = 1
D) y = -2
29)
1 3
1 7
30) - , and , 5 5
5 5
30)
A) y = 4x + 10
B) y = 2x
C) y = 2x - 2
5
D) y = 2x + 1
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Answer the question.
31) The ordered pair (2, 1) is a solution of the equation 2x - 3y = .
Clear fractions then solve by substitution.
7x 5y
32)
+ = 4
3
4
31)
32)
5x
- 2y = 21
6
Evaluate the function.
33) Given f(x) = (x + 1)2 , find f(3).
33)
34) Given f(x) = 4x2 - 5x - 7, find f(-3).
34)
Give the ordered pairs for the points labeled on the graph.
35)
8
y
4
C
-8
-4
8 x
4
-4
-8
D
35)
Graph the line through the given point with the given slope.
1
36) (8, 2), m = 2
36)
y
10
5
-10
-5
5
10
x
-5
-10
37) (-2, -1), m = 2
37)
y
10
5
-10
-5
5
10
x
-5
-10
Graph the linear inequality.
38) y < -4
38)
y
10
5
-10
-5
5
10
x
-5
-10
Provide the proper response.
39) If the product of the slopes of two lines is -1, what do we know about the lines?
40) If two nonvertical lines have the same slope, they are .
39)
40)
Solve by the substitution method.
41) x + 4y = 27
2x + 3y = 24
41)
42) 0.3x + 0.2y = 1.3
x - 0.6y = 5.6
42)
Solve the system by graphing.
43) 2x + y = 1
x + 3y = -12
43)
y
10
5
-10
-5
5
10
x
-5
-10
Solve the system by the elimination method.
44) 7x + 8y = 67
3x + 6y = 39
44)
Write a system of equations for the problem, and then solve the system.
45) A biologist collected 305 fern and moss samples. There were 37 fewer ferns than moss
samples. How many fern and moss samples did the biologist collect?
45)
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
Graph the equation by using the slope and y -intercept.
1
46) y = x - 1
2
y
10
5
-10
-5
5
-5
-10
10
x
47) 2x - 3y = 12
10
y
5
-10
-5
x
5
-5
-10
Graph the linear inequality.
48) x + 3y ≥ 5
y
10
5
-10
-5
5
10
x
10
x
-5
-10
Graph the solution of the system.
49) x + y < 8
-4x + y > - 3
y
10
5
-10
-5
5
-5
-10
50) x ≤ 2y + 9
x + y < 0
y
10
5
-10
-5
5
-5
-10
10
x