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
Answer: B
Objective: (3.7) Decide if Equation is a Function
2) x = y 2 + 5
A) Yes
2)
B) No
Answer: B
Objective: (3.7) Decide if Equation is a Function
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
3)
Answer: B
Objective: (3.3) Identify Parallel and Perpendicular Lines
4) 6x + 2y = 8
9x + 3y = 15
A) Parallel
4)
B) Neither
C) Perpendicular
Answer: A
Objective: (3.3) Identify Parallel and Perpendicular Lines
5) y = 2x - 4
6x + 3y = 7
A) Neither
5)
B) Perpendicular
C) Parallel
Answer: A
Objective: (3.3) Identify Parallel and Perpendicular Lines
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
6)
Answer: C
Objective: (4.1) Determine Number of Solutions of System
7) 6x - y = 22
x + 6y = 16
A) Infinite number
7)
B) No Solution
Answer: C
Objective: (4.1) Determine Number of Solutions of System
C) One
8) x + 2y = 0
1
y = - x
2
8)
A) No Solution
B) One
C) Infinite number
Answer: C
Objective: (4.1) Determine Number of Solutions of System
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)
Answer: A
Objective: (3.5) Find Equation of Parallel or Perpendicular Line
Find the domain and range of the function.
10) y = x - 6
A) Domain: (-∞, ∞), range: (-∞, ∞)
C) Domain: (-∞, ∞), range: [0, ∞)
10)
B) Domain: [6, ∞), range: (-∞, ∞)
D) Domain: [6, ∞), range: [0, ∞)
Answer: D
Objective: (3.7) Find Domain and Range of Function
Find the intercepts for the graph of the equation.
11) 2x + y = -6
B) (-6, -2) (-2, -6)
A) (-3, 0) (0, -6)
11)
C) (-2, 0) (-2, 0)
D) (0, -2) (0, -2)
Answer: A
Objective: (3.2) Find x- and y- Intercepts
Find the slope of the line going through the given pair of points.
12) (6, 4) and (-9, -3)
1
7
A)
B) - C) - 3
3
15
12)
15
D)
7
Answer: A
Objective: (3.3) Find Slope Through Pair of Points
13) (5, -7) and (5, 3)
3
A)
10
13)
B) 10
C) Undefined
10
D)
3
C) 1
D) 16
Answer: C
Objective: (3.3) Find Slope Through Pair of Points
14) (-9, 7) and (4, 7)
A) 3
14)
B) 0
Answer: B
Objective: (3.3) Find Slope Through Pair of Points
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
B) About 20 dollars
D) About 35.5 dollars
Answer: A
Objective: (3.2) Solve Apps: Graphing Linear Equations
Solve by the substitution method.
16) 3x + 3y = 5
9x = 10 + 9y
1 5
, A)
18 18
C) {(x, y)| 3x + 3y = 5}
16)
B)
25 5
, 18 18
D) ∅
Answer: B
Objective: (4.2) Solve System by Substitution
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
17)
Answer: C
Objective: (3.4) Solve Apps: Linear Equations
Solve the system by elimination.
18) -3x + 2y = -6
6x - 4y = -12
A) {(-18, 12)}
C) {(x, y)|-3x + 2y = -6}
Answer: D
Objective: (4.3) Solve System by Elimination II
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) ∅
Answer: C
Objective: (4.3) Solve System by Elimination I
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
Answer: A
Objective: (3.7) Decide if Graph Represents a Function
21)
21)
y
10
5
-10
-5
5
10
x
-5
-10
A) Not a function
B) Function
Answer: A
Objective: (3.7) Decide if Graph Represents a Function
Tell whether or not the relation is a function.
22) {(-9, 1), (-9, -2), (1, -5), (3, -2), (7, -7)}
A) No
22)
B) Yes
Answer: A
Objective: (3.7) Decide if Ordered-Pair Relation is a Function
23) {(-5, -2), (-2, 5), (2, -3), (6, 5)}
A) Yes
23)
B) No
Answer: A
Objective: (3.7) Decide if Ordered-Pair Relation is a Function
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
Answer: D
Objective: (3.4) Write Equation Given Table of Values (Slope-Intercept Form)
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
Answer: C
Objective: (3.4) Write Equation of Line From Graph
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?
A) $13 seats: 29,000; $6 seats: 13,000
B) $13 seats: 22,750; $6 seats: 19,250
C) $13 seats: 13,000; $6 seats: 29,000
D) $13 seats: 19,250; $6 seats: 22,750
Answer: C
Objective: (4.4) Solve Apps: Linear Systems II
26)
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
t
4
12
A) Boat: 9 mph; current: 3 mph
C) Boat: 15 mph; current: 9 mph
27)
d
4(x + y)
B) Boat: 6 mph; current: 3 mph
D) Boat: 3 mph; current: 6 mph
Answer: B
Objective: (4.4) Solve Apps: Linear Systems III
Write an equation of the line through the given point with the given slope. Write the equation in slope -intercept form.
28) (4, 5); m = - 3
28)
1
1
A) y = -3x + B) y = -3x + 17
C) y = - x + 17
D) y = -3x - 17
17
3
Answer: B
Objective: (3.4) Write Equation Given Slope and Point
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)
Answer: D
Objective: (3.5) Write Equation Given Two Points (Slope-Intercept Form)
1 3
1 7
30) - , and , 5 5
5 5
A) y = 4x + 10
30)
B) y = 2x
C) y = 2x - 2
5
D) y = 2x + 1
Answer: D
Objective: (3.5) Write Equation Given Two Points (Slope-Intercept Form)
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 = .
31)
Answer: 1
Objective: (3.1) *Know Concepts: Reading Graphs/Linear Equations
Clear fractions then solve by substitution.
7x 5y
32)
+ = 4
3
4
5x
- 2y = 21
6
Answer: {(6, -8)}
Objective: (4.2) Clear Fractions and Solve by Substitution
32)
Evaluate the function.
33) Given f(x) = (x + 1)2 , find f(3).
33)
Answer: 16
Objective: (3.7) Evaluate Function
34) Given f(x) = 4x2 - 5x - 7, find f(-3).
34)
Answer: 44
Objective: (3.7) Evaluate Function
Give the ordered pairs for the points labeled on the graph.
35)
8
y
4
C
-8
-4
8 x
4
-4
D
-8
Answer: C(-4, 1); D(5, -5)
Objective: (3.1) Give Ordered Pairs for Points on Graph
35)
Graph the line through the given point with the given slope.
1
36) (8, 2), m = 2
y
10
5
-10
-5
5
10
x
-5
-10
Answer:
y
10
5
-10
-5
5
10
x
-5
-10
Objective: (3.4) Graph Line Given Slope and Point
36)
37) (-2, -1), m = 2
37)
y
10
5
-10
-5
5
10
x
-5
-10
Answer:
y
10
5
-10
-5
5
10
x
-5
-10
Objective: (3.5) Graph Line Given Slope and Point
Graph the linear inequality.
38) y < -4
38)
y
10
5
-10
-5
5
x
10
-5
-10
Answer:
y
10
5
-10
-5
5
10
x
-5
-10
Objective: (3.6) Graph Linear Inequality
Provide the proper response.
39) If the product of the slopes of two lines is -1, what do we know about the lines?
39)
Answer: They are perpendicular.
Objective: (3.3) *Know Concepts: Slope
40) If two nonvertical lines have the same slope, they are .
40)
Answer: parallel
Objective: (3.3) *Know Concepts: Slope
Solve by the substitution method.
41) x + 4y = 27
2x + 3y = 24
41)
Answer: {(3, 6)}
Objective: (4.2) Solve System by Substitution
42) 0.3x + 0.2y = 1.3
x - 0.6y = 5.6
Answer: {(5, -1)}
Objective: (4.2) Solve System by Substitution (Decimals)
42)
Solve the system by graphing.
43) 2x + y = 1
x + 3y = -12
43)
y
10
5
-10
-5
5
10
x
-5
-10
Answer: {(3, -5)}
Objective: (4.1) Solve Linear System by Graphing
Solve the system by the elimination method.
44) 7x + 8y = 67
3x + 6y = 39
44)
Answer: {(5, 4)}
Objective: (4.3) Solve System by Elimination I
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?
Answer: Fern samples: 134; moss samples: 171
Objective: (4.4) Solve Apps: Linear Systems II
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
10
x
-5
-10
Answer:
y
10
5
-10
-5
5
10
x
-5
-10
Objective: (3.4) Graph Equation Using Slope and y-Intercept
47) 2x - 3y = 12
10
y
5
-10
-5
x
5
-5
-10
Answer:
10
y
5
-10
-5
5
x
-5
-10
Objective: (3.4) Graph Equation Using Slope and y-Intercept
Graph the linear inequality.
48) x + 3y ≥ 5
y
10
5
-10
-5
5
10
x
-5
-10
Answer:
y
10
5
-10
-5
5
-5
-10
Objective: (3.6) Graph Linear Inequality
10
x
Graph the solution of the system.
49) x + y < 8
-4x + y > - 3
y
10
5
-10
-5
5
10
x
-5
-10
Answer:
y
10
5
-10
-5
5
10
x
-5
-10
Objective: (4.5) Graph System of Linear Inequalities
50) x ≤ 2y + 9
x + y < 0
y
10
5
-10
-5
5
10
x
-5
-10
Answer:
y
10
5
-10
-5
5
10
x
-5
-10
Objective: (4.5) Graph System of Linear Inequalities