8/18/15
With Solutions
MATH 151
TEST 2 REVIEW
TO THE STUDENT:
 To best prepare for Test 2, do all the problems on separate paper.
 The answers are given at the end of the review sheet.
PART 1 – NON-CALCULATOR
DIRECTIONS:
 The problems on this part of the Review Sheet are similar to those you can expect on the
non-calculator part of the test. For that reason, you should do these problems without
your graphing calculator.
 Show all your steps.
 Support all answers with appropriate reasoning.
 If a graph is requested, label it completely.
 If a table is requested, include and circle the relevant rows.
 Answer application problems using complete sentences.
Chapters 1 – 4 Review
1. Use the graph to answer the following.
a. Does the graph represent a function?
b. Identify the domain and range.
c. Evaluate f (4) and f (2) .
d. Identify the x- and y-intercepts.
e. Find the slope of the line.
f. Find a formula for f ( x) .
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
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Solution #1
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2. Find the slope-intercept form of the line that passes through (–6, 3) and is perpendicular
3
to y   x .
Solution #2
4
3. Let f be a linear function. Find the slope, x-intercept, and y-intercept of the graph of f.
–2
–6
x
f ( x)
–1
–2
0
2
2
10
4. Solve the equation or inequality:
1
a.
(1  x)  2 x  3x  1
2
d. 3  2  4 x  5
b. 2(1  x)  4 x  (2  x)
e.
c.
x  1  2 or x  1  4
3x  2  4
Solution to #4c
5. Solve each system, if possible.
x  y  2
x  2y  3
a.
b.
2x  2 y  5
3 x  2 y  2
6. Solve the system.
x  2 y  z  2
3 x  y  z  12
x  y  2 z  1
Solution to #6
Trigonometry
Solutions to Trig #1 - 5
1. Sketch in standard position:
a. 110º
b. 
5
3
b. 
2
3
2. Convert each angle from radians to degrees:
a.

4
2
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3. Convert each angle from degrees to radians:
a. 180º
b. –250º
4. Find a positive and negative angle coterminal with –330º.
5. Use a 45º – 45º triangle to find the exact value of cos 45º.
Chapter 5 Review
1. Give an example of a binomial and of a trinomial.
2. Identify the degree and coefficient of:
a. 4x5
b. 5xy6
3. Combine like terms: 6 x3 y  4 x3  8x3 y  5x3 .
4. Combine the polynomials: (4x2  6x  1)  (3x2  7 x  1) .
Solution to #4
5. Evaluate f ( x)  2 x2  3x  2 at x  1 .
6. Use the graph to evaluate f (2) .
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
       

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
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





Solution to #6

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7. Multiply:
a. 2 x(1  x  4 x2 )
d.
(4 x  y)(4 x  y)
b. (12 xy 4 )(5x2 y)
e. ( x  3)2
c. (6 x  3)(2 x  9)
f.
Solutions to #7b), e)
(a  b)(a2  ab  b2 )
8. Factor out the greatest common factor: 12x4  8x3 16 x2 .
9. Use grouping to factor the polynomial:
a. 2 x3  2 x2  3x  3
b. z 3  z 2  z  1
Solution to #9
10. Use the graph to do the following:
a. Find the x-intercepts.
b. Solve the equation P( x)  0 .
c. Find the zeros of P( x) .
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
Solution to #10
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
11. Factor completely.
a. x2  5x  50
b. 9 x2  25x  6
c. 4 x2  22 x  10
d. x3  4x2  3x
Solution to #11b), c)
4
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12. Use the table to factor the expression. Check your answer by multiplying.
X
Y1
-5
20
-3
0
-1
-12
1
-16
3
-12
5
0
7
20
Y1=X^2–2X–15
Solution to #12
13. Use the graph to factor x2  3x  28 . Check your answer by multiplying.

Solution to #13

       






 
 
 
 
14. Factor completely:
a.
t 2  49
b.
x2  4 x  4
c.
x3  27
d.
10 y3 10 y
e.
f.
g.
m4  16n4
25a2  30ab  9b2
a6  27b3
Solutions to #14 e)- g)
15. Solve:
a.
b.
4 x2  28x  49  0
3x 2  2 x  5
c.
d.
x3  x
x3  x2  72 x  0
Solutions to #15 b), c)
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Chapter 6 Review
1
at x = 3.
x 1
3
2. Evaluate f ( x) 
at x = –3 and 2.
x2
2x
3. Evaluate f ( x)  2
at x = –2 and 3.
x 4
1
4. Let f ( x)  2
. Give the domain of f.
4x 1
1. Evaluate f ( x) 
2
5. Use the graph of f to evaluate the expressions:
a. f(0) and f(2)
Solution to #4
Solution to #5
b. f(–3) and f(–2)
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







6. Solve the rational equations:
3 x
2
a.
x
1
1

b.
x3 5
7. Simplify the rational expressions:
x2  4
a.
x2
x2  6 x  7
b.
2 x2  x  3
x
2x  2

x2 x2
4
 1
d.
2  3x
c.
c. 
3  2x
2x  3
Solutions to #7b), c) & #8e)
6
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8.
9.
Simplify the products or quotients:
1 4 y2
a.

2y 8
x2  2 x  1 x  3
b.

x2  9
x 1
1
1
c.
 4
3y 9 y
d.
e.
Simplify the sums or differences:
2
2
a.

y2 y2
4
2
b.

2
2
a b a b
c.
x2  2 x x  2

x 2  25 x  5
x 2  2 x  15 x  3

x2  4x  3 x  1
a
b

a b a b
Solutions to #9a) & #10d)
10. Solve the rational equations:
4 5 1
a. 

x 2x 2
1
3
b.

x  4 2x 1
2 1
 1
c.
x2 x
11. Use the graph to solve
d.
e.
1
1
 1
x4 x
1
1
2


2
x 1 x 1 3
3
1
 x . Then check your answer.
x 1 2
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

Solution to #11
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12. Simplify the complex fractions:
4
a. ab .
2
bc
3
2
x
b.
3
2
x
c.
1 1

x 2
1 2

4 x
Solution to #12c)
PART 2 - GRAPHING CALCULATOR
DIRECTIONS:
 You may use your graphing calculator on this part of the review sheet.
 Support all answers with appropriate reasoning.
 Follow the same directions for supplying graphs and tables as in the non-calculator part.
 Always answer application problems using complete sentences.
Chapters 1 – 4 Review
1.
The table below shows equivalent temperatures in degrees Fahrenheit and Celsius.
ºF
ºC
–40
–40
32
0
59
15
95
35
212
100
Solutions to #1, #3
a. Find f ( x)  m( x  h)  k so that f receives the Fahrenheit temperature as input
and outputs the corresponding Celsius temperature.
b. If the temperature is 104ºF, what is the equivalent temperature in degrees Celsius?
2.
During strenuous exercise, an athlete burns 690 calories per hour on a stair climber
and 540 calories per hour on a stationary bicycle. During a 90-minute workout the
athlete burns 885 calories. How much time (in hours) is spent on each type of exercise
equipment?
3.
The price of admission to a county fair is $2 for children and $5 for adults. If a group
of 30 people pays $78 to enter the fairgrounds, find the number of children and the
number of adults in the group.
4.
A rectangle has an area of 165 square feet. Its length is 4 feet more than its width.
Find the dimensions of the rectangle.
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Trigonometry
1. Find the length of the arc intercepted by a central angle   60 and a radius r = 6 feet.
2. Use the figure to determine the radian measure of angle  . Then approximate the
degree measure  to the nearest tenth of a degree.
3
3
12
Θ
3. The shadow of a vertical tower is 40.6 meters long when the angle of elevation of the
sun is 34.6º. Find the height of the tower.
Chapter 5 Review
1. Use the graphing calculator to graph f ( x)  x 2 , and give in interval notation:
a. the domain
b. the range
Solution to #1
2. Solve the equation symbolically and graphically: x2  16  0 .
3. Solve the equation symbolically and graphically: x2  2 x  3  0 .
4. The formula f ( x)  1.466x2  20.25x  9 models the monthly average high
temperature in degrees Fahrenheit in Columbus, Ohio. In this formula, let x = 1 be
January, x = 2 be February, and so on.
Solution to #4
a. What is the average high temperature in May?
b. Make a table of f(x), starting at x = 1 and incrementing by 1. During what
month is the average temperature the greatest?
c. Graph f in [1, 12, 1] by [30, 90, 10] and interpret the graph.
5. A rectangular pen has a perimeter of 50 feet. If x represents its width, write a
polynomial that gives the area of the pen in terms of x.
6. If a golf ball is hit upward with a velocity of 66 feet per second (45 mph), its height h in
feet above the ground after t seconds can be modeled by h(t )  16t 2  66t .
a. Determine when the ball strikes the ground.
b.
When is the height of the ball 50 feet?
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Solution to #1
Chapter 6 Review
1. Use the graphing calculator to graph f ( x) 
3x
. Give the equation of the vertical
x 3
asymptote.
Solution to #2
1
 1  2x .
x
****************************************************************************
Test 2 Review Answer Key
2. Solve the rational equation graphically:
Part 1. Non-Calculator.
Chap. 1-4 Review
b. Domain and Range: (–∞, +∞) c. f (4)  3 ; f (2)  0
1
d. x-intercept is 2; y-intercept is –1
e. m = ½
f. f ( x)  x  1
2
4
y  x  11
3
1
slope: 4; x-intercept:  ; y-intercept: 2.
2
1
4
2
 3 5
a. 
b. (–∞, ) c. (–∞,1) U (3,∞) d.   ,  e.  , 2
3
5
3
 4 4
 1 11 
a.  ,  b. No solutions
4 8 
(3, 2, 1)
1. a. Yes
2.
3.
4.
5.
6.
Trigonometry
1. a.
2. a. 45º
3. a. 
b.
b. –120º
25
b. –
18
4. 30º, –690º
1
5.
2
10
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Chap. 5 Review
1. Various.
2. a. Degree: 5; coefficient: –4
b. Degree: 7; coefficient: 5
3
3
3. 14x y  x
4.  x2  x
5. 7
6. –4
7. a. 2 x  2 x2  8x3 b. 60x3 y5
c. 12x2  48x  27
d. 16x2  y 2
e. x2  6 x  9
f. a3  b3
8. 4x2 (3x2  2 x  4)
9. a. ( x  1)(2 x2  3) b. ( z  1)( z 2  1)
10. a –c. 0, 3
11. a. ( x 10)( x  5) b. ( x  3)(9 x  2) c. 2( x  5)(2x 1) d. x( x  3)( x 1)
12. ( x  3)( x  5)
13. ( x  7)( x  4)
14. a. (t  7)(t  7) b. ( x  2)2 c. ( x  3)( x2  3x  9) d. 10 y( y 1)( y  1)
e. (m  2n)(m  2n)(m2  4n2 ) f. (5a  3b)2 g. (a2  3b)(a4  3a2b  9b2 )
7
5
15. a.
b. 1,
c. –1, 0, 1 d. –9, 0, 8
2
3
Chap. 6 Review
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
1
8
–3; 0.75
Undefined; 1.2
1
x
2
a. 3; 1 b. 2; undefined
a. 1
b. 2
c. No solutions
d. 2
x7
a. x  2 b.
c. 1
2x  3
y
x 1
x
x5
a.
b.
c. 3y3 d.
e.
4
x3
x5
x3
2
8
2(a  b  2)
a  2ab  b2
a.
b. 
c.
( y  2)( y  2)
(a  b)(a  b)
(a  b)(a  b)
a. 3
b. 11
c. –2, 1
d. –2
e. –2, ½
–2, 3
2c
2x  3
2( x  2)
a.
b.
c.
2x  3
x 8
a
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Part 2. Graphing calculator.
Chap. 1-4 Review
5
1. a. f ( x)  ( x  32) b. 40ºC
9
2. Stair climber: ½ hour; stationary bicycle: 1 hour
3. 24 children, 6 adults
4. 11 ft by 15 ft
Trigonometry
1. 2π feet ≈ 6.28 feet
2. Θ = ¼ radian ≈ 14.3º
3. 28 meters
Chap. 5 Review
a. Domain: (–∞, +∞) b. Range: [0, +∞)
–4, 4
–1, 3
a. 73.6ºF
b. July
c. Temperatures increase from January to July, then decrease from July to December
5. 25x  x2
6. a. After 4.125 sec
b. After 1 sec and after 3.125 sec
1.
2.
3.
4.
Chap. 6 Review
1. x = 3
y

2. x = 1, –0.5


x=1
x







x = -.5



12