CCDM112N Final Review New Version

CCDM 112N
REVIEW FOR FINAL EXAM
Directions: Read each question carefully. Give exact answers unless the question requests otherwise.
Include correct units when appropriate.
1. (1.4) Simplify the following expressions.
a. 3(2x
5y)
4( x 2y)
b. 2(5x
6y)
(2x
3y)
c. 2(
x 3y)
5( x y)
d. 7(
x 6) 3(2x
9)
2. (1.8) Use the order-of-operations to simplify the following expressions:
a. 4 20 (7 2)(3 1)
b. 1 2 15
27 2
3. (1.1) Use d = rt to solve the following problems. Include correct units in your answer.
a. You and your friends decide to travel from Las Cruces to Tucson for a weekend trip this summer. If it
is a 280 mile trip and your average speed is 70 miles per hour, how long will it take you to reach your
destination?
b. Suppose that you travel from Las Cruces to Albuquerque, a 230 mile trip. If you travel an average
speed of 75 miles per hour, how long will it take you to make this trip? Round answer to the nearest
tenth.
4. (1.1) The polynomial S 2LW
2LH
2WH
describes the surface area of a box. Find the surface area of a
box with a length of 8 inches, width of 6.5 inches and height of 4 inches, by evaluating the polynomial. Include
correct units.
5. (1.8) The height h (in feet) of a baseball after t seconds can be modeled by the equation
h 16t
2 100t
4 . Find the height of the baseball in four seconds. Include correct units.
CCDM 112N Introductory Algebra, Blitzer 6 th Ed. Updated Fall 2012

6. (2.3) Solve the following equations:
a. 5(
x 4) 5x
10(2
x)
b. 5(
x 3) 6x
10(3
x)
c.
1
2
1 3 1
x x
d.
4 4 6
1
3
1 1
x x
5 5
1
3
7. (2.5) Translate the following problems into an algebraic equation and solve:
a. Twice the difference of a number and three is equal to eight.
b. Eight less than the product of three and a number is twenty – two.
8. (2.5) Translate the following word problems into an equation and solve algebraically. Interpret your results,
including correct units.
a. The length of a building is twice its width. If the perimeter is 72 feet, determine the length and the
width.
b. The length of a rectangle is seven inches more than its width. If the perimeter is 26 inches, find the
length and the width.
9. (2.7) Solve the following inequalities and graph on a number line:
a. 2(
x 5) 5 21
b. 3(4x 6) 10x
10. (3.1) Determine whether each equation is linear or nonlinear:
a. 3x 5y
8
b. y x 2 5
c. y 3 6x
CCDM 112N Introductory Algebra, Blitzer 6 th Ed. Updated Fall 2012

11. (3.1, 3.2) Graph the following linear equations. Label at least two points on the graph. :
a. 4x 2y
8
b. 2x
4y
8
10
10
- 1 0 10
- 1 0 10
- 1 0
12. (3.3) Find the slope of the line through the given points, then state whether the line is increasing or
decreasing.
a. (0, -1), (3, 2) b. (-2, 7), (-1, 2)
- 1 0
c. Explain how you determine whether a line is increasing or decreasing.
13. (3.4) For the linear equations, rewrite each equation in slope – intercept form, then state the slope
and the y – intercept (in point form).
a. 3x 5y
8
b. 4x
8y
8
14. (3.3) Order the following linear equations from least to most steep.
5
a. y 5x
2 b. y x c. 1 y x 6 d. y 4x
1
3
3
Explain how you arrived at your answer.
CCDM 112N Introductory Algebra, Blitzer 6 th Ed. Updated Fall 2012

15. (3.5) Write the equation of the line in slope-intercept form given the slope and the y-intercept:
15
a. m = -2; (0, 3) b. m = ; (0, -2) 4
16. (3.5) Write the equation of the line in slope-intercept form given the slope and a point on the line
(hint: use y y m x )
1
( x1
a. m = 6; (4, 3) b. m = -3; (6, -2) c.
1
m ; (4, -3)
2
17. (3.4) The cost of a rental car, C, as a function of the number of miles driven, x, is given by C 0.13x
23
a. What is the initial cost?
b. Find the cost of driving 100 miles. Include correct units.
c. How many miles will be driven if the cost is $350.00? Include correct units.
18. (3.4) The value, V, of a car as a function of the number of years after it was purchased, x, is given by
V 1500x
18,000
a. What is the initial value?
b. Find the value of the car after 3 years. Include correct units.
c. How many years after purchase is the car worth $3,000? Include correct units.
CCDM 112N Introductory Algebra, Blitzer 6 th Ed. Updated Fall 2012

19. (4.2, 4.3) Solve the following systems of equations using substitution or elimination.
a.
7x
4y
4
5x
y 26
b.
3x
5y
17
y
15
4x
c.
3x
y 11
6x
2y
2
d.
x
5y
18
3x
2y
11
(4.4) Translate the following word problems into a system of equations and solve algebraically. Include
correct units in your answer.
20. A restaurant manager buys 50 lb of sausage and 80 lb of hamburger for a total cost of $300. A second
purchase, at the same price, includes 100 lb of sausage and 120 lb of hamburger for a cost of $480. Find the
cost of the sausage and the hamburger.
21. If David has 19 bills in his wallet worth $125, all fives and tens, how many of each bill does he have?
Answer Key
1. a. 10x 23y
b. 8x 15y
c. 3x 11y
d. x 15
2. a. 12 b. 4
3. a. t 4
hours b. t 3. 1 hours
4. S=220 square inches
5. h=148 feet
CCDM 112N Introductory Algebra, Blitzer 6 th Ed. Updated Fall 2012

5
6. a. x = 2 b. x = 5 c. x d. x = 4
3
7. a. 2(
n 3) 8; n 7 b. 3n
8
22; n 10
8. a. Equation: 2(2w ) 2w
72 Dimensions: width is 12 feet, length is 24 feet.
b. Equation: 2(
w 7) 2w
26 Dimensions: width is 3 inches, length is 10 inches.
9. a. x ≥ -8, graph on number line: closed circle at -8, arrow pointing to the right
b. x < 9, graph on number line: open circle at 9 arrow pointing to left
10. a. linear b. nonlinear c. linear
11. a. graph is an increasing line passing through (0, -4) and (2, 0)
b. graph is a decreasing line passing through (0, 2) and (4, 0)
12. a. m = 1; increasing line b. m = -5; decreasing line
c. for m > 0, line is increasing, for m < 0, line is decreasing
3 8
3
8
13. a. y x , slope: m , y-intercept: 0
,
5 5
5
5
b. 1 1
y x 1 , slope: m , y-intercept: 0,
1
2
2
14. c b d a; the larger the slope, the steeper the line.
15. a. y 2x
3 b. 15 y x 2
4
16. a. y 3 6( x 4)
b. y ( 2)
3(
x 6)
c.
y 6x
21
y 3x
16
1
y ( 3)
( x 4)
2
1 y x 5
2
17 a. $23 b. $46 c. 2515.38 miles
18. a. $18,000 b. $13,50 c. 10 years
19. a. (4, 6) b. (-4, 1) c. (-2,-5) d. (-7, 5)
20. Equations:
Solution: Cost of hamburger: $3.00 per pound, cost of sausage: $1.20 per pound.
21. Equations: Solution: David has six ten dollar bills and thirteen five dollar bills.
CCDM 112N Introductory Algebra, Blitzer 6 th Ed. Updated Fall 2012