Download Chapter 1 Question 1. Evaluate the following expressions. (a) 52 (b

Name:
Chapter 1
Question 1. Evaluate the following expressions.
(a) 52
(c) (−5)2
(b) −52
(d)
3
1
−
3
Question 2. Evaluate the following expressions.
(a) 20 − 5(2)3 ÷ 4
(c) 3(5 − 7)2 − 6(3)
(b) −9 + (8 − 5)2
(d) (9 − 13)2 + 15 ÷ (−3)
Question 3. Simplify each expression by collecting like terms.
(a) −8y + 6 − 5x + 2 + y − 3
(b) −9y − 2x − 5x
Question 4. Multiply using the distributive property and collect like terms if possible.
(a) 3(6n + 7)
(d) 4{12y 2 + 3[7y 2 − 2y(y + z)]}
(b) −8(6x + 3) + 6(9x + 7)
(e) [−8p − (2p − 3)] + [−5p − (−7 − 5p)]
(c) 4x(5x − 2) − 2(x2 − 3x)
(f ) (3x − 5) − [2x − (3x + 7)]
Question 5. Evaluate the following expressions for the specified values.
(a) 4x + 9 for x = 8
(c) 2 − x2 for x = −10
(b) −3x2 − 2x + 7 for x = −2
(d) (2x)2 + 2(5x + 1) for x = −2
Math 81 Beginning Algebra
Name:
Chapter 2
Question 1. Determine if the given value is a solution to the given equation.
(a) Is 3 a solution to the equation 2(3 − x) = 1 − (x − 2)?
(b) Is 2 a solution to the equation 3(x − 2) = −4(5 + x)?
Question 2. Solve for x and check your solution. If the solution is not an integer express your
answer as a reduced fraction.
(a) 5 − 8 + x = −12
(c) −45 = −5x
(b) −2.8 + x = 4.7
(d) 12x − 6x = −48
Question 3. Libby’s four quiz grades in her history class are 89, 87, 80, and 81. What score does
Libby need to obtain on her next quiz to get an average on her quizzes of 85?
Question 4. Solve for x and check your solution. If the solution is not an integer express your
answer as a reduced fraction.
(a) −14x + 9 = 2x + 7
4
x
(b) 14x + 2(7 − 2x) = 20
4
x
(c) 0.5(1.2x − 3.4) = −1.4x + 5.8
(d) 3(x + 6) = −2(4x − 1) + x
4
x
4
x
(e)
x x
3
− =
2
8
4
(f )
1
(x + 3) = 4x − 2(x − 3)
4
(g)
1
1
(7x − 14) − 2 = (x − 2)
7
3
(h) 0.2(x − 3) = 4(0.2x − 0.1)
4
x
Question 5. Write an algebraic expression. Use the variable x to represent the unknown value.
(a) 19 more than a number.
(c) Triple the sum of a number and 4.
(b) Two-thirds of a number.
(d) Twice a number decreased by three
Question 6. Solve each scenario.
(a) 10 less than double a number is the same as (c) Two airplanes take off at the same time.
7 times the number.
One flies east at 110 miles per hour and the
other flies west at 90 miles per hour. How
far apart will they be in 6 hours?
(b) The measure of the first angle of a triangle is (d) Erica invested a total of $5, 000 in two accounts. The first account pays 3% simple in3 times the measure of the third angle. The
terest per year and the second accounts pays
measure of the second angle of a triangle is
4% simple interest per year. After 1 year her
20 less than the third. Draw a picture of
she made $176 in interest, how much did she
the triangle and label its angles. Solve for
invest in each account?
all three angles of the triangle.
Question 7. Solve each inequality and graph the result.
(a) 9 + 2x ≤ 6 − x
−5
−4
−3
−2
−1
0
1
2
3
4
5
(b) 2x − 3 + x > 5(x + 1)
−7
−6
−5
−4
−3
−2
−1
0
1
2
3
−1
0
1
2
3
4
5
6
7
−4
−3
−2
−1
0
1
2
3
3
(c) 7 − x > 4
5
−3
(d)
−2
x
3
−1≤ x+4
2
2
−7
−6
−5
Name:
Chapter 3
Question 1. Plot and label the following points.
A: (2, −3)
B: (−1, 0)
C: (0, −5)
D: (−3, −6)
E: (4, 5)
F: (−2, 3)
y
6
4
2
x
−6
−4
−2
−2
2
4
6
−4
−6
Question 2. Give the coordinates of each point.
y
6
4
G
J
K
2
x
−6
−4
H
−2
−2
2
4
6
I
−4
−6
Question 3. Graph each line.
(b) 2y + 4x = −8 + 2y
y
(a) 5y + x = −15
y
x
(c) 3y = 2x + 6
y
x
x
Question 4. Complete the ordered pairs so that each is a solution to the given equation.
(a) y = 7 − 3x
(b) 2x + 5y = 12
(c) y = 2x − 6
(i) (0, )
(i) (1, )
(i) ( , −4)
(ii) ( , 10)
(ii) ( , 4)
(ii) ( , −8)
Question 5. Find the slope of the line passing through each pair of points.
(a)
1
2, −
and (5, −3)
2
(b) (−1, 2) and (4, 2)
(c) (3, −7) and (3, 2)
(b) 2x − 3y = −12
y
(c) y = −2x
Question 6. Graph each line.
(a) y = − 21 x + 3
y
y
x
x
Question 7. Write the equation of a line satisfying the given conditions.
(a) Passing through (3,-4) with slope −6
(d) Passing through (−1, 4) and (2, 1).
1
(b) Passing through (−1, 4), with slope − .
3
(e) Passing through (3, 7) and (−6, 7).
(c) Passing through (3, −5) and (0, −7).
(f ) Passing through (2, −6) and (−1, 6).
5
x
Question 8. What is the slope of the line perpendicular to to the line whose equation is
1
y = − x − 5?
4
1
Question 9. Determine the equation of the line perpendicular to y = − x − 5 passing through
4
the point (1, −2)
Question 10. Given the following functions, find the indicated values.
(b) g(x) = −2x2 + 3x + 4
(a) f (x) = 7 − 6x
(c) h(x) =
2
x+4
(i) f (0)
(i) g(−1)
(i) h(−2)
(ii) f (−4)
(ii) g(3)
(ii) h(6)
Question 11. Write the equation in slope intercept form of the line shown in the graph.
y
5
4
3
2
1
x
−5 −4 −3 −2 −1
−1
1
2
3
4
5
−2
−3
−4
−5
Question 12. Write the equation in slope intercept form of the line shown in the graph.
y
5
4
3
2
1
x
−5 −4 −3 −2 −1
−1
1
2
3
4
5
−2
−3
−4
−5
6
Question 13. Is the set of ordered pairs f = {(2, 1), (3, 1), (5, 1), (10, 1)} a function? Explain why
or why not.
Question 14. Determine which of the following graphs represents a function. If it is, simply state
“yes,” if not explain why it fails to be a function.
Question 15. Economists in the Labor Department are concerned about the continued job loss in
the manufacturing industry. The number of people employed in manufacturing jobs in the united
states can be predicted by the equation y = −269x + 17, 020 where x represents the number of
years since 1994 and y is the number of employees in thousands in the manufacturing industry. Use
this data to answer the following questions.
(a) How many people were employed in manufacturing in 1994? In 2000? In 2008?
(c) What is the slope of this equation?
What is its significance?
(b) Use your answer(s) from question (a) to
draw a graph of the equation
y = −269x + 17, 020.
(d) What is the y-intercept of this equation
and what is its significance?
y
Number of people employed (in thousands)
18, 000
16, 000
14, 000
12, 000
10, 000
0
2
4
6
8
10
12
14
16
18
20
x
Number of years since 1994
7
Name:
Chapter 4 Review
Question 1. Solve each of the following systems by graphing.
(a) x + 2y = 8
x−y =2
(b) 2x + y = 6
3x + 4y = 4
y
y
x
x
Question 2. Solve each system by substitution.
(a) 3x − 2y = −9
2x + y = 1
(b) 4x + 5y = 2
3x − y = 11
Question 3. Solve each system by elimination.
(a) −2x + 5y = −12
3x + y = 1
Professor: W. Ila Peterson
(b) 7x − 4y = 2
6x − 5y = −3
Math81
Beginning Algebra
Question 4. Solve each system by any appropriate method.
(a) x = 3 − 2y
3x + 6y = 8
(c) 5x − 2y = 15
3x + y = −2
(b) x = −5y + 10
5y = 10 − x
(d) 3x + 8y = 0
9x + 2y = 11
Question 5. Amanda works as a salesperson for a home security company. Each pay period
Amanda earns $900 plus a 5% commission on her sales for that pay period. At a different security
company Carly, who also sells home security systems, earns $1, 200 each pay period and a 3%
commission on her sales. For what amount of sales will both Amanda and Carly get paid the
same?
Question 6. Jarod is having a problem with rabbits getting into his vegetable garden, so he decides
to fence it in. The length of the garden is 11 feet more than three times the width. He needs 70
feet of fencing to do the job. Find the length and the width of Jarod’s vegetable garden fence.
Question 7. A boat travels downstream 150 miles in 5 hours. The return trip takes 7.5 hours.
Find the speed of the boat without a current and the speed of the current.
Question 8. Devon purchased tickets to an airshow for 5 adults and two children the total was
$128. The cost of a child’s ticket was $6 less than the cost of an adult ticket. Write and solve a
system of linear equations to find the cost of one adult’s ticket and the cost of one child’s ticket.
Name:
Chapter 5
Question 1. Simplify each of the following expressions. Write your answer with positive exponents.
(a) (−6a2 )(3a5 )
(b)
(3xy 2 )(3x3 y 4 )
−5xy 2
(c)
25x6 y 6
(−2b2 )4
(d)
(−5b4 )3
(e)
2
1
2
2
1
2
2
1
2
2
1
2
(−3a3 b2 )2
2
1
2
5ab2
c3
x0 y 3
4w5 z 2
(f )
(g)
2x−6
(h) −3
y
(i)
3 2
1
2
2
1
2
(2x−5 y)−3
(j)
2 2
1
2
3x−3 y −4
2x−5 y
2
1
2
2 2
1
2
Question 2. Write in scientific notation.
(a) 156, 340, 000, 000
(c) 0.000783
(b) 0.00000174
(d) 123, 780
Question 3. Write in decimal notation.
(a) 4.32 × 10−5
(c) 8.137 × 107
(b) 6.034 × 106
(d) 3.5 × 10−8
Question 4. Evaluate by using scientific notation and the laws of exponents. Leave your answer
in scientific notation. (For full credit all numbers should be converted to scientific notation)
(b) (0.003)4
(a) (42, 000, 000)(1, 500, 000, 000)
Question 5. Today’s fastest modern computers can perform one operation in 1 × 10−11 second.
How many operations can such a computer perform in one minute?
Question 6. During feeding season, gray whales eat 3.4 × 105 pounds of food per day. If the
feeding period lasts 140 days, how many pounds of food in total will a gray whale consume during
the feeding period?
Question 7. Perform the indicated operation and simplify.
(a) 2x − (−3x2 + 3x − 6)
(g) (x − 4)(x + 4)
(b) (3x2 − 4x + 5) − (2x2 − 3x + 5)
(h) (x − 4)2
(c) (3x2 + 4x) + (−4x2 − 2x − 5)
(i) (2x − 3)(2x + 3)
(d) −5a(4a − 3b)
(j) (3m − 10)2
(e) 3x2 (2x2 − 4x + 1)
(f ) −3x(2x2 − 3xy + 4y 2 )
(k) (2x + 5)2
Question 8. Find a polynomial that describes the shaded area in the figure.
2x
x
y
2y + 1
12