Name____________________
Great Mills High School Math Department Summer Review
Intermediate Algebra
This packet contains review material. You have been taught and tested on this material in prior math courses.
However, math is a cumulative study; it builds upon itself. Recalling these prerequisite mathematical concepts
and processes is critical to your success in this course.
The purpose of this review packet is three-fold:
1. Review/refresh prerequisite skills
2. Reinforce the expectation that you are prepared to take this course
3. Provide a smooth transition into a higher-level math course
This material will be graded as follows:
1. Completion of this packet is a process grade for the class.
2. This packet will be returned to you and each problem will be reviewed. Following review, you will
take a process-grade group quiz.
3. Lastly, there will be a product-grade individual quiz on this material.
For each topic addressed, there are examples, explanations, and/or references, followed by a short set of
practice problems. You are expected to complete this packet on your own.
Be sure to show your work. If you need additional space, use lined notebook paper and
This packet is due on August 21, 2013, the first day of school.
Topics:
1.
2.
3.
4.
5.
6.
7.
8.
Patterns – Linear, Quadratic, Cubic and Geometric
Linear Equations and Graphs
Linear Inequalities
Graphs of Non-Linear Functions
Systems of Equations in Two Variables
Probability, Simulations and Making Predictions
Measures of Central Tendency
Misleading Data Representations
1. Patterns – Linear, Quadratic, Cubic and Geometric
This unit has corresponding practice on www.ixl.com under Algebra, topics P.1 – P.7.
Linear Patterns
Given: 8, 15, 22, 29, …
a. Write an equation which represents this linear pattern.
b. What is the 12th term?
c. What term has a value of 50?
Quadratic Patterns
Given: 3, 4, 7, 12, 19. …
a. Write an equation which represents this quadratic pattern.
b. What is the value of the 15th term?
c. What term has a value of 102?
Cubic Patterns
Given: -9, -2, 17, 54, 115, 206, …
a. Write an equation which represents this cubic pattern.
b. What is the value of the next term?
c. What term has a value of 719?
Geometric Patterns
Given: 3, -15, 75, -375, 1875, …
a. What is the value of the next term?
2. Linear Equations and Graphs
This unit has corresponding practice on www.ixl.com under Algebra, topics S.1 – S.18
a. What is the slope-intercept form of the equation of the line in the graph below?
y
6
4
2
x
2
4
6
8
10
12
14
b. Screen-printing a batch of shirts requires 2 minutes per shirt in addition to 2 minutes of initial
set-up time. Write an equation that shows the relationship between the number of shirts s and
the time t.
c. Bonita has already prepared 4 kilograms of dough and will continue preparing 1 kilogram of
dough every hour. How much dough did Bonita prepare if she worked for 5 hours? Write and
solve an equation to find the answer.
d. A corporate team-building event costs $2, plus an additional $2 per attendee. How many
attendees can there be, at most, if the budget for the corporate team-building event is $10?
Write and solve an equation to find the answer.
e. Graph this function using intercepts:
x+y=9
y
9
8
7
6
5
4
3
2
1
-9
-8 -7 -6
-5 -4 -3 -2
-1
x
1
2
3
4
5
6
7
8
9
-1
-2
-3
-4
-5
-6
-7
-8
-9
f. Line r has a slope of 5/3. Line s is parallel to line r. What is the slope of line s?
g. Line d has a slope of 9/7. Line e is perpendicular to d. What is the slope of line e?
h. Line k has an equation of
. Line l which is parallel to line k, passes through the point
(-6, -3). What is the equation of line i?
3. Linear Inequalities
This unit has corresponding practice on www.ixl.com under Algebra, topics K.1 – S.15 and T.1 – T.5
a. Solve the inequality and draw the graph on a number line.
i. 5 – 2r > 1
iii.
iv.
ii.
b. Does the point (3, 7) satisfy the inequality y < 2x +1
c. Graph the inequality y < 2x + 1
y
9
8
7
6
5
4
3
2
1
-9
-8 -7 -6
-5 -4 -3 -2
-1
x
1
-1
-2
-3
-4
-5
-6
-7
-8
-9
2
3
4
5
6
7
8
9
d. Graph the inequality 3x – y ≥ 8
y
9
8
7
6
5
4
3
2
1
-9
-8 -7 -6
-5 -4 -3 -2
-1
x
1
2
3
4
5
6
7
8
9
-1
-2
-3
-4
-5
-6
-7
-8
-9
4. Graphs of Non-Linear Functions
This unit has corresponding practice on www.ixl.com under Algebra, topics Q.1 – Q.12.
a. For the graph below find the range, domain, maximum, minimum, determine if it is a function
or not a function, determine if it is continuous or not continuous, and find all the zeros.
y
i.
ii.
iii.
iv.
v.
vi.
vii.
range
domain
maximum
minimum
function
continuous
zeros
__________
__________
__________
__________
yes or no
yes or no
__________
4
3
2
1
x
-4
-3
-2
-1
1
-1
-2
-3
-4
2
3
4
5. Systems of Equations in Two Variables
This unit has corresponding practice on www.ixl.com under Algebra, topics U.1 – U.15.
a. Solve each system of equations using an appropriate method:
i.
ii.
iii.
b. Lucia is training for a triathlon and needs to swim a certain distance for today's workout. If she
swims at the rec center pool, she will complete a 157-yard warmup and then swim laps in a
lane that is 42 yards long. If Lucia swims at the indoor pool at her gym, she will complete a 113yard warmup, plus a main set that consists of 44 yards per lap. If Lucia swims the correct
number of laps, she can complete the same distance in either pool. How long will Lucia's
workout be in total? How many laps will that take?
c. The drama club is selling gift baskets to raise money for new costumes. During the fall play,
they sold a combined 3 regular gift baskets and 5 deluxe gift baskets, earning a total of $280.
During the spring musical, they sold 16 regular gift baskets and 20 deluxe gift baskets, earning a
total of $1,200. How much are they charging for the different sized gift baskets?
d. Two groups of volunteers are cleaning up the football stadium after the Homecoming game.
Volunteers from the Band Booster Club have already cleaned 10 rows of bleachers and will
continue to clean at a rate of 1 row per minute. The leadership class has completed 5 rows and
will continue working at 2 rows per minute. Once the two groups get to the point where they
have cleaned the same number of rows, they will take a break and decide how to split up the
remaining work. How many minutes will each group have cleaned by then?
Write a system of equations, graph them, and write the solution as an ordered pair.
Cleaning Bleachers
30
25
Rows
20
15
10
5
0
0
2
4
6
Minutes
8
10
12
Probability, Simulations and Making Predictions
This unit has corresponding practice on www.ixl.com under Algebra, topics II.1 – II.7
a. You roll a 6-sided die.
What is P(1)? Simplify your answer and write it as a fraction or whole number.
b. During 14 spins, a spinner landed on red 2 times. If you spin the spinner once, what is the
experimental probability that it will land on red?
c. You flip a coin and spin the spinner. How many outcomes are possible?
d. Eric is packing a lunch. He has three different choices for sandwiches and five different choices
for fruits. How many different lunches are possible for Eric to pack?
6. Measures of Central Tendency
a. Find the mean, median and mode of the data set below:
15
28
32
18
21
25
19
18
20
22
20
22
b. Use the data below to draw a box-and-whisker graph:
15
28
32
18
21
25
19
18
c. A pottery factory kept track of the number of broken plates per shipment last week.
Use the data to complete the histogram below.
Broken plates per shipment
41 18 59 54 17 32 41 51 51 44 21 12 37 25
0-9
10-19 20-29 30-40 41-50 51-60 61-70
d. Students were surveyed as to how many stuffed animals they had at home. This box-andwhisker plot shows the results.
0
10
20
30
40
50
60
What percent of the students own 50 or more stuffed animals?
70
7. Misleading Data Representations
a. Megan polled the 12 customers who had been going to a particular barbershop the longest.
Is this sample of the customers at the barbershop likely to be biased? Explain your reasoning.
b. Based on the graphs below, Dylan claims that the number of students who earned a B in math
last year is the same as the number of students who earned a B in math this year. Is Dylan
correct? Explain your answer. What characteristic of the graph may have led Dylan to believe
his statement is correct?
Grades This Year by Subject Area
14
12
10
Number of A's
8
Number of B's
6
Number of C's
4
Number of D's
Number of F's
2
0
English Science
Social
Studies
Art
Math
P.E.
Grades Last Year by Subject Area
24
22
20
Number of A's
18
Number of B's
16
Number of C's
14
Number of D's
Number of F's
12
10
English Science
Social
Studies
Art
Math
P.E.