Integrated Math I Summer Packet Answers
PART 1 – BASIC SKILLS
Number Sense (This material is expected to be completed without a calculator.)
1) Complete the statement with the appropriate symbol
, ,  .
2) Complete the statement with the appropriate symbol
, ,  .
12.5
2


12.4
3) Complete the statement with the appropriate symbol
, ,  .


9
3


4
4) Complete the statement with the appropriate symbol
, ,  .


5
6
3
4
5) Complete the statement with the appropriate symbol
, ,  .
6) Complete the statement with the appropriate symbol
, ,  .
3
4
3


 3.1


2
7) Place the following numbers in order form least to
greatest: 4,7,  2, 2,  4
8) Place the following numbers in order form least to
greatest: 4,0.04, 0.0004,0.4, 40
9) Place the following numbers in order form least to
10) Place the following numbers in order form least to
greatest: 7, 6.28,  6.3,  6.03,  6
greatest:
4 5 3 11 7
, , , ,
3 3 2 6 6
Percent
***Please round all answers to the nearest tenth when needed.
11) Write the following decimal as a percent:
12) Write the following decimal as a percent:
0.375
0.08
13) Write the following percent as a decimal:
14) Write the following percent as a decimal:
30%
6.25%
15) What is 20% of 50?
16) 46 is what percent of 107?
17) 62% of what is 89.3?
18) What percent of 126 is 22?
19) What is 270% of 60?
20) What percent of 88.6 is 70?
Order of Operations (This material should be completed without a calculator.)
21) Simplify: 3  2  10
23) Simplify: 32  ( 3) 2
22) Simplify: 2(1  4) 2
24) Simplify:
3  9  5
45
25) Simplify: 8  [(4  7)  (8  1)]
26) Simplify: 4  [8  (2  4)]
27) Simplify: 10  [(4  5)2  (12  14)]4
28) Simplify: 7  (3  8) 2
(1  2)(32 )
29) Simplify:
6  3
30) Simplify: 3[11  (1  3)]
Solving Equations
31) Solve for x: 3 x  36
32) Solve for x: x  2.8  1.9
33) Solve for x:  4  3 x  11
34) Solve for x: 5 x  4  26
35) Solve for x: 5 x  12  2 x  3
36) Solve for x: 4 x  14  6 x  8
37) Solve for x: 5( x  4)  4( x  5)
38) Solve for x: 3 x  4  5 x  x  4  x
39) Solve for x: 3 x  2( x  4)  5( x  1)  3
40) Solve for x: 3( x  6)  5 x
Fractions (This material should be completed without a calculator.)
41) Which fraction is larger?
2
7
or
3
15
43) Circle any values that are equivalent:
42) Arrange these fractions from smallest to largest:
1 0
1
7 9
, ,  ,  ,
3 4
2
8 100
44) Evaluate
4 6 1 9 15 33
, , ,
,
,
5 8 2 27 20 44
45) Evaluate
1 3 8
 
2 7 3
46) Evaluate
2 4

5 5
47) Evaluate
1  4
 
3  5
49) Evaluate
1 2
2 1
3 3
5 3

4 4
48) Convert to an improper fraction:
4
3
5
50) Evaluate
5
4
3  2
8
5
Exponents
51) Simplify. Leave in exponent form.
43  42
53) Simplify. Leave in exponent form.
6 r  5r 2
55) Simplify. Leave in exponent form.
(3x)2
57) Simplify. Leave in exponent form.
8 x3
4 x5
59) Write in scientific notation:
456000000
52) True or False?
43  4 2  45
54) Simplify. Leave in exponent form.
2 x 2 y  3 x 5 y 2
56) Simplify. Leave in exponent form.
28
23
58) Simplify. Leave in exponent form.
 2 xy 3   x3 y 3 
 2  4 2 
 y   2x y 
60) Write in standard notation:
2.371  10 7
PART 2 – CONCEPTS AND APPLICATIONS
Linear Equations
1) Solve for m:
8  2m  4
2) Which of the following equations is not equivalent to the equation: 8 x  5 x  5  12  9
a)
b)
c)
d)
x2
13 x  5  21
13 x  26
13 x  21
3) Mike and Jake work for an apple picking company. They get paid $9 per bushel picked. After a Saturday
of working, Jake was bragging that he made $27 more than Mike made. If the total amount of money made
between both men was $153, how many bushels did Mike pick?
Proportions
4) Solve the following equation for x:
x  3 2x

7
5
5) List five fractions that are proportional to
3
4
6) Your dad recently started working for an architecture company. His first project is to design a new
skyscraper for the city of Chicago. The following picture represents his building. If the scale is
1 inch  160 ft. , how tall is your father’s building going to be? Measure the front (ground to highest point)
(Yes, you do have to measure with a ruler, round to nearest quarter inch)
Rigid Transformations
7) Answer True or False for each of the following:
a) If the letter “M” is completely above the x-axis, and it is reflected across the x-axis, the result is a
different uppercase letter?
b) If you had a picture of a dog, and you rotated it 90 clockwise and then shifted it 6 units to the right,
your new image would be the exact same as if you first shifted 6 units to the right, then rotated it 90
Congruency
8) True or False: Since all squares have four 90 angles, and all sides in a square are the same length, all
squares are congruent to each other
9) Given the following complete figure on the left, using a ruler and the given segment on the right, create a
congruent picture.
A’
B
B’
C
D
E
A
Basic Geometric Shapes
10) The table below lists some different shapes, and properties. In each box place an “X” indicating
of the shape has the property.
Square Rectangle Kite Trapezoid
Isosceles Rhombus Parallelogram
Trapezoid
All angles are
right angles
All sides are
congruent
11) Complete each of the following by indicating if it is Always, Sometimes, or Never true.
a) A square is a rectangle
b) A rectangle is a square
c) A quadrilateral has four sides
d) A pentagon has a greater perimeter than a triangle.
12) Zac and Jenny are remodeling their bathroom. Given the blue-print below, determine how many
boxes of tiles they need to buy, if each box has 12 tiles, each measure one-square-foot (12” x 12”).
(Note: Tile will be used in all unoccupied floor sections).
TOILET Room: 8ft. x 12 ft.
Toilet: radius = 1ft.
Vanity: 9ft. x 2 ft.
Tub: 5ft. x 3ft.
VANITY TUB Labeling and Understanding Geometric Diagrams
13) For the triangles above, name all pairs of congruent segments.
14) Given the following diagram, name 1 in two different ways. Also, put a smiley face in DBC .
A
D
1
B
C
Area
15) On the graph below, plot the points (-3, 1), (6,1), and (2,-4) . Then find the area of the triangle formed
when the points are connected with straight lines segments.
Functions
16) If f (x)  3x  5 , find f (2)
17) Joanie and Chachi attempted to solve an equation. It read: if 22  5 x  12 , solve for x. Chachi said the
correct answer is 98. Joanie said the answer 6.8. Who is correct Joanie or Chachi? Why?
18) Given the following table:
0
x
y
-4
Find the Domain and Range.
2
-5
4
-6
7
-7
9
-10
19) Let the following graph represent a function f ( x)
a) Find f (0)
b) Find f (2)
c) If you found f (4)  f (5) , would the answer positive, or negative?
20) The dosage in milligrams D of Invermectin, a heartworm preventative, for a dog who weighs x pounds is
136
given by D ( x) 
x
25
a) Find the proper dosage for a dog that weighs 30 pounds.
b) If a doctor gave 152 milligrams of Invermectin to a dog named Skippy, how many pounds does Skippy
weigh? This is not a “ruff” problem!
21) A salesperson earns $600 per week plus a commission of 20% of their sales. Find the minimum amount
of sales needed to receive a total income of at least $1500 per week.
22) On the graph below, sketch the graphs of
a) f ( x)  2x  5
b) g( x)  3
23) Find the y – intercept of the function f (x)  4x  3
24) How many x – intercepts does the graph f ( x)  45 have
25) Find the equation of the vertical line that goes through the point (3,7) .
26) Graph a line with a slope of
describes the situation.
1
that passes through the origin. Also create the equation of the line that
4
27) If you knew the slope of a line is -4, in what directions would you move from the y – intercept to create
an accurate graph?
28) Find the equation of the line that goes through the points (3, 4) and (-1, -5).
29) Stibnite is a silvery white mineral with a metallic luster. It is one of the few minerals that melts easily in
match flame or at temperatures of approximately 977  F or greater. Using the conversion formula
5
C  ( F  32) , find the lowest temperature, in degrees C , at which stibnite will melt.
9
Reading and Writing Inequalities
30) Write the inequality: four times a number,
n , is less than 6.
31) Six Flags requires that you are 48 inches tall to ride a roller coaster. Which of the following inequalities
best represents their requirement if h is height measured in inches?
a. h  48
b. h  48
c. h  48
d. h  48
32) Solve the following inequality for x: 5 x  3  1
Slope
33) What is the slope of the graphed line? Write your answer as a fraction.
34) In 1990, the enrollment of Lemont High School was 900 and by 2010, the enrollment had grown to 1450.
 students 
 from 1990 to 2010.
 year 
Find the rate of change 
Evaluating Expressions
35) Evaluate the following expressions for the given variables.
3x  4 y
 x  7; y  3 
a  b
2
c
 a  1; b  2; c  3
36) Explain why the following expression cannot result in a negative number.
a  b
2
 cd
37) The perimeter for a rectangle can be found using the formula P  2 w  2l . The Adam’s family wants
to put in a rectangular fence for their dog. The length of their yard is 65 feet and the width is 30 feet. How
much fencing will they need?
Constructing Table Values
38) Given the equation y  3 x  2 , fill in the table of values.
x
y
1
2
3
4
5
Scatter Plots and Correlation
39) Create the scatter plot given the following table.
x
y
1
4
5
7
9
2
6
5
6
8
Statistics
40) Circle the data point in the following data sets that would appear to be an outlier.
a.
b.
c. 10, 13, 11, 12, 900, 14, 8, 16, 17
41) In measuring the heights of the players of a 6th grade basketball team, explain why adding the height of
LeBron James to this set of data would create an outlier?
42) The following list is the number of homeruns hit by Barry Bonds every year of his career.
16,25,24,19,33,25,34,46,37,33,42,40,37,34,49,73,46,45,45,5,26,28
a) What is the MEAN per year of Barry Bonds’ homeruns?
b) What is the MEDIAN of Barry Bonds’ homeruns?
c) What is the MODE of Barry Bonds’ homeruns?
d) What number would represent an OUTLIER of the list? Why do you think that number happened?
Representing Functions Graphically or with Tables
43) Match the following functions with the table of values. Place the correct function name above the right
column.
g  x   3 x  1
f ( x)  2 x  5
x
1
2
3
4
5
x
5
5
5
5
5
1
2
3
4
5
hx  5
x
7
9
11
13
15
44) List all of the functions that are increasing as time increases.
1
2
3
4
5
2
5
8
11
14
Arithmetic Sequences
45) Write the next three terms of the sequence: 5, 8, 11, 14, …
46) What is the pattern illustrated in the following sequence: 2, 7, 12, 17, …
47) Alex makes $15 a week in allowance after four weeks, he has $105. If he continues to save at the same
rate, how much money will he have at the end of 7 weeks?
Using Scales and Labels on Graphs
48) Label the axes of the following grid so that the horizontal axis represents time in seconds and goes from
0-20 and the vertical axis represents speed in miles per hour and goes from 0-50.
49) For making a graph that compares the amount of miles driven to the amount of gas used, why would you
only want your axes to represent positive values?
50) Nicole is tracking the temperature for the month of July. Below is her graph for the first 7 days. If it is
52 degrees on the 9th day of July, what will she have to do with the labels on her vertical axis to adjust for
this change on her
graph?