Math 7
Common Core State
Standards Review Packet
Name: __________________________
Period: ______
Problem #1
You found the same sweatshirt on sale at three different stores.
Store
Original price
Target
Walmart
Tilly’s
$28
$31
$36
Percent
Discount
5%
12%
25%
A. Which store has the lowest price for the sweatshirt?
B. What is the difference between the highest and lowest sale price of the sweatshirt?
Problem #2
Your mom gives you $100 to spend on school clothes. Regular prices
and discounts for six items are shown (tax is included).
Item
Shirt
Shoes
Pants
Hat
Socks
Jacket
Regular Price
$20
$45
$35
$25
$5
$65
Discount
35% off
10% off
35% off
10% off
10% off
45% off
Sale Price
You want to buy as many individual items as you can with the $100. You can only buy one of
each item.
2 Problem #3
You do not want to spend more than $18.00 on a new shirt. Which of the
following descriptions of prices for shirts could you buy? You can choose more
than one. Which one is the lowest price? Highest price?
A.
B.
C.
D.
E.
10% off $19.00
15% off $20.00
25% off $28.00
$14.95, plus a $3.25 shipping fee
$15.55, plus a $2.40 shipping fee
Problem #4
You ordered a burger and a soda. If sales tax is 8%, how much change will you get if you paid
with a $20 bill?
Menu Main Dish Salad $7.00 Burger $5.50 Steak $12.00 Spaghetti $6.50 Chicken $11.50 Hot Dog $8.00 3 Soda Milk Tea Water Juice Drinks $3.50 $2.50 $2.00 $1.50 $4.00 Problem #5
Your ASB class wants to repaint the media center walls. They made 80
gallons of turquoise paint by mixing 48 gallons of green paint with 32
gallons of blue paint. What part of every gallon is from green paint? Blue
paint? Write in the fraction, decimal, and percent.
Problem #6
Hannah, Trisha, and Mihaela will share the cost to rent a vacation house in Big Bear
for a week. Hannah will pay 40% of the cost. Trisha will pay 0.35 of the cost. Mihaela
will pay the remainder of the cost.
Part A:
Mihaela thinks that she will pay 1/3
of the cost. Is she correct? Use
mathematics to justify your answer.
Part B:
The cost to rent a vacation house
for the week is $800. How much
will Hannah, Trisha, and Mihaela each pay to
rent this house for a week?
4 Problem #7
Identify the number(s) that makes each statement true. You may select more than one number
for each statement.
A.
−4.8 + ______ = a positive number
☐ −5.2
B.
______ − 1 ! = a negative number
☐
C.
−2.15 – ______ = a negative number
☐ −1.75
☐ 1.34
D.
______ + 5 = zero
☐ −5
☐ 5
E.
______ • !.!" = one
☐ 3.25
☐ −3.25
!
!!
!
!
☐ 4.9
☐−
!
!
Problem #8
The tires Holly wants to buy for her car cost $200 per tire. Pep Boys is offering the
following deal. Buy 3 tires and get the 4th tire for 75% off! Holly will buy 4 tires
using the deal. The sales tax is 8%.
Part A:
What is the total cost for four tires
after discount with sales tax?
Part B:
How much money will Holly save by
using the deal versus paying the full
price for all 4 tires? (with sales tax)
A.
B.
5 $150
$162
C. $185
D. $216
Problem #9
Allyson asked a random sample of 40 students from her school to
identify their birth month. There are 800 students in her school.
Allyson’s data is shown in this table.
Which of these statements is best supported by the data?
A.
B.
C.
D.
Exactly 25% of the students in Allyson’s school have April as
their birth month.
There are no students in Allyson’s school that have a February
birth month.
There are probably more students at Allyson’s school with an
April birth month than a July birth month.
There are probably more students at Allyson’s school with a
July birth month than a June birth month.
If there are 800 students, how many students were born in July
and August? How many percent is that?
Problem #10
In the inequality −3x + 6 ≥ 18, write each number in the box to show whether the number
satisfies the given inequality.
8, −4, 4, 1, −6, −8, −2, 6, 3, 0
Solutions for the Given Inequality
Not Solutions for the Given Inequality
6 Problem #11
Daniel’s weekly salary is $455 per week. He received a 20% raise. How can he
calculate his new weekly salary? Check the correct ways to calculate his NEW
salary. Then find the new salary with the raise.
Multiply $455 by 0.20
Divide $455 by 0.20
Solve for x:
!""
!
=
!"#
!""
Multiply $455 by 1.20
Divide $455 by 1.20
Solve for x:
!""
!
=
!"
!""
Problem #12
Use the expression in the box to form three true equations:
1.
-4 _______________ = -4x + 16
2.
!
3.
!
_______________ = -3 + 3x
-0.113 _______________ = 0.452x + 0.452
7 (x – 4) (x + 4) (–x + 4) (4 – 4x) (–4 + 4x) (–4x – 4x) (4x + 4) (–4x – 4) Problem #13
Adrik and Sebastian need 216 posts to build a fence.
A) They have 88 posts and need p more. Write and solve an equation to show how to solve for
the number of posts they need.
B) Each post requires 8 nails for installation. There are 250 nails in a box. How many number
of boxes will they need?
C) They will build another fence that is 48 feet long. The posts can be a minimum of 5 feet
apart and a maximum of 9 feet apart. The posts should be equally separated. Design a fence
that uses the fewest posts possible. How far apart should each post be placed?
Problem #14
Choose True or False for each equation:
A. 37 x 4 = 1,480 ÷ 10
True
False
B. 215 x 39 = 2,487 ÷ 3
True
False
C. 4,086 x 7 = 32,202
True
False
D. 9,130 x 86 = 785,180
True
False
8 Problem #15
Five friends ordered 3 large sandwiches at Subway.
Sean ate
!
Peter ate
!
Terron ate
Lucas ate
of a sandwich.
!
of a sandwich.
!
!
!
!
!
of a sandwich.
of a sandwich.
How much sandwich is leftover for Daniel?
Problem #16
All books in the store are being discounted by 30%.
A) Let x represent the regular price of any book in the store. Write an
expression that can be used to find the sale price of any book in the store.
Expression:
_______________________________
B) Gavin bought a book on sale at the store. The sale price of the book was $8.96.
Write and solve an equation to determine the regular price of the book to the nearest
cent.
Regular Price:
_______________________________
9 Problem #17
Consider a circle that has a circumference of 28π centimeters (cm).
Part A: What is the area, in cm2, of this circle? Show all work necessary
to justify your response.
Part B: What would be the measure of the radius, in cm, of a circle with
the area that is 20% greater than the circle in Part A? Show all work
necessary to justify your response.
Problem #18
Part A: Determine if each of these statements is always true, sometimes true, or never
true. Circle your response.
1.
The sum of the measures of two complementary angles is 90°.
Always True
2.
Sometimes True
Never True
Two adjacent angles are complementary.
Always True
4.
Never True
Vertical angles are also adjacent angles.
Always True
3.
Sometimes True
Sometimes True
Never True
If the measure of an angle is represented by x, then the measure of its
supplement is represented by 180 – x.
Always True
5.
Sometimes True
Never True
If two lines intersect, each pair of vertical angles are supplementary.
Always True
Sometimes True
Never True
Part B: For each statement you chose as “Sometimes True,” provide one example of
when the statement is true and one example when the statement is not true. Your
examples should be a diagram with the angle measurements labeled.
10 Problem #19
Circle YES or NO to indicate whether each of these expressions is equivalent to:
2(2x + 1)
A.
4x + 2
YES
NO
B.
2(1 + 2x)
YES
NO
C.
2(2x) + 1
YES
NO
D.
2x + 1 + 2x + 1
YES
NO
E.
x+x+x+x+1+1
YES
NO
Problem #20
A representative sample of 50
students from a middle school is
surveyed by the year
book staff.
Each student is asked what math
class he or she is taking.
Based on the representative sample,
check TRUE or FALSE to identify
whether each statement is valid.
Math Class
Number of Students
Math Collab
Math 6
Math 7
Math 8
Algebra 8
6
10
18
4
12
•
Twice as many students are taking
Algebra 8 than are taking Math Collab.
TRUE
FALSE
•
In a group of 25 students, it is expected
that 4 of the students are taking Math 8.
TRUE
FALSE
•
20% of the student at the middle
school are taking Math 6.
TRUE
FALSE
•
In a group of 150 students, it is expected
that 45 of the students are taking Math 7.
TRUE
FALSE
11 Problem #21
1. What is the mean?
2. What is the mode?
3. What is the median?
4. What is the range?
Problem #22
The original price of the jacket is $60. Which coupon is a better deal? How much
better?
Coupon A: $20 OFF ANY ITEM
Coupon B: 40% OFF ANY PURCHASE
12 Problem #23
How many more teaspoons of paprika than red pepper are needed?
How much butter will be needed if the recipe is tripled?
Problem #24
The spinner has 8 equal-sized sections, each labeled 1, 2, 3, or 4. Check the
outcomes to the category that correctly describes the probability of the outcome.
1
2
4
2
4
2
3
3
Probability
Less Than
1/3
Landing on 1
Landing on 2
Landing on 3
Landing on 4
13 Probability
Greater Than
1/3
Problem #25
An equation is shown: a • b = c
Given this equation, fill in one value into each box to complete four different
equations. Assume a, b, and c are NOT 0.
☐=c
☐ • ☐ = −c
☐=a
−a •
a
b
c
−b
−a
☐ =a
−b
−c
Problem #26
You have $10 to spend on school supplies. This table shows how much each item at
the school shop costs. No tax is charged.
Item
Price
Select ALL of the following combinations that you could
Folder
$1.29
buy with $10.00.
Pen
$0.70
Notebook
$2.35
☐
5 folders and 5 pens
Eraser
$0.89
☐
6 pens and 6 erasers
☐
1 pen and 4 notebooks
☐
3 folders and 7 erasers
14 Problem #27
The entry fee to a carnival is $4.00. Each ride requires a ticket that costs
$0.50. You spent a total of $12.00. Write and solve the equation to find the
number of tickets you purchased.
Equation:
________________________
Answer: _____________________
Problem #28
1. Write an equivalent expression for 3(x + 5) – 2
_________________
2. Ben thinks the two expressions 2(3a – 2) + 4a
and 10a – 2 is equivalent? Is he correct?
_________________
3. Write an equivalent expression for 3a + 12
_________________
4. A rectangle is twice as long as wide. Write an
expression to find the perimeter of the rectangle
and the area of the rectangle.
_________________
15 _________________
Problem #29
1. Allison had $26 to spend in school supplies. After buying 10 pens, she had $14.30
left. How much does each pen cost?
2. The sum of three consecutive even numbers is 48. What is the middle number?
3. Solve:
!
!
n + 5 = 20
Problem #30
1. Write and solve an equation to find the measure of angle x.
2. Write and solve an equation to find the measure of angle x.
16