1.
Unit 2 Study Guide or Practice Problems Answer Key
Students reviewed problems 1-18 starting 11-06**
Lines of latitude are imaginary lines that circle the globe in an east-west
direction. They measure distances north and south of the equator. The
equator represents 0 degree latitude. What latitude is opposite of 65 degrees
north latitude? (NS3)
A.) -65 south
B.) 130 south
C.) 65 south
D.) 130 north
2. What is the value of this expression? (EE1) NEEDS MORE PRACTICE
=12.49
3. A triangle has sides with lengths of 5x – 7, 2x – 5, and 4x – 2. What is the
perimeter of the triangle? (EE1)
A.) 9x -12
B.) 13x – 14
C.) 11x – 14
D.) 25x
4. Rewrite the expression 10(x +5) using the Distributive Property. (EE1)
A) 10x + 50
B) 10x + 5
C) 10x + 15
D) 15x
5. Kimberly needs to buy two sweaters and 5 pairs of pants. She does not want to
spend more than $170. Which inequality best represents this situation? (EE2)
A) 2s + 5p < 170
B) 2s + 5p > 170
C) 2s + 5p <170
D) 2s + 5p > 170
6. The 7th grade classes are going on a field trip to the ball park. The school must
pay $10 per hour for each hour they stay at the park plus a $250 upfront fee.
Write an expression for this scenario, using h to represent the number of hours
the students are at the museum. (EE2)
$250 + 10h
7. Jayden is shopping for school supplies. He has $55 to spend on a calculator and
notebooks. He will buy one calculator for $20. Let n represent the cost of one
notebook. Write an expression that describes this situation.
$55 = $20 + n or n = $35 or n = $55-$20
8. Solve:
(E
Test the solutions IF you cannot solve the equation.
(2)(-3) divided by -3 = +1
A.) w =-3
B.) w = -4
C.) w = 3
9. What is the value of y for 10y + 15 = 5y – 45. (EE3)
A.) y = -12
B.) y = -30
D.) w = 0
C.) y = 30
D.) y = -60
10. Michael scored x points in the first basketball game of the season. The
expressions below represent how many points he scored during the first three
games of the season. (EE3)
Game 1: x
Game 2: x + 6
Game 3: x – 3
Michael scored a total of 72 points in all 3 games. How many points did he score
in Game 1?
1. (Set expressions for games 1, 2, and 3 = to 72 points. Solve for x.)
x + x +6 + x – 3 = 72
2. (Combine like terms)
3x + 3 = 72
3. (Solve for x)
3x + 3 – 3 = 72 – 3
3x = 69
Divide both sides by 3 to isolate the x
x = 23
4. Put or substitute values in for x to get points for
Game 1 = x = 23 points scored in Game 1
Game 2 = x + 6 = 23 + 6 = 29 points in Game 2
Game 3 = x - 3 = 23 – 3 = 20 points in Game 3
5. Circle, Box, or Cloud your final answers.
11. Gary is 20 years less than half his father’s age. If Gary is 13 years old, how old
is his father? (EE4a) G = Gary’s Age F = Father’s Age
1.
Set up an equation based on the variables provided.
G = F/2 – 20
2. Multiply each term by 2. Note 2/2 = 1 so it cancels out.
(2) G = (2) F/2 – (2) 20
2G = F - 40
3. Now G = 13 based on information from the word problem. Substitute or plug
in 13 into the equation.
2(13) = F – 40
26
= F – 40
4. Add 40 to both sides of the equation to help isolate and solve for F.
26
+ 40 = F – 40 + 40
4.
5. Your zero pair -40 + 40 cancels out. F is your final answer. Box your final
answer. Write a complete sentence.
66 = F or F = 66
Gary’s father is 66 years old when Gary is 13 years old.
12. A rental car costs $125 for one day plus an additional $0.50 per mile. What is
the cost of renting a car for one day and driving it 70 miles? (EE4a)
$125 + 0.50(70) = $125.00 + 35.00 = $160.00
It would cost $160.00 to rent the car for 1 day if you
drive 70 miles.
13. Ben joins a DVD movie club. He pays $10 for each DVD and a $5 shipping fee
for the entire order. If Ben spent $115, how many DVDs did he buy? (EE4a)
$115 = $5 + $10d d stands for number of DVD’s that Ben can buy or purchase.
$115 – 5 = $110 $110 divided by $10 = 11 DVDS
14. Margo has $180 to spend. She wants to buy as many DVDs as possible after
buying a CD that costs $8. The DVDs cost $20 each at most. What is the
greatest number of DVDs she can buy? (EE4b)
Subtract 180 – 8 = 172 divided by cost for each DVD (20)
Answer is 8.66 DVDs. So final answer Margo can buy 8 DVDs.
Challenge Problem DOK 4
15. Members of a gym pay $10 per class plus a one-time $100 membership fee.
Non-members pay $25 per class. How many classes would a member have to
take to save money compared to taking classes as a non-member? (EE4b)
Members would need to take at least _____________classes.
Solve this equation to determine when becoming a member saves the
customer money.
Member cost = $100 + 10c
Non-Member cost = $25c
Set the equations equal.
$100 + 10 c = $25 c
Now solve for c. Subtract 10c from both sides.
$100 + 10 c – 10 c = 25 c – 10 c
$100 = 15 c Divide both sides by 15 to isolate the variable.
100/15 = 15c/15
6.66 = c
So it would take 6.66 classes for the cost to be equal.
Remember c represents number of classes needed so that costs
would be equal if you were a member or a non-member.
So final answer would need to be greater than c.
Members would need to take at least 7 classes to save money as a
member.
16. Mr. Jones invited 10 children to his son’s ball game. He plans to give each child
at least 3 small items in a ball bag. He wants to have 5 extra gifts to give away
as prizes. Describe the inequality that represents the number of bags he must
buy. (EE4b) Write the inequality that represents the number of individual
items he must buy.
Number of Bags = b
b > 10
Number of Small Items = s
s > 35
17. Adriun’s motorcycle can travel 401.5 miles on 4.5 gallons of gasoline.
What is the number of miles per gallon? (Divide) RP1 Unit 3
401.4 divided by 4.5 = 89.22 miles per gallon of gas
18. Mrs. Moore made skirts for cheerleaders. She used ¾ yard of material for
each skirt. She used 20 yards in all. How many skirts did she make? (Divide)
20 divided by ¾ yard. RP1 Unit 3
20 x 4/3 = 80/3 = 26.66 So Mrs. Moore can make 26 skirts.
Example to help with #16
Example:
Mrs. Jones had 20 bouncy balls. Write the inequality that represents the number
of bouncy balls she has in her room before she gives them away to students.
Number of bouncy balls is represented by the variable ( b ).
20 is the most number of balls she will have before she distributes the balls.
b < 20
Students who have not mastered will want to spend some time practicing writing and
graphing inequalities. Google inequalities practice or inequality videos or games.
These are the inequality symbols.
< less than or equal to
> greater than or equal to
< less than
> greater than
DO NOT FORGET TO PRACTICE YOUR RACE STRATEGIES and to
WRITE YOUR MATH SOLUTIONS IN COMPLETE SENTENCE.
PRACTICE PRACTICE PRACTICE.
R – Restate and Re-Read the problem
A – Analyze the numbers and words
C – Choose your strategy. (What operation did you apply?)
E – Evaluate and Explain your answer. Did you answer the
question? Does it make sense?
Always Box, Circle , or Bubble your Answer.
Always include your Units!
Use your math vocabulary. Make sure you
can use these words in a sentence.
addition
additive inverse
subtraction
difference
multiply
multiplicative inverse
divide
product
division
quotient
operation
percent
distributive property
evaluate
percentage
substitute
graph
solve
illustrates
simplify
calculation
rationalize
calculate
ratio
rate
fraction
unit rate
resulting
distance
Students completed Unit 2 assessments before the
break. Scores for 7EE1 and 7EE2 are already posted.
Some students already show mastery for 7EE3 and
7EE4. These will also post soon. Students with blank
scores did not demonstrate mastery for those
standards before the break. They will have assigned
tasks and problems to complete when we return.
Students who have not mastered 7EE3 and 7EE4 will
need to spend additional time and practice on those
problems over the next few weeks in addition to
learning problems for RP1 Ratios Units. A few students
have also already demonstrated mastery for RP1.
Students who are working in the Crosswalks
workbooks can continue practice in domain 3 that
starts on pg 122. Lesson 16, 17, and 18 will help with
word problems. Students working ahead on Ratios and
Rates will preview lessons 9, 10 and 11 pg 88 -110.
Lessons have also been updated and added to
usatestprep to help students with online practice as
needed. The goal for each student is mastery of each
mathematical standard presented.
Students please enjoy your break, but do take
advantage of extra time to practice and master new
skills. Try to squeeze in 30 minutes to 60 minutes each
day to help boost your personal test scores and
achievement. Also practice reading and writing over
the break. I would love for my students to bring in an
extra credit story that talks about how math was used
over the break to solve a problem or complete a task.
It will need to be a full paragraph 5 to 7 sentences.
Underline the key math words. Use complete
sentences.
Title on Page: Everday Math Over the Holidays !!!