7th Grade Math EOY Review - Remediation

Algebraic Reasoning

100

A plumber has been called in to replace a broken kitchen sink. The material needed costs $341.25 and the total expected cost of the job is $424.09. How many hours will the plumber need to work in order to get the job completed at a rate of $20.79?

First, find the labor cost: 424.09−341.25=82.84

Labor cost = $82.84 

Now, divide the labor cost by the hourly rate:

82.84 / 20.79  ≈3.99  about 4 hours

200

The length of the rectangle is twice its width. The perimeter of the rectangle totals 45 feet. What is the width of the rectangle?

• Let the width = x feet.

• Then the length = 2x feet (since it's twice the width).

The formula for the perimeter of a rectangle is:  Perimeter=2(length+width) 

Substituting:

45=2(2x+x) 

45=2(3x)    45=6x

Now solve for x:

x=7.5 

300

Write an inequality to represent the situation. Three boxes hold at least 120 cookies total. Then solve how many cookies are available per box?

3𝑏 ≥ 120 

𝑏 ≤ 40

400

Miguel takes out a loan that adds interest each year on the initial amount. What is the interest Miguel will pay on the loan if he borrowed $5,000 at an annual interest rate of 4.5% for 15 years? (Use the formula 𝐼 = 𝑃𝑟𝑡, where 𝐼 is the interest, 𝑃 is the principal or initial investment, 𝑟 is the interest rate per year, and 𝑡 is the number of years.)

Where:

• P=5000

• r=0.045 (4.5% as a decimal)

• t=15

Substituting into the formula:

I=5000×0.045×15

Miguel will pay $3,375 in interest on the loan.

500

SurfPro Shop and The Surfer Store both sold surfboards for $350. In February, SurfPro Shop wanted to increase their profits so they increased the prices of their boards by 15%. When this increase failed to bring in more money, they decreased their price again by 10% in November. To beat their competitor who had increased prices, The Surfer Store decided to decrease their price of surfboards by 10% in March. However, when they started to lose money on the new pricing scheme, they increased the price of surfboards in November by 15%. If no other changes were made after November, which store now has the better price for surfboards? What is the difference between their prices?

SurfPro Shop:

• Starting price: $350

• February: increase by 15%

New price after 15% increase:

350+(0.15×350)=350+52.50=402.50

• November: decrease by 10%

New price after 10% decrease:

402.50−(0.10×402.50) = 402.50 − 40.25 =$362.25

The Surfer Store:

• Starting price: $350

• March: decrease by 10%

New price after 10% decrease:

350−(0.10×350)=350−35=315

• November: increase by 15%

New price after 15% increase:

315+(0.15×315) = 315+47.25 = $362.25

Lock in :)

100

What are the solutions to the inequality

 4.2 + 𝑧 ≤ −5.3?

The solutions are all values of z such that 

z ≤ −9.5

200

Melanie is buying a candle for a gift. She has 80.07 inches squared of wrapping paper and all of the candles she is looking at have a radius of 1.5 in. What height candle can Melanie buy if she uses all of the wrapping paper she has?

height is approximately 7 inches

300

DOUBLE - Kell works at an after-school program at an elementary school. The table below shows how much money he earned every day last week. Who would make more money for working 10 hours? 

Everyone makes the same amount per hour $8.40

400

 Each small circle has a radius of 5 centimeters. What is the area of the big circle? what is the area of the shaded area?

big circle 706.5  

all small circles added area is 549.5

shaded area 26.1666...

500

Joe was planning a business trip to Canada, so he went to the bank to exchange $200 U.S. dollars for Canadian (CDN) dollars. On the way home from the bank, Joe’s boss called to say that the destination of the trip had changed to Mexico City. Joe went back to the bank to exchange his Canadian dollars for Mexican pesos. What is the value of Mexican pesos that Joe has now? 

Rate of $1.02 CDN per $1 U.S.                                 Rate of 20.8 pesos per $1 CDN

Joe starts with $200 U.S.
The exchange rate is $1.02 CDN per $1 U.S.

200×1.02=204 CDN dollars.                             Now he has 204 CDN dollars.
The exchange rate is 20.8 pesos per 1 CDN dollar. So: 204 × 20.8 = 4243.2 pesos
Joe now has 4,243.20 pesos.

Number Sense

100

Solve 

1/2 ^5 = 1/32

200

Solve

40

300

Daliah purchases eggs by the dozen for her two children. Each day, Zane eats 1/4 carton and Amare eats 1/6 carton. A carton of 12 eggs costs $1.65. How much does Daliah spend on eggs for her two children in 30 days?

Daily consumption: 1/4 + 1/6 = 5/12                So together they eat 5/12 x 30 eggs = 12.5 carton eggs of a carton each day.

Each carton costs $1.65. So: 12.5×1.65=20.625

Daliah spends $20.63 (rounded to the nearest cent).

400

-3

43.2

500

(DAILY DOUBLE) All of the 7th grade homeroom classes collected recycling, with the top three classes splitting the grand prize of $800 toward building their own gardens. Mr. Brogle’s class turned in 237 pounds of recycling, Mrs. Abiola’s class turned in 192 pounds and Mr. Wheeler’s class turned in 179 pounds. How should these top three divide the money so that each class gets the same fraction of the prize money as the fraction of recycling they collected?

• Mr. Brogle’s class:

237/608 × 800 ≈ 311.84

• Mrs. Abiola’s class:

192/608 × 800 ≈ 252.63

• Mr. Wheeler’s class:

179/608 × 800 ≈ 235.53

Geometry

100

(TRIPPLE POINTS) An ocean resort decided to build a large room in the shape of a cylinder to host events. The room is 34 feet in diameter with a height of 9 feet. They are going to paint the floor, wall and ceiling blue to make attendees feel like they are floating in the sky. Determine the surface area to be painted so they may order the needed supplies.

approximately 2777.17 square feet

200

When baking an apple pie, a strip of aluminum foil needs to be placed around the edge of the crust until the last 20 minutes of baking so that it will not burn. If using a 9 1/2 -inch diameter pie pan, how long should the strip of foil be?

C=3.14 ×9.5 = 29.83 inches long

300

Bena is building a kite based on the design shown below. Determine how much ripstop nylon she will need to purchase for the sail material. 

5400 centimeters squared

400

Find the area of the figure

Step 1: Convert mixed numbers to decimals. The area is 76.25 square feet

• 8 1/2=8.5

• 4 3/4=4.75

• 5 1/8=5.125

• 1 1/2=1.5

• 3 1/4=3.25

500

(DAILY DOUBLE) Amy and Eunice are participating in a bike-a-thon this weekend. Amy has 29-inch road bike wheels and Eunice has 26-inch mountain bike wheels, where the bike wheel measurements are based on their diameter. How many more revolutions will Eunice's bike need to make to reach the finish line as compared to Amy's bike?

• 1 mile = 5,280 feet

• 1 foot = 12 inches

• 5,280 × 12=63,360 inches

• 63,360 × 5 miles = 316,800 inches  
  
  

Amy's bike circumference ≈ 91.106 inches 3468.49 revolutions to finish

Eunice's wheel circumference ≈ 81.681 inches 3878.5 revolutions to finish

410.01 more revolutions for Eunice to finish the race as compared to Amy. (without using the distance formula)

Data & Probability

100

What is the sample space for pulling a face card from a standard deck of cards? 

What is the sample space for rolling a 12-sided fair die?

KKKKQQQQJJJJ

1 2 3 4 5 6 7 8 9 10 11 12 

200

There are 7 red, 5 blue and 12 green marbles in a bag.                                                                 Part A. What is the probability of choosing a red marble?                                                                 Part B. What is the probability of not choosing a green marble?                                                         Part C. What is the probability of choosing a yellow marble?                                                            Part D. What is the probability of choosing a red or blue marble?  

red 5/24   approx. 20.8%

not green 1/2   50%                            

yellow impossible 0

red or blue 1/2 50%

300

What is the shape of this distribution: symmetric or skewed? Is there an outlier?? Which measure of center and variability would you use?

skewed, median, and IQR

400

A random sampling of juniors and seniors at the local high school were surveyed about the average amount of time they spent per night on homework. Calculate and compare the measures of center for the data sets.

juniors - use the mean

seniors - use the median because there is an outlier

500

A random sampling of juniors  seniors at a high school were surveyed about the average amount of time they spent per night on homework. Calculate and compare the measures of variability for the data sets.

juniors - use the range

seniors use the IQR because there is an outlier