Unit 4 Test Study Guide

Unit 4
Test Study Guide

A RATIO is a comparison of 2 values.
Like fractions, ratios should always be written in SIMPLEST FORM.

Ratio

A RATE is a ratio that compares 2 different quantities.
A UNIT RATE is a rate with a denominator of 1.
To change the to a unit rate, DIVIDE the numerator by the denominator

Rates

​Topic 1: Ratio & Rates

2. An aquarium has 14 angelfish, 12 clownfish and 18 seahorses in one exhibit.

Write a ratio in simplest form:

clownfish to angelfish and seahorses

4. Write the ratio in simplest form.

3 cups of sugar to 27 cups of milk

6. Write the ratio in simplest form.

85 pieces of candy to 10 bags

Fill in the Blanks

Multiple Choice

10. 10. Calculate the unit rate. Round to the nearest tenth or cent when necessary.

12. After running 5 miles, Kevin’s total time was 42 minutes. Find his time per mile.

• 8.4 min / mi

• 0.1 mi / min

Multiple Choice

12. 12. Determine if Option A or Option B is the better deal.

• Option A:

  6 granola bars for $6.48

• Option B:

  5 granola bars for $5.50

A PROPORTION is an equation that states that 2 ratios are equal.
To determine whether a pair of ratios form a proportion, check their CROSS PRODUCTS.
To solve proportions, CROSS MULTIPLY to create a one-step equation.
When using a proportion to solve word problems, it is important to STAY CONSISTENT.

Proportions

​Topic 2: Proportional Relationships & Solving Proportions

14. Determine if a proportional relationship exists. If yes, give the constant rate.

16. Determine if the ratios form a proportion.

Fill in the Blanks

Multiple Choice

20. 20. Erin is making lemonade. She needs $$1\frac{3}{4}$$ cups of white sugar to make 8 cups of lemonade. She has a 32 cup pitcher to fill.

22. How many cups of sugar will she need?

• 146 cups

• 7 cups

• 1 cup

A SCALE DRAWING or MODEL is used to represent an object that is too big or too small to be shown in its actual size. The dimensions of the object on the scale drawing or model are PROPORTIONAL to the dimensions of the actual object. The SCALE is the RATIO of the size of the model to its actual size.

Scale = MODEL/ACTUAL

A scale can have the same units or different units.

You can use a scale to find a missing measure on the model or the

actual object. Simply set up and solve a proportion.

Scale Drawings & Models

​Similar figures have the same SHAPE but a different SIZE.

Figures are similar if:

• CORRESPONDING ANGLES ARE CONGRUENT

• CORRESPONDING SIDES ARE PROPORTIONATE

The ratio of corresponding sides is called the SCALE FACTOR.
Because the sides of similar figures are proportional, you can use a PROPORTION to find a missing side length. Simply match up two pairs of corresponding sides.

Similar Figures

​Topic 3: Scale Drawings & Models

22. On a map with a scale of 0.25 inch = 30 miles, the distance between two cities is 8.3 inches.

Find the actual distance between the cities.

Multiple Choice

24. Morgan and Natalie’s heights can be compared using a scale of 1.5 inch : 2.5 inches.

If Morgan is 36 inches tall, find Natalie’s height.

**Give your answer in feet.

• 6 feet, 2 inches

• 9 feet, 6 inches

• 5 feet

​Similar figures have the same SHAPE but a different SIZE.

Figures are similar if:

• CORRESPONDING ANGLES ARE CONGRUENT

• CORRESPONDING SIDES ARE PROPORTIONATE

The ratio of corresponding sides is called the SCALE FACTOR.
Because the sides of similar figures are proportional, you can use a PROPORTION to find a missing side length. Simply match up two pairs of corresponding sides.

​Indirect measurement uses the properties of SIMILAR TRIANGLES to find measurements that are difficult to

measure directly.

One type of indirect measurement involves SHADOWS.

​Topic 4: Similar Figures & Indirect Measure

​26. Give the scale factor of Figure A to Figure B.

​28. If the figures below are similar, find the value of x.

Multiple Choice

30. A palm tree casts a 19 foot shadow. A beach umbrella in the sand next to the palm tree casts a 6.5 foot shadow.

If the umbrella is 4 feet tall, calculate the height of the palm tree.

• 14.4 feet

• 11.7 feet

• 13.9 feet

Fill in the Blanks

In a PERCENT PROPORTION: Depending on the wording of the problem, you may find the

following two formulas beneficial in setting up your proportion:

Stores frequently DISCOUNT or MARKUP items.

• Discounts are SUBTRACTED from the original price.

• Markups are ADDED to the original price.

• The SELLING PRICE (or sale price) is the amount the customer ends up paying.
A PERCENT OF CHANGE is the ratio of the amount of change to the original amount.
When the original amount goes UP, it’s called a PERCENT INCREASE.

When the original amount goes DOWN, it’s called a PERCENT DECREASE.

​Topic 5: Percents

Round to the nearest hundredth if necessary.

34. Find 15% of 30.

Round to the nearest hundredth if necessary.

36. 150 is what percent of 250?

Multiple Choice

38. 28 is 40% of what number?

• x=11.2

• x=142.9

• x=70

Round to the nearest hundredth if necessary.

40. Andrew took a math test with 40 questions.

If he scored an 85%, how many questions did he get
correct?

Round to the nearest hundredth if necessary.

42. A box of diapers is marked down 10%.

How much are the diapers if they originally cost $28.75?

Multiple Choice

44. An $80 printer is selling for 37.5% off.

Find the final price of the printer if sales tax is 5.5%.

• $52.75

• $50.00

• $30.00

• $2.75

Multiple Choice

46. Nina buys a $59.99 video game on sale for 15% off.

She then uses a coupon that takes 20% off the sale price.

If sales tax is 7%, how much did she pay in total?

• $40.79

• $43.65

• $50.99

Multiple Choice

48. The James family purchased their home in 2000 for $175,000.

They sold their home in 2017 for $250,000.

Find the percent change in the value of their home.

Classify as a percent increase or decrease.

• 42.9%

  increase

• 42.9%

  decrease

• 30%

  increase

• 30%

  decrease

INTEREST is the amount of money paid or earned for the use of money by a bank or other financial institution.

• For BORROWING MONEY (loans, credits cards, etc.), interest is paid.

• For SAVING MONEY (savings accounts, investing, etc.), interest is earned.

Simple Interest Formula: I=prt

To solve problems involving simple interest, use the formula:

I = INTEREST

p = principal

r = rate

t = time

​Topic 6: Simple Interest

Solve. **Round to the nearest tenth or cent when necessary.

50. Simon put $15,000 in an account with a simple interest rate of 4.5%.

Calculate the amount of interest earned at the end of 8 years.

Solve. **Round to the nearest tenth or cent when necessary.

52. Chelsey put $450 into an account with a simple interest rate of 2.5%.
When she withdrew the money she had earned a total of $67.50 in interest.
How long did she leave the money in the account?

Multiple Choice

54. What was the simple interest rate on a $8,000 investment that was left in an account for 18 months and earned $360 in interest?

• 0.25%

• 3%

• 33.3%

• 4%

Great job...
Memorize your formulas!

HOMEWORK:

Study Guide #1-55, odds only (in Edulastic)