Semester Exam Review

Benchmark
Review

It is very important that you pay attention and follow along while we walk through the review.

Parts of a Circle

• Radius: line segment that goes from the center to the edge of the circle (HALF the DIAMETER)

• Diameter: line segment that goes from edge to edge on a circle (TWICE the RADIUS)

• Circumference: the distance around the outside of a circle (AKA perimeter)

Labelling

Label the parts of a circle.

Drag labels to their correct position on the image

Diameter

Center

Circumference

Radius

What is PI

Multiple Choice

Which definition describes $$\pi$$ ?

• The ratio of the circumference of a circle to its diameter.

• The ratio of the circumference of a circle to its radius.

• The radius of a circle times 2 times 3.14.
  

• The diameter of a circle times 2 times 3.14.

Multiple Choice

The circumference of a circle is 36.4 centimeters. The diameter of the circle is 13 centimeters.

Which expression best represent the value of $$\pi$$ ?

• $$\frac{13}{36.4}$$

• $$\frac{36.4}{6.5}$$

• $$\frac{36.4}{13}$$

• $$\frac{6.5}{36.4}$$

Multiple Choice

What is the RADIUS of this circle?

• 18

• 36

• 9

• 8

Multiple Choice

If the radius of a circle is 6 inches then what is the diameter?

• 12 inches

• 18 inches

• 24 inches

• 36 inches

We will use the formula:

​

C= πd

​When we are given diameter.​

​

We will use the formula:

​

C= 2π​r

When we are given radius.​

​How to find the circumference of a circle

​C = d x π

​

Set it Up:

​

C = 6.2 x ​π
C = 6.2 x 3.14

​Given Diameter​

Given Radius​

​

​C = 2 x r x π

​

Set it Up:

​

C = 2 x 14 x ​π
C = 2 x 14 x 3.14

​Set It Up

Multiple Choice

A circle has a diameter of 7.6 feet. Which measurement is closest to the circumference of the circle in feet?

• 23.9ft

• 45.3ft

• 47.7ft

• 11.9ft

Multiple Choice

A company's logo was designed using circles of 3 different sizes. The diameter of the two circles are shown. Which measurement is closest to the area of the largest circle in square centimeters?

• $$56.52cm^2$$

• $$141.30cm^2$$

• $$1,017.36cm^2$$

• $$254.34cm^2$$

Area of a Circle

Area is the amount of space a circle takes up.
Basically the space inside of the circle.

Multiple Choice

What is the formula for AREA of a circle?

• $$A=\pi r^2$$

• $$A=2\pi r$$

Multiple Choice

Which of these do I need to find the area of a circle?

• Diameter

• Radius

• Circumference

Multiple Choice

What does r² mean?

• r × 2

• r × r

Multiple Choice

A sundial has a circular base with a diameter of 90 feet as shown in the picture.

Which measurement is closest to the area of the circular base of the sundial in square feet?

• $$3,627.5\ ft^2$$

• $$282.6\ ft^2$$

• $$141.3ft^2$$

• $$6,358.5ft^2$$

To get the unit rate, divide the numerator by the denominator.

Multiple Select

What are common rates/unit rates?

(select all that apply)

• miles per hr

• price per lb

• miles per gal

• hrs per gal

• lb per price

Match

Imani compared the number of fluid ounces per bottle of sunscreen to the cost of four different brands of sunscreen. The information she gathered is shown in the table.

Use the table to match each brand with its cost per fluid ounce.

• Brand W

• Brand X

• Brand Y

• Brand Z

$0.60/ounce

$0.75/ounce

$0.65/ounce

$0.50/ounce

• $0.60/ounce

• $0.75/ounce

• $0.65/ounce

• $0.50/ounce

Classifying Rational Numbers

Labelling

Complete the venn diagram to show the relationships among integers, rational numbers, and natural numbers and whole numbers. Move the correct answer to its box.

Drag labels to their correct position on the image

Rational

Natural

Whole

Constant of Proportionality

Multiple Choice

Which equation is used to represent the constant of proportionality?

• $$x=ky$$

• $$y=x$$

• $$y=kx$$

Multiple Choice

How do you solve for k ?

• $$k=\frac{x}{y}$$

• $$y=kx$$

• $$k=y+x$$

• $$k=\frac{y}{x}$$

Multiple Choice

Identify the constant of proportionality in the equation.

• k = 2x

• k = 2

• k = 4

• none (not proportional)

Multiple Choice

The constant of proportionality in the equation $$y=\frac{1}{2}x$$ is _______. 

• $$x$$

• $$y$$

• $$\frac{1}{2}$$

• $$2$$

Multiple Choice

Write an equation in $$y=kx$$ form for the table given.

• $$y=16x$$

• $$y=8x$$

• $$y=12x$$

Is this proportional?

To solve, check each ordered pair for a rate of change.
10/1 = 10
20/2 = 10
70/7 = 10
100/10 = 10
Yes, the rates are constant, so this is proportional.

Multiple Choice

Which of the tables above has a constant of proportionality of $0.20?

• A & C

• A

• B

• All of them

Characteristics of Proportional Graphs.

• It has to be a straight line.

• The straight line has to pass through the origin.

Multiple Choice

The origin is located where in the coordinate plane?

• (0, 0)

• (10,10)

• (100, 100)

• (50, 50)

Graphing

A recipe for trail mix calls for $$1\frac{1}{2}$$ cups of walnuts for every dried fruit. Create a graph to represent y, the cups of walnuts required for x number of dried fruits.

Select two points on the coordinate grid. A line will connect the points,

Percent Proportions

Vocab Review

part (is)- partial amount
whole (of)- full amount
percent (%)
100 (you put your percents over 100 to make them a fractions)

Multiple Choice

A student earned a grade of 85% on a math test that had 20 problems. How many problems on his test did the student answer correctly?

**Set up your proportion**

• $$\frac{x}{20}=\frac{85}{100}$$

• $$\frac{20}{85}=\frac{x}{100}$$

• $$\frac{x}{85}=\frac{20}{100}$$

Percent Change Proportion

We can solve for the percent change using the proportion at the right.

​(AOC)

​(OA)

Multiple Choice

Which of the follow proportions could be used to find the percent that Amber's wage increase?

Remember:

$$\frac{amount\ of\ change}{original\ amount}=\frac{\%}{100}$$  

• $$\frac{8}{10}=\frac{x}{100}$$  

• $$\frac{2}{10}=\frac{x}{100}$$  

• $$\frac{2}{8}=\frac{x}{100}$$  

• $$\frac{10}{8}=\frac{x}{100}$$  

Multiple Choice

What percent did Amber's wage increase?

Remember: 
$$\frac{2}{8}=\frac{x}{100}$$  can be used to find the percent increase.

• 25%

• 4%

• 50%

• 400%

Multiple Choice

Which of the following proportions could be used to find the percent that Alex's grade decreased?

• $$\frac{8}{72}=\frac{x}{100}$$

• $$\frac{72}{80}=\frac{x}{100}$$

• $$\frac{8}{100}=\frac{x}{80}$$

• $$\frac{8}{80}=\frac{x}{100}$$

Multiple Choice

By what percent did Alex's math grade decrease?

Remember:

$$\frac{8}{80}=\frac{x}{100}$$  

• 80%

• 10%

• 1,000%

• 64%

Congruent and Similar Figures

What makes two figures CONGRUENT?

• Same shape and size

• Congruent symbol ≅

What makes two figures SIMILAR?

• Similar symbol ∼

• Same shape or figure

• Ratios of the lengths of their corresponding sides are equal

• Corresponding angles are congruent

Match

Match each symbol with the correct term.

Congruent

Similar

Pi

Approximately

• Congruent

• Similar

• Pi

• Approximately

Find the Missing Side Length