8/3/2019 GR8ASS

1/33

Annual Review: Math 8

Name: ___________________

Comments: _______________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

8/3/2019 GR8ASS

2/33

Section One: Rational Numbers

1. Fractions

a. Identifying Fractions

What is the name for the top number in a fraction _____________________

What is the name for the bottom number in a fraction _____________________

Is it true orfalse, that aproperfraction has a lower number on top, and a higher

number on the bottom?

_____________________

What kind of fraction has a whole number in front _____________________

What kind of fraction has a bigger number on top _____________________

b. Converting to Fractions from Non-Fractions

Convert the following Numbers into Fractions:

1 _____________________ 5 _____________________

2.5 _____________________ 7.25 _____________________

0.125 _____________________ 9.75 _____________________

c. Converting to Non-Fractions from Fractions

Convert the following Fractions into Numbers:

_____________________ _____________________

1 _____________________ 4 _____________________

2 _____________________ _____________________

8/3/2019 GR8ASS

3/33

2. Ratios

a. Identifying Ratios

What is a ratio: ___________________________________________________

_______________________________________________________________

_______________________________________________________________

Write this ratio out as a phrase 2 : 5 _____________________

Write out the ratio Three to One _____________________

The first number of a ratio is the same as what part of a fraction

_____________________

The second number of a ratio is the same as what part of a fraction

_____________________

b. Converting to Ratios

Convert the following fractions to ratios

_____________________ _____________________

_____________________ _____________________

c. Converting from Ratios

Convert the following ratios to fractions

1 : 1 _____________________ 1 : 3 _____________________

2 : 4 _____________________ 3 : 7 _____________________

8/3/2019 GR8ASS

4/33

3. Percentage

a. Identifying Percentage

What does percentage mean: _______________________________________

_______________________________________________________________

_______________________________________________________________

What operation do you use when you want to find out what some percentage of a

number is?

_____________________

Describe the process of calculating percentages. Use three steps

1 ___________________________________________________________

2 ___________________________________________________________

3 ___________________________________________________________

b. Converting to Percentage

Convert the following numbers to percentages

1.0 _____________________ 0.5 _____________________

0.125 _____________________ 1.3 _____________________

c. Converting from Percentage

Convert the following percentages to numbers

1% _____________________ 50% _____________________

99% _____________________ 150% _____________________

8/3/2019 GR8ASS

5/33

4. Decimals

a. Identifying Decimals

In this decimal, name theplace value of each of the following numbers

For the number: 123.456

What is name of theplace value held by the:

1 _____________________ 2 _____________________

3 _____________________ 4 _____________________

5 _____________________ 6 _____________________

b. Converting to Decimals

Convert each of the following numbers or expressions to decimals:

1 _____________________

Two and three quarters _____________________

One and twenty-five thousandths _____________________

c. Converting from Decimals

Convert each of the following decimals into the indicated type of number

0.95 (into a percentage) _____________________

3.3333... (into a fraction) _____________________

0.5 (into a ratio) _____________________

8/3/2019 GR8ASS

6/33

5. Summary

a. Converting between different types of rational number

Complete the following table. All the boxes in each row are equivalent numbers.

WORDS DECIMAL FRACTION PERCENT RATIO

One

0.5

30%

5 : 6

Ten and a half

9.9

110%

6 : 5

One hundredth

0.05

5%

1 : 10

8/3/2019 GR8ASS

7/33

Section Two: Integers

1. Identification

a. What is an Integer

Define Integer _________________________________________________

_________________________________________________________________

Circle the integers; cross out the non-integers:

+5 -8 + -1.25 + 13

2. Addition

Add the following integers. Add:

-3 and +4 _________________ +1 and +3 _________________

-5 and -2 _________________ +7 and -7 _________________

3. Subtraction

Subtract the first number from the second. Subtract:

+3 from +7 _________________ -3 from +1 _________________

+5 from -5 _________________ -4 from -4 _________________

4. Multiplication

Multiply the following numbers together. Multiply:

+3 and +4 _________________ -1 and +1 _________________

-4 and +2 _________________ -7 and -3 _________________

8/3/2019 GR8ASS

8/33

5. Division

Divide the first number by the second. Divide:

+8 by +2 _________________ -1 by +1 _________________

+9 by -3 _________________ -6 by -2 _________________

6. Summary

Using order of operations (BEDMAS), evaluate the following expressions:

+1 + +2 + +3 + +4 _________________

+1 - +2 - +3 - +4 _________________

+1 - -2 + +3 - -4 _________________

+1 - +2 + -3 - +4 _________________

+4 +2 + +3 x +1 _________________

(+4 + +2) (+3 + +1) _________________

(+4 + +2) (+3 - +1) _________________

(+4 - +2) (+3 - +1) _________________

-4 -2 + -3 x -1 _________________

(-4 + -2) (-3 + -1) _________________

(-4 + +2) (+3 - +1) _________________

(+4 - -2) (+3 + -1) _________________

8/3/2019 GR8ASS

9/33

Section Three: Exponents

1. Identification

a. What is an exponent

Define an exponent, or power? ______________________________________

_________________________________________________________________

_________________________________________________________________

In the expression Xy

X is the _________________ y is the _________________

2. Squares

a. Identifying Squares?

Why do we call a number with the exponent 2 a square? _________________

_________________________________________________________________

_________________________________________________________________

b. Evaluating Squares

What is the value of the following expressions:

102 _________________ 122 _________________

202 _________________ 1002 _________________

c. Perfect Squares

Circle the perfect squares; cross out the non-perfect squares

1 3 4 9 12 16 24 30 36 48 64

8/3/2019 GR8ASS

10/33

3. Squared roots

a. Identifying squared roots?

Define a Squared Root: ________________________________________

______________________________________________________________

______________________________________________________________

b. Evaluating Squared Roots

Evaluate each expression:

_________________ _________________

_________________ _________________

c. Estimating Squared Roots

Estimate the following squared roots; draw a number line when showing your work

_________________ _________________

_________________ _________________

4. Summary

a. What happens when you take the squared root of a squared number?

Evaluate these expressions:

( )2 _________________ (72) _________________

8/3/2019 GR8ASS

11/33

Section Four: Geometry

1. Squares and Rectangles

a. Height and Width

On the next sheet of paper, please draw rectangles (or squares) with the following

heights and widths:

A) Base 1, Height 1

B) Base 2, Height 3

C) Base 5, Height 9

D) Base 9, Height 19

E) Base 7.5, Height 11.6

F) Base 3 , Height 5

b. Perimeter

Calculate the perimeter of each shape from the section above:

A) ________________ B) ________________

C) ________________ D) ________________

E) ________________ F) ________________

c. Area

Calculate the area of each shape from the section above:

A) ________________ B) ________________

C) ________________ D) ________________

E) ________________ F) ________________

8/3/2019 GR8ASS

12/33

A B

C D

E F

8/3/2019 GR8ASS

13/33

2. Other Quadrilaterals

a. Height and Width

On the next sheet of paper, please draw the appropriate shapes with the indicated

dimensions:

A) Trapezoid Base 4, Height 3, Top 2

B) Parallelogram Base 7, Height 3, Side Length 5

C) Rhombus Base 5, Height 3, Side Length 5

D) Trapezoid Base 6, Height 3, Top 4

E) Parallelogram Base 15, Height 5, Side Length 13

F) Rhombus Base 17, Height 15, Side Length 17

b. Perimeter

Calculate the perimeter of each shape from the section above:

A) ________________ B) ________________

C) ________________ D) ________________

E) ________________ F) ________________

c. Area

Calculate the area of each shape from the section above:

A) ________________ B) ________________

C) ________________ D) ________________

E) ________________ F) ________________

8/3/2019 GR8ASS

14/33

A B

C D

E F

8/3/2019 GR8ASS

15/33

8/3/2019 GR8ASS

16/33

3. Triangles

a. Height and Width

Draw a triangle of the indicated type and dimensions on the next page. The variable a

and b stand for the shorter two legs of the right triangles, while c stands for the

hypotenuse.

A) Right Triangle Sides: 3, 4, c

B) Right Triangle Sides: 5, 12, c

C) Right Triangle Sides: , 3, c

D) Right Triangle Sides: a, , 6

E) Right Triangle Sides: 5, b,

F) Isosceles Triangle Base 5, Height 6, Side Lengths c

b. Pythagorean Formula

Write out the Pythagorean Formula: ____________________________________

c. Hypotenuse

Calculate the missing side lengths of the triangles drawn above:

A) ________________ B) ________________

C) ________________ D) ________________

E) ________________ F) ________________

d. Area

Using the completed side lengths, calculate the area of each shape drawn above:

A) ________________ B) ________________

C) ________________ D) ________________

E) ________________ F) ________________

8/3/2019 GR8ASS

17/33

A B

C D

E F

8/3/2019 GR8ASS

18/33

8/3/2019 GR8ASS

19/33

4. Circles

a. Circle Properties

Write out the formulae for circles:

r = _____ d = _____ c = _____ a = _____

b. Drawing Circles

On the following page, draw circles from the table at the bottom of the page (A-B):

c. Pi

Define the number Pi ( ) ______________________________________

____________________________________________________________

____________________________________________________________

What is a useful approximation of Pi: ~ _____ (the value we use in class)

d. Calculating Circle Properties

Complete this table, for the circles drawn above

Circle Radius Diameter Circumference Area

A 1cm

B 1cm

C 10m

D 10m

E 9.42cm

F 31 400m2

8/3/2019 GR8ASS

20/33

A B

C D

E F

8/3/2019 GR8ASS

21/33

Section Four: Word Problems

For each word problem you will be awarded points for each of the following criteria:

1. Identifying the problem and writing/drawing out a summary or diagram

2. Indicating which formulae and strategies you are using

3. Showing all work

4. Writing out the correct answer

For example:

Question: You need to build a fence big enough to enclose a pasture at least 100m 2.

How do you do this with the fewest resources possible?

1. Identifying the problem and writing/drawing out a summary or diagram

I draw a few different shapes and write 100m2 on the inside.

2. Indicating which formulae and strategies you are using

I write out the area formula for each shape. I write out that I intend to work backwards

to calculate the perimeter of each shape, because that is the amount of fence I would

need. I will then pick the shape with the smallest perimeter, or the cheapest fence.

3. Showing all work

Working backwards, I solve for the perimeter (or circumference) of each shape. I keep

all my equations balanced by lining up the equals sign vertically. I make sure that I

make no mistakes, and I double check my answers.

4. Writing out the correct answer

I will indicate which object has the smallest perimeter, and then write that I chose to

make a fence of that shape, in order to make costs as low as possible.

8/3/2019 GR8ASS

22/33

1. You need to bake a cake for class. You have a recipe for 6 people, but there

will be 14 people in class. You need to figure out what number to multiply the

quantities in the recipe by to go from 6 to 14 people. Then you need to apply this

number to the quantities in the following recipe:

150 g all-purpose flour

330 g sugar

4 tablespoons unsweetened cocoa powder

1 teaspoon baking powder

1 teaspoon vanilla extract

180 g butter

90ml boiling water

3 eggs

120 g chocolate chips

150 g chopped walnuts or pecan nuts

First: what fraction do you multiply 6 by to get 14?

Second: multiply all ingredients by this fraction

Third: Write out the converted recipe neatly

8/3/2019 GR8ASS

23/33

2. Next year you will be placed into a class with a 5:2 ratio of returning students

to new-students. You are responsible for arranging a pizza party for the class.

You know that there will be 10 returning students in the class, so you need to

calculate the total number of students. Then, calculate the cost for a party, with

the following costs per student:

Pizza 10.00$ : 8 slices of pizza

Soda 4.50$ : 12 cans

Candy 1.10$ : 1 candy bar

Popcorn 2.00$ : bag

You need to order three slices of pizza per student. You also need one can of soda and

one candy bar for each student. Each bag of popcorn can be shared between up to

four students.

The store manager is nice enough to sell you pizza by the slice and soda by the can

if you calculate the partial cost of each item. Must buy a whole number of bags ofpopcorn.

First: Calculate the number of students in the class

Second: Calculate the unit-price of each item (this may be a fraction)

Third: Calculate the total cost of your party, and write it out neatly

8/3/2019 GR8ASS

24/33

3. While on vacation, you discover that you are not permitted to take and foreign

currency out of the country you are visiting. You must spend all the money you

have. Tax in this country is 5%, so you need to chose the items which, when

tax is added, combine to the total amount of money you have. You have one

thousand euros cash, one thousand euros in travellers checks, and 100 euros

in change. You may buy any combination of the following, but only one of each

item:

Original European artwork 500 euro

European sports-car hood ornament 200 euro

Medieval knights armor 1500 euro

Case of French wine 300 euro

Cutting edge European cell-phone 400 euro

Basket of exotic European sausages 50 euro

Meter-wide wheel of cheese 150 euro

Folding Peugeot bicycle 1850 euro

First: Calculate the cost of each item with tax

Second: Calculate the total amount of money you have

Third: select items until your cost is the same as your available money, and write out

your shopping lest neatly

8/3/2019 GR8ASS

25/33

4. Ally gave Billy $11.23

Billy gave Cindy twice what Ally gave her. Cindy gave Dolly twice what she received.

Dolly gave Ellie three times what she received, and she also gave Fanny three times

what Billy gave Cindy.

Ellie and Fanny put their money together to buy a waffle-iron. How much money did

Ellie and Fanny receive from Dolly?

8/3/2019 GR8ASS

26/33

5. Mr. Schmoo is redecorating his house. He is tiling all of his floors. He currently

has one of his rooms tiled, and he really likes the tiles, so he is going to pull

it all up, and then mix his old tiles with the new ones. Mr. Schmoo lives in a

rectangular house, ten meters long by twelve meters wide. His bathroom, which

is two meters wide by three meters long, is already tiled. His walls take away

some of the floor space he needs to tile; all together he has fifty-six meters of

quarter-meter-thick walls. How many boxes of tiles does Mr. Schmoo need?

A box of tiles covers one square meter, and can be arranged in a number of patterns,

so none will be wasted if you calculate the correct remaining area of the floor.

8/3/2019 GR8ASS

27/33

6. Mr. Schmoo just finished re-tiling his floors when he discovered that his walls

were rotten! Mr. Schmoo has a friend who will drywall and finish the outsides

of the house, if Mr. Schmoo sets up the frames for the walls. Each side of Mr.

Schmoos house can be broken up into a specific number of squares.

Each of the short sides of Mr. Schmoos house are made up of two squares, each 25m 2

in area. Each of the long sides of Mr. Schmoos house are made up of three squares,

each 16m2 in area. Mr. Schmoo has a 12m x 1m window running along the top of each

of the long sides. To frame each wall, enough timber needs to be purchased to outline

each square. Where two squares meet, the timbers will be attached to each other.

What is the overall length of timber that Mr. Schmoo needs to creates frames for all the

sections of his walls.

8/3/2019 GR8ASS

28/33

7. The average temperature in Bella Coola is 8*c. The Average high temperature in

Bella Coola is 12.2*c, and the average low is 3.7*c. The Extreme temperatures

in Bella Coola are 37.8*c and -27.9*c. What is the range (distance between the

average high and low) of the temprature in Bella Coola? What is the maximum

range (distance between the maximum high and low) of the temperature in Bella

Coola?

8/3/2019 GR8ASS

29/33

8. Mrs. Flobble bought three paintings in Europe the year she graduated from

High School. The paintings were entitled Damp Scotland, Robust Germany,

and Gay Paris. She paid the equivalent of One thousand Canadian dollars (1

000 CAN$) for each painting. Now, thirty years later, each painting is worth a

different amount. Each painting has gained some value for its age, but also lost

some value because of its condition.

Damp Scotland became 50 CAN$ more valuable every three years. Unfortunately, it

was painted on cheap canvas, and lost 10 CAN$ of value every ten years.

Robust Germany became 75 CAN$ more valuable every five years. Unfortunately, it

was painted with cheap paint, and lost 15 CAN$ of value every five years.

Gay Paris became 100 CAN$ more valuable every ten years. It was painted on

excellent canvass with wonderful paint, but its frame was made out of cheap wood, so itlost 1 CAN$ value every three years.

What are Mrs. Flobbles paintings worth?

8/3/2019 GR8ASS

30/33

9. Farmer McGruuven owns a big field, 120m wide and 50m long. He has to set up

five enclosures, with the following guidelines:

McGruuvens pigs need a pen with 1600m2 of space. McGruuvens pigs need a square

enclosure, because it makes them feel safe.

McGruuvens sheep need a pen which is 30m on two sides, and 25m on the other two.

This is because the sheep are scared of the pigs, and squares remind them of pigs.

McGruuvens goats need 1050m2 of space, but they, like the sheep, do not want a

square enclosure. In fact, the goats want the long sides of their pen 5m longer than the

short sides.

McGruuven has two horses, a big one and a little one, who want to share a pen

together. The big one wants a side 40m to run along; the small one wants a side 25mshorter than that.

Lastly, McGruuvens prized Emu, Golden Glory, needs a pen eight times as long as it is

wide, so it can run back and forth all day. This pen needs to be 200m2 in area, so that

Golden Glory doesnt get sad.

Please draw Farmer McGruuvens field, and place the enclosures together so they fit in

the feild. Then calculate the total length of the fencing needed to build the pens. If you

share pen-walls between two pens, then you only need to count their length once.

8/3/2019 GR8ASS

31/33

10.Mr. Schmoo is going on a trip (to celebrate his new home). He doesnt want to

go to far from home, but he only has two choices of where to go. He could go to

Jabootistan, or Kalamazoo. Mr. Schmoo has his own plane, so he may travel in

a straight line.

Jabootistan is 500km west of Humpreys cove. Humphreys cove is 375km south of Mr.

Schmoos house.

Kalamazoo is 600km East of Diggily Bay. Diggily bay is North of Mr. Schmoos house,

but he isnt sure how far.

How far away from Mr. Schmoos house must Diggily bay to make Kalamazoo farther

away than Jabootistan?

8/3/2019 GR8ASS

32/33

11.BONUS: Farmer McGruuven wants to build a pen for his Hippo, Henrietta. If

he has 500m of fencing, what is the greatest possible area of enclosure he can

build?

8/3/2019 GR8ASS

33/33

Section Five: Basic Operations

Under the six following headings you will find every possible calculation I may ask you

to make on the final exam. Read the instructions carefully, so that you can complete

the questions properly. You will find the answers keys to all the work printed on the

reverse of each page. Use these answers to check yourself; do not use these answers

to fill in questions without trying them.

YOU MUST BE ABLE TO ANSWER EVERY QUESTION IN THIS REVIEW

ON YOUR OWN IN ORDER TO PASS THE COURSE

i) Fractions (starting with parts of a group)

Remember that for addition and subtraction, you need common denominators

For multiplication, you multiply the top by the top and the bottom by the bottom

For division you multiply the first fraction by the inverse (the flip) of the second

To reduce improper fractions, add 1, then reduce the top term by the bottom term

ii) Decimals and percentages (comparing decimals)

Remember that, after a decimal, the place values are: Tenths, hundredths, and thousandths

To find the percentage of a number, multiply the number by the decimal equivalent of the percent

iii) Money (money addition)

Use decimal adding/subtracting rules; remember to include the unit in your answer (dollars$)

iv) Integers (comparing integers)

When you add integers, start with the first number, then move in the direction of the second integers sign

With subtraction, start with the first number then move in the opposite direction of the second integerssign

With multiplication and division you perform the operation as usual, but then choose the sign based on

the signs of the numbers multiplied. Same signs give a positive answer; different signs give a negative

one

v) Algebra (missing numbers)

In general, if you cannot find a missing number, try using the reverse operation on the answer.

For Example: 7 x _ = 49 ; to find the missing number, divide the answer by 7 ; 49 / 7 = 7

vi) Geometry

Always write out your formulae, and work through each question thoughtfully, step by step

all sheets found on: http://www.math-drills.com/