Grade 9 Applied Math Workbook

Lesson 2: Introduction To Integers Name:

6 Represent the following numbers using a tile display.

Use a small shaded square to represent +1 (the red tile)

Use a small unshaded square to represent -1 (the white tile)

a) - 5 b) + 4 c) - 7

d) 0 e) + 1 f) - 2

7 State the opposite of the following integers.

a) - 6 b) - 100 c) + 10 d) 5

8 State the integer that must be combined with the following integers to result in the zero

model.

a) 16 b) - 10 c) + 8 d) -1528

5

TIPS Assignment -

Write an integer expression for each of the following. Do NOT evaluate.

a) The temperature is 14EC, and drops 10EC.

b) You deposit $40 to your bank account,

and then write a check for $15 and

another check for $15.

Lesson 3: Combining Integers 1 Evaluate the following using algebra tiles. Model the expression and show the final answer using tiles and a

number.

a) -3 + 5 b) -2 - 4 c) 4 - 5 d) -3 + 3 2. Evaluate the following WITHOUT a calculator. (Remember: No calculators will be

permitted on the test.)

a) - 2 - 3 b) - 1 - 4 c) - 5 + 2 d) - 3 + 1 e) - 4 + 7 f) - 9 - 6 g) 7 + 9 h) - 12 + 4 i) - 22 - 4 j) - 2 - 6 – 4 k) - 1 - 2 - 3 l) - 3 + 5 - 9 m) 6 - 4 – 6 n) 3 - 5 - 7 o) -3 + 4 + 5 - 2 3. Gasoline is made from crude oil. The price of crude oil often changes from day to day. Suppose that a barrel of

crude oil cost $41.60 at the end of the day on Monday. For the rest of the week, the price changed as shown in this table.

Tuesday Wednesday Thursday Friday - $ 0.09 - $ 0.42 + $ 0.76 - $ 1.14

a) Write an expression to model the value of the stock at the end of the week.

b) Evaluate the expression to model the value of the stock at the end of the week. 4. At the beginning of the month, a family had $640 in their bank account. During the month, they made the

following deposits and withdrawals:

Deposits: $875, $700, $875, $700 Withdrawals: $225, $40, $75, $225, $55, $225, $199, $225

a) Write an expression to model the bank balance at the end of the month.

b) Evaluate the expression to model the bank balance at the end of the month.

Lesson 4: Introduction to Rational Numbers

1 Write the fraction that represents the shaded part of each diagram.

a) b) c) d)

2 Place each number beside the corresponding letter, and reduce if possible.

| | | | | | | | | | | | | | -2 D -1 C A 0 F B 1 E

A B C D E F _____

3 Place each letter on the number line

| | | | | | | | | | | | | | -4 -3 -2 -1 0 1 2

A 2

3 B 1

4

5 C

1

2 D 3

2

3 E 2

1

3 F ‐ 2.65

4 i) Rewrite each rational number in decimal form.

a) 1

4 b) 2

1

4 c) 1

1

3

ii) Rewrite the fractions from smallest to largest.

5 i) State the opposite of each rational number.

ii) Express its opposite in decimal form.

a) 1

4 b) 2

1

7 c) 1

1

2

3 i) Express each rational number in fraction form, then reduce it to lowest terms.

ii) Rewrite the fractions from largest to smallest.

a) 0.6 b)-1.4 c) 0.875 d) 0.75 e)-0.2

4 Express each mixed number as an improper fraction

a) 21

4 b) 2

3

4 c) 1

2

3 d) 2

4

7 e) 1

3

5

Lesson 5: Combining Rational Numbers 1. Simplify. Remember to reduce all answers to lowest terms.

a) 5

6

1

6 b)

3

4

1

4 c) 1

3

3

4

d) 2

3

3

4 e)

3

8

5

4 f)

2

32

5

6

g) 11

2

1

8 h) 35

6 i)

1

21

5

6

j) 11

3

3

4 k) 5

2

3 l) 1

3

1

2

1

4

m) 11

2

2

31

5

6 n) 2

3

4

1

53

2 How many slices are in two pizzas if each pizza is cut into twelve slices.

3 At the start of the week, Mom’s car reads 1

8 of a tank. At the end of the

week, she adds 3

4 of a tank. The drive to the cottage takes

1

3 of a tank of

gas. a) How much gas is left when she arrives at the cottage?

b) Will she have enough gas to make the return trip home? Explain.

Lesson 6: Introduction to Polynomials 1 Complete the sentences below using the following words. binomial, coefficient, constant, exponent, like terms, monomial, term, trinomial, unlike terms, variable

a) In the term, 4x 2, the 4 is the and x is a . The

expression 5a 2 has one . Therefore, this expression is a . b) The expression 2b - 5 has two terms. Therefore, it is a . In this

expression, the second term is a . c) The expression 3y 2 - 2y - 4 is an example of a . d) 3a 2, -5a 2, and 9a 2 all have the same variable and the same .

Therefore, these three terms are . 3a 2, 4b, and 11 are .

2 State the coefficient of each term. a) 10 d 2 b) -3x c) y d) -y 3 State whether each of the following expressions is a monomial, binomial or trinomial or

polynomial. Then, state its degree.

a) 5h b) -9k + 6 c) 77b – 55

d) 2xy 2 + 6y + 8 e) 6x 4y + 5x 3 - 8x 2 + 2x + 9 4 Identify the like terms.

a) 5x 2, 7x, 8xy, 54x, 67, -8y 2, 9x b) 6k, -10, 8k 3, 7k, -9k 2, 12, k 3

Lesson 7: Combining Polynomials 1 Simplify by collecting like terms. State the degree of the final polynomial answer.

a) 3x - 6x b) -2x 2 + 4x 2 c) 3y + 6y d) 4xy - 2xy e)6n + 9 - 3n + 5 f) 4p - p - 6 + 2 g) 2x + 3x + 8y - 7y h) z 3 + 3z 2 - 6 - 3z 3 + 6z - 3 i) 4y 2 - y + 3 + 2y 2 + 2y - 1

k) m 2 - 4m + 1 + 6m 2 - 7m - 10

j) 3x 2 + 7x - 7 - 8x 2 + 5x + 3

l) 5v 2 - v + 6 - 12v 3 - v - 6

Lesson 8: Combining Polynomials Assignment For the triangle to the right, a) Determine the length of each b) Determine the perimeter of side if x = 5 units. the triangle if x = 5 units. (HINT: use your results from a) Side 1 = Side 2 = Side 3 = c) Write an expression for the d) Use the expression from part c perimeter of the triangle. Simplify to determine the perimeter of the expression. The triangle when x = 5 units. e) Compare your results for parts f) Which method was easier? Why (b) and (d). What do you notice?

Lesson 9: Multiplying and Dividing Integers 1 Evaluate the following WITHOUT a calculator. (No calculators will be permitted on the test.) a) 7 x (-4) b) - 5 x (- 8) c) 45 (- 2) d) -12 x (- 3) e) (- 12)(3) f) 11 x 5 g) (- 8) (- 10) h) (- 4) (- 5) i) - 16 ÷ (-8) j) 24 ÷ 3 k) 25 ÷ (-5) l) -24 ÷ (-8) 2 Owing money can be expressed as a negative number. Earning money can be

expressed as a positive number. Write a multiplication expression to model each situation. (For example, suppose you cut three lawns and were paid $10 for each lawn. This can be expressed mathematically as 3 x 10.) Then, evaluate each expression.

a) On three different days, you borrowed $2 from your friend for french fries. b) For three nights a week, you babysat the neighbour’s children. You were paid $10

each time you babysat. 3 One year, the highest temperature in town was 41̊ C and the lowest temperature

was -25 ̊C. What was the range in temperatures for this town? (Hint: Range = highest value - lowest value.)

Lesson 10: Order of Operations 1 Evaluate the following statements in the space shown.

(18 - 6) ÷ 4 2³ + 5 x 6

3(8 - 2) + 6²

6 24 2

3 4 35

10

5 3

3² - 4 x 2 9 4 6

7 1

519 11

18 92

2 The formula h = -5t 2 + 10t + 1 gives the height, in metres, of a

ball above the ground t seconds after it is tossed into the air. Determine the height of the ball after

a) 0s b) 1s c) 2s

Lesson 11: Combining Integers Revisited

1 Evaluate without a calculator. Calculators will NOT be permitted on the test.

a) 3 - (- 9) b) 1 + 3 + (-6)

c) 14 + (- 3) - (- 5) d) 7 - (-3) + 3

2 Follow the order of operations (BEDMAS) to simplify each expression.

a) -3 (2 + 7) - 1 b) (- 4 - 1) x 2 - ( 1 - 3) c) 5 (-2) - 3(- 1) + 14 ÷ 7

d) -2 (2 + 3) - 1 e) 4 ( -3) + 2 ( -2) f) 18 ÷ 2 - (4 x 5)

g) 6 (- 2) + 4 (- 4) - 21 ÷ 7 h) -2( 15 ÷ 3) - 3 ( 27 ÷ 3)

i) (-2)² - 3(-1)³ j) 3 ( -2)³ - ( -3) -3 ( -1 - 1)²

Lesson 12: Multiplying and Dividing Rational Numbers 1 Evaluate without using a calculator.

a) 2

5

3

4 b)

2

3

6

4x c)

5

62

1

5

d)

2

2

31

2

5x e)

5

83 f)

4

9

2

3

g) 4

5

3

10

h) 2

1

4

5

6 i)

4

5

1

10

2 Mrs. May’s children always take Dad’s Oatmeal cookies for lunch. If they

ate 23

4 packages of cookies in five school days,

a) How many packages did they eat each day? Express your answer as a fraction.

b) If there are 20 cookies in each bag, how many cookies did they eat each day?

c) If Mrs. May needs to buy cookies for school lunches for the next two weeks, excluding the two Pizza Days at school, how many packages of cookies should she buy to ensure she has enough cookies. (Please make sure your answer is reasonable.) 3 The waiters at a restaurant have agreed to give one-third of their tips to the

kitchen staff. If a waiter collects $32.75 in tips, how much does he end up keeping?

4 Lisa claims that she can find the answer for

2 1

2

3 in her head. She says

the answer is 32

3. Do you agree? Justify your answer

Lesson 13: Review 1 Evaluate a) - 6 + 13 b) 7 x (-2) c) (- 3) x (- 6) d) ( - 8) x 4 e) 5(- 9) f) (- 42) ÷ (- 6) g) (- 32) ÷ 4 h) (-12) (3) i) - 25 ÷ (-5) j) - 48 ÷ 6 k) 17 - 12 - (-5) l) - 12 x 4 2 One night the temperature fell from - 5 ̊ C to - 15 ̊ C in 3 h. What was the rate of

temperature change per hour? 3 The following outside temperatures were recorded at school at 10:00 am for one

week. Calculate the average outside temperature. Monday + 2 ̊ C, Tuesday + 3 ̊ C Wednesday - 2 ̊ C Thursday - 6 ̊ C Friday - 7 ̊ C

4 The elevation of Mount Everest is 8850 m. The elevation of the Dead Sea is -400 m. What is the difference between the two elevations?

5 Mountain climbers in the Canadian Rockies must prepare for cold temperatures as they approach the top of a mountain. The temperature drops approximately 6 ̊ C for every 1000 m they climb. The height of Mount Logan is 5960 m. The temperature at the bottom of Mount Logan is 14 ̊ C. a) Write an expression to determine the temperature at the top of the mountain. b) Determine the temperature at the top of the mountain. 6 For each of the following polynomials, state their degree and classify them as a monomial, binomial or trinomial. a) 2x – 3 b) 6n c) k 2 + 3k – 7 d) -8y 2 e) 2y 3 - 9y 2 + 6y f) 8q + 5 7 Simplify the following expressions. a) 4a + 2a + 9 + 2 b) 13x - 5x + 7 + 12 c) 2y - 6 + 5y + 1 d) 8n 2 + 3n + 5 - 2n 2 + 4n + 2

8 Evaluate each of the following expressions. Show all of your work.

a) 72

5

b)

3

1

4

3

2 c) 3

1

4

13

2

d)

3

5

6

7 e) 4

2

36

3

4

9 A teaspoon is a common unit of measure for baking. A set of three small measuring

spoons is labelled: 1teaspoon, 1

2 teaspoon,

1

4 teaspoon. Describe two ways to

measure out 3

4 of a teaspoon.

Lesson 1: Solving One-Step Equations with Multiplication and Division

1 Solve the following equations. Use mental math, not a calculator.

a) 2x = 6 b) -3x = 6 c) -2x = - 4

d) 5x = 10 e) 4x = 16 f) 3x = - 15

g) -x = - 5 h) 2x = -8 i) -6x = 12

2 Solve the following equations. Use mental math, not a calculator.

a) b) c)

d) e) f)

A

4

Equations Assignment

Luis knows that the area of a rectangle is 225 cm and the length of the2

rectangle is 45 cm. Help Luis find the width of the rectangle using the

formula, A = Rw.

Lesson 3: Kitchen Relationships

1 For each of the following relationships,

a) Complete the table, label the x axis and y axis on the graph

b) State an equation that relates the variables (include let statements to introduce the variables.)

c) Graph the relation on the grid to the right of each table.

Number of

Tablespoons (b )

Number of

Teaspoons (p)

0

1

2

3

4

Let b represent

Let p represent

Equation: p =

Number of Cups

(c)

Number of Fluid

Ounces (f )

0

1

2

Let c represent

Let f represent Equation: f =


Number of Fluid

Ounces (f )

Number of

Tablespoons (b )

0

1

2

3

4

5

Let b represent

Let f represent

Equation: b =

Number of

Litres (L)

N Number of

Millilitres (m)

0

0.25

0.5

0.75

1

Let L represent

Let m represent

Equation: m =


1 For the six relations on Pages 3 - 5, complete the table below.

Equation Constant of Variation

2 Use the graphs on Pages 3 - 5 to find more reasonable measurements for

the following converted quantities. Show the interpolation or extrapolation

on the graphs by drawing the vertical and horizontal lines.

a) 21 tsp = tbsp

b) tsp = 2.5 tbsp

c) 10 tbsp = fl oz

d) 32 fl oz = cups

3 State whether you used interpolation or extrapolation in each part of

Question 2. Explain your answer.

a)

b)

c)

d)

Lesson 5: Relationships Beyond the Kitchen Part 1

Independence Day

For the following relationships, fill in the blanks to complete each statement.

1 Distance vs. Time travelled in a car.

Statement: The depends on the

so is the dependent variable and

is the independent variable.

2 The amount of candy you get on Halloween vs. the number of houses you

visit.




3 The number of detentions a student receives vs. the number of times a

student is late.




4 The number of hours worked vs. the amount earned.




Whenever you graph a relationship, the independent variable is plotted on the

axis and the dependent variable is plotted on the axis.

Lesson 5: Kitchen Relationships Part 1

1 The cost of a taxi ride is shown in the table below.

a) Complete the table of values for the total cost in dollars for a taxi ride.

d (distance in km) C (total cost in $)Cost per kilometer

($/km)

0 0

1

2

3 0.90

7

8

9 2.70

b) State the independent variable. c) State the dependent variable.

d) Determine the rate of change

of cost versus the distance

travelled.

e) What does the rate of change

of cost versus the distance

travelled represent?

f) What does this tell you about the relationship between total cost and

distance travelled?

Lesson 5: Kitchen Relationships Part 1

2 A salesman’s commission on his sales is shown in the table below.

a) Complete the table of values for his total commission.

s (total sales in $)C (Total commission

in $)

Commission per dollar

sold

0 0

100

200

300 30

700

800

900 90

b) State the independent variable. c) State the dependent variable.

d) Determine the rate of change

of commission versus total

sales.

e) What does the rate of change

of commission versus total

sales represent?

f) What does this tell you about the relationship between commission and total

sales?


1 Using the data from Lesson 5, write an equation including LET statements for

a) The taxi ride b) The salesman’s commission

2 Use the equations created in Question 1, to determine

a) the cost of a 15.5 km taxi ride. b) the number of kilometres

travelled for $ 2.25.

c) the commission earned on $ 250

of sales

d) the sales when a commission of

$150 is paid.


A

4

C

5

Name:

Writing Equations Assignment

ABC Construction Company pays $1000 per house to the framer (person who puts

up the frame.)

[3, C] 1 Write an equation relating the pay per house to the total

income for the framer. Remember to introduce the variables

using LET statements.

2 Determine the

[1, C]

[2, A] a) amount of money

earned when 7

houses are framed.

[1, C]

[2, A] b) the number of

houses framed for

$12000.

Lesson 7: Relationships Beyond the Kitchen Part 3 Practicing Your Scales Recall: Range of Data = Highest Data – Lowest Data Scale = Range . Number of Boxes

Round to a nice number 1 Using the data from Lesson 5 and assuming you have a 15 (horizontal) x 20 (vertical) grid,

determine the horizontal and vertical scales for a) The taxi ride Dependent Variable _________________ Axis _________ Boxes ________

Independent Variable _______________ Axis _________ Boxes ________ Distance (km)

0 1 2 3 7 8 9 Range of Data =

Scale =

Cost ($)

0 0.9 2.7 Range of Data =

Scale =

a) The salesman’s commission Dependent Variable _________________ Axis _________ Boxes ________

Independent Variable _______________ Axis _________ Boxes ________ Sales ($)

0 100 200 300 700 800 900 Range of Data =

Scale =

Earnings ($)

0 30 90 Range of Data =

Scale =


1 Sketch a graph of the taxi ride on the grid below. Do not forget to label each axis

and place a title on the graph.

Distance (km) Cost ($)

0 0

1 0.3

2 0.6

3 0.9

7 2.1

8 2.4

9 2.70

2 Use interpolation or extrapolation to estimate

a) the cost of a 4 km taxi ride.

b) the cost of a 12.5 km taxi ride.

c) the distance travelled for $3.

d) the distance travelled for 50¢.

3 State whether you used interpolation or extrapolation in each part of Question 2.

a)

b)

c)

d)

4 Verify each answer in Question 2 using the equation you created on Lesson 6.


1 Sketch a graph of the salesman’s commission on the grid below. Do not forget to label each

axis and place a title on the graph.

Total Sales ($) Commission ($)

0 0

100 10

200 20

300 30

700 70

800 80

900 90

2 Use interpolation or extrapolation to estimate

a) the commission on sales totalling

$975.

b) the commission on sales totalling

$530.

c) the total sales when the commission is

$64.

d) the total sales when the commission is

$120.

3 State whether you used interpolation or extrapolation in each part of Question 2.

a)

b)

c)

d)

4 Verify each answer in Question 2 using the equation you created on Lesson 6.

T

24

Name:

Lesson 9: Direct Variation TIPS Assignment

1 In Extreme Boards, the first mandatory event is called “Slalom.” In this event,

competitors must travel back and forth on a curved surface.

Number of Tricks, n Style Score, S

0 0

2 4

4 8

6 12

The boarder can earn points for performing trick moves at the top of each swing.

[2] a) Is the Style Score a direct variation of the number of tricks? Explain your answer.

[1] b) Determine the constant of variation for this relation.

[3] c) Write an equation that relates Style Score, S, and the number of tricks, n.

(Remember the LET statements.)

[3] d) When Ally’s turn comes, the top style score is 18. How many tricks must Ally

perform successfully to beat this score?

Name:

Lesson 9: Direct Variation TIPS Assignment

2 Suzanne’s pay for the past three weeks is shown in the table below.

[2] a) Determine Suzanne’s hourly rate of pay for each week.

Hours Worked, h Pay ($), P Hourly Rate

($/h)

20 180

15 135

22 198

[2] b) What does this tell you about the relationship between pay and hours worked?

Explain.

[7] c) Graph pay versus hours worked

[2] d) Use the graph to determine Suzanne’s earnings if she works

i) 10 hours ii) 25 hours

[2] e) How many hours must Suzanne work to earn $250.00?

Name:

Lesson 10: Direct Variations Assignment1 The table shows several different

heights and areas for triangles with a

base of 10 cm.

[2, A] a) Complete the table below.

Height (cm) 0 2 5 10 20

Area (cm²) 0 10 25 50 100

k = DV ÷ IV

[2, C]

[4, A] a) Graph the relationship on the grid below.

[3, C] b) Write an equation that relates the area and the height of the

triangle. (Don’t forget to include LET statements.)

Recall: DV = k (IV )

Name:

Lesson 10: Direct Variations Assignment

[1, C]

[2, A] c) Use interpolation or extrapolation to determine the area of a

triangle with a height of 25 cm. Remember to show your work

on the graph and include a sentence answer.

[1, C]

[2, A] d) Use the equation to determine the area of a triangle with a

height of 25 cm. Remember to include a sentence answer.

[1, C]

[2, A] e) Use interpolation or extrapolation to determine the height of

a triangle with an area of 75 cm . Remember to show your2

work on the graph and include a sentence answer.

[1, C]

[2, A] f) Use the equation to determine the height of a triangle with an

area of 75 cm . Remember to include a sentence answer.2

Lesson 11: Test Part 1 Review

1 Solve the following equations for the unknown variable.

a) 2x = - 8

b) p = 11

c) -6x = 20

d) y = - 9

2 Circle whether each of the following relations is or is not a direct variation. Then, state

the constant of variation.

a) C = 2t

Direct or Not direct

COV

b) P = 50h + 100


COV

c) y = - 2x


COV

d) y = x - 5


COV

3 Samantha babysits her little brother. Her hours of work and pay for one evening are shown

in the table below.

Hours worked 0 1 2 3

Pay ($) 0 5 10 15

a) In this relationship, state the

i) independent variable ii) dependent variable

b) State the constant of variation in the equation. (Remember: k = .)

c) Write an equation to express this relationship. (Remember to include LET

statements.)

d) Use the equation to determine

how many hours she babysits

if she earns $22.50.

e) Is this relationship a direct or not a

direct variation? Explain your answer.


3 f) Graph the relation.

g) Look at the graph and explain why this is a direct variation.

h) Use interpolation or extrapolation to determine the

i) her pay for babysitting 7.5 hours.

ii) how many hours she babysits if she earns $12.50.

h) State whether you used interpolation or extrapolation in each part of ( g ).

i) ii)

4 Create a cheat sheet for the test that includes a definition of

• hypothesis • inference • interpolation

• extrapolation • direct variation • constant of variation

• rate of change • independent variable • dependent variable

Lesson 13: Introduction to Ratios

Vegetable Dip (Serves 6)

250 mL sour cream

160 mL mayonnaise

15 mL finely chopped onion

15 mL chopped fresh dill

20 mL chopped fresh parsley

10 mL seasoned salt

Mix all ingredients. Chill for several hours.

Use as a dip for fresh vegetables.

1 Express the following ratios in lowest terms.

a) sour cream to mayonnaise b) onion to sour cream

c) dill to parsley d) dill to salt

e) mayonnaise to salt f) mayonnaise to dill

g) onion to salt h) mayonnaise to parsley

Lesson 14: - Solving Proportions in the Kitchen

Use the Vegetable Dip Recipe on Lesson 13 and proportions to determine the quantity of each ingredient

required for the following numbers of people. Hint: if 24 people are being served.

24 people 15 people

Sour Cream

Mayonnaise

Onion

Dill

Parsley

Salt

Lesson 16: Solving Proportions Out of the Kitchen 1 Based on current cancer rates, 19 out of 50 Canadian women will develop cancer during their lifetime and 43 out of 100 Canadian men will develop cancer during their lifetime. a) Predict how many women out b) Predict how many men out of 30 of 700 are likely to develop are likely to develop cancer cancer. during their lifetime. 2 In 2003, 1.1 million students collected over $5.4 million dollars in pledges for the Terry Fox Run. At this rate, how much money could 1.6 million students raise? 3 A new skateboard park is being constructed in Fletcher’s Meadow. If the ratio of

the height of the ramp to the base is 2:3 a) Determine the base of a ramp b) Determine the height of a ramp

with a height of 15m with a base of 4m.

Lesson 19: Unit Rates

1 Beginning in St. John’s, Newfoundland Terry Fox ran 294 km every week.

a) Express this as a unit rate (per

day).

b) If Terry ran for 143 days, use

the unit rate to determine how

far Terry Fox ran for Cancer

Research.

2 After 143 days, Terry stopped running in Thunder Bay, Ontario. He had

raised $23 million at that time.

a) On average, how much money

did Terry raise per day of his

run?

b) At that time, Canada’s

population was about 24 million

people. On average, how much

had Terry Fox raised from

every Canadian Citizen?

3 About 300,000 people participated in the very first Terry Fox Run which

was held about 1 year after Terry stopped his marathon. If each participant

raised $11.68 each, how much money was raised in total?

Lesson 19: Unit Rates

4 Some doctors suggest taking vitamin E to help prevent cancer. A pharmacist

sells two brands of vitamin E:

Rexall: 175 g for $9.98

or

Life: 260 g for $12.99

Which BRAND is cheaper? Justify your answer.

5 India has been involved with the Terry Fox run for about 10 years. One

India Rupee costs about $0.02 Cdn.

a) Express the ratio of rupee to Canadian dollars in lowest terms.

b) India has raised 400 000 rupees for cancer research. How much is

this worth in Canadian dollars?

Name:

Lesson 20: Conversion Factors Assignment

** Show all work for full or part marks.

You are throwing a party for 30 people. These are the recipes you used.

Vegetable Dip (Serves 6)

250 mL sour cream

160 mL mayonnaise

15 mL finely chopped onion

15 mL chopped fresh dill

20 mL chopped fresh parsley

10 mL seasoned salt

Apple Crisp (Serves 5)

4 cups sliced apples (about 4 medium)

cup packed brown sugar

cup flour

cup oats

cup butter

tsp ground cinnamon

tsp ground nutmeg

1 Determine the conversion factor for each recipe.

Hint: New Measure = k (Old Measure)

[2, A] a) Apple Crisp [2, A] b) Vegetable Dip

[2, C] 2 Can the same conversion factor be used for BOTH recipes?

Explain your answer.

Name:

Lesson 20: Conversion Factors Assignment

[13, A] 3 Use the conversion factor to determine the quantity of each

ingredient required. All measurements must be REASONABLE.

Apple Crisp Vegetable Dip

Apples Sour Cream

Brown Sugar Mayonnaise

Flour Onion

Oats Dill

Butter Parsley

Cinnamon Salt

Nutmeg

Lesson 22: Scale Diagrams

The diagram below represents an overhead view of a typical classroom.

The “scale” of the diagram is 1 square to 50 centimetres.

Recall: Scales may be written using a colon.

1 square : 50 cm.

This means the length of one side of 1 square on the diagram

represents 50 cm inside the classroom.

1 Determine the number of squares required for 1 metre (100 cm).


2 Count the number of squares along the long wall of the diagram.

squares

Determine the actual length of the classroom in metres.

3 Count the number of squares along the short wall of the diagram.

squares

Determine the actual width of the classroom in metres.

4 Determine the actual perimeter of the classroom in metres.

5 A table will be placed in the classroom. The table is 2 m long and 1.5 m wide.

a) Convert these measurement to centimetres.


b) Use the scale of 1 square : 50 centimeters to determine the diagram

measures of the table.

c) Draw the table on the diagram accurately using the diagram measures.

6 Four desks will be added to the room. Each desk is 1 m long and 1 m wide.

a) Convert these measurement to centimetres.

b) Use the scale of 1 square : 50 centimeters to determine the diagram

measures of each desk.

c) Draw all four desks on the diagram accurately using the diagram measures.

d) Remember to add a door as was discussed in the reading.

e) Complete your diagram and remember to label the contents of the room and

put your scale on the diagram.

Lesson 24: One Number as a Percent of Another Number

Complete the table below.

Fraction Decimal Percent

60%

1.3

0.74

1.4%

Lesson 24: One Number as a Percent of Another Number

1 Express each of the following as a percent.

a) 230:200 b) 17 to 40 c) 18 out of 30

d) 36.6 to 12.2 e) 1.2 to 80 f) 35 to 20

2 Determine to the nearest tenth of a percent, the percent increase from

a) $50 to $57.50 b) $200 to $400

c) 5 cm to 12 cm d) 18EC to 32EC

3 Determine to the nearest tenth of a percent, the percent decrease from

a) 120 m to 100 m b) $80 to $53.33 c) 18.4 s to 15.9 s

Lesson 25: Fractions, Decimals and Percent 1 Determine the given percent of each number. (Use a constant of variation.) a) 40% of 600 b) 7% of $150 c) 6.5% of $230000 d) 4.5% of 675 e) 8.25% of $89000 f) 8% of $49.75 2 Determine each number. (Use a proportion) a) 20% of what number is 68? b) 40% of what number is 52? c) 45% of what number is 35? d) 7.25% of what number is 1885? 3 A basketball shirt with a regular price of $89.95 is on sale for 25% off.

Both 8% PST and 7% GST apply to the sale price. What is the cost, including taxes on the sale price?


1 What is a ratio? (Include some examples.)

2 Reduce each of the following ratios to lowest terms.

a) 27 : 18 b) 150 cm : 5 m

3 What is a proportion? (Include some examples.)

4 Solve each of the following proportions.

a) x : 6 = 20 : 24

b) c)

5 Several Fletcher’s Meadow, Heart Lake and Brathwaite students were surveyed and 15% of

students stated that they ENJOY learning MATH. If 431 students enjoy learning math, how

many students were surveyed.

6 What is a unit rate? (Include some examples.)

Lesson 27: Review

7 State each of the following as a unit rate.

a) Harveys charges $12.85 for 2 burger

combos.

b) Sasha drove 750 km in 9 hours.

8 Two grocery stores have a sale on Freezies

Metro 40 Freezies for $13.99

Fortinos 50 Freezies for $15.99

Which store has the better buy?

9 A recipe that serves 4 people calls for 1 cup of chicken broth and cup of chopped onions.

a) Express the ratio of chicken

broth : onions in lowest terms.

b) Determine the conversion factor if the

recipe must serve 20 people.

c) Use the conversion factor to determine the amount of

i) chicken broth required for the

new recipe.

ii) onions required for the new recipe.

10 Express the following expressions as a percent, correct to the nearest percent.

a)

b) 36 out of 51 c) 250 : 210

Lesson 27: Review

11 Solve the following expressions.

a) 76% of 15 b) 30 % of what number is 52

12 State the formula used to calculate a percent increase/decrease

13 Plasma T. V.s are selling for $3999.99 at Best Buy. Next week they go on sale for

$3250.99. What is the discount as a percent of the regular price?

MFM 1P0 Unit 3: Uh-Oh, It’s NOT Direct!

Page 1 of 32

Unit 3:

Uh-Oh, It’s NOT DIRECT!


Page 2 of 32

Lesson 1: Investigation: Uh-Oh, It’s NOT Direct!

A banquet hall charges $100 for the hall and $20 per person for dinner. a) Complete the following table.

Number of People, n Total Cost ($), C Cost per Person

0 100 20

1 120 20

2 140 20

3 160 20

7 7(20) + 100 = 240 20

10 10(20) + 100 = 300 20

15 15(20) + 100 = 400 20

b) How is this table different than the table for a direct variation?

When no people attend the banquet, there is still a charge. In a direct, there would be no charge when no people attend.

c) What is the rate of change of cost with respect to the number of people

attending the dinner? The rate of change of cost with respect to the number of people attending the dinner is $20/person

d) Did we need to complete the table to determine this value? Explain.

No, we did not need to complete the table to determine the value because the rate of change was stated in the original question

e) What does the rate of change of cost represent?

The rate of change of cost with respect to the number of people represents the cost per person.


Page 3 of 32

Lesson 1: Investigation: Uh-Oh, It’s NOT Direct! f) Sketch the graph of this relationship. g) How does the graph of this relationship differ from the graph of a direct

variation? The graph of a partial variation does not pass through (0,0) h) How is the graph of this relationship the same as the graph of a direct

variation ? They both have a straight line i) Write LET statements to introduce the two variables in this relationship,

then write an equation to express this relationship.

You will need your knowledge of direct variations and an understanding of the differences between direct variations and this relationship to express the relationship using an equation.

Let C represent the total cost of the banquet, in dollars Let n represent the number of people attending the banquet

C = 20n + 100

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20


Page 4 of 32

Lesson 2: Partial Variations Part 1 Lesson 2: Partial Variations Part 1 1 To rent a car for the weekend it costs $10 plus $0.25/km.

b) Sketch the graph.

c) Write LET statements to introduce the two variables in this relationship, then write an equation to express this relationship.


Page 5 of 32

Lesson 2: Partial Variations Part 1 2 A race car had a head start of 50 km. It travels at a constant speed of 200

km/h. a) Complete the chart.

b) Sketch the graph.

c) Write LET statements to introduce the two variables in this relationship, then write an equation to express this relationship.


Page 6 of 32

Lesson 3: Direct and Partial Variations Assignment Decisions, Decisions, Decisions

You are helping a friend decide which cell phone package is best for her to buy. The cost of purchasing the phone is the same in all cases. Crystal Net: Charges $0.30 per minute. Rover: Charges $12 per month, plus $0.20 per minute. Ring Mobility: Charges $15 per month, plus $0.10 per minute.

1 State whether the company’s have a direct or partial variation. Crystal Net Rover Ring Mobility 2 State the rate of change of Cost with respect to time for each

company. Crystal Net Rover Ring Mobility 3 State an equation to represent each relationship including LET

statements for the variables. (Note: Only two LET statements are required because the three companies may use the same variables.) Remember: For DIRECT VARIATION: DV = m (IV)

For PARTIAL VARIATION: DV = m (IV) + b Crystal Net Rover Ring Mobility


Page 7 of 32

Lesson 4: Partial Variations Part 2 2 A telephone company offers a discount plan for overseas calls.

a) Is this a direct or partial variation? Explain your answer.

b) What is the rate of change of total cost with respect to the number of minutes talked? c) What is the slope of this graph?

d) What does the rate of change of total cost with respect to the number of minutes talked represent?

e) What is the fixed cost of this graph?

f) What is the y - intercept?

g) Write an equation including LET statements to represent this relation.

Cost of Overseas Phone Calls

Cost ($)

Duration (min)

h) Use the graph to estimate

i) The duration of a call that costs $7.00

ii) The duration of a call that costs $15.

iii) The cost of a 40 minute call.

iv) The cost of a 90 minute call.

10 20 30 40 50 60 70 80 90 10

51015202530


Page 8 of 32

Lesson 5: Graphing From an Equation 1 The Reliable Repair Company charges $25 for a visit plus $60 per hour for labour. a) What is the slope of the line representing this relationship? How does this value relate to

the repair charges? b) What is the y - intercept of the line representing this relationship? How does this value

relate to the repair charges? c) Write an equation including LET statements to relate the two variables. d) Graph the relation. (Don’t forget to

telescope the axis to make life simpler.)

e) Use the graph to determine the cost of a repair that takes 5 hours.

f) Use the equation to determine the

cost of a repair that takes 3 hours. g) Use the graph to determine the

number of hours of labour spent if the bill was for $160.


Page 9 of 32

Lesson 6: Graphing From an Equation Part 2

1 A soccer league holds an awards banquet at the end of the season. The banquet hall charges $20 per person for the meal plus $500 for the use of the hall.

a) Write an equation to model the cost of the banquet. (Don’t forget LET statements.)

b) Identify the slope and the y - intercept in your formula slope: _________ y - intercept:____________

c) How can you tell the equation describes a partial variation? d) Use the equation to sketch a graph of

the data. e) Use the equation to complete the

table of values for the banquet costs.

Number of People, n

Banquet Cost B ($)

0

20

50

75

100

150


Page 10 of 32

Lesson 6: Graphing From an Equation Part 2

2 The cost to rent a snowboard for one day is $40. You can rent it for a reduced cost, as shown.

Number of Extra Days

Cost ($)

0 40

1 55

2 70

3 85

a) What is the cost for each extra day?

Explain how you determined this.

b) What is the y-intercept of this variation?

What is the slope of this variation? c) Write an equation to express cost, C,

in terms of additional day, D. (Don’t forget LET statements.)

d) Use the equation to calculate the

total rental cost for a total rental of 8 days.


Page 11 of 32

Lesson 7: Assignment - The Best Value 2 A law office plans to do some landscaping around their building. They have two estimates: Company A: $240 for a full landscape plan plus $30 per hour to do the work Company B: $60 per hour to do the work (which includes the landscape plan) a) Graph Company A and Company

B on the same axis for upto 9 hours (Use a different colour for each.)

b) For which time value are the costs the same for both Company A and Company B?

c) For which time value is

Company A a better deal than Company

d) State an equation including LET statements to relate the cost and total time of

each company. Company A Company B e) Complete each of the following sentences. I would choose Company A if ... I would choose Company B if ...


Page 12 of 32

Lesson 10: Slope 1 For each graph, state the rise, run and slope.

a)

Rise =

Run =

Slope =

b)

Rise =

Run =

Slope =

c)

Rise =

Run =

Slope =

d)

Rise =

Run =

Slope=

-4 4

-4

4

x

y

-4 4 8 12

4

4

8

12

x

y

8 16

8

-20 20

-20

20


Page 13 of 32

Lesson 10: Slope e)

Rise =

Run =

Slope =

f)

Rise =

Run =

Slope = 2 Lines with slope rise to the right.

The greater the positive slope, the steeply the line rises.

The smaller the positive slope, the steeply the line rises. 3 Lines with slope fall to the right.

The greater the negative slope, the steeply the line falls.

The smaller the negative slope, the steeply the line falls. 4 The slope of a line is zero (0).

The slope of a line is undefined.

-4 4

-4

4

x

y

-4 4

-4

4

x

y


Page 14 of 32

Lesson 13: Graphing Linear Relations and First Differences 1 Fill in the following blanks for the following linear relations. a) y = 2x + 5

slope

y - intercept

Is it a direct or partial variation?

b) y = 3

4x + 3

slope

y - intercept


c) y = - 4 + x

slope

y - intercept


d) y = -x

slope

y - intercept



Page 15 of 32

Lesson 13: Graphing Linear Relations and First Differences 2 Complete the table of values and determine the first differences for each relation. Then,

graph each relation. Graph (a) on the first grid and (c) on the second grid. Use different colours for each line. (Label each graph.)

a) y = 2x + 5

x y 1st Differences

b) y = 3

4x + 3

x y 1st Differences

c) y = - 4 + x

x y 1st Differences

d) y = -x

x y 1st Differences


Page 16 of 32

Lesson 14: Assignment The Catering Problem

Maxwell’s Catering Company prepares and serves food for large gatherings like weddings and company parties. They charge a base fee for renting the hall plus a cost per person.

Menu A Chef’s Salad Chicken Kiev

Broiled Potatoes Mixed Vegetables

Ice Cream Coffee or Tea

Menu B French Onion Soup

Chef’s Salad Roast Beef

Baked Potato Steamed Broccoli

Cheese Cake Coffee or Tea

Menu C Shrimp Coctail Chef’s Salad

Steak & Lobster Baked Potato

Glazed Carrots Dessert Crepes Coffee or Tea

The following formulas are used to calculate the ordered pair (n, C ). The number of people served is n. The total cost in dollars is C. Menu A: C = 12n + 200

Menu B: C = 16n + 200 Menu C: C = 20n + 200 1 Complete the table of values for each relation:

Menu A

n C ($)

1ST D

Menu B

n C ($)

1ST D

Menu C

n C ($)

1st D


Page 17 of 32

Lesson 14: Assignment - The Catering Problem 2 Graph the three relations on the same axis. Graph each Menu with a different

colour. 3 Identify the slope and the C-intercept of the Menu C line. How do these values

relate to the total cost?

How it relates

Slope:

C -intercept:

4 Compare the first differences for the three Menus. How are the first differences

related to the a) graph? b) equation?


Page 18 of 32

Lesson 14: Assignment - The Catering Problem 5 Compare the graphs of each of the three Menus. How are the graphs the a) same? b) different? 6 For Menu B, what does the ordered pair (120, 2120) mean?

7 Brad and Jennifer, oops I mean Angelina have invited 70 people to their Wedding

anniversary. How much will it cost for

Menu A? Menu B? Menu C? 8 Lui and Sami are planning their wedding. They have $3500 to spend on dinner. They

would like to have Menu C. What is the greatest number of guests they can have at dinner?


Page 19 of 32

Lesson 15: Non-Linear Relationships Part 1 Remember: To calculate first differences, choose x - values that increase or decrease by

1. 1 Consider the relation, y = 2x + 1 a) Does the data represent a linear or

non-linear relationship? b) If it is linear, is it a direct or partial

variation. c) State the slope of the relation. d) State the y -intercept of the

relation. e)

Sketch the graph of the relation.

f) Determine the first differences.

x y

First Differences

g) What is significant about the value of the first differences?


Page 20 of 32

2 Consider the relation y = -3x

a) Does the data represent a linear or non-linear relationship?

b) If it is linear, is it a direct or partial variation.

c) State the slope of the relation. d) State the y -intercept of the

relation. Lesson 15: Non-Linear Relationships Part 1 e) Sketch the graph of the relation. f) Determine the first differences.

x y

g) What is significant about the value of the first differences?

First Differences

3 Consider the relation, y = 2x 2


Page 21 of 32

a) Does the data represent a linear or


variation. c) Sketch the graph of the relation.

Lesson 15: Non-Linear Relationships Part 1 4 Consider the relation, y = x 2 + 2 a) Does the data represent a linear or


variation. c) Sketch the graph of the relation. d) Determine the first differences.


Page 22 of 32

x y

First Differences

e) What is significant about the value of the

first differences? 5 Consider the relation, y = x 2 - 3x a) Does the data represent a linear or


variation.


Page 23 of 32

Lesson 15: Non-Linear Relationships Part 1 c) Sketch the graph of the relation. d) Determine the first differences.

x y

First Differences

e) What is significant about the value of the first differences? 6 How are the equations of the linear and non-linear relations different? 7 How are the first differences of linear and non-linear relations different?


Page 24 of 32

Lesson 16: Graphing Non-Linear Relations and First Differences 1 Determine which of the following relations are linear or non-linear. a)

b)

c)

d)

e)

f) y = x 2 - 2 g) y = -5x h) y = x 3 - 1 i) y = 3x + 4

-2 2 4 6

-2

2

4

6

x

y

-2 2 4 6

-2

2

4

6

x

y

-2 2 4 62

2

4

6

8

x

y

4 8 12 16 20 24

4

8

12

16

20

x

y

2 4 6 8 10 12 14 1

2468101214

x

y


Page 25 of 32

Lesson 18: Solving One-Step Equations

[2] 1 a) To solve x + 4 = 9, from each side of the equation.

b) To solve m - 6 = 2, to each side of the equation. [6] 2 Solve the following equations. Show all work.

a) y + 3 = 0 b) x + 4 = 9 c) k - 5 = 0

d) n - 2 = -3 e) m - 6 = 2 f) p + 4 = -8

g) 3 + x = 8 h) y - 5 = -1 i) x + 3 = - 1 [2] 3 Use a LEFT SIDE / RIGHT SIDE check to determine if x = 3 is a solution to

x + 4 = 7.


Page 26 of 32

Lesson 19: Solving Multi-Step Equations 1 Solve each of the following equations. a) 3x - 5 = 13 b) 2j + 9 = 11 c) m - 3 = 19 d) -v = 6 e) -8t = 24 f) 9z - 4 = 14

g) q

53 h)

c

4= - 7

i) -5w = - 35

m) -2h + 1 = -5 n) 3 - p = 11 2 Jacques is enclosing a rectangular swimming pool deck with 144 m of fencing. What is the width of the rectangle if the length is 40 m?


Page 27 of 32

Lesson 22: Unit Review 1 State whether each of the following relations is a direct or partial variation. a) y = - 3x b) A banquet hall

charges $50 for the hall and $30 per person.

c) C = 1.5t + 5

d) Pay-As-You-Go Cell

Phone Company charges $0.25 per minute talked.

e)

2 State the slope and “ y” -intercept of the following. Then, sketch each graph. a) y = - 3x

slope =

y - intercept =

-4 4

-4

4

x

y

-4 4

-4

4

x

y


Page 28 of 32

Lesson 22: Unit Review 3 A banquet hall charges $50 for the hall and $30 per person. a) Write an equation, including LET

statements for the relation. b) Graph the relation.

c) Use the equation to determine the

total cost of the banquet for 150 people.

d)Use the graph to determine the total cost of the banquet for 6 people. (Don’t forget to show your work on the graph and the final answer here.)

4 Pay-As-You-Go Cell Phone Company charges $0.25 per minute talked plus $5 for the month. a) Write an equation, including LET

statements for the relation. b) Graph the relation.


Page 29 of 32

Lesson 22: Unit Review c) Use the equation to determine the

total cell phone bill when a person talks for 300 minutes.

d) Use the graph to determine the total cell phone bill when a person talks for 50 minutes.

5 For each of the following relations, state the rise, run, slope, y -intercept, and equation. a) rise = run = slope = y - intercept = equation :

b)

rise = run = slope = y - intercept = equation :

-4 4

-4

4

x

y

-4 4

5

x

y


Page 30 of 32

Lesson 22: Unit Review 7 Complete the table of values, then graph each of the following relations. a) y = x + 4

x y (x, y)

-2

0

3

b) y = x ² + 1

x y (x, y)

-2

-1

0

1

2

-6 6

-6

6

x

y

-6 6

-6

6

x

y


Page 31 of 32

Lesson 22: Unit Review 8 Determine the first differences for the following relations. Then, state whether the

relations are linear or non-linear. a)

x y

-1 3

1 8

3 13

5 18

7 23

Conclusion:

1ST Differences

b)

x y

-7 0

-5 2

-3 5

-1 7

1 10

Conclusion:

1ST Differences

c) y = 3x + 1

x y = 3x + 1

-1

1

3

5

Conclusion:

1ST Differences

d) y = 2x ² - 1

x y = 2x ² - 1

-2

-1

0

1

2

Conclusion:

1ST Differences


Page 32 of 32

9 Using the scatterplot to the right: a) Identify the independent variable. b) Which point represents a body length of 20 cm and a tail length of 30 cm? c) Which point represents a body length of 60 cm and a tail length of 60 cm? d) What do the coordinates of point G represent?

Animal Body Length vs Tail Length

Tail Length (cm) G F C D A E B

Body Length (cm)

15 Answer True, T or False, F. A partial variation is a straight line through (0, 0). The graph of a scatterplot always has a positive or negative relationship.

10 20 30 40 50 60 70 8

10

20

30

40

50

60

70

Page 1 of 18

Grade 9 Applied Math

Unit 4 Geometry

Page 2 of 18

Lesson 1: Complimentary Angles, Supplementary Angles and The Opposite Angle Theorem

The sum of the angles in any right angle is always ________________. Therefore,

<A + <B = .

AND Therefore,

< A + < B + < C = .

Regardless of the number of angles, the sum of the angles in a right angle is always . These angles are referred to as ____ . Example 1: Determine the value of the unknown angles in each of the following

right angles. a)

b)

A B

A B

C

30.7°

y17.4°

x55.5°

MFM 1P0 Unit 4: Geometry Student Notes

Page 3 of 18


The sum of the angles in any straight line is always .

Therefore,

< A + < B = .

Therefore,

< A + < B + < C = .

Regardless of the number of angles, the sum of the angles in a straight line is always . These angles are referred to as . Example 2: Determine the value of the unknown angles in each of the following

straight angles. (Note: Diagrams are not to scale.) a)

b)

A B

A B

C

m 64.6°18.6°

10.5° x

25.1°


Page 4 of 18


c)

When two or more lines intersect, the angles that are opposite one another are always .

Therefore, < A = < < B = <

y y 3y4x

5x

A

D C

B


Page 5 of 18


AND

Therefore, < A = < < B = < < C = <

Regardless of the number of intersecting lines, opposite angles are always . Example 3: Determine the value of the unknown angles in each of the following

opposite angles. a)

A

F

E D

C

B

45°

D C

B


Page 6 of 18


b)

x+1

F

E Dx+4

x+1


Page 7 of 18


1 In each diagram, calculate the measure of the unknown angle. a)

b) c)

d) e) f)

39° a 115° b c

x + 3

30°

40°

ya52°

130°

bb


Page 8 of 18

2 Calculate the measure of the unknown angles. You must state and solve two equations to find the four unknown angles.

x + 3

x + 3

y + 40

y


Page 9 of 18

Lesson 2: Interior and Exterior Angles of Triangles and Quadrilaterals The Sum of the Angles in a Triangle • The sum of the interior angles in a triangle is . • The measure of an exterior angle is equal to the sum of

__________________________________________. • The sum of the exterior angles in a triangle is .

Therefore, < A + < B + < C = . AND

< D = . < E = .

< F = . AND < D + < E + < F = .

The Sum of the Angles in a Quadrilateral • The sum of the interior angles of a quadrilateral is . • The sum of the exterior angles of a quadrilateral is .

Therefore, < A + < B + < C + < D = . AND < E + < F + < G + < H = .

Note: To form exterior angles, each side of the polygon is extended only once.

A

BE

C FD

A

H G

FE

D C

B


Page 11 of 18

Lesson 2: Interior and Exterior Angles of Triangles and Quadrilaterals b)

c)

38o x80o

p n

mg

42o

85o

95ok

97o j i


Page 12 of 18

Lesson 2: Interior and Exterior Angles of Triangles and Quadrilaterals 1 In each diagram, calculate the measure of the unknown angle. a)

b)

c)

d)

e)

f)

e

138° 22°a

7 5E b

70°

25°

x y

148°84°

72°c

df

78°126°

93°

75°

125°

130°

ef

g


Page 13 of 18

Lesson 03: Parallel Line Theorems Alternate Angles

Corresponding Angles

Example 1: Solve for the unknown angles. a)

b)

a

b

a

b

ab

50o

c

d ef g

c

d b50o50oe a

f g

a

b

Co-interior Angles


Page 14 of 18

Lesson 03: Parallel Line Theorems 1 In the diagram to the right, • and are equal because they are opposite

angles (X pattern) • and are equal because they are

corresponding angles (F pattern) • and are equal because they are alternate

angles (Z pattern) • and add to 180 ° because they are co-

interior angles ( C pattern)2 Determine the measure of each angle marked with a letter in these

diagrams. List the angle relationship for each calculation. a) a = Reason:

b = Reason:

b) c = Reason:

d = Reason: e = Reason:

y

w

z x

ba60 °

c40 °

70 °

ed


Page 15 of 18

Lesson 03: Parallel Line Theorems

c) f = Reason: g = Reason: h = Reason:

3 If two lines appear to be parallel but are not marked with parallel arrows,

can you apply any of the parallel line theorems? Explain your answer. 4 A parallelogram is formed by two sets of intersecting parallel lines. a) Sketch a parallelogram. Don’t forget to label the parallel sides. b) Label each interior angle, a, b, c and d. c) State all relationships that exist between the four interior angles?

f

hg

75°


Page 16 of 18

Lesson 04: Algebra in Geometry Recall: 1 The sum of the angles in any right angle is always . 2 The sum of the angles in any straight line is always . 3 When two or more lines intersect, the angles that are opposite one another

are always . 4 • The sum of the interior angles in a triangle is .

• The measure of an exterior angle of a triangle is equal to the of the measures of the two interior and opposite angles.

• The sum of the exterior angles in a triangle is . 5 • The sum of the interior angles of a quadrilateral is .

• The sum of the exterior angles of a quadrilateral is . 6 Alternate Angles are .

Corresponding Angles are .

Co-interior Angles add to be .

a

b

a

b

a

b


Page 17 of 18

Lesson 04: Algebra in Geometry Example 1: Solve for the unknown angles. a)

b)

x - 7

2x + 12x + 1

2x + 5 x - 5

2x + 52x + 5


Page 18 of 18

Lesson 04: Algebra in Geometry 1 Rewrite the following expressions using multiplication. Then expand each

expression. The first one is done for you. a) x + 6 + x + 6 + x + 6

= 3 (x + 6) = 3x + 18 b) k + 4 + k + 4 + k + 4 + k + 4 + k + 4 + k + 4 + k + 4 + k + 4 c) 2x - 3 + 2x - 3 + 2x - 3 + 2x - 3 d) - 4m - 1 - 4m - 1 - 4m - 1 - 4m - 1 - 4m - 1 - 4m - 1 2 Determine the measures of each of the following angles using an algebraic

“shortcut.” -x + 5

-2x-x + 5

-x + 5

1 5

Lesson 1: More Exponents Exponential Form: 25 = 2 x 2 x 2 x 2 x 2 5 times

1. Write each of the following as powers a) 5 x 5 =

b) 12 x 12 x 12 x 12 x 12 x 12 x 12 x 12 x 12 x 12 =

c) s x s x s x s x s =

d) 6a x 6a x 6a x 6a x 6a x 6a x 6a =

e) 2 x u x u x u x u x u x u =

f) 7 x 7 x 7 x 7 = 4 4 4 4

Exponent Rules: i) Power of 1: 51 = 5 ii) Multiplication Law: 54 x 53 = 54+3 = 57 iii) Division Law: 56 52 = 56-2 = 54 iv) Zero Law: 50 = 1 v) Power Law: (53) 2= 53*2 = 56 vi) Negative Law: 5-2 = ( ) 2

5 is the exponent 2 is the Base 25

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2. Using the Exponent Rules, solve the following questions. a) 74 x 73 x 72 b) 44 x 49 42

= 7 4 + 3 + 2

= 79 c) 27 22 x 21 d) ((-2)4) 2

e) 45 x ((4)2) 3 413 f) (-19)0

g) 40 x 70 – 90 h) 6-4

3. Using the Exponent Rules, evaluate the following:

a) k2 x k4 b) k3 ( k2 – 1) c) p (p2 p4)

Lesson 2: Surface Area and Volume

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Surface Area of any object is the sum of all the areas of all the faces of the object. Example: Take this cube of side length 3cm. There are 6 faces to a cube (4 sides, 1 top, 1 bottom). The area of 1 face is s x s = 3 x 3 = 9cm2 S.A. of the cube = 6 * 9 = 54 cm2

Solve for the surface areas of the following objects:

a) l = 3 cm w = 7cm h = 4 cm (Notice here that the top and bottom rectangles are the same the 2 different side rectangles are the same) S.A. of a rectangular prism = Area of all 6 faces = 2(area of 1st side) + 2(area of 2nd side) + 2(area of 3rd side) = = Volume is the amount of space that a figure occupies. Volume of any object = Area of the base x height V = B x H

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Example: The same cube of side length 3. This means the length, width and height of the cube is 3 cm. Volume = Area of the base x height = (3 x 3 ) x 3 = 27 cm3

Solve for the volumes of the following objects: a) The rectangular prism has length = 4cm width = 3cm and height = 7cm Volume = _________________ x __________ = = = b) Triangle base = 12 ft Triangle height = 20 ft Height of the prism = 25 ft

Volume of a Triangular Prism = Area of the Triangle x Height of prism =

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Documents

Grade 9 Applied Math Workbook