Outline for Math 8 Exam Collingwood School 20% Carlbeck, … · 2019-11-17 · Collingwood Math...

Collingwood Math Eight

Outline for Math 8 Exam Collingwood School

20% Carlbeck, Ditson, Rogers, Town, Van der West

Tuesday June 16th 8:30am

Below you will find a list of all the topics we have covered this year. Next to each topic is an Exercise

number that refers to a section in the text book. If there are no initials in front of the number, then this

section is in your blue hard cover book (New Elementary Math) and if you see the initials CM it means

your green coil book (Canadian Math). Beside each unit header there is a percentage. This represents the

percent of questions on the exam that come from this unit.

Tips for being successful on your exam:

Review your notes from every chapter

Redo any quizzes or tests you may have

Work through the review package and make sure to go over concepts that you

have trouble with

Set up tutorial times with your teacher if you need extra help. Do this early,

leaving things to the last minute does NOT = success

Unit 1: Number Connections (Chapter 1)

Multiples, Factors, Primes, Prime Factorization 1.3 and 1.4

HCF using Prime Factorization 1.5

LCM using Prime Factorization 1.6

Number Patterns and Variables 1.8

Unit 2: Fractions and Decimals (Chapter 2)

Fractions (Equivalent, Reduction, Comparison 2.1

Addition and Subtraction of Fractions 2.2

Multiplications and Division of Fractions 2.3

Decimals 2.4

Conversions between Fractions and Decimals 2.6

Unit 3: Integers (Chapter 4)

Adding and Subtracting Integers 4.1 (Q 1 - 8) & 4.2 (Q 1 - 5)

Multiplying Integers and Square and Cube Roots 4.3 (Q 1 – 9) Dividing Integers 4.4 Real Numbers and Order of Calculation 4.5 Order of Calculation (operation) con’t Handout 1

Unit 4: Algebraic Expressions (Chapter 5)

Writing Algebraic Expressions 5.1

Evaluations of Algebraic Expressions 5.2

Algebraic Terms 5.3

Use of Brackets 5.4

Collecting Like Terms 5.5

Unit 5: Algebraic Equations (Chapter 5 New Elem, Chapter 6 Can. Math)

Solving Type I Equations CM 6.1

Solving Type II Equations CM 6.2


Solving Type III Equations CM 6.3

Solving Type IV Equations CM 6.4

Equations Review CM 6.5

Open Sentences 6.1

Equations 6.2

Equations with Fractional/Decimal Coefficients 6.3

Evaluations of Formulae 6.4

Unit 6: Rate, Ratio, and Percent (Chapter 7)

Speed and Rate Speed (1) Handout

Speed and Rate Speed (2 & 3) Handout

Speed, Rate and Unit Rate 7.1 (Q 1- 12)

Ratio 7.2

Percentage 7.4 and CM 8.1

Ratio/Percent Word Problems CM 8.2

Ratio/Percent Word Problems CM 8.3

Percentage Problems CM 8.8

Unit 7: Geometry (Chapter 9 & 10)

Introduction to Geometry (Terms & Angles) Handout MH 3.1 & 3.2

Parallel Lines Handout MH 3.4

Types of Triangles Handout

Properties of Triangles Handout

Algebra and Geometry 9.1 and 9.2

Algebra and Angles 9.3

Algebra and Parallel Lines 9.4

Unit 8: Graphing Linear Equations (All Handouts)

Plotting points on a coordinate plan

Plotting lines in slope-intercept form

Plotting lines in standard form

Finding the x-intercept and y-intercept

Finding the slope of a line

Finding the equation of a line given a graph


Math 8 Exam Preparation

Unit 1 – Number Sense

1. Complete the tables and explain the pattern

a. b.

Pattern: ________________ Pattern: ________________

2. What is a natural number?

3. What is a multiple number?

4. What is a prime number?

5. Evaluate using the order of operations

a. 3 x 3571381 b. 0

2

5713

10)9293(2

6. Find the prime factors for the following (write using index notation)

a. 56 b. 540

7. Find the HCF for the following groups of numbers

a. 60, 96 b. 420, 990

8. Find the LCM for the following

a. 12, 15 b. 65, 135, 175

9. Write a formula for m and nth term for the following sequences.

a. 1, 4, 9, 16, … b. 6, 12, 18, 24, … c. 2, 5, 8, 11, … d. 76, 67, 58, 49, …

Extra Practice – New Elementary Text Book

Section 1.2 page 6 #1-6 even letters

Section 1.3 page 10 #1-2 even letters, 3, 4




Section 1.7 page 20 #1-2 even letters, 3, 4

Section 1.8 page 24 #1-4, 5 even letters, 6,7

In Out

3 10

5 16

6 19

7

28

In Out

2 3

4 15

6 35

7

99


Answers

1a. 1b

In Out

7 22

9 28

Multiply by 3 then add 1 Square then subtract 1

2. A natural number is….. See page 7 in your textbook

3. What is a multiple…… See page 8 in your textbook

4. What is a prime number….. See page 10 in your textbook

4a. 510 b. x12 c. 84

5a. 270 b. 2

6a. 23x7 b. 22x33x5

7a.

60 = 2 x 2 x 3 x 5

96 = 2 x 2 x 2 x 2 x 2 x 3

HCF 2 x 2 x 3 = 12

b. 420 = 2 x 2 x 3 x 5 x 7

990 = 2 x 3 x 3 x 5 x 11

HCF 2 x 3 x 5 = 30

8a. 12 = 2 x 2 x 3

15 = x 3 x 5

LCM 2 x 2 x 3 x 5 = 60

8b. 65= 5 x 13

135 = 3 x 3 x 3 x 5

175 = 5 x 5 x 7

LCM 3 x 3 x 3 x 5 x 5 x 7 x 13 = 61 425

9a. m = n2 b. m = 6n c. 3n - 1 d. m = 85 – 9n

In Out

7 48

10 28



Unit 2 – Fractions/Decimals

1. Mrs. Dixon divided 8

5lb of candy among 3 friends. How much candy did each friend

receive?

2. Mr. Lamorie has 250 video games. He bought 10

7of the games himself. The number of

games Mr. McLean gave him is 5

3of the number of games he bought. How many games did

Mr. McLean give to Mr. Lamorie?

3. Evaluate

a. 3

1

4

1 b.

3

1

5

2 c.

8

3

12

51 d.

8

33

12

512

e. 3

2

2

1 f.

10

9

8

3 g.

81

80

10

9 h.

2

4

32

4

15

i.

18

139

9

85

6

512 j. )914()37( k.

3

2

6

1

12

22

15

7

4. Express each decimal as a fraction in the simplest form.

a. 1.6 b. 6.0 c. 0.0002 d. 0.85

5. Round off each of the following to 2 decimal places.

a. 0.1955 b. 8

7 c.

9

8 d.

7

11

6. Calculate the following.

a. 8.3 x 20.8 -

3.0

8.4 b. (2.8 +

8.0

64.0)

3.0

7.2 c. 25.235.7

53

43

d. 27

2639 e. )1410()2521( f.

41

32 410

7. Calculate

a.

4

32.125.3

2

14 b.

16

15

5

2

7.0

3.65.2

Extra Practice – New Elementary Textbook


Section 2.3 Page 44 #1-6 even letters




Answers

1. 24

5

3

1

8

5 Each friend received

24

5lb of candy.

2. 17510

7250 bought games. 105

5

3175 games.

Mr McLean game 105 games to Mr. Lamorie

3 a. 12

7 b.

15

11 c.

24

191 d.

24

19

e. 3

1 f.

12

5 g.

9

8 h.

121

84

i. 9

428 j.

2

3 k.

33

7

4 a. 5

31 b.

3

2 c.

5000

1 d.

20

17

5. a. 0.2 b. 0.88 c. 0.89 d. 1.14

6. a. 156.64 b. 14.75 c. 5.7

d 40.5 e. 0.6 f. 51

128

7. a. 32.5 b. 22.125



Unit 3 – Integers

1. Identify the following if Irrational, Undefined and/or Whole Numbers

121 П 3 9 9

0

0

12 8

2. Evaluate the following

a. -5 - (-12) b. (-122) – (- 71) c. 190 – (-1001)

d. -(-125) e. – 285 – (- 124) – (+921) f. (-12)(-30)


a. 144 b. 3 125 c. 4 81

d. 121 e. 1296 f. 3 1728


a. 9 – 11 ÷ (-11) b. 82

10120

c. – 2 – 1 – 3(4)

d. 21

2724

e. )1210)(4()43(2 f.

72

110) - 3(2

g. (-1)17 h. (-2)4 – 32 i.

25

50

10

90

j. 2

3 62

k. )17(273 l. 2

243

5. Solve the following

a. 1442 x b. 982 2 x c. 2512x

6. Evaluate

a. 375.04

3

8

15.0

b.

8

1

4

1

2

1

4

1

8

1

2

1

c. 41

21

31 2

3

431

d. [5.3 + (-7.5)] – (-1.4 – 2.6) x (-0.5)

e. –(4)2 – 12 + 6 x (-4) f. 7 – 3[(-4) + (-9) (-3) – (+2)] + (-4)


Answers to Unit 3 – Integers

1.

121 П 3 9

9

0

0

12 8

Whole Irrational Irrational Whole Undefined Undefined

2. a. 7 b. -51 c. 1191

d. 125 e. -1082 f. 360

3. a. 12 b. 5 c. 3

d. undefined e. 36 f. 12

4. a. 10 b. 2 c. -15

d. 1 e. -16 f. 5

g. -1 h. 7 i. 11

j. 16 k. 14 l. -12

5. a. 12x b. 7x c. 4,6 x

6. a. 8

1 b.

4

5

c. 12

37 d. -4.2

e. - 52 f. 12

Extra Practice- New Elementary Textbook

4.1 #1-8

4.2 #1-4 even letters, 8-10

4.3 #1 even letters, 2-7, 9

4.4 #1-30 even numbers

4.5 #1-5, 7 even letters, 8

*4.6 #1-20 even numbers



Unit 4 – Algebraic Expressions

1. Write an algebraic expression for each of the following

a. The number of cm in k metres

b. The number of meters in h millimeters

c. Choose a number. Multiply it by 2 and subtract 5.

d. The area of a rectangle if the length is 8 metres.

e. The perimeter of a square.

f. The area of a triangle with a base of 16 meters

g. The sum of four consecutive numbers

2. A rectangle has a length of 4a cm and width of 3a cm.

a. Write an algebraic expression for the perimeter of the rectangle.

b. Write an algebraic expression for the area of the rectangle.

c. Find the perimeter and area if a = 2.5 cm

3. Evaluate the following by taking x = 3. y = 4, z = 5

a. yxz b. xz

xy

c.

x

yz

z

x

24

4. Evaluate the following using r = -2. s = 4, t = -6

a.

s

tsr b.

t

s

s

rt c. 432 rst

5. Simplify the following

a. aa 94 b. )9)(4( aa c. b

ab

2

12

d. )6)(6( yx

e. yx 24 f. b

a

10

5

g. )2)(4( 2xxy h. 22 212 rrr

i. ba

ab2

2

26

13

j.

ba

ba2

22

26

39

k. )()( baba l. )()( baba

m. 26)3)(2( xxx n. xzy

zyx

)(33

)(22

o.

r

r

r

rrr

3

15

2

43

232

p. yxxzyx 2 q. pqqp 22 r. )()( xzyzyxyxz

6. Extract the common factors from the following

a. aa 94 b. 1 ba 124 c. abaa 3618 2

d. 100515 ba e. 21086 xxyx f. 2222 2010105 yxxyyxxy


Answers Unit 4 – Algebraic Expressions

1. a. k100 metres b. 1000

h millimeters c. 2n – 5

d. 8w m2 e. 4s units f. 2

16hm2 = h8 m2

g. x + (x + 1) + (x + 2) + (x + 3) = 4x + 6

2. a. 14 a cm b. 12 a2 cm2 c. 35 cm & 75 cm2

3. a. 35 b. 6 c. 2

1

4. a. 6 b. 3

11 c. 84

5. a. a13 b. 236a c. a6 d. xy36

e. yx 24 f. b

a

2 g. yx38 h. rr 211 2

i. a

b

2 j.

2

3b k. a2 l. 0

m. 0 n. 3

2 o. 254 rr p. zyx 22

q. qp 44 r. 0

6. a. 94 a b. ba 672 c. baa 263

d. 2035 ba e. xyx 5432 f. xyyxxy 42215



5.2 #1-4 even letters






Unit 5 – Algebraic Equations

1. Solve and double check

a. 1004 a b. 55.2

w c. 019 b d.

4

1

3

1x

e. 9912 x f. 127

3q g. 2826 q h. 4

4

)19(

x

i. 5.212

w

j. 2

1

8

1

4

3b k. 111 z l. 21170 x

m. n. o.

2. Solve and double check

a. qq 28126 b. 44

)4(

x c. 5.21

2

w

d. aa 7834 e. 5

2

2

11

5

3

2

1 xx f. )12()1( xx

g. 9812 w h. )7(2)2(7 xx i. xx 21)13(4

3

j. 125126 xx k. 2523 xx l. 4

1

3

1

3

2

2

1 xx

m. 2

112

ww n.

4

4

3

2

xx o.

5

)1(2

6

)2(

xx

3. Solve the following:

a. If find a when t = 120, q = 20 and r = 10

b. If find r is b=3, h=4 and k=12

c. If find t when

Answers to Unit 5 – Algebraic Equations

1. a. a = 25 b. w = 12.5 c. b = -19 d. x =12

7

e. x = 10 f. q = 28 g. q = 5 h. x = -3

i. w = 7 j. b = 6

5 k. z = -12 l. x = 9

m. x = 7 n. x2 = 16, x = 4 o. x = ±3


2. a. q = 7

40 b. x = 12 c. w = 7

d. a = 15 e. x = 10

1 f. x = -2

g. w = 50 h. x = 5

28 i. x =

75

3

j. x = 24 k. x = 7

5 l. x =

4

3

m. w = 3

5 n. x = -20 o. x =

17

2

3. a. b. c.







Unit 6 – Rate, Ratios & Percents

1. Sam ran at a speed 450 m/min for 30 seconds. How far did he run?

2. Mr. Clark had to arrive at the airport at 4:00 pm. The airport is 60 km from his house. If

he starts at 2:30 pm from his house, at what speed should he drive so as to reach the

airport exactly on time?

3. David and Sarah took 6 hours to cover 2/3 of a road trip. They covered the remaining

120 km in 4 hours. Find the average speed for the whole trip.

4. A car and a bus were traveling at uniform speeds. They were 250 km apart at noon and

passed each other 2 pm. If the car was traveling at 80 km/hr, find the speed of the bus.

5. A bus driver drove at an average speed of 80 km/h for the first 105 min and then at an

average speed of 40 km/h for the next 43 h. What was his average speed for the whole

journey?

6. Express each of the following ratios as simple as possible.

a. 2.5:3.5 b. 4

3:

3

2 c. 85 m to km d. 50 cm2 : 1 m2

7. Express the following as percents

a.

4

25 b. 0.155 c.

27

125 d.

9

1

8 Solve for the missing value in each case

a. 14% of 175 is x b. x% of 30 is 48 c. 224 of x is 80%

9. Ning scored 99 on her last test. She answered 10% of the questions incorrect. What

was the test out of?

10. The ratio of boys to girls in a school choir is 5:4. There are 32 girls. If another 6 girls

join the choir, what will be the new ratio of boys to girls?

11. Liana bought a new basketball. The tax was $3.15, which was 7%. How much was the

basketball before tax?

12. Complete the following conversions

a. 450 minutes = _____ hours b. 142 g = ______ kg

c. 2.8 days = _____ hours _____ min d. 100 m/s = _____ km/h

13. Tess bought a computer for $1200. She decided to sell it 3 years later for $400.

What was the percent decrease of the computer?


Answers to Unit 6 – Rate, Ratios & Percents

1. metresmtsD 225min5.0min/450

2. hkmhr

km

t

Ds /40

15

600

5.1

60

3. kmtrip 1203

1 Total Distance = 360km Total time = 10 hours

hkmhr

km

t

Ds /36

10

360

4. Car kmhrshkmtsD 1602/80

Bus Distance = 250 km – 160 km = 90 km

Bus Speed hkmhr

km

t

Ds /45

2

90

5. Remember: you can NOT average – average speeds. You need total distance & total time.

First leg of journey Second leg of journey

kmhrhrkmtsD 140)75.1()/80(1 kmhrhrkmtsD 30)4

3()/40(2

Total Average Speed =

hrkmhr

km

hrhr

kmkm

t

Ds

t

tt /68

5.2

170

75.075.1

30140

6 a. 5:7 b. 8:9 c. 17:200 d. 1:200

7a. 16% b. 15.5 % c. 205.6% d. %1.11

8a. 100

14

175

x b.

10030

48 x c.

100

80224

x

5.24x 160x 280x

9. 100

9099

x x = 110, The test was out of 110 marks

10. 40:38 = 20:19


32 + 6 new = 38 Girls

40 Boys

8

32

Girls

Boys

11. 100

715.3$

x x= 45 The discus cost $45 before tax.

12 a. 7.5 hours b. 0.142 kg

c. 67 hours 12 minutes d. 360 km/h

13. Where 800 is the amount the computer decreased by.

X = 66.7% Therefore the computer decreased by 66.7%

Extra Practice:

7.1 page 174 – 175 #1-11

7.2 page 180 – 181 #1-6, 9-20

7.4 page 190 #1-6

Mickelson chapter:


Geometry Review

1) Find the value of x:

2) Find the value of x and y:

3) Find the values of x, and y in the following figures:

a. b.

4) Calculate the value of x in the following diagram:

152

78

x

2x + 5

3x - 25

y

603x

2x + 5

7x + 13

y - 10y + 16

4x + 15


5) Find the value of x and y

6) Find the value of x, y, and z in the following diagrams:

a. b.

c.

7) Find the of x:

60

117

y

x

2x

82

48

z2y

3x

2x

x

29

x

24

67


8)

9)

10) Draw two parallel lines. Label the angles and show the three angle properties for parallel lines.

11) The angles of a triangle are 2n0, 3n

0, 3n

0

a. Name the kind of triangle which has these angles

b. Find the value of n.

12) The exterior angles of a quadrilateral are 2x0, 3x

0, 95

0, and 115

0. Calculate

a. Find the value of x

b. The largest interior angle.

13) The interior angles of a pentagon are 3x0, 2x

0, x

0, 4x

0, and 5x

0 respectively. Find

the value of x.

14) Find the number of sides for a regular polygon if each interior angle is 17 times

its exterior angle.

15) One angle of a triangle is 27o. The second angle is twice as large as the third angle. Find the size

of each angle in the triangle.

16) Find two complementary angles where one angels is 12o larger than the other angle

y

163x + 10

x + 10

120

36

2x


17) One angle of a scalene triangle is 30o. The second angle is twice as large as the third angle.

What is the size of each angle?

Answers: 1. 220

2. x = 200, y = 120

0 3. a) x = 18

0 b) x = 15.5

0 y = 87

0 4. x = 130

0 5. x = 31.5

0 y=

91.50

6. a) x = 250 b) x = 20

0 y = 30

0 z = 60

0 c) x = 29 7. 43

0 8. x = 30

0 y =24

0 9. x = 42

0 10.

Alternate interior, co-interior, corresponding 11) a. isosceles b. 22.50 12) 30

0, 120

0, 13) 36

0 14) 36

sides 15) 51o and 102

o, 16) 39

o, 51

o 17) 50

o, 100

o

Extra practice: Please see your orange and pink handouts. You are able to complete all

these questions. If you would like a new one or would like to answer key please come and see

me and I will email it to you.


Graphing Review

1. Graph the following points. (make sure to label everything!) a. (2, 3) b. (-4, 5) c. (-5, -1) d. (6, -4)

2. Label the following all of the quadrants


3. Find the coordinates of the following points:

A ________ B ________ C ________ D ________


4. Using the table of values provided, graph the following line. Be sure to list at least 3 points. (4 marks)

22

1 xy

5. Using the table of values provided, graph the following line. Be sure to list at least 3 points. (4 marks)


Calculate which of the following points lie on the line 2x +6y – 6 = 0 ? Circle ALL the points that lie on the line. (2 marks) a) ( -2,2/3 ) b) ( 1,-2/3 ) c) ( 3, 0 ) d) ( 6,-1 ) e) ( 4, 7 ) 6. Calculate the slope between the following points. Label the slope as undefined or ‘zero slope’ if needed: (1mark each) a) ( 1,7 ) and ( 3,9) b) ( 4, -5 ) and ( 4, -11) 7. Graph the line 3y + 2x + 6 = 0. Find the slope, y intercept and x intercept. (4 marks)

Slope: _________________ Y intercept: _______________ X intercept:_______________

8. If the point ( -3, 4) lies on the line y = mx + 7 find the slope. (2marks) 9. Find the equation of a line with the y intercept of 2 and passes through the point ( 5,-8 ). (2 marks)


10. Write the equation for the following line: (1 mark)

Equation: _______________________

** We just finished this unit and the key will be very long, please find answers from PCR.

Extra Practice: Worksheets: Worksheets are on collingwoodmath.weebly.com

Graphing Points: Points in a coordinate plane

Graphing a line:

1) Slope Intercepts Form

2) Standard Form

Finding the slope of a line

Finding the x-intercepts and y-intercepts of a line

Finding the equation of a line

_ 4

_ 2

_ - 2

_ - 4

_ - 5 _ 5

Outline for Math 8 Exam Collingwood School 20% Carlbeck, … · 2019-11-17 · Collingwood Math...

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Transcript of Outline for Math 8 Exam Collingwood School 20% Carlbeck, … · 2019-11-17 · Collingwood Math...