Outline for Math 8 Exam Collingwood School 0% Carlbeck, Ditson, Rogers, Town, Van der West Tuesday June 6 th 8:0am 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 : Number Connections (Chapter ) Multiples, Factors, Primes, Prime Factorization. and.4 HCF using Prime Factorization.5 LCM using Prime Factorization.6 Number Patterns and Variables.8 Unit : Fractions and Decimals (Chapter ) Fractions (Equivalent, Reduction, Comparison. Addition and Subtraction of Fractions. Multiplications and Division of Fractions. Decimals.4 Conversions between Fractions and Decimals.6 Unit : Integers (Chapter 4) Adding and Subtracting Integers 4. (Q - 8) & 4. (Q - 5) Multiplying Integers and Square and Cube Roots 4. (Q 9) Dividing Integers 4.4 Real Numbers and Order of Calculation 4.5 Order of Calculation (operation) con t Handout Unit 4: Algebraic Expressions (Chapter 5) Writing Algebraic Expressions 5. Evaluations of Algebraic Expressions 5. Algebraic Terms 5. 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. Solving Type II Equations CM 6.
Solving Type III Equations CM 6. Solving Type IV Equations CM 6.4 Equations Review CM 6.5 Open Sentences 6. Equations 6. Equations with Fractional/Decimal Coefficients 6. Evaluations of Formulae 6.4 Unit 6: Rate, Ratio, and Percent (Chapter 7) Speed and Rate Speed () Handout Speed and Rate Speed ( & ) Handout Speed, Rate and Unit Rate 7. (Q - ) Ratio 7. Percentage 7.4 and CM 8. Ratio/Percent Word Problems CM 8. Ratio/Percent Word Problems CM 8. Percentage Problems CM 8.8 Unit 7: Geometry (Chapter 9 & 0) Introduction to Geometry (Terms & Angles) Handout MH. &. Parallel Lines Handout MH.4 Types of Triangles Handout Properties of Triangles Handout Algebra and Geometry 9. and 9. Algebra and Angles 9. 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
Unit Number Sense Math 8 Exam Preparation. Complete the tables and explain the pattern a. In Out b. 0 5 6 6 9 7 8 Pattern:. What is a natural number? In Out 4 5 6 5 7 99 Pattern:. What is a multiple number? 4. What is a prime number? 5. Evaluate using the order of operations a. x 7 5 8 b. (9 9) 0 7 5 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. 40, 990 0 8. Find the LCM for the following a., 5 b. 65, 5, 75 9. Write a formula for m and n th term for the following sequences. a., 4, 9, 6, b. 6,, 8, 4, c., 5, 8,, d. 76, 67, 58, 49, Extra Practice New Elementary Text Book Section. page 6 #-6 even letters Section. page 0 #- even letters,, 4 Section.4 page #-4 even letters Section.5 page 5 #- even letters Section.6 page 7 #- even letters Section.7 page 0 #- even letters,, 4 Section.8 page 4 #-4, 5 even letters, 6,7
Answers a. b In Out 7 9 8 In Out 7 48 0 8 Multiply by then add Square then subtract. A natural number is.. See page 7 in your textbook. What is a multiple See page 8 in your textbook 4. What is a prime number.. See page 0 in your textbook 4a. 5 0 b. x c. 8 4 5a. 70 b. 6a. x7 b. x x5 7a. 60 = x x x 5 96 = x x x x x HCF x x = b. 40 = x x x 5 x 7 990 = x x x 5 x HCF x x 5 = 0 8a. = x x 5 = x x 5 LCM x x x 5 = 60 8b. 65= 5 x 5 = x x x 5 75 = 5 x 5 x 7 LCM x x x 5 x 5 x 7 x = 6 45 9a. m = n b. m = 6n c. n - d. m = 85 9n
Unit Fractions/Decimals Math 8 Exam Preparation. Mrs. Dixon divided 8 5 lb of candy among friends. How much candy did each friend receive?. Mr. Lamorie has 50 video games. He bought 0 7 of the games himself. The number of games Mr. McLean gave him is 5 of the number of games he bought. How many games did Mr. McLean give to Mr. Lamorie?. Evaluate a. 5 b. c. d. 4 5 8 5 8 e. 9 9 80 f. g. h. 5 8 0 0 8 4 4 5 8 7 i. 5 9 j. ( 7 ) (4 9) k. 6 9 8 5 6 4. Express each decimal as a fraction in the simplest form. a..6 b. 0. 6 c. 0.000 d. 0.85 5. Round off each of the following to decimal places. a. 0.955 b. 8 7 c. 9 8 d. 7 6. Calculate the following. 4.8.7 0.64 a. 8. x 0.8 - b. (.8 + ) 0. 0. 0.8 6 d. 9 e. ( 5) (0 4) 7 c..5.5 7 4 5 0 f. 4 4 7. Calculate a..5. 4 4 b. Extra Practice New Elementary Textbook Section. page 4 #-6 even letters Section. Page 44 #-6 even letters Section.4 page 49 #-8 even letters Section.6 page 6 #-8 even letters 6. 5.5 0.7 5 6
Answers. 5 5 Each friend received 8 4 4 5 lb of candy. 7. 50 75 bought games. 75 05 0 5 Mr McLean game 05 games to Mr. Lamorie games. a. 7 b. 5 c. 9 d. 4 9 4 e. f. 5 g. 9 8 84 h. i. 4 a. 4 8 j. 9 b. 5 7 k. c. 5000 7 d. 0 5. a. 0. b. 0.88 c. 0.89 d..4 6. a. 56.64 b. 4.75 c. 5.7 8 d 40.5 e. 0.6 f. 5 7. a..5 b..5
Unit Integers Math 8 Exam Preparation. Identify the following if Irrational, Undefined and/or Whole Numbers П 9 0 9 0 8. Evaluate the following a. -5 - (-) b. (-) (- 7) c. 90 (-00) d. -(-5) e. 85 (- 4) (+9) f. (-)(-0). Evaluate the following a. 44 b. 5 c. 4 8 d. e. 96 f. 78 4. Evaluate the following 0 0 a. 9 (-) b. c. (4) 8 4 7 ( -0) d. e. ( 4) ( 4)(0 ) f. 7 90 50 g. (-) 7 h. (-) 4 i. 0 5 j. 6 k. 7 ( 7) l. 4 5. Solve the following a. x 44 b. 98 x x c. 5 6. Evaluate a. 0.5 0. 75 8 b. 4 8 4 4 8 c. 4 d. [5. + (-7.5)] (-.4.6) x (-0.5) 4 e. (4) + 6 x (-4) f. 7 [(-4) + (-9) (-) (+)] + (-4)
Answers to Unit Integers. П 9 0 9 8 0 Whole Irrational Irrational Whole Undefined Undefined. a. 7 b. -5 c. 9 d. 5 e. -08 f. 60. a. b. 5 c. d. undefined e. 6 f. 4. a. 0 b. c. -5 d. e. -6 f. 5 g. - h. 7 i. j. 6 k. 4 l. - 5. a. x b. x 7 c. x 6, 4 6. a. c. 5 b. 8 4 7 d. -4. e. - 5 f. Extra Practice- New Elementary Textbook 4. #-8 4. #-4 even letters, 8-0 4. # even letters, -7, 9 4.4 #-0 even numbers 4.5 #-5, 7 even letters, 8 *4.6 #-0 even numbers
Unit 4 Algebraic Expressions Math 8 Exam Preparation. 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 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 6 meters g. The sum of four consecutive numbers. A rectangle has a length of 4a cm and width of a 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 =.5 cm. Evaluate the following by taking x =. y = 4, z = 5 z b. a. x y z xy x x yz c. 4z x 4. Evaluate the following using r = -. s = 4, t = -6 t a. s s r b. rt s 4 c. t s r s t 5. Simplify the following a. 4a 9a b. ( 4a )(9a) c. e. 4x y f. i. m. ab 6a b ( x x)( x) 6 n. j. 5a 0b 9a b 6a b x( y) z y( z) x ab b g. ( 4xy)(x ) h. k. ) ( 6x )(6y d. ) r r r ( a b) ( a b l. ( a b) ( a b) o. r r 4r r 5r r x y z x x p. y q. p q q p r. zx y x( y z) y( z x) 6. Extract the common factors from the following a. 4a 9a b. a b d. 5a 5b 00 e. 6x 8xy 0x f. 4 c. 8a 6a ab 5xy 0x y 0xy 0x y
Answers Unit 4 Algebraic Expressions h. a. 00 k metres b. 000 millimeters c. n 5 d. 8w m e. 4s units f. g. x + (x + ) + (x + ) + (x + ) = 4x + 6 6h m = 8 h m. a. 4 a cm b. a cm c. 5 cm & 75 cm. a. 5 b. 6 c. 4. a. 6 b. c. 84 5. a. a b. e. 4x y f. i. b a j. m. 0 n. q. 4p 4q r. 0 6a c. 6a d. 6 xy a b g. 8x y h. r r b k. a l. 0 o. 4r 5r p. x y z 6. a. a 4 9 b. 7a 6b c. a6a b d. 5a b 0 e. x 4y 5x f. 5xy x y 4xy Extra Practice- New Elementary Textbook 5. #-6 even numbers 5. #-4 even letters 5. #-4 even letters 5.4 #-4 even letters 5.5 #-4 even letters
Unit 5 Algebraic Equations Math 8 Exam Preparation. Solve and double check w a. 4a 00 b. 5.5 e. x 99 f. 7 w i.. 5 j. 4 8 c. b 9 0 d. x 4 ( x 9) 4 q g. 6q 8 h. 4 b k. z l. 70 x m. n. o.. Solve and double check a. 6 q 8 q ( x 4) w b. 4 c.. 5 4 d. 4 a 78 a e. x x 5 5 f. ( x ) (x ) g. w 98 h. 7( x ) ( x 7) i. (x ) x 4 j. 6x 5x k. x 5x l. x x 4 w w n. m. x x 4 4 o. ( x ) ( x ) 6 5. Solve the following: a. If find a when t = 0, q = 0 and r = 0 b. If find r is b=, h=4 and k= c. If find t when Answers to Unit 5 Algebraic Equations. a. a = 5 b. w =.5 c. b = -9 d. x = 7 e. x = 0 f. q = 8 g. q = 5 h. x = - i. w = 7 5 j. b = 6 k. z = - l. x = 9 m. x = 7 n. x = 6, x = 4 o. x = ±
. a. q = 7 40 b. x = c. w = 7 d. a = 5 e. x = 0 f. x = - g. w = 50 8 h. x = 5 i. x = j. x = 4 5 k. x = 7 l. x = 4 75 m. w = 5 n. x = -0 o. x = 7. a. b. c. Extra Practice- New Elementary Textbook 6. #-4 even letters 6. #-0 even letters 6.4 #-4 even numbers
Math 8 Exam Preparation Unit 6 Rate, Ratios & Percents. Sam ran at a speed 450 m/min for 0 seconds. How far did he run?. Mr. Clark had to arrive at the airport at 4:00 pm. The airport is 60 km from his house. If he starts at :0 pm from his house, at what speed should he drive so as to reach the airport exactly on time?. David and Sarah took 6 hours to cover / of a road trip. They covered the remaining 0 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 50 km apart at noon and passed each other 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 05 min and then at an average speed of 40 km/h for the next 4 h. What was his average speed for the whole journey? 6. Express each of the following ratios as simple as possible. a..5:.5 b. : 4 c. 85 m to km d. 50 cm : m 7. Express the following as percents a. 4 5 b. 0.55 c. 7 5 d. 9 8 Solve for the missing value in each case a. 4% of 75 is x b. x% of 0 is 48 c. 4 of x is 80% 9. Ning scored 99 on her last test. She answered 0% of the questions incorrect. What was the test out of? 0. The ratio of boys to girls in a school choir is 5:4. There are girls. If another 6 girls join the choir, what will be the new ratio of boys to girls?. Liana bought a new basketball. The tax was $.5, which was 7%. How much was the basketball before tax?. Complete the following conversions a. 450 minutes = hours b. 4 g = kg c..8 days = hours min d. 00 m/s = km/h. Tess bought a computer for $00. She decided to sell it years later for $400. What was the percent decrease of the computer?
Answers to Unit 6 Rate, Ratios & Percents. D st 450m / min 0.5min 5metres D 60km 600 s 40km/ t.5hr 5. h trip 0 D 60km s 6km/ h t 0hr. km Total Distance = 60km Total time = 0 hours 4. Car D st 80km/ h hrs 60km Bus Distance = 50 km 60 km = 90 km Bus Speed D 90km s 45km/ h t hr 5. Remember: you can NOT average average speeds. You need total distance & total time. First leg of journey Second leg of journey D s t (80km/ hr) (.75hr) 40km D s t (40km/ hr) ( hr) 0km 4 Total Average Speed = s Dt t 40km 0km 70km 68km hr.75hr 0.75hr.5hr t / t 6 a. 5:7 b. 8:9 c. 7:00 d. :00 7a. 6% b. 5.5 % c. 05.6% d.. % 8a. x 75 4 00 b. 48 x 0 00 c. 4 x 80 00 x 4.5 x 60 x 80 9. 99 x 90 00 x = 0, The test was out of 0 marks 0. 40:8 = 0:9
Boys 40 Boys Girls 8 + 6 new = 8 Girls. $.5 x 7 00 x= 45 The discus cost $45 before tax. a. 7.5 hours b. 0.4 kg c. 67 hours minutes d. 60 km/h. Where 800 is the amount the computer decreased by. X = 66.7% Therefore the computer decreased by 66.7% Extra Practice: 7. page 74 75 #- 7. page 80 8 #-6, 9-0 7.4 page 90 #-6 Mickelson chapter:
Geometry Review ) Find the value of x: x - 5 x + 5 ) Find the value of x and y: x y 60 ) Find the values of x, and y in the following figures: a. b. 7x + 4x + 5 x + 5 y + 6 y - 0 4) Calculate the value of x in the following diagram: x 78 5
5) Find the value of x and y 60 x y 7 6) Find the value of x, y, and z in the following diagrams: a. b. 48 x x 8 y z c. x 9 x 7) Find the of x: 4 67 x
8) x + 0 y 6 x + 0 9) x 0 6 0) Draw two parallel lines. Label the angles and show the three angle properties for parallel lines. ) The angles of a triangle are n 0, n 0, n 0 a. Name the kind of triangle which has these angles b. Find the value of n. ) The exterior angles of a quadrilateral are x 0, x 0, 95 0, and 5 0. Calculate a. Find the value of x b. The largest interior angle. ) The interior angles of a pentagon are x 0, x 0, x 0, 4x 0, and 5x 0 respectively. Find the value of x. 4) Find the number of sides for a regular polygon if each interior angle is 7 times its exterior angle. 5) One angle of a triangle is 7 o. The second angle is twice as large as the third angle. Find the size of each angle in the triangle. 6) Find two complementary angles where one angels is o larger than the other angle
7) One angle of a scalene triangle is 0 o. The second angle is twice as large as the third angle. What is the size of each angle? Answers:. 0. x = 0 0, y = 0 0. a) x = 8 0 b) x = 5.5 0 y = 87 0 4. x = 0 0 5. x =.5 0 y= 9.5 0 6. a) x = 5 0 b) x = 0 0 y = 0 0 z = 60 0 c) x = 9 7. 4 0 8. x = 0 0 y =4 0 9. x = 4 0 0. Alternate interior, co-interior, corresponding ) a. isosceles b..5 0 ) 0 0, 0 0, ) 6 0 4) 6 sides 5) 5 o and 0 o, 6) 9 o, 5 o 7) 50 o, 00 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. Graph the following points. (make sure to label everything!) a. (, ) b. (-4, 5) c. (-5, -) d. (6, -4). Label the following all of the quadrants
. 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 points. (4 marks) y x 5. Using the table of values provided, graph the following line. Be sure to list at least points. (4 marks)
Calculate which of the following points lie on the line x +6y 6 = 0? Circle ALL the points that lie on the line. ( marks) a) ( -,/ ) b) (,-/ ) c) (, 0 ) d) ( 6,- ) e) ( 4, 7 ) 6. Calculate the slope between the following points. Label the slope as undefined or zero slope if needed: (mark each) a) (,7 ) and (,9) b) ( 4, -5 ) and ( 4, -) 7. Graph the line y + x + 6 = 0. Find the slope, y intercept and x intercept. (4 marks) Slope: Y intercept: X intercept: 8. If the point ( -, 4) lies on the line y = mx + 7 find the slope. (marks) 9. Find the equation of a line with the y intercept of and passes through the point ( 5,-8 ). ( marks)
0. Write the equation for the following line: ( mark) _4-5 _ 5 _- _- 4 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: ) Slope Intercepts Form ) Standard Form Finding the slope of a line Finding the x-intercepts and y-intercepts of a line Finding the equation of a line