Year 8 Maths Revision Exercises PDF

YEAR 8 REVISION EXERCISES NAME: _________ WHOLE NUMBER AND DECIMALS  Y8 – Whole Number and Decimals – Revision Exercises 1. Adding Whole Numbers: 93145 + 81319 51666 + 72022 64755 + 96704 18494 + 90697 2. Subtracting Whole Numbers: 3. Mult...

YEAR 8 REVISION EXERCISES NAME: _________ WHOLE NUMBER AND DECIMALS  Y8 – Whole Number and Decimals – Revision Exercises 1. Adding Whole Numbers: 93145 + 81319 51666 + 72022 64755 + 96704 18494 + 90697 2. Subtracting Whole Numbers: 3. Multiplying Whole Numbers: 4. Dividing Whole Numbers: 5. Adding Decimal Numbers: 3.79 + 5.28 4.75 + 3.294 9.76 + 2.381 +24.7 6. Subtracting Decimal Numbers:  5.92 – 3.87 28.105 – 7.99 73 – 4. 859 7. Multiplying Decimal Numbers: 8.93 x 4.1 0.723 x 2.5 135 x 0.58 8. Dividing Decimal Numbers: 9. Place Value: a. What is the place value of the 3 in 89273.56? b. What is the place value of the 9 in 89273.56? c. What is the place value of the 6 in 89273.56? d. What is the place value of the 8 in 89273.56?  e. What is the place value of the 5 in 89273.56? 10. Rounding: a. Round 72549.5 to the nearest ten. b. Round 72549.5 to the nearest one. c. Round 72549.5 to the nearest thousand. d. Round 72549.5 to the nearest ten thousand. e. Round 72549.5 to the nearest hundred. 11. Factors, Primes and Multiples: a. List all the factors of 36: b. List the first 7 prime numbers: c. List the first 5 multiples of 6: d. Are even numbers prime? Why or why not? e. List all the factors of 45: 12. Highest Common Factor and Lowest Common Multiple: Find the highest common factor of the following: a. 15 and 20 a. 24 and 36 a. 45 and 81 a. 6 and 24 Find the lowest common multiple of the following: a. 3 and 5 a. 4 and 12 a. 5 and 7 a. 12 and 15 13. Word Problems: a. Mandy buys 5 packs of organic milk from the neighbourhood store. If each pack is priced at $3.96, how much does Mandy spend in all on the purchase of milk? b. Peter cuts a piece of string into three lengths. One is 4.26cm long, one is 7.54cm long and the third is 3.9cm long. How long was the string before it was cut?  c. George's dad bought 696.60 centimetres of string. If he cut the string into 12 equal pieces, what would be the length of each piece? d. Sally's high school played 970 soccer games this year, 113 of the games were played at night. She attended 355 games. How many soccer games did Sally miss? e. Calvin paints pictures and sells them at art shows. He charges $56.25 for a large painting. He charges $25.80 for a small painting. Last month he sold six large paintings and three small paintings. How much did he make in all? Y8 – Whole Number and Decimals – Answers 1. Adding Whole Numbers: 2. Subtracting Whole Numbers: 3. Multiplying Whole Numbers: 4. Dividing Whole Numbers: 5. Adding Decimal Numbers: 3.79 + 5.28 = 9.07 4.75 + 3.294 = 8.044 9.76 + 2.381 +24.7 = 36.841 6. Subtracting Decimal Numbers: 5.92 – 3.87 = 2.05 28.105 – 7.99 = 20.115 73 – 4. 859 = 68.141 7. Multiplying Decimal Numbers: 8.93 x 4.1 = 36.613 0.723 x 2.5 = 1.8075 135 x 0.58 = 78.3 8. Dividing Decimal Numbers: 9. Place Value: a. Ones place b. Thousands place c. Hundredths place d. Ten thousands place e. Tenths place 10. Rounding: a. 72550 b. 72550 c. 73000 d. 70000 e. 72500 11. Factors, Primes and Multiples: a. 1,2,3,4,6,9,12,18,36 b. 2,3,5,7,11,13,17 c. 6,12,18,24,30,36 d. No, in general even numbers are not prime because they can be divided by 2. However, 2 is the only even prime number because you can only divide it by one and itself. e. 1,3,5,9,15,45 12. Highest Common Factor and Lowest Common Multiple: Highest Common Factor is… a. 5 b. 12 b. 9 b. 6 Lowest Common Multiple is… a. 15 a. 12 a. 35 a. 60 13. Word Problems: a. 3.96 x 5 = $19.80 b. 15.7cm c. 58.05 cm d. Sally missed 615 games e. 56.25 x 6 + 25.80 x 3 = 337.5 + 77.4 = $414.90  ORDER OF OPERATIONS AND INTEGERS  Y8 – Order of Operations and Integers – Revision Exercises 1. BEDMAS a. 18 ÷ 3 x 9 b. (5 + 2) x (1 – 7) c. -3 x -3 x -3 d. 24 ÷ 3 x 9 e. (4 – 9) x -3 f. 8 + 5(9 – 3) ÷ 3 g. 4(12 + 3) + 8(5 - 6) h. 62 + (3 x 9) ÷ 9 i. 14 - 6(22 + 52) + 33 2. Integers * Before you try these practice questions, draw a number line to help you with your working. You can also do this in the exam. Draw a number line from -20 to 20 in the space below: a. -5 + -9 b. -7 + 9 - 17 - -5 c. -21 - -8 + -12 − 72 d. -3 + -6 - -8 e. (-8)2 ÷ 2 f. 24 ÷ -3 x 7 g. 9 Y8 – Order of Operations and Integers – Answers BEDMAS Answers: a. 54, b. -42, c. -27, d. 72, e. 15, f. 18, g. 52, h. 39, i. -133 INTEGER Answers: a. -14, b. -10, c. -25, d. -1 e. 32, f. -56, g. -8  FRACTIONS AND PERCENTAGES  Y8 – Fractions and Percentages – Revision Exercises 1. Simplifying Fractions: Simplify the following fractions. 2. Equivalent Fractions Write an equivalent fraction for each of the following. 1 3 7 5 a. b. c. d. 2 4 8 9 3. Converting improper fractions to a mixed number: Convert to a mixed number. 10 7 13 27 a. b. c. d. 3 2 4 10 4. Converting a mixed number to an improper fraction: Convert to an improper fraction. 1 2 6 5 a. 2 b. 3 c. 4 d. 6 4 3 11 8 5. Adding or subtracting fractions with like denominators: Solve by adding or subtracting. 6. Adding or subtracting fractions with un-like denominators: Solve by finding a common denominator then adding or subtracting. 7. Multiplying Fractions: Solve by multiplying. 8. Adding, Subtracting or Multiplying Mixed Numbers: Solve. 9. Converting between percentages and decimals: Convert to percentages: a. 0.26 b. 0.462 c. 1.91 d. 0.08 e. 0.2 f. 2.07 g. 0.05 h. 3.50 Convert to decimals: a. 50% b. 25% c. 10% d. 45% e. 91% f. 5.2% g. 43% h. 0.8% 10. Converting between fractions and decimals: Convert to fractions and simplify: a. 50% b. 25% c. 10% d. 45% e. 90% f. 5% g. 4% h. 80% Convert to fractions and simplify: a. 0.2 b. 0.55 c. 0.80 d. 0.45 e. 0.90 f. 0.08 g. 0.10 h. 0.05 Convert to decimals: 𝟐 𝟓𝟑 𝟖 𝟗 𝟑𝟕 𝟒 𝟑𝟑 𝟐𝟒 a. b. c. d. e. f. g. h. 𝟏𝟎 𝟏𝟎𝟎 𝟏𝟎 𝟐𝟎 𝟓𝟎 𝟓 𝟔𝟎 𝟖𝟎 Convert to percentages: 𝟐 𝟓𝟑 𝟖 𝟗 𝟑𝟕 𝟒 𝟑𝟑 𝟐𝟒 a. b. c. d. e. f. g. h. 𝟏𝟎 𝟏𝟎𝟎 𝟏𝟎 𝟐𝟎 𝟓𝟎 𝟓 𝟔𝟎 𝟖𝟎 11. Finding a fraction of a quantity: Solve to find the fraction of the amount. Be sure to include units. 12. Finding the total amount when given a fraction of an amount. Solve to find the amount. a. 15 is 1/5 of what number? b. 6 is 1/7 of what number? c. 12 is 2/3 of what number? d. 155 is 5/6 of what number? 13. Finding a percentage of an amount. Replace the percentage with a fraction or decimal to evaluate these. a. 15% of $8 a. 30% of 150 L a. 12% of $40 a. 8% of 1800 g 14. Percentage Increase and Decrease: Increase or decrease the following percentages. a. Increase 70 by b. Increase 16 by c. Increase 55 by d. Increase 42 by 20% 25% 12% 27% a. Decrease 80 by b. Decrease 24 by c. Decrease 72 by d. Decrease 90 by 30% 15% 16% 5%  Y8 – Fractions and Percentages – Answers 4 3 4 1 1. Simplifying Fractions: a. b. c. d. 7 5 7 3 2. Equivalent Fractions: Note that answers may vary depending on what you multiply by!! 4 6 14 50 Example answers: a. b. c. d. 8 8 16 90 3. Converting improper fractions to a mixed number: 1 1 1 7 a. 3 b. 3 c. 3 d. 2 3 2 4 10 4. Converting a mixed number to an improper fraction: 9 11 50 53 a. b. c. d. 4 3 11 8 2 7 3 8 4 5. Adding or subtracting fractions with like denominators: a. b. c. d. = 3 8 11 50 25 6. Adding or subtracting fractions with un-like denominators: 7 10 2 16 48 a. b. = 1 c. d. = 2 e. 8 10 9 8 25 7. Multiplying Fractions: 3 8 21 6 3 a. 𝑏. 𝑐. 𝑑. = 70 35 80 70 35 8. Adding, Subtracting or Multiplying Mixed Numbers: 23 11 12 1 52 43 95 1 19 7 12 a. − = = 1 b. + = = 9 c. − = =4 8 8 8 2 10 10 10 2 3 3 3 9. Converting between percentages and decimals: Convert to percentages: a. 26% b. 46.2% c. 191% d. 8% e. 20% f. 207% g. 5% h. 350% Convert to decimals: a. 0.5 b. 0.25 c. 0.1 d. 0.45 e. 0.91 f. 0.052 g. 0.43 h. 0.008 10. Converting between fractions and decimals: Convert to fractions and simplify: 1 1 1 9 9 1 1 8 a. b. c. d. e. f. g. h. 2 4 10 20 10 20 25 10 Convert to fractions and simplify: 1 11 4 9 9 2 1 1 a. b. c. d. e. f. g. h. 5 20 5 20 10 25 10 20 Convert to decimals: a. 0.2 b. 0.53 c. 0.8 d. 0.45 e. 0.74 f. 0.8 g. 0.55 h. 0.3 Convert to percentages: a. 20% b. 53% c. 80% d. 45% e. 74% f. 80% g. 55% h. 30% 11. Finding a fraction of a quantity: a. $15 b. 21 mm c. $15 d. $350 12. Finding the total amount when given a fraction of an amount: a. 75 b. 42 c. 18 d. 186 13. Finding a percentage of an amount. a. $1.20 b. 45 L c. $4.80 d. 144 g 14. Percentage Increase and Decrease: a. 84 b. 20 c. 61.6 d. 53.34 a. 56 b. 20.4 c. 60.48 d. 85.5 ALGEBRA  Year 8 Algebra Revision Exercises 1. Simplifying algebraic expressions – The Rules of Algebra Simplify the following using the rules of Algebra. a. p + p = b. 2s – s = c. 5 x a = d. m x 12 = f. 1d x c x b = g. a x a = 2. Simplifying algebraic expressions – Like Terms Identify the like terms in each group. 3. Simplifying algebraic expressions - Addition and Subtraction 4. Simplifying algebraic expressions - Multiplication and Division Multiplication: Division: 5. Simplifying algebraic expressions – Multiplication and Division with exponents a. d x d = b. m2 x m3 = c. 5h x 2h4 d. 3 x 4a x 2ab = e. 3a2 x 2b2 x 3ab3c = f. 12a ÷ 3 = g. 21bc ÷ 7c= h. 34s ÷ 17s = i. 32d5 ÷ 4d3 = j. 10b2 ÷ 5b6 = 6. Identifying number patterns Complete the pattern. Write a rule to describe the pattern. 7. Writing function rules x 1 2 3 4 15 y 1 6 11 16 Difference: Write a rule to________________________ explain the relationship between y and x. y = ______________________ What would the value of y be if x = 15? Equation: _________________________ Complete this table. Shape number (n) 1 2 3 4 5 12 Number of shaded squares 7 11 15 (s) Write a rule to show how many shaded squares make up each shape number. S = ……………………………. How many shaded squares would there be in shape number 20? ______________ Read the question below complete the table and write the two rules. 8. Substitution 9. Writing algebraic equations from word problems. One Step Problems a. A shop makes $15 profit (p) for each bag sold. Which expression shows the profit made when b number of bags are sold. p = b + 15 p = b - 15 p = b x 15 p = b ÷ 15 b. Tim is 25cm taller than his brother John. Which expression represents Tim's height (t) compared to John's height (j). t = j + 25 t = j - 25 t = j x 25 t = j ÷ 25 c. Which expression represents John's height (j) compared to Tim's height (t). j = t + 25 j = t - 25 j = t x 25 j = t ÷ 25 d. Elle has read m pages from her 300 page book. How many does she have left to read. 300 + m 300 - m 300 x m 300 ÷ m e. A clothing store is having a sale. Write an expression that describes how much a $70 shirt would cost (c) once you take the discount (d) off the total price. f. A store stocks Local products (L) imported products (i) and second hand products (s). Write an expression that represents the total number (t) of products in the store. Two Step Problems a. An adult ticket to Kelly Tarlton's is $40 and a child's ticket is $30. Which expression shows the total cost (t) for adults (a) and children (c)? t = 40a + 30c t = 40a - 30c t = 40a x 30c t = 40a ÷30c b. To hire a taxi you pay a start fee of $8 and then $6.50 for each kilometre (k). Which expressions shows the total cost (c) for catching a taxi? c = 8 x 6.5k c = 8 ÷ 6.5k c = 8 + 6.5k c = 8 - 6.5k c. Melinda needs an electrician. The call out cost is $60 plus $45 an hour (h). Write an algebraic expression that she could use to calculate the total cost (c) of hiring an electrician. d. How much would it cost Melinda if the electrician worked at her house for 3 hours? e. To rent a Jet Ski costs $40 an hour (h) plus $2 for every litre of fuel (f). Write an algebraic expression that shows how much it costs to hire (c) a jet ski? f. How much would it cost to hire a Jet Ski if you used it for 1.5 hours and used 5 litres of petrol? g. A family pass at Laser Strike costs $25 plus $10 per game (g). Write an expression that describes the total cost (c) h. How many games could a family play if they had $45 to spend? i. How many games could a family play if they had $70 to spend? j. Tom buys a ticket in the school raffle. He multiplies his number by 4 and then takes away 5 to get 27. Write an expression that represents this process. Use n to represent Tom's raffle number. k. What was Tom's raffle number? Y8 – Algebra – Answers 1. Simplifying algebraic expressions – The Rules of Algebra a. 2p b. s c. 5a d. 12m f. bcd g. a2 2. Simplifying algebraic expressions – Like Terms a. 8a, 5a b. -2m, 3m c. m2, 3m2 d. t2, -t2 e. 3cd, dc f. -bc, 5cb g. -2t, 3t h. -6w, w i. 3s, 2.3s j. -0.2y, 2y 3. Simplifying algebraic expressions - Addition and Subtraction p. 4g + 3 q. 4l + 1 r. 2v + 7w s. 5p + 6q t. 3y + 2z u. 3j + 2k e. 3a + 3b f. 3t + 3t2 g. ad + 5d h. -m + 4n 4. Simplifying algebraic expressions - Multiplication and Division Multiplication: a. 20abn b. 6xy c. 18mn d. 6a2b e. 12pq2 f. 15k2l Division: a. 2m b. 5x c. 5p d. 2a d. 3 e. 3 f. 2 g. 3n h. 6b i. 4p 5. Simplifying algebraic expressions - Multiplication with exponents a. d2 b. m5 c. 10h5 d. 24a2b d. 18a3b5c f. 4a g. 3b h. 2 i. 8d2 j. 2/b4 or 2b-4 6. Identifying number patterns a. 35, 41: Rule = n + 6 b. 27, 24: Rule = n - 3 c. 54, 56: Rule = n + 2 d. 37, 27: Rule = n -10 7. Writing function rules y = 5x – 4 If x = 15, y = 71 s = 4n + 3 83 shaded squares Tables: 20, 24, 28, 32, 36, 40, 44 t = 4n + 4 c = 4n + 8 8. Substitution a. 16 b. 32 c. 25 a. 0 b. 3 c. 47 d. 9 e. 12 c. 4 9. Writing algebraic equations from word problems. a. p = b x 15 b. t = j + 25 c. j = t – 25 d. 300 - m e. c = 70 - d f. t = i + L + s a. t = 40a + 30c b. c = 8 + 6.5k c. c = 60 + 45h d. $195 e. c = 40h + 2f f. $70 g. c = 25 + 10g h. 2 games i. c = 4 games j. 4n – 5 = 27 k. 8 MEASUREMENT  Y8 – Measurement – Revision Exercises 1. Perimeter 2. Perimeter with missing measurements. 3. Area of rectangles, squares. 3. Area of parallelograms. 4. Area of triangles. 5. Area of irregular or compound shapes. 6. Unit Conversions. Distance Mass Volume 7. Word problems. 8. Circumference. Calculate the circumference of these circles. 9. Area of a circle. Calculate the area of these circles. 10. Volume of rectangular prisms. Calculate the volume of these prisms. All measurements are in centimetres. 11. Volume of a cylinder. Calculate the volume of these cylinders. 12. Volume of a triangular prism. Calculate the volume of these prisms. All measurements are in centimetres. 13. Surface area of a prism Calculate the total surface area of these prisms. 2100, 3500  Y8 – Measurement – Answers 1. Perimeter a. 14 cm b. 80 cm c. 18 cm 2. Perimeter with missing measurements. a. 294 mm b. 368 m c. 32 m d. 13 m e. 23 km 3. Area of rectangles, squares. a. 6 m2 b. 4 cm2 c. 9 m2 3. Area of parallelograms. a. 45 mm2 b. 10.12 cm2 4. Area of triangles. a. ½ x base x height or (base x height) ÷ 2 a. 18 cm2 b. 18 m2 c. 40 m2 a. 9 cm2 b. 18 m2 c. 24 m2 d. 42 cm2 e. 119 m2 f. 45.9 m2 5. Area of irregular or compound shapes. a. 21 m2 b. 2000 m2 c. 48 m2 d. 10 cm2 e. 130 cm2 f. 104 cm2 6. Unit Conversions. Distance a. 20 cm b. 40.5 cm c. 823.8 cm d. 200 cm e. 1900 cm f. 45000 cm a. 4 m b. 0.28 m c. 3.25 m d. 4.82 m e. 1.23 m f. 7.777 m g. 4.341 m h. 1.87 m i. 0.198 m Mass Volume a. 3.452 L b. 7.895 L c. 10 L d. 12.674 L e. 56.78 L f. 0.235 L a. 2568 ml b. 3999 ml c. 10566 ml d. 1780 ml e. 7305 ml f. 350 ml 7. Word problems. a. 16.8 m b. 19 cm c. 34.2 cm a. 121 cm2 b. 384 cm2 c. 126 cm2 d. 4.27 m2 a. 81 cm2 b. 32 m2 a. 12 b. 3 days c. 4 days d. 2 boxes of each a. 10 b. 1.625 L, 1.250 L c. 5 glasses, 125 ml 8. Circumference. a. 31.4 mm b. 18.84 cm c. 87.92 mm 9. Area of a circle. a. 12.56 m2 b. 28.26 cm2 c. 50.24 cm2 10. Volume of rectangular prisms. a. 216 cm3 b. 126 cm3 c. 200 cm3 d. 720 cm3 e. 630 cm3 f. 200 cm3 11. Volume of a cylinder. a. 401.92 cm3 b. 1099 cm3 c. 1356.48 cm3 12. Volume of a triangular prism. a. 100 cm3 b. 480 cm3 c. 720 cm3 d. 312 cm3 e. 120 cm3 f. 1620 cm3 13. Surface area of a prism a. 52 cm2 b. 8600 cm2 STATISTICS  Y8 – Statistics – Revision Exercises 1. Calculate the mean, median, mode and range of a data set Find the mean median mode and range of the following data sets. 1) 7, 8, 8, 8, 18, 10, 18, 11 Mean _________ Median _________ Mode _________ Range _________ 2) 19, 12, 6, 11, 7, 7, 8 Mean _________ Median _________ Mode _________ Range _________ 3) 16, 13, 10, 18, 18, 11, 6, 8, 15, 15 Mean _________ Median _________ Mode _________ Range _________ 4) 8, 8, 10, 16, 18 Mean _________ Median _________ Mode _________ Range _________ 5) 18, 15, 9, 12, 17, 19 Mean _________ Median _________ Mode _________ Range _________ 2. The Statistical Enquiry Cycle Write two characteristics of each part of the Statistical Enquiry Cycle. Problem Characteristic 1: Characteristic 2: Plan Characteristic 1: Characteristic 2: Data Characteristic 1: Characteristic 2: Analysis Characteristic 1: Characteristic 2: Conclusion Characteristic 1: Characteristic 2: 3. Interpreting Stem-and-Leaf Plots Below is a stem-and-leaf plot of the ages of people in a family. Use this to answer the questions below. 1. How old is the oldest family member? 2. What is the most common age? (The mode) 3. What is the range of the ages in the family? 4. What is the mean of the ages of family members in their 40’s? 4. Interpreting Bar Graphs Below is a bar graph using the data collected in a survey about favorite sports. Use this to answer the questions below.  1. What is the least favorite sport, according to the survey? 2. How many people chose Tennis and Basketball as their favorite sports? 3. How many more people chose Soccer as their favorite sport rather than Baseball? 4. What fraction of the total people surveyed chose Hockey as their favorite sport? Y8 – Statistics – Answers 1. Calculate the mean, median, mode and range of a data set 1) Mean = 11 Median = (8+10)÷2 = 9 Mode = 8 Range = 18-7 = 11 2) Mean = 10 Median = 8 Mode = 7 Range = 19-6 = 13 3) Mean = 13 Median = (13+15)÷2 = 14 Mode = 15 and 18 Range = 18-6 = 12 4) Mean = 12 Median = 10 Mode = 8 Range = 18-8 = 10 5) Mean = 15 Median = (15+17)÷2 = 16 Mode = No Mode Range = 19-9 = 10 2. The Statistical Enquiry Cycle Problem (From the yellow PPDAC picture) Understanding and defining the problem OR How do we go about answering this question Plan (From the yellow PPDAC picture) What to measure and how? OR Study design? OR Recording? OR Collecting? Data (From the yellow PPDAC picture) Collection OR Management OR Cleaning Analysis (From the yellow PPDAC picture) Sort data OR Construct table, graphs OR Look for patterns OR Hypothesis generation Conclusion (From the yellow PPDAC picture) Interpretation OR Conclusions OR New ideas OR Communication 3. Interpreting Stem-and-Leaf Plots 1. The oldest family member is 66 years old, represented by 6|6 2. The most common age is 4 years old, represented by 0|4 3. The range of the ages in the family is 66 – 1 = 65 years 4. The mean of the ages of family members in their 40’s is (40 + 44 + 48 + 49) ÷ 4 = 45.25 years 4. Interpreting Bar Graphs 1. The least favorite sport is Hockey. 2. 12 people chose Tennis and Basketball as their favorite sports. 3. 3 more people chose Soccer as their favorite sport rather than Baseball 2 4. The total people surveyed is 9 + 7 + 5 + 2 + 6 = 29 so of people surveyed chose 29 Hockey