AUSTRALIAN ISLAMIC COLLEGE Western Australian Curriculum Mathematics 2018 Year 8 Holiday Homework Name: Student ID: Teacher: Instructions: Show your working. Demonstrate clear understanding. Include the importance of mathematics wherever possible. Due Date: Term 3 Week 1 There will be a validation test Week 2 Wednesday based on the Holiday Homework Course Content: Carry out the four operations with integers, using efficient mental and written strategies and appropriate digital technologies (ACMNA 183) Investigate terminating and recurring decimals (ACMNA 184) Solve problems involving the use of percentages, including percentage increases and decreases, with and without digital technologies (ACMNA 187) Solve problems involving profit and loss, with and without digital technology (ACMNA 189 Solve a range of problems involving rates and ratios, with and without technologies (ACMNA 188) Simplify algebraic expressions involving the four operations (ACMNA 192) Extend and apply the distributive law to the expansion of algebraic expressions (ACMNA 190) Use index notation with numbers to establish the index laws with positive integral indices and the zero index (ACMNA 182) Solving linear equations using algebraic and graphical techniques (ACMNA 194 Declaration of Authenticity: I hereby declare that this submission is my own work and to the best of my ability it contains no plagiarised material. Signed: Date
1 Use an algorithm to find these sums and differences. a 1 6 5 + 8 7 b 2 5 3 1 6 4 2 Use an algorithm to find these products and quotients. a 79 5 b 189 7 3 Find the lowest common multiple (LCM) of 8 and 10. 4 Find the highest common factor (HCF) of 18 and 24. 5 Evaluate the following. a 16 b 7 2 c 25 2 d 11 e 64 3 f 8 g 5 3 3 h 27
6 a Use factor trees to write 108 and 225 as products of prime factors. b Hence, find the LCM and HCF of 108 and 225. Give your answers in prime factor form. 7 Evaluate the following. a 4 9 b -7 + 3 c -13 6 d 10 + (-8) e -12 + 25 f -17 + (-6) g 38 + (-45) h 40 (-29) i -86 (-57)
8 Evaluate the following products and quotients. a -4 8 b 36 (-4) c 9 (-5) d -56 8 e -12 (-7) f -108 (-9) 9 The temperature one morning in Moscow was -2 C. During the day, the temperature rose by 4 C and then dropped by 7 C. What is the temperature after the rise and fall? Show your working. 10 Stuart sold 8 couches and 11 armchairs at his furniture store yesterday. He made a $10 loss on each couch and a $12 profit on each armchair. What was his overall profit or loss? 11 Evaluate the following. a 10 + (-4) 6 b 9 + (-12) (-6 (-2) 5)
12 Evaluate these expressions using a = -3 and b = 8. a -9 a b a + b (-4) c -2 (5 + a 7) b 13 Remember that x 2 = x x and x 3 = x x x. a Evaluate these expressions. i (-5) 2 ii (-7) 2 iii (-2) 3 iv (-3) 3 b Will the square of a negative number always be positive? Explain why. c Will the cube of a negative number always be negative? Explain why.
14 Rewrite the following fractions in simplest form. 5 18 a b c 20 30 88 56 15 Evaluate the following. 2 a b c 3 4 3 1 7 2 +1 5 9 4 1 4 2 5 6 d 1 2 e f 5 1 4 8 5 3 2 9 1 7 8 2 3 11 16 Convert the following decimals to fractions in their simplest form. a 0.225 b 3.68
17 Evaluate the following. a 5 b c 6 2 8 7 9 + 1 6 1 1 2 2 2 3 d 3 e f 7 4 11 5 12 3 2 7 8 10 11 5 18 Convert the following fractions into decimals by finding an equivalent fraction whose denominator is a power of 10. a 3 5 b 87 50 19 Express the following fractions as recurring decimals. a 2 9 b 6 11
20 Write the following fractions as decimals, correct to two decimal places. a 2 7 b 7 12 21 Convert the following percentages to fractions or mixed numbers in their simplest form. a 62.5% b 375% 22 Convert the following fractions and mixed numbers into percentages. a 4 5 b 2 1 3 23 Convert the following percentages to decimals. a 80.9% b 164% 24 Convert the following decimals to percentages. a 0.732 b 4.8 25 Express: a 18 as a percentage of 60 b 70cm as a percentage of 2.5 m
26 Find: a 66 2 of 123 b 140% of 75 3 % 27 Find the new value when: a $65 is increased by 20% b $180 is decreased by 45% 28 Find the selling price when: a a $490 painting is discounted by 30% b a $175 antique chair is marked up by 8% 29 Calculate the percentage change (profit/loss) when: a $24 becomes $54 b $80 becomes $68 30 If 18% of an amount of money is $36: a how much is 75% of that amount? b what is the full amount of money?
31 A television has been discounted by 40%. If the sale price was $72, what was the original price? 32 A bag contains 4 red marbles, 5 blue marbles and 3 green marbles. Write down the ratio of: a red to blue to green marbles b green marbles to red marbles c blue marbles to other marbles d blue marbles to total marbles 33 Complete each pair of equivalent ratios. a 3 : 10 = 12 : b 4 : 7 = : 56 34 Simplify these ratios. a 7 : 28 b 125 : 300 35 Simplify these ratios. 1 2 2 a : b : 4 7 9 5 6
36 First change the quantities to the same unit, and then express each pair of quantities as a ratio in simplest form. a 24 mm to 3 cm b 300 g to 1.5 kg c 800 ml to 1.2 L d 14 hours to 2 days 37 a Divide 63 m in the ratio of 4 : 5. b Divide $240 in the ratio of 2 : 3 : 38 Expand the brackets in each expression and then combine like terms where possible. a 5(4x 7) b -3(9 + 2y) c 2(x + 9) + 5x d 9yx + 7x(3 y) 6x + 10y 39 Find the highest common factor of: a 18 and 24 b 20x and 45xy c 12ab 2 and 16ba
40 Factorise the following expressions. a 12 8m b 9n + 24 c 6a 15ab d 18cde + 12def e 42x 30x 2 f 24x 2 + 40xy 41 Write an expression for the following situations. a The total cost, in dollars, of p pencils that each cost 70c b The area of a rectangle if its length is x cm and its width is 5 cm less than its length c The total cost of hiring a gardener for h hours if he charges a $30 call-out fee and $60 per hour
42 Simplify the following using the index law for multiplication. a x 2 x 3 b y 3 y 7 c z 5 z d 4w 8 9w w 4 e 2 p 6 q 4 6 pq 2 f 5s 2 t 7s 5 t 7 43 Simplify the following using the index law for division. a x 6 x 4 b 25z 7 5z c 9k 5 56a 6 b 2 d 27k 2 14a 3 b 44 Simplify the following expressions using the index laws. ( ) 0 8x 0 k 3 a 8x b c ( ) 5 ( ) 4 4( a 2 b) 0 c 3 d 3a 0 b 5 c 0 e mn 2 f ( ) 2 3x( y 2 z 7 ) 4 5( 3p 0 q) 2 r 6 g 6e 6 f 0 h i
45 Express each of the following as a simplified rate. a 24 mm rainfall in 3 days b $90 in 6 hours 46 Find the average rate for each situation. a A football team scored 63 goals over 7 games. b Russell was 115 cm tall when he turned 6 years old, and 187 cm when he turned 18 years old. 47 Solve the following ratio and rate problems. a A triangle has height and base dimensions in a ratio of 3 : 7. If a particular triangle has a height of 9 cm, what is the length of its base? b Laura, Sam and Paul have won a prize. They decide to share it in the ratio of 2 : 4 : 5. If Paul receives $100, how much do Laura and Sam receive, and what was the total value of the prize?
c A tap is dripping at a rate of 300 ml every 5 minutes. How much water drips in 9 minutes? d Jared earns $97.20 for working for 6 hours. How much will he earn if he works for 8 hours? 48 Convert the following rates into the units given in the brackets. a 200 ml/min (L/h) b 36 km/h (m/s) 49 a Calculate the average speed in km/h of a train travelling 480 km in 6 hours. b Calculate the average speed in km/h of an athlete who runs 4 km in 20 minutes.