Easington Academy. Easington Academy Mathematics Department

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2 Contents HW 1 HW 2 HW 3 HW 4 HW 5 HW 6 HW 7 HW 8 HW 9 HW 10 HW 11 HW 12 HW 13 HW 14 HW 15 HW 16 HW 17 HW 18 HW 19 HW 20 HW 21 HW 22 HW 23 HW 24 HW 25 HW 26 HW 27 HW 28 HW 29 HW 30 HW 31 HW 32 HW 33 HW 34 HW 35 HW 36 HW 37 HW 38 HW 39 HW 40 HW 41 HW 42 HW 43 HW 44 HW 45 Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Maths Skills Areas of shapes Surface area and volume Metric and imperial measures Powers, expressions and formula Brackets Equations Adding and subtracting fractions Multiplying and dividing fractions Calculating with mixed numbers and decimals Fractions, decimals and percentages Percentage problems The language of probability Calculating probability Experimental probability Solve geometric problems Parallel lines Interior and exterior angles Straight line graphs Midpoints Direct proportion Averages and range Tables Charts and graphs Shapes and symmetry Translations, reflections and enlargements

3 HW 46 Rotations and combined transformations HW 47 Fractions and decimals HW 48 Ratios HW 49 Using equations 1 HW 50 Using equations 2 HW 51 Multiples, factors and primes HW 52 Probability HW 53 Analysing data HW 54 Sequences HW 55 Percentages HW 56 Written methods

4 HW 1 1. Divide thirty-one point five by ten. 2. Round to the nearest whole number. 3. Which is bigger, 40% of 90 or ½ of 80? 4. Put these in order of size, smallest first. 60% 0.4 ½ 5. What is the fraction twelve twentieths in its simplest form? 11. One book costs one pound ninety-five pence. How much do six books cost? 12. What fraction of two pounds is twenty pence? 13. What is the difference between 289 and What temperature is 20 degrees lower than 6 degrees Celsius? 15. Six cakes cost How much do ten cakes cost? If x = 2, calculate the value of: Which is bigger: or? Increase 30 by 15% 8. Divide 300 in a ratio of 3:7 9. If 400ml of milk is used for 8 pancakes, how much is used for 6? x 3 + x 17. Solve: 2x 5 = Find the nth term of this sequence If y=3x + 2, find the value of y when x = Use π=3 10. Add: and Calculate the length of the circumference of a circle with diameter of 6cm

5 HW 2 1. Divide 47.5 by Round 19.3 to the nearest whole number. 3. Which is bigger, 60% of 90 or ½ of 100? 4. Put these in order of size, smallest first % ⅕ 5. What is the fraction 10/14 in its simplest form? 11. One book costs How much do six books cost? 12. What fraction of two pounds is fifty pence? 13. What is the difference between 179 and What temperature is 15 0 lower than 7 0 c? 15. Six cakes cost How much do ten cakes cost? If x = 3, calculate the value of: Which is bigger: 30% or? 3 7. Decrease 20 by 15% 8. Divide 80 in a ratio of 3:2 9. If 200g of fat is used for 8 cakes, how much is used for 3 cakes? 10. x 3 + x 17. Solve: 2x 3 = Find the nth term of this sequence If y=3x + 2, find the value of y when x = -3 Add: 5 1 and 2 1 Use π=3 20. Calculate the length of the circumference of a circle with diameter of 8cm

6 HW 3 1. What is nineteen point three five multiplied by ten? 2. Round seven point seven six to one decimal place. 3. Which is bigger, 80% of 150 or ¾ of 200? 4. Put these in order of size, smallest first % ⁴ ₅ 5. What is the fraction ten twelfths in its simplest form? 11. One book costs How much do four books cost? 12. What fraction of a pound is seventy pence? 13. What is the difference between 129 and What temperature is ten degrees higher than -7 C? 15. Five cakes cost How much do seven cakes cost? If x = -2, calculate the value of: Which is bigger: 0.3 or? 3 7. Increase 60 by 10% 8. Divide 56 in a ratio of 5:3 9. If 150g of sugar is used for 5 cakes, how much is used for 7 cakes? 10. Work out: x 3 + x 17. Solve: 3x + 17 = Find the nth term of this sequence If y=2x - 3, find the value of y when x = Use π=3 20. Calculate the area of a circle with radius of 4cm

7 HW 4 1. What is thirty point zero five multiplied by ten? 2. Round six point nine five to one decimal place. 3. Which is bigger, 70% of 200 or ¾ of 160? 4. Put these in order of size, smallest first % ⁴ ₅ 5. What is the fraction five twentieths in its simplest form? 11. One book costs How much do three books cost? 12. What fraction of a pound is eighty pence? 13. What is the difference between 89 and What temperature is nine degrees higher than -3 C? 15. Five cakes cost How much do seven cakes cost? If x = 3, calculate the value of: Which is bigger: or? Decrease 64 by 10% 8. Divide 56 in a ratio of 4:3 9. If 450g of flour is used for 3 pies, how much is used for 4 pies? 10. Work out: x 3 - x 17. Solve: 2x + 7 = Find the nth term of this sequence If y=5x - 3, find the value of y when x = Use π=3 20. Calculate the length of the circumference of a circle with diameter of 9.2cm

8 HW 5 1. Divide two hundred and thirty point one by one hundred. 2. Round nine point four two to one decimal place. 3. Which is bigger, 40% of 200 or ⅓ of 150? 4. Put these in order of size, smallest first % ⁴ ₅ 5. What is the fraction eight twentieths in its simplest form? 11. One book costs 95p. How much do five books cost? 12. What fraction of a pound is twenty-five pence? 13. What is the difference between 95 and What temperature is ten degrees higher than -7 C? 15. Eight cakes cost How much do three cakes cost? If x = -3, calculate the value of: Which is bigger: 15% or? 5 7. Increase 40 by 20% 8. Divide in a ratio of 4:5:9 9. If 80% is 72 marks, what is full marks? 10. x 2 - x 17. Solve: 2x + 7 = Find the nth term of this sequence If y=4x + 5, find the value of y when x = 0 Work out: 5 x 6 5 Use π=3 20. Calculate the area of a circle with diameter of 6cm

9 HW 6 1. Divide 37.9 by ten. 2. Round to one decimal place. 3. Which is bigger, 80% of 90 or ½ of 140? 4. Put these in order of size, smallest first % ⅕ 5. What is the fraction ten twelfths in its simplest form? 6. Which is bigger: 0.6 or 0.58? 7. Decrease 600 by 20% 8. Divide 25kg in a ratio of 2:3:5 9. If a litre of water is provided for 20 people, how much for 50 people? One book costs How much do 4 books cost? 12. What fraction of 3.00 is fifty pence? 13. What is the difference between 164 and What temperature is twenty degrees lower than nine degrees Celsius? 15. Seven cakes cost How much do ten cakes cost? 16. If x = 1, calculate the value of: x 3 - x 17. Solve: 2x + 3 = Find the nth term of this sequence If y=3x - 5, find the value of y when x = -1 Work out: 5 x 4 3 Use π=3 20. Calculate the length of the circumference of a circle with radius of 5cm

10 HW x Round 5.53 to one decimal place. 3. Which is bigger, 40% of 120 or ¼ of 200? 4. Put these in order of size, smallest first % ³ ₅ 5. What is the fraction ¹⁵ ₂₀ in its simplest form? 6. Which is bigger: or 0.15? 7. Increase 40 by 5% 8. Divide 72kg in a ratio of 1:3:5 9. I used 8bags of sand for 12m 2, how much will I need for 15m 2? One book costs How much do two books cost? 12. What fraction of a pound is forty pence? 13. What is the difference between 178 and 401? 14. What temperature is twelve degrees higher than -6 C? 15. Five cakes cost How much do seven cakes cost? 16. If x = 2, calculate the value of: x 2 - x 17. Solve: 2x - 2 = Find the nth term of this sequence If y=4x - 1, find the value of y when x = -2 Work out: 5 3 of 7kg Use π=3 20. Calculate the area of a circle with diameter of 10cm

11 HW 8 1. Divide 67.9 by one hundred Round 6.95 to one decimal place 3. Which is bigger, 40% of 200 or ¼ of 400? 4. Put a ring around the decimal which is equal to three-fifths Which fraction is equal to ⅓? ⁶ ₃₀ ⁴ ₁₂ ⁵ ₁₆ 6. 3 Which is bigger:12.5% or 20? 7. Decrease 680 by 10% 8. Divide 132kg in a ratio of 3:3:5 9. 4bags of cement do 18m 2, how many m 2 can be done with 7bags? What is two-fifths of twentyfive? 13. What is thirty multiplied by sixty? 14. What temperature is ten degrees higher than -22 C? 15. In a group of 36 children, there are twice as many boys as girls. How many girls are there? 16. If x = -2, calculate the value of: x 2 + 2x 17. Solve: 5x + 1 = If T(n) = 6n +2, what is the 3 rd term? 19. If y=4x + 3, find the value of y when x = -2 Work out: 5 x 4 3 Use π=3 20. Calculate the length of the circumference of a circle with radius of 7cm

12 HW x Round 3.61 to one decimal place. 3. Which is bigger, 20% of 400 or ¼ of 360? 4. Put a ring around the decimal which is equal to ⁶ ₂₀ What is four-fifths of twenty? 13. What is ninety multiplied by seventy? 14. What temperature is ten degrees lower than 4 C? 5. Which fraction is equal to ⅛? 15. In a group of 45 children, ⁴ ₆ ⁴ ₃₀ ² ₁₆ there are twice as many boys as girls. How many girls are there? If x = 4, calculate the value of: Which is bigger: 17.5% or? 6 x 2 + 2x 7. Increase 1200 by 2% 8. Fruit : Sugar in 2 : 3. If 15kg of sugar is used, how much fruit? 9. If 75% is 45, what is the full cost? Solve: 3x - 3 = 2x 18. If T(n) = 7 - n, what is the 2 nd term? 19. If x + y = 10, find the value of y when x = 3 Work out: 3 2 of 2 Use π=3 20. Calculate the area of a circle with radius of 2cm

13 HW x Round to one decimal place. 3. Which is bigger, 40% of 1000 or ¼ of 1200? 4. Put a ring around the decimal which is equal to ⁴ ₂₀ Which fraction is equal to ⅔? ⁴ ₈ ⁶ ₉ ⁵ ₁₅ 6. Which is bigger: 10 3 or 5 3? 7. Decrease 1200 by 25% 8. Paint is Red : Blue in a ratio 3 : 4. If 6 litres of blue is used, how much red? 9. If 75% is 60, what is the full cost? What is two thirds of twentyfour? 13. What is sixty multiplied by seventy? 14. What temperature is ten degrees lower than -7 C? 15. In a group of 42 children, there are twice as many boys as girls. How many girls are there? 16. If x = 3, calculate the value of: x 2 + 2x 17. Solve: 3x - 3 = x If T(n) = 3+ 2n, what is the 5 th term? 19. If x + y = 6, find the value of y when x = Work out: Use π=3 20. Calculate the length of the circumference of a circle with radius of 2.8cm

14 HW Divide 263 by one hundred = 2. Round to one decimal place 3. Which is bigger, 40% of 210 or ¼ of 320? 4. Put a ring around the decimal which is equal to ⅘ What is five-eighths of sixtyfour? 13. What is fifty multiplied by seventy? 14. What temperature is ten degrees higher than -16 C? 5. Which fraction is equal to ⅗? 15. In a group of 48 children, there ⁴ ₁₂ ⁶ ₁₀ ⁵ ₁₅ are three times as many boys as girls. How many girls are there? If x = -4, calculate the value of: Which is bigger: or 12%? 8 2x 2 + x 7. Increase 160km by 30% 8. Boys : Girls are in a ratio 3 : 4. If there are 12 boys, how many girls? 9. 5miles = 8km. How many km in 40 miles? Solve: 4x + 3 = 2x If T(n) = 5-2n, what is the 4 th term? 19. If x + y = 8, find the value of y when x = -1 Work out: Use π=3 20. Calculate the area of a circle with diameter of 14cm

15 HW x = 2. Round 9.39 to one decimal place. 3. Which is bigger, 30% of 110 or ¼ of 180? 4. Put a ring around the decimal which is equal to ⁷ ₁₀ Which fraction is equal to ⅛? ⁴ ₃₂ ⁶ ₃₀ ⁵ ₁₅ 6. Which is bigger: 8 3 or Decrease 2500 by 1% 8. Fir trees : Yew trees is 3:4. There are 18 fir trees, how many yew trees? 9. 5miles = 8km. How many km in 250 miles? 12. Find 25% of What is thirty multiplied by eighty? 14. What temperature is twelve degrees higher than -15 C? 15. In a group of 36 children, there are three times as many boys as girls. How many girls are there? 16. If x = 4, calculate the value of: 2x Solve: 2(x 3) = If T(n) = 4 + 3n, what is the 2 nd term? 19. If y = 2x+ 3, find the value of y when x = Work out: Use π=3 20. Calculate the length of the circumference of a circle with diameter of 10.4cm

16 HW Divide 97 by one hundred = 2. Round to the nearest whole number. 3. Which is bigger, 20% of 300 or ¼ of 200? 4. Put a ring around the decimal which is equal to ⁸ ₂₀ Which fraction is equal to ⅗? ⁴ ₂₀ ⁶ ₃₀ ⁹ ₁₅ 6. 3 Which is bigger: 13% or Increase 680 by 15% 8. A & B share the cost in a ratio of 3:2. The cost is 85; much does A pay? 9. 5miles = 8km. How many miles in 80km? Find 60% of What is forty multiplied by seventy? 14. What temperature is ten degrees lower than -8 C? 15. In a group of 30 children, there are four times as many boys as girls. How many girls are there? 16. If x = -3, calculate the value of: 2x Solve: 2(x + 2) = If T(n) = 2-7n, what is the 1 st term? 19. If y = 2x+ 3, find the value of y when x = -3 Work out: 8 5 of 10 litres Use π=3 20. Calculate the area of a circle with diameter of 1.8m

17 HW x Round to one decimal place. 3. Which is bigger, 70% of 300 or ¼ of 600? 4. Put a ring around the decimal which is equal to ⅖ Which fraction is equal to ⅚? ⁸ ₂₂ ²⁵ ₃₀ ⁵ ₁₅ 6. Which is bigger: 30% or 15 4? 7. Decrease 80 by 40% 8. A & B share the cost in a ratio of 3:2. A pays 126, how much does B pay? 9. The exchange rate is: 1 = $1.54. How many would I get for $ = Find 15% of What is forty multiplied by ninety? 14. What temperature is fifteen degrees lower than -7 C? 15. In a group of 45 children, there are four times as many boys as girls. How many girls are there? 16. If x = -4, calculate the value of: 2x Solve: 3(x 1) = Find the nth term of this sequence Work out: litres 19. If y = 2x- 5, find the value of y when x = -4 Use π=3 20. Calculate the length of the circumference of a circle with radius of 1.6m

18 HW Divide 1.7 by one hundred. 11. Calculate Round to one decimal place. 3. Which is bigger, 40% of 180 or ¼ of 320? 4. Put a ring around the decimal 3 which is equal to Which fraction is equal to ⅔? ⁴ ₁₄ ⁶ ₉ ⁵ ₁₅ 6. Which is bigger: 8 1 or Increase 48m by 20 % 8. A & B share the cost in a ratio of 3:2. A pays 126, how much does B pay? 9. The exchange rate is: 1 = How many would I get for Work out: What is 45% of three hundred? 13. What is forty multiplied by seventy? 14. What temperature is twelve degrees lower than -3 C? 15. In a group of 60 children, there are three times as many boys as girls. How many girls are there? 16. If x = 5, calculate the value of: 2x 2 + x 17. Solve: 2(x + 3) = Find the nth term of this sequence If y = 2x + 5, find the value of y when x = -4 Use π=3 20. Calculate the area of a circle with radius of 7cm

19 HW If x = 2, calculate the value of: Which is bigger: or? 7 5 x 3 + x 2. Which is bigger: 0.45 or 5 2? 3. Increase 30 by 15% 4. Decrease 40 by 15% 5. Divide 300 in a ratio of 3:7 6. Divide 30 in a ratio of 3:2 7. If 60 marks is 40%, what is full marks? 8. If 400ml of milk is used for 8 pancakes, how much is used for 6? 9. Add: 3 1 and Work out: 12. If x = -2, calculate the value of: x 3 + x 14. Solve: 2x 5 = Solve: 3x + 1 = Find the nth term of this sequence If T(n) = 3n 1, what is the 3 rd term? 17. If y=3x + 2, find the value of y when x = y = 3x + 2 is the equation of a straight line graph. What is its gradient? Use π = Calculate the area of a circle with radius of 5cm 2 of 8 5 Use π = Calculate the length of the circumference of a circle with diameter of 6cm

20 HW If x = 3, calculate the value of: Which is bigger: or? 4 3 x 3 + x 2. Which is bigger: 30% or 3 1? 3. Increase 60 by 15% 4. Decrease 20 by 15% 5. Divide 500 in a ratio of 3:7 6. Divide 80 in a ratio of 3:2 7. If 120 marks is 60%, what is full marks? 8. If 200g of fat is used for 8 cakes, how much is used for 3 cakes? 9. Add: 5 1 and Work out: 12. If x = -3, calculate the value of: x 3 + x 14. Solve: 2x 3 = Solve: 3x + 5 = Find the nth term of this sequence In the sequence 4n 1, what is the 3 rd term? 17. If y=3x + 2, find the value of y when x = y = 5x - 2 is the equation of a straight line graph. What is its gradient? Use π = Calculate the area of a circle with radius of 2cm 2 of 8 3 Use π = Calculate the circumference of a circle with diameter of 8cm

21 HW If x = 2, calculate the value of: Which is bigger: or? 4 5 x 3 - x 2. Which is bigger: 0.3 or 3 1? 3. Increase 60 by 10% 4. Decrease 40 by 10% 5. Divide 56 in a ratio of 5:3 6. Divide 28 in a ratio of 3:4 7. If 30 marks is 40%, what is full marks? 8. If 150g of sugar is used for 5 cakes, how much is used for 7 cakes? 9. Work out: If x = -2, calculate the value of: x 3 - x 14. Solve: 2x 1 = Solve: 3x + 17 = Find the nth term of this sequence If T(n) = 2n + 3, what is the 3 rd term? 17. If y=2x - 3, find the value of y when x = y = 4x - 1 is the equation of a straight line graph. What is its gradient? Use π = Calculate the area of a circle with radius of 4cm Work out: 5 3 of 7 Use π = Calculate the length of the circumference of a circle with diameter of 7cm

22 HW If x = 3, calculate the value of: Which is bigger: or? 3 5 x 3 - x 2. Which is bigger: 67% or 3 2? 3. Increase 42 by 10% 4. Decrease 64 by 10% 5. Divide 56 in a ratio of 4:3 6. Divide 72 in a ratio of 3:5 7. If 80% is 60 marks, what is full marks? 8. If 450g of flour is used for 3 pies, how much is used for 4 cakes? 9. Work out: If x = -3, calculate the value of: x 3 - x 14. Solve: 4x 5 = Solve: 2x + 7 = Find the nth term of this sequence In the sequence 3n - 5, what is the 3 rd term? 17. If y=5x - 3, find the value of y when x = y = 6x + 5 is the equation of a straight line graph. What is its gradient? Use π = Calculate the area of a circle with radius of 6cm Work out: 4 of 5 7 Use π = Calculate the length of the circumference of a circle with diameter of 9cm

23 HW If x = 3, calculate the value of: Which is bigger: or 0.58? 8 x 2 + x 2. Which is bigger: 15% or 5 1? 3. Increase 40 by 20% 4. Decrease 60 by 20% 5. Divide in a ratio of 4:5:9 6. Divide 42 in a ratio of 1:2:3 7. If 80% is 72 marks, what is full marks? 8. If a litre of water is provided for 5 people, how much for 7 people? 9. Work out: If x = -3, calculate the value of: x 2 + x 14. Solve: 2(x 1) = Solve: 2x + 7 = Find the nth term of this sequence If T(n) = n - 7, what is the 5 th term? 17. If y=4x + 5, find the value of y when x = y = 3x + 2 is the equation of a straight line graph. Where does it cross the y-axis? Use π = Calculate the area of a circle with diameter of 5cm Work out: 5 x 6 5 Use π = Calculate the length of the circumference of a circle with radius of 3cm

24 Areas of shapes HW 21 1 Work out the area of each triangle 2 This triangle has a height of 4 cm and an area of 16 cm 2 Ellen says, The base of the triangle is 4 cm because 4 x 4 = 16. Is she correct, explain your answer. 3 The diagram shows the dimensions of a badge What is the total area of the badge 4 Work out the area of this parallelogram 5 Use the formula A = ½(a + b)h to work out the area of this trapezium 6 Ade works out the area of this trapezium. This is what he writes Area = ½ x x 8 = = m 2 (a) Explain the mistake that he has made (b) Work out the correct area

25 Surface area and volume HW 22 1 Here is a cuboid with length 4 cm, width 8 cm and height 2 cm. (a) Sketch a net of the cuboid (b) (c) Write on it the area of each face Find the surface area of the cuboid 2 Work out the surface area of this cube 3 An open cardboard box has length 32 cm, width 12.5 cm and height 16.5 cm. Work out the area of cardboard needed to make the open box. 4 Work out the volume of this cube 5 A biscuit tin is a cuboid of length 18cm, width 9cm and height 6cm. What is the volume of the tin 6 A cube has a side length of 15cm. How many cubes will fit into a box that measures 75cm by 60cm by 30cm.

26 Metric and imperial measures HW 23 1 Work out these conversions. (a) 5 litres = cm 3 (b) 2.7 litres = cm 3 (c) 3600 cm 3 = litres (d) 240 cm 3 = litres 2(a) (b) (c) (d) (e) A butcher receives an order for 10 pounds (lb) of beef mince. Approximately how many kilograms is this Sean runs 8 miles. How far is this on kilometres Anna orders 900 litres of oil for her central heating oil tank. How many gallons is this One jelly mould holds 1.5 pints of jelly How much jelly is needed for six jelly moulds. Give your answer in litres The central strip of a cricket field between the two wickets has a width of 10 feet. What is the width in metres.

27 Powers, expressions and formulae HW 24 1(a) Write m x m x m x m as a power (b) Write b 6 as a product (c) Write each product using index notation (i) a x a x a x c x c (ii) 2n x 3n x 4n 2 The formula for the total surface area A of a cube of side d is A = 6d 2. Calculate the surface area when d = 7.5cm 3 Simplify these expressions (a) w 2 x w 3 (b) y x y 2 (c) 4 x g 3 x 3 x g 3 (d) c 6 c 2 (e) v 3 v (f) 5 x e 4 e 3 4 Simplify these expressions (a) s 2 + s 2 + s 2 + s 2 (b) 2a 2 + 5b 2 2b 2 + a 2 (c) 4p 3 + 3p + 2p 3 5(a) (b) 6(a) (b) Write a simplified formula for the area A cm 2 of this rectangle. Use your formula to find A when a = 4 cm Write an expression for the volume of each cuboid Work out the volume of cuboid C when k = 3cm 7 An ice cube tray is filled with w ml of water. It makes 15 ice cubes (a) (b) (c) Write a formula for the volume V ml of water in an ice cube Use your formula to find V when w = 450 ml Write a formula for the total volume V of n ice cubes 8 A 120 bill for a meal is divided equally between n people. Write an expression for the amount each person pays.

28 Brackets HW 25 1 Expand these expressions and simplify where possible (a) m(2 + n) (b) 2b(b 3) (c) -4(2t + 5) (d) 5u 2(u 3) (e) 4(r 1) 2(r + 2) (f) c(4c + 3) c 2(a) (b) Write the highest common factor of 8n and 12m Factorise 8n + 12m completely 3 Factorise these expressions (a) 8s 8 (b) m (c) 3h + 9 (d) t (e) 54p + 18r (f) 30j 42q (g) k k 2 (h) 16v 2 4v (i) 15a a

29 Equations HW 26 1 Solve these equations (a) h 7 =12 (b) w 2 = 10 (c) -4m = 24 (d) 3a + 2 = 20 (e) 2(d + 5) = 12 (f) 3r 2 = r + 8 (g) 5(c 2) = 2(c + 1) (h) 3(x + 2) = 4x 1 (i) 2(5 n) = 10n The formula v = at gives the speed v metres per second (m/s) of a sports car after t seconds. Use the formula to find t when a = 11 and v = 110 m/s 3 Solve each equation by working out the unknown length 4 A bolt has a mass of 20g and a nut has a mass of n g. (a) Write an expression with brackets for the total mass of 5 nuts and 5 bolts (b) The total mass of 5 nuts and 5 bolts is 125 g. Solve an equation to find the mass of a nut

30 Adding and subtracting fractions HW 27 1 Complete the following additions (a) (b) 2 Work out: (a) (b) (c) 3) Work out these additions and subtractions by writing them with the same denominator. (a) (b) (c) (d) 4 Work out:

31 Multiplying and dividing fractions HW 28 1 Work out (a) (b) (c) 2 Work out these multiplications. Simplify your answer fully. (a) (b) (c) 3 Write down the reciprocals of these numbers. 4 Work out these divisions. (a) (b) (c) (d)

32 Calculating with mixed numbers and decimals HW 29 1 Write down the first 5 decimal places of the following recurring decimals. (a) 2 Convert each fraction to a decimal. Write recurring decimals using dot notation. 3 Write these mixed numbers as improper fractions. 4 Work out these mixed number additions. Leave your answer as a mixed number. 5 Work out these mixed number subtractions. Leave your answers as mixed numbers. 6 Work out these calculations. (a) (b) (c) (d) (b)

33 Fractions, decimals and percentages. HW 30 1 Copy and complete the diagram below 2 Write these mixed numbers as a decimal and percentage. 3 Write these terminating decimals as fractions or mixed numbers in their simplest forms 4 Fifteen out of 45 members of a knitting club are children. a) What fraction of the knitting club members are children? b) What percentage of the knitting club members are children? 5

34 Percentage problems HW 31 1 For each of these, write the first amount as a percentage of the second amount. a) 48cm out of 1m b) 15mm out of 50mm c) 750m out of 3000m 2 Increase these amounts by the given percentage a) 46 by 20% b) 60 by 10% c) 80 by 15% d) 56 by 25% 3 Decrease these amounts by the given percentage a) 85 by 5% b) 90 by 10% c) 20 by 30% d) 72 by 15% 4 What would be multiplier be for, a) A 40% increase? b) 30% decrease? c) 4% increase? 5 Sita invests 800 for 3 years at 4% simple interest per year. Copy & complete the workings to find out how much her investment is worth at the end of the 3 years. 6 Aneira invests 400 for 4 years at 3.5% simple interest per year. How much will her investment be worth after the 4 years? (Hint, use the method from Q5) 7 10% of an amount is 12. a) Work out 1% of the amount. b) Work out 100% of the amount 8 5% of an amount is 30g. a) Work out 1% of the amount b) Work out the original amount 9 Sarah wants to buy a car. She sees this advert. a) How much is the deposit? b) Which method of payment is more expensive? By how much?

35 The language of probability HW 32 1 Here is a fair spinner. a) Which section is most likely to be landed on. b) Which section is least likely to be landed on 2 Misha rolls an ordinary dice numbered 1 to 6. Using the words listed below, describe each of the following events - Impossible, unlikely, even, likely, certain a) Rolling a number 5 b) Rolling an odd number? c) Rolling the number 9? d) Rolling a number greater than 2? e) Rolling a number less than 7? 3 Draw the probability scale and then place the letters from each event on the scale.

36 Calculating probability HW 33 1 This four-sided dice has a shape drawn on each side a) How many possible outcomes are there? b) The dice is rolled once. What is the probability of it landing on a face that shows a triangle? 2 Alessandra put 5 blue counters, 4 red counters and 1 pink counter in a bag. What is the probability that the counter is a) Blue? b) Red? c) Pink? d) Blue or pink? e) Not pink? 3 Alessandra then writes her name on card, with one letter on each one, and puts them in a different bag. What is the probability that she pulls out a a) Letter A? b) Letter A or S? c) Not the letter S? d) The letter L or N? 4 Astronomers predict that there is a 45% chance of a solar storm tomorrow. What is the probability that there will not be a solar storm tomorrow?

37 Experimental probability HW 34 1) Sanchez s teacher secretly put 10 cubes in a bag. Some were blue, some yellow and some black. Sanchez took one out and recorded its colour in the tally chart below. He then put the cube back and repeated this 20 times. a) Copy and complete the table below b) Which colour is most likely to be picked from the bag? 2 The tally chart shows the visits to some Post Office cashier desks on a Saturday morning. a) Copy and complete the table below b) Which cashier desk was visited by the most customers? c) Work out the estimated probability that the next customer will visit cashier desk 3. Write your answer as a percentage.

38 Solving geometrical problems HW 35 1 Work out the size of any angles marked with a letter 2 Work out the size of each angle marked with a letter. 3) Find the value of x in each of these diagrams.

39 Parallel lines HW 36 1 Look at the diagram and fill in the spaces using the following words. Opposite, corresponding or alternate. 2 Work out the angles marked with letters. Give a reason for your answer. 3 Write down the angles marked with letters. Give a reason for each answer.

40 Interior and exterior angles HW 37 1 Work out the angles marked with letters. Give a reason for your answer each time. 2 Work out angle x. Give a reason for your answer. 3 Work out the size of angles x and y. Give a reason for your answer. 4 Work out angles a and b. Give a reason for your answer.

41 Straight-line graphs HW 38 1 Work out the gradients of each of these lines 2 Using the graphs shown, copy and complete this table. Where do you think the line y = 3x + 5 will cross the y-axis? 4) Write down the equations of these lines A: B: C: D:

42 Midpoints HW 39 1 Work out the midpoints between the following coordinates: a) (0,3) and (6, 9) b) (1, 5) and (7, 1) c) (-1, 4) and (3, 2) d) (7, 4) and (-3, 0)

43 Direct proportion HW 40 1) 2) a) Copy and complete the table b) Are gallons and litres in direct proportion? Explain 3) Decide if the following quantities are in direct proportion. Explain why.

44 Averages and range HW 41 1) Ten families live down a street. Here are the numbers of children in those families. 1, 3, 5, 2, 3, 2, 0, 2, 2, 3. a) Find the mode b) Work out the range c) Check that the total number of children is 23 d) Work out the mean number of children per family 2) The frequency table shops the numbers of children in families in another street. a) How many families have more than two children? b) How many families are there altogether? c) Find the mode d) Work out the mean number of children per family 3) Here are Pat s and Sam s marks in their maths homework this term. Pat: 8, 2, 9, 6, 10, 1, 10 Sam: 7, 8, 7, 7, 6, 7, 8, 8 a) Work out the median and range for Pat. b) Work out the median and range for Sam. Median: c) Who would be the better person to help you with your maths homework? Explain your answer

45 Tables HW 42 1 This two way table shows the information about the animals treated in a vets surgery a) Copy and complete the table b) How many cats were treated? c) What is the total number of animals treated? d) What fraction of the total number of animals treated were cats? e) What fraction of the animals treated were dogs? 2 Here are the masses of turkeys on sale in a butcher s shop (kg) 10.5, 15.2, 16.0, 14.7, 11.0, 10.9, 14.0, 13.2, 15.9, a) What does 10 m < 12kg mean? b) Copy and complete the table c) State the modal class

46 Charts and graphs HW 43 1 This pie chart shows the meals people ate in a restaurant. a) What fraction of the people ate i) Chicken? ii) Fish? iii) Lamb? v) Chicken or fish? iv) Vegetarian? 2 The stem and leaf diagram shows the ages of people using a swimming pool in one day. a) What does 4 0 mean? b) How many people in their 40s were in the pool? c) How old was the youngest person in the pool? d) What was the mode? e) Find the median age of people in the swimming pool 3 For each graph, decide whether it shows a positive correlation, negative correlation or no correlation.

47 Shapes and Symmetry HW 44 1 Write down the number of lines of symmetry for each of these shapes 2 Aaron says, A rectangle has these four lines of symmetry. Is Aaron correct? Explain your answer. 3 Which pairs of arrows are congruent? 4 Write down the order of rotational symmetry of each of these shapes 5 Copy and complete this table Shape Number of lines of symmetry Order of rotational symmetry Square Equilateral triangle Parallelogram kite

48 Translations, reflections and enlargements HW 45 1 Copy this shape on to squared paper Draw the image of the shape after these translations a) 3 squares right, 2 squares down. Label this shape A b) 4 squares left, 1 square up. Label this shape B 2 Describe each translation. a) shape A to shape B b) shape B to shape C 3a) Draw the original shape from question 1 enlarged by scale factor 2. b) Write down the ratio of the length of the sides of the original shape to the enlarged shape. 4 Copy this diagram. Draw the image of the shape after a reflection in the line: a) Y = 1. Label your reflected shape A b) X = -1. Label your reflected shape B

49 Rotations and combined transformations HW

50 Fractions and decimals HW 47 1 Write each decimal as a fraction in its lowest terms. a 0.6 b 0.25 c 0.55 d 0.64 e 0.92 f g h Change these decimals to mixed numbers. Give your answers in their lowest terms. a 1.8 b 9.45 c d e Change these fractions to decimals. Do not use a calculator. a f b e g j Use a calculator to write each fraction as a decimal. a b e Gina asked some boys in Year 8 which is their favourite sport to watch on television. The table shows the results. Golf Football Tennis Cricket Motor Racing a How many boys did Gina ask? b What fraction of the total chose golf? Give your answer in its lowest terms. c Change your answer to part b into a decimal. d What fraction of the total chose cricket? Give your answer in its lowest terms. e Change your answer to part d into a decimal. Use a calculator. c h c d i d

51 Ratios HW 48 1 Write the proportion of each shape that is shaded as a fraction in its simplest form. a b c 2 Use the shapes in question 1. Write the ratio of shaded area to unshaded area. 3 The bar chart shows the number of books read by a group of 36 pupils in three months. 4 Simplify these ratios. a What proportion of pupils read 5 b books? Give your answer as a fraction in its simplest form. What proportion of pupils read 5 or more books? Give your answer as a fraction in its simplest form. c What is the ratio of pupils who read 5 books to all the other pupils? d What is the ratio of pupils who read 5 or more books to pupils who read less than 5 books? a 6 : 3 b 4 : 12 c 5 : 20 d 15 : 25 e 40 : 24 f 60 : 35 g 42 : 28 h 16 : 8 i 9 : 45 j 10 : 55 k 49 : 14 l 36 : 48 5 The following pairs of ratios are equivalent. Work out the unknown values. a 1 : 3 = 4 : x b 11 : p = 33 : 18 c n : 7 = 18 : 42 d 2 : 9 = y : 36 e 5 : 25 = 1 : q f 1 : 3 : 6 = 3 : g : h

52 Using equations 1 HW 49 1 Solve these equations. a p + 7 = 9 b x 4 = 5 c 3b + 2 = 14 d 5k 3 = 27 e 6q + 3 = 9 f = 6 t 2 Solve these equations. a 5x + 8 = 3x + 12 b 11 3t = 5t 13 c 3(m + 2) = 21 d 2(3g + 4) = 5(g + 3) 3 For each of these shapes, write an equation and solve it to find the value of the letter. Then work out the size of each angle in the shapes. b c a x a 12 p x a 3 3p 15 p + 55 x 2p + 20

53 Using equations 2 HW 50 1 In triangle ABC, AB = AC. The perimeter of triangle ABC is 30 cm. A a Write B an equation for C the perimeter of the triangle. (x 3) cm b Solve your equation to find x. c Write down the lengths of AB and BC. 2 The perimeter of this rectangle is 24 cm. a Write an equation for the perimeter of the triangle. b Solve your equation to find K. c Write down the lengths of the sides of the rectangle. 3 The perimeter of this trapezium is 40 cm. a Write an equation (2y + 3) for cm the perimeter of the trapezium. b Solve your equation to find y. c (x + 6) cm y cm K cm (y + 2) cm (x + 6) cm (4K 3) cm y cm Write down the lengths of the sides of the trapezium.

54 Multiples, factors and primes HW 51 1 a Write the first ten multiples of 3. b Write the first ten multiples of 4. c Write the numbers that are common multiples of 3 and 4. d What is the lowest common multiple of 3 and 4? 2 Find the lowest common multiple of each set of numbers. a 4, 7 b 9, 12 c 3, 4, 5 3 a Write one number which fits all three of these statements. It is a multiple of 6. It is a multiple of 8. It ends in 2. b Explain why a number which ends in 5 cannot be a multiple of 6. 4 a Write down all the factors of 24. b Write down all the factors of 40. c Write down the factors that are common to 24 and 40. d What is the highest common factor of 24 and 40? 5 Find the highest common factor of each set of numbers. a 30, 48 b 84, 210 c 48, 84, a 11 has two factors: 1 and 11. What type of number is 11? b Investigate the number of factors that each number from 1 to 20 has. It may help you to use a table like the one shown. Comment on your results. Number Factors Number of factors , 2 2

55 Probability HW 52 1 Jade has one black sock on. There are 19 socks in her draw. 11 are black and the rest are different colours. She picks out one sock from the draw at random. a What is the probability that it is black? b What is the probablilty that it is not black? 2 Salik buys a ticket in a raffle. The probability that Salik will win first prize is 2%. What is the probability he will not win first prize? 3 A spinner is divided up in to lots of sections. It only has the numbers 1 to 4 on it. The probability of spinning a 4 is 0.1. The probability of spinning a 1 is 0.5. The probability of spinning a 2 is the same as the probability of spinning a 3. What is the probability of spinning a 2? 4 Kerry has some coloured counters in a bag. a b She is going to take a counter from the bag at random. The table shows the probabilities of taking a red, blue, green or yellow counter. Colour Red Blue Green Yellow Probability Explain how you know that all the counters in the bag are either red, blue, green or yellow. Kerry says The total number of counters in the bag is 20. Why is Kerry not correct? 5 Here are two spinners, A and B. Luca spins the pointer on each spinner. He adds the two scores together. a b Draw a sample space diagram to show all the possible outcomes. Use the diagram to find the probability of these outcomes. 1 8 i an even number ii a square number iii less than 8 iv at least 11 v a prime number

56 Analysing data HW 53 1 Jade has one black sock on. There are 19 socks in her draw. 11 are black and the rest are different colours. She picks out one sock from the draw at random. a What is the probability that it is black? b What is the probablilty that it is not black? 2 Salik buys a ticket in a raffle. The probability that Salik will win first prize is 2%. What is the probability he will not win first prize? 3 A spinner is divided up in to lots of sections. It only has the numbers 1 to 4 on it. The probability of spinning a 4 is 0.1. The probability of spinning a 1 is 0.5. The probability of spinning a 2 is the same as the probability of spinning a 3. What is the probability of spinning a 2? 4 Kerry has some coloured counters in a bag. a b She is going to take a counter from the bag at random. The table shows the probabilities of taking a red, blue, green or yellow counter. Colour Red Blue Green Yellow Probability Explain how you know that all the counters in the bag are either red, blue, green or yellow. Kerry says The total number of counters in the bag is 20. Why is Kerry not correct? 5 Here are two spinners, A and B. Luca spins the pointer on each spinner. He adds the two scores together. a b Draw a sample space diagram to show all the possible outcomes. Use the diagram to find the probability of these outcomes. 1 8 i an even number ii a square number iii less than 8 iv at least 11 v a prime number

57 Sequences HW 54 1 For each of the sequences below i describe the term-to-term rule ii write the next three terms in the sequence a b c d e f a The first term of a sequence is 12. The term-to-term rule is add 5. i ii What is the third term of the sequence? What is the sixth term of the sequence? b The sixth term of a different sequence is 5. The term-to-term rule is subtract 2. i ii What is the fifth term of the sequence? What is the first term of the sequence? 3 The 2nd, 3rd, 4th and 5th terms of each sequence are given. i ii Find the term-to-term rule for each sequence. Find the first term of each sequence. a 5, 11, 17, 23 b 16, 25, 34, 43 c 2 1, 1, 2, 2 2 d 2.25, 2.20, 2.15,

58 Percentages HW 55 1 Write each percentage as a fraction in its simplest form. a 20% b 32% c 55% d 84% e 7% f 2.5% 2 Write each decimal as a percentage. a 0.75 b 0.13 c 0.04 d e f Grace asked 40 pupils in her year to name their favourite fruit. Her results are shown in the table. a Apple Pear Strawberry Melon Banana Work out what fraction of the group chose each type of fruit. Write each fraction in its simplest form. b What percentage of the group chose each type of fruit? 4 Harry used his calculator to change 1 7 He said To the nearest percent, 1 7 to a percentage. is 14%. His friend Dan said So to the nearest percent, 2 7 Show that Dan is wrong. is 28%. 5 Work out each amount by changing the percentage to a fraction. a 15% of 60 b 36% of 25 c 22% It may of 65 help to simplify some of the d 7% of 120 e 40% of 80 f 9% of 56 6 Find these amounts without using the % key on your calculator a 38% of 75 b 42% of 15 m c 54% of 125 km d 3.5% of 620 kg e 125% of 78 g f 17% of 338 m g 7.1% of 5500 h 37.5% of 88 mm

59 Written methods HW 56 1 Work these out. a b c d e f Tina flies from Manchester to Paris. At Manchester airport her case is weighed and the scales show 15.3 kg. In Paris she buys presents for her family, they weigh 3 kg, 1.45 kg, 2.9 kg and 0.83 kg. a What is the total weight of the presents in kilograms? b Tina puts the presents in her case when she flies home. What does it weigh now? c Tina may take a case on board weighing up to 25 kg without paying excess baggage charges. Does her case weigh less or more than 25 kg? How much less or more? 3 i Estimate the answer to each calculation by rounding. Show your working clearly. ii Work out each answer. a b c The currency exchange rate between British pounds and American dollars is 1 = US $ How many dollars would you get for 350? 5 Henry bought the items on the list. He paid with a 20 note. Work out his change. Show all your working. 6 What is the cost of 2.4 metres of fabric at 8.65 a metre? 7 Work these out. 3 pencils at 28p each a b c pads of paper at 2.35 each 2 magazines at 2.89 each

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