Higher booklet answers_(3)_(1)_(1)

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Higher booklet answers_(3)_(1)_(1)

  1. 1. GCSE Mathematics ESSENTIAL REVISION QUESTIONS MathsWatch Higher Book with answers to all questions www.mathswatch.com enquiries to info@mathswatch.com
  2. 2. CONTENTS Grades C/D......................................... 3 to 40 B............................................. 41 to 54 A/A* ...................................... 55 to 71
  3. 3. 85 Essential Questions at C to D (1 to 72 are non-calculator) 1T) a) 4t + 7t Grade C a) 11t b) 4t × 7t b) 28t2 c) 6y + 2w – 5y Clip 102 c) y + 2w d) 6y × 3t d) 18yt or 18ty e) 4e2 × 3e3 e) 12e5 f) m7 ÷ m5 f) m2 y5 g) y3 g) y2 h) 3y3 6y 4 h) 2y 1S) a) 3t + 8t a) 11t b) 2t × 9t b) 18t2 c) 12y + 3w – 5y c) 7y + 3w d) 4y × 2t d) 8yt or 8ty e) 3e5 × 2e7 e) 6e12 f) x4 ÷ x3 f) x r7 g) r4 g) h) 3r2 r3 6r 5 h) 2r 3 2T) a) Expand 5(3y – 1) a) 15y – 5 b) Expand 3x(2x + 4) b) 6x2 + 12x c) Expand and simplify 2(3x + 5) – 3(4x – 2) c) –6x + 16 d) Expand and simplify 5(2y – 3) + 2(y – 1) d) 12y – 17 e) (2x + 3)(x – 4) e) 2x2 – 5x – 12 Grade C 2S) a) Expand 3(2y – 4) Clip 103 a) 6y – 12 b) Expand 5x(3x + 2) b) 15x2 + 10x c) Expand and simplify 5(2x + 1) – 2(3x – 4) c) 4x + 13 d) Expand and simplify 4(3y – 2) + 2(3y – 2) d) 18y – 12 e) (3x – 4)(2x – 1) e) 6x2 – 11x + 4 Page 3 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 3
  4. 4. 3T) Find the nth term of the following patterns a) 3, 5, 7, 9, 11 . . . . . a) 2n + 1 Grade C b) 8, 13, 18, 23, 28, . . . . . Clip 112 b) 5n + 3 c) 9, 6, 3, 0, –3, . . . . . c) –3n + 12 3S) Find the nth term of the following patterns a) 2, 6, 10, 14, 18 . . . . . a) 4n – 2 b) 7, 16, 25, 34, 43, . . . . . b) 9n – 2 c) 5, 2, –1, –4, –7, . . . . . c) –3n + 8 4T) Number of Frequency smarties 29 2 30 5 31 2 32 1 a) From the table above, find the mean number of a) 30.2 smarties in a tube. b) 30 b) Find the median number of smarties in a tube. Grade C Clip 133 4S) Number of Frequency smarties 29 2 30 1 31 5 32 2 a) From the table above, find the mean number of a) 30.7 smarties in a tube. b) 31 b) Find the median number of smarties in a tube. Page 4 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 4
  5. 5. 5T) Factorise the following: a) 2x + 6 a) 2(x + 3) b) 2x + 8 b) 2(x + 4) c) 2x + 12 Grade C c) 2(x + 6) d) 3x + 6 Clip 104 d) 3(x + 2) e) x2 + x e) x(x + 1) f) 2x2 – 6x f) 2x(x – 3) g) 3h(3h + 2) g) 9h2 + 6h h) 2x(4x – 5) h) 8x2 – 10x 5S) Factorise the following: a) 2t + 10 a) 2(t + 5) b) 3m – 12 b) 3(m – 4) c) 4y + 8 c) 4(y + 2) d) 2x2 + 6 d) 2(x2 + 3) e) t2 + t e) t(t + 1) f) 5t2 + 10t f) 5t(t + 2) g) 7t2 – 14t g) 7t(t – 2) h) 9h2 – 30h h) 3h(3h – 10) 6T) a) If a piece of wood is measured as 8cm to the a) Greatest is 8.5cm nearest cm, what is the greatest possible Least is 7.5cm length and the least possible length? b) Greatest is 19.85cm b) If a piece of wood is measured as 19.8cm to the nearest tenth of a cm, what is the greatest possible Least is 19.75cm length and the least possible length? Grade C Clip 125 6S) a) If a piece of wood is measured as 5cm to the a) Greatest is 5.5cm nearest cm, what is the greatest possible Least is 4.5cm length and the least possible length? b) If a piece of wood is measured as 6.7cm to the b) Greatest is 6.75cm nearest tenth of a cm, what is the greatest possible Least is 6.65cm length and the least possible length? Page 5 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 5
  6. 6. 7T) a) If a = 3 and t = –2 find the value of (i) 3a a) (i) 9 (ii) a2 Grade D (ii) 9 (iii) 5a2 (iii) 45 (iv) 4a – 2t Clip 66 (iv) 16 (v) 2(3a + t) (v) 14 (vi) 2 (vi) 4a − t 7 b) Colin said “when x = 3, then the value of 4x2 is 144” b) Sue because 4x2 is 4 × x2 Sue said “when x = 3, then the value of 4x2 is 36” Who was right? Explain why. 7S) a) If a = 4 and t = –5 find the value of a) (i) 12 (i) 3a (ii) 16 (ii) a2 (iii) 80 (iii) 5a2 (iv) 26 (iv) 4a – 2t (v) 14 (v) 2(3a + t) (vi) 3 (vi) 4a − t 7 b) Colin said “when x = 5, then the value of 4x2 is 400” b) Sue because Sue said “when x = 5, then the value of 4x2 is 100” 4x2 is 4 × x2 Who was right? Explain why 8T) a) Write 2340000 in standard form. a) 2.34 × 106 b) Write 0.00042 in standard form. b) 4.2 × 10–4 c) Write 7.8 × 106 as a normal number. c) 7800000 d) Write 4.71 × 10–5 as a normal number. d) 0.0000471 Grade C Clip 97 8S) a) Write 630000000 in standard form. a) 6.3 × 108 b) Write 0.00000715 in standard form. b) 7.15 × 10–6 c) Write 9.17 × 105 as a normal number. c) 917000 d) Write 8.23 × 10–6 as a normal number. d) 0.00000823 Page 6 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 6
  7. 7. 9T) Write the following numbers as the product of their prime factors a) 48 Grade C a) 2 × 2 × 2 × 2 × 3 b) 60 Clips 95 & 96 b) 2 × 2 × 3 × 5 c) Find the Highest Common Factor of 48 and 60 c) 12 d) Find the Lowest Common Multiple of 48 and 60 d) 240 9S) Write the following numbers as the product of their prime factors a) 90 a) 2 × 3 × 3 × 5 b) 120 b) 2 × 2 × 2 × 3 × 5 c) Find the Highest Common Factor of 90 and 120 c) 30 d) Find the Lowest Common Multiple of 90 and 120 d) 360 10T) a) Draw an angle of 70 degrees and then use ruler Grade C Clip 127 and compasses to bisect it. b) Draw a line of length 9cm and then bisect it Grade C Clip 129 using compasses. c) Use compasses to draw a triangle ABC with AB Grade D Clip 80 equal to 9cm, AC 7cm and BC 4cm 10S) a) Draw an angle of 60 degrees and then use ruler and compasses to bisect it. b) Draw a line of length 11cm and then bisect it using compasses. c) Use compasses to draw an isosceles triangle with the base equal to 8cm and the other two sides of length 12cm 11T) What is 2 × 5 + 7 × 3? Grade D 31 Clip 59 11S) Work out the answer to 38 – 3 × 4 26 12T) What is 2.3 × 0.15? 0.345 Grade D 12S) What is 2.7 × 0.13? 0.351 Clip 60 13T) –3 x < 4 Grade C Clip 108 x is an integer. Write down all the possible values. –3, –2, –1, 0, 1, 2, 3 13S) –2 x 3 x is an integer. Write down all the possible values. –2, –1, 0, 1, 2, 3 Page 7 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 7
  8. 8. 14T) Here are the front elevation, side elevation and the plan of a 3-D shape. Draw a sketch of the 3-D shape. Grade D Front elevation Side elevation Clip 81 Plan 14S) Here are the front elevation, side elevation and the plan of a 3-D shape. Draw a sketch of the 3-D shape. Front elevation Side elevation Plan 3 of 600 15T) a) Work out 10 Grade D a) 180 b) Work out 5 of 800 8 Clip 55 b) 500 c) Work out 5 × 42 c) 30 7 15S) a) Work out 7 of 400 10 a) 280 b) Work out 2 of 900 9 b) 200 c) Work out 3 × 56 8 c) 21 Page 8 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 8
  9. 9. 16T) If you share out £240 between Alice and Bill in the £60 ratio 5 : 3, how much more does Alice get compared with Bill? Grade C Clip 94 16S) If you share out £60 between Alice and Bill in the £24 for Alice and ratio 2 : 3, how much does each of them get? £36 for Bill 17T) Sara and Fred share tips from their job in the ratio £14 2 : 5. If Fred receives £35 how much does Sara get? Grade C Clip 94 17S) Sara and Fred share tips from their job in the ratio £24 3 : 4. If Sara receives £18 how much does Fred get? 18T) Some plant heights are measured as shown in the table, below. Height in cm Frequency 0 < h 20 4 20 < h 40 3 40 < h 60 2 60 < h 80 1 a) Find an estimate for the mean height of a plant. a) 30 b) In which interval does the median height lie? b) 20 < h 40 18S) Some plant heights are measured as shown in the table, below. Height in cm Frequency 0 < h 20 1 20 < h 40 2 40 < h 60 4 60 < h 80 3 a) Find an estimate for the mean height of a plant. a) 48 b) In which interval does the median height lie? b) 40 < h 60 Grade C Clip 133 Page 9 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 9
  10. 10. Page 10 mathswatch@aol.co.uk www.mathswatch.com ©MathsWatch Page 10 Reflection in y = –x c) 210987654321 210987654321 210987654321 210987654321 210987654321 76543210987654321 210987654321 76543210987654321 210987654321 76543210987654321 210987654321 76543210987654321 210987654321 210987654321 76543210987654321 76543210987654321 210987654321 210987654321 T 76543210987654321 76543210987654321 U 210987654321 210987654321 76543210987654321 76543210987654321 210987654321 76543210987654321 210987654321 76543210987654321 move U back on to the shaded shape. Decribe fully the single transformation that will c) centre of rotation and label the new shape U Rotate T 90º clockwise using (0, 0) as the b) Reflect the shaded shape in the x axis and label it T 19S) a) Grade D Clips 74, 75, 77 Reflection in y = –x c) 76543210987654321 76543210987654321 76543210987654321 76543210987654321 76543210987654321 76543210987654321 76543210987654321 76543210987654321 U 76543210987654321 76543210987654321 76543210987654321 76543210987654321 210987654321 210987654321 210987654321 210987654321 210987654321 T 210987654321 210987654321 move U back on to the shaded shape. 210987654321 210987654321 210987654321 210987654321 210987654321 Decribe fully the single transformation that will c) 210987654321 210987654321 210987654321 210987654321 210987654321 centre of rotation and label the new shape U Rotate T 90º anticlockwise using (0, 0) as the b) Reflect the shaded shape in the y axis and label it T 19T) a)
  11. 11. 20T) a) Enlarge triangle A scale factor 3 using (2, 4) as centre of enlargement b) Enlarge triangle A scale factor ½ using (4, 0) as centre of enlargement Grade D Clip 76 20S) a) Enlarge triangle A scale factor 2 using (4, 5) as centre of enlargement b) Enlarge triangle A scale factor ½ using (-2, 2) as centre of enlargement Page 11 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 11
  12. 12. 21T) Find the exterior angle of this regular octagon 45 degrees Grade D Clip 70 21S) Find the exterior angle of this regular hexagon 60 degrees 22T) a) In the triangle below, find an expression, in terms a) 4x + 8 of x, for the perimeter of the triangle. Simplify your expression. b) x = 9 cm b) If the perimeter of the triangle 2x 2x is 44 cm, find the value of x. Grade C 8 Clip 106 22S) a) In the rectangle below, find an expression, in terms a) 8x + 6 of x, for the perimeter of the rectangle. Simplify your expression. b) x = 5 cm 3x + 5 x–2 b) If the perimeter of the rectangle is 46 cm, find the value of x. Page 12 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 12
  13. 13. 23T) Find the size of angle n, giving reasons A ABC = 60°(angles on st. line = 180) n = 78° (angles in add B C Grade D up to 180) Clips 68, 69 23S) Find the size of angles x and y, giving reasons A x = 56° (angles in =180, base angles are equal) ABC = 56°(base angles of isos. are equal) y = 124° (angles on st. line = 180°) B C 24T) Find the size of angle x, giving reasons Grade D ° Clip 67 BRS = 30°(angles on straight line add up to 180°) ° x = 30° (alternate angles) 24S) Find the size of angles x and y, giving reasons x = 86° (angles in quadrilateral add up to 360°) y = 74° (alternate angles) Page 13 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 13
  14. 14. 25T) Solve the following equations a) 2x = 7 a) 3.5 b) x – 8 = 4 c) 2x + 3 = 11 Grade C b) c) 12 4 d) x +5=7 Clip 105 d) 6 3 e) 3 e) 2(5x – 2) = 26 f) 5 2 x – 3 = –1 g) 3.5 f) 5 g) 3x + 4 = 5x – 3 25S) Solve the following equations a) 3x = 12 a) 4 b) x – 9 = 3 b) 12 c) 3x + 2 = 14 c) 4 x +6=4 d) –6 d) 3 e) 7 e) 2(3x + 2) = 46 f) 7.5 2 x – 6 = –3 g) –3 f) 5 g) 4x + 3 = 2x – 3 26T) Draw a stem and leaf diagram to show the following 3 4 6 information. 4 1 7 7 9 The heights of 12 plants in cm are: 5 1 2 2 8 3.6, 5.2, 4.1, 3.4, 5.8, 6.2, 4.7, 5.2, 6 2 4 4.7, 6.4, 5.1, 4.9 Key 4 | 1 means 4.1 Grade D Clip 89 26S) Draw a stem and leaf diagram to show the following 5 0 2 9 information. 6 2 4 7 8 The weights of 10 people in kg are: 7 1 5 59, 52, 81, 67, 75, 62, 50, 64, 68, 71 8 1 Key 6 | 2 means 62 27T) For each of the following, state whether it is a length, area, volume or none of them (a, b, m, q, r, x are lengths) mq p2 r r3 V A L V A A a 2b 2ab r ab(m + q) q x Grade C Clip 124 27S) For each of the following, state whether it is a length, area, volume or none of them (a, b, m, q, r, x are lengths) pqr r2 A V A V V L ab 2ab2 r2 + rx ab(m + q) 2 x Page 14 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 14
  15. 15. 28T) a) Anne buys 46 litres of diesel at £1.32 per litre. a) £60.72 How much does she spend altogether on diesel? b) James spends £65.72 on 53 litres of petrol. b) £1.24 How much was each litre of petrol? Grade D Clip 60 28S) a) Sara buys 34 litres of diesel at £1.43 per litre. a) £48.62 How much does she spend altogether on diesel? b) Sid spends £57.12 on 42 litres of petrol. b) £1.36 How much was each litre of petrol? 2 3 1 1 29T) a) 3 + 8 a) 24 b) 3 1 5 – 4 Grade D b) 7 20 3 8 Clips 56 c) 2 c) × 9 3 4 and 57 d) 2 1 d) 4 3 ÷ 6 3 2 1 5 29S) a) 4 + 3 a) 12 5 2 11 b) 7 – 5 b) 35 c) 3 6 9 c) 10 × 8 40 d) 4 3 d) 22 5 ÷ 10 3 P 30T) Draw a pie chart to show the following information B C Plain Crisp flavour Frequency Cheese Cheese 80° 8 Plain 19 Grade D Plain 190° Beef Beef Prawn 6 3 Clip 86 Prawn 60° 30° 30S) Draw a pie chart to show the following information B P C Plain Crisp flavour Frequency Cheese 8 Cheese 160° Plain 6 Plain 120° Beef 1 Beef 20° Prawn 3 Prawn 60° Page 15 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 15
  16. 16. 31T) Find the areas of the following shapes a) 7m b) a) 21m2 3m 4cm b) 10cm2 c) 160cm2 5cm c) 18cm 4cm 12cm 11cm Grade D Clip 73 31S) Find the areas of the following shapes a) b) a) 54m2 9m 6m 7cm b) 42cm2 c) 222cm2 12cm c) 24cm 4cm 13cm 14cm Page 16 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 16
  17. 17. 32T) Find the surface area of this cuboid. 92cm2 Grade C 3cm Clip 121 2cm 8cm 32S) Find the surface area of this cuboid. 190cm2 5cm 3cm 10cm 33T) Make the letter in the bracket the subject of the formula. v-u a) v = u + at (a) Grade C a) a= t b) x – t = bc a (x) Clip 107 b) x = a(bc + t) 33S) Make the letter in the bracket the subject of the formula. v2 - u2 a) v2 = u2 + 2as (a) a) a= 2s b) x +y=c (x) a b) x = a(c – y) 34T) Find the following: a) 10% of £700 a) £70 b) 15% of £80 Grade D b) £12 c) 35% of £600 c) £210 d) 17.5% of £48 Clip 52 d) £8.40 34S) Find the following: a) 40% of £260 a) £104 b) 15% of £900 b) £135 c) 85% of £800 c) £680 d) 17.5% of £240 d) £42 Page 17 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 17
  18. 18. 35T) Sally’s mother lives 80km from Sally. This is the journey to her mother’s house. a) 100km/h 100 b) 30 mins Distance in km from home c) 30km/h 80 60 40 20 0800 0900 1000 1100 1200 Time a) Sally has a rest at 8.30. What speed had she been travelling at until 8.30? b) How long did she rest for? c) What speed did she travel at for the last part of the journey to her mother’s house? d) For the return journey, Sally travelled at 60km/h without a break. Complete the travel graph to show this. Grade C Clip 117 35S) Sally’s mother lives 90km from Sally. This is the journey to her mother’s house. a) 120km/h b) 30km/h 100 Distance in km from home 80 60 40 20 0800 0900 1000 1100 1200 Time a) What speed did Sally travel at until her first rest? b) What speed did she travel at for the last part of the journey to her mother’s house? c) For the return journey, Sally travelled at 80km/h without a break. Complete the travel graph to show this. Page 18 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 18
  19. 19. 36T) a) Complete the table for the equation y = 2x2 – 3x x –2 –1 0 1 2 3 Grade C –2 –1 0 1 2 3 y 14 Clip 116 14 5 0 –1 2 9 b) Draw the graph of y = 2x2 – 3x on the axes at the bottom of the page c) Use your graph to find the value of y c) 3.6 when x = 2.3 d) Use your graph to find the value of y d) 9 when x = –1.5 e) Use your graph to solve 2x2 – 3x = 5 e) x = –1 and x = 2.5 f) Use your graph to solve 2x2 – 3x = 8 f) x = –1.3 and x = 2.9 y 14 13 12 11 10 9 8 7 6 5 4 3 2 1 O x -2 -1 1 2 3 -1 -2 Page 19 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 19
  20. 20. 36S) a) Complete the table for the equation y = 3x2 – x x –2 –1 0 1 2 Grade C –2 –1 0 1 2 y 14 Clip 116 14 4 0 2 10 b) Draw the graph of y = 3x2 – x on the axes at the bottom of the page c) Use your graph to find the value of y c) 5.3 when x = 1.5 d) Use your graph to find the value of y d) 8.25 when x = –1.5 e) Use your graph to solve 3x2 – x = 10 e) x = –1.7 and x = 2 y 14 13 12 11 10 9 8 7 6 5 4 3 2 1 O x -2 -1 1 2 3 -1 -2 Page 20 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 20
  21. 21. 5 37T) Draw a set of axes going from –5 to +5 y = 3x + 1 4 3 a) Draw the graph of y = 2x – 3 b) What is the gradient? Grade C b) 2 2 1 37S) Draw a set of axes going from –5 to +5 Clip 113 -5 -4 -3 -2 -1 O -1 1 2 3 4 5 -2 a) Draw the graph of y = 3x + 1 y = 2x – 3 -3 b) What is the gradient? b) 3 -4 -5 38T) The table below shows the probability of an oddly shaped 4-sided dice landing on 1, 2, 3, or 4. a) Work out the value of x a) 0.24 b) If the dice is rolled 1000 times how many 2s b) 370 would you expect to get? 1 2 3 4 Grade C 0.15 0.37 0.24 x Clip 132 38S) The table below shows the probability of an oddly shaped 4-sided dice landing on 1, 2, 3, or 4. a) Work out the value of x a) 0.23 b) If the dice is rolled 1000 times how many 3s b) 140 would you expect to get? 1 2 3 4 0.29 0.34 0.14 x other answers 39T) Draw a plane of symmetry on this shape are possible Grade D Clip 83 39S) Draw a plane of symmetry on this shape other answers are possible Page 21 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 21
  22. 22. 40T) Frequency Frequency Height Frequency 0 to 10 1 7 7 10 to 20 4 6 6 20 to 30 3 5 5 30 to 40 2 4 4 a) On the first set of axes, 3 3 draw a frequency diagram 2 2 b) On the second set of axes, draw a frequency polygon 1 1 0 0 0 10 20 30 40 50 0 10 20 30 40 50 Grade D Height Height Frequency Frequency Clip 88 7 7 6 6 5 5 ANSWERS for 40T 4 4 × 3 3 × 2 2 × 1 1 × 0 0 0 10 20 30 40 50 0 10 20 30 40 50 Height Height 40S) Frequency Frequency Height Frequency 0 to 10 3 7 7 10 to 20 7 6 6 20 to 30 2 5 5 30 to 40 1 4 4 a) On the first set of axes, 3 3 draw a frequency diagram 2 2 b) On the second set of axes, draw a frequency polygon 1 1 0 0 0 10 20 30 40 50 0 10 20 30 40 50 Height Height Frequency Frequency 7 7 × 6 6 5 5 ANSWERS for 40S 4 4 3 3 × 2 2 × 1 1 × 0 0 0 10 20 30 40 50 0 10 20 30 40 50 Height Height Page 22 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 22
  23. 23. 41T) a) In a room there are 7 boys and 3 girls. a) 70% What percentage of the people are boys? b) 35% b) In a room there are 13 boys and 7 girls. What percentage of the people are girls? c) 60% c) Sally scores 24 marks out of 40 in a Science test. What was her percentage score? Grade D Clip 54 41S) a) In a room there are 11 boys and 9 girls. a) 55% What percentage of the people are boys? b) In a room there are 13 boys and 12 girls. b) 48% What percentage of the people are girls? c) 90% c) Emma scores 54 marks out of 60 in a Science test. What was her percentage score? 42T) A point, P, moves so that the locus of P is always 2 cm from the line AB. Draw the locus of P. Grade C Clip 130 B A 42S) A point, P, moves so that the locus of P is always equidistant from lines AB and AC. Draw the locus of P. B A C Page 23 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 23
  24. 24. 43T) a) Sketch a scatter diagram with positive a) correlation × × × × × ×× ×× ‘hair length’, ‘hair colour’, ‘intelligence,’ ×× × ‘circumference of wrist’, ‘height’, ‘ice cream ×× sales’, ‘weight’, ‘outside temperature’ ‘sale of extra-warm jackets’, ‘eye colour’ b) (i) height and weight b) From the list above select two sets of data which would have or Ice cream sales and temp. (i) a positive correlation (ii) hair length and hair colour (ii) no correlation or hair colour and intelligence Grade D Clip 87 etc 43S) a) Sketch a scatter diagram with negative a) ×× correlation ×× × × × ‘hair length’, ‘hair colour’, ‘intelligence,’ ×× × ×× ‘circumference of wrist’, ‘height’, ‘ice cream × × sales’, ‘weight’, ‘outside temperature’ ‘sale of extra-warm jackets’, ‘eye colour’ b) From the list above select two sets of data which b) (i) temp. and sale of jackets would have (ii) eye colour and intelligence (i) a negative correlation or hair length and weight (ii) no correlation etc 44T) a) What are the first four multiples of 7? a) 7 14 21 28 b) Write down all the factors of 30. b) 1 2 3 5 6 10 15 30 c) What are the first six prime numbers? c) 2 3 5 7 11 13 44S) a) What are the first four multiples of 5? a) 5 10 15 20 b) Write down all the factors of 40. b) 1 2 4 5 8 10 20 40 c) Which two prime numbers come next, after 13? c) 17 19 Grade D Clip 44 45T) Solve the inequality 2x + 3 < 11 x<4 45S) Solve the inequality 5x – 7 > 43 x > 10 Grade C Clip 109 46T) Evaluate 53 125 Grade D Clip 45 16 46S) Evaluate 24 Page 24 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 24
  25. 25. 47T) Find the volume of this triangular prism. Volume = 84cm3 6cm 7cm Grade C 4cm Clip 122 47S) Find the volume of this triangular prism. Volume = 160cm3 4cm m 10c 8cm 48T) a) Write as a power of 7 73 × 75 Grade C a) 78 b) Write as a power of 2 Clip 111 b) 26 28 ÷ 22 48S) a) Write as a power of 5 a) 57 52 × 54 × 5 b) Write as a power of 3 b) 35 39 ÷ 34 49T) Complete the two-way table which shows the favourite soup of 100 people. Oxtail Tomato Chicken Total Oxtail Tomato Chicken Total Male 25 42 Male 25 12 5 42 Female 18 11 Female 29 18 11 58 Total 54 30 16 100 Total 16 100 Grade D Clip 85 49S) 110 students studied History and Geography as shown in the two-way table. History Geography Both Total History Geography Both Total Female Female 11 12 35 58 Male 8 Male 4 8 40 52 Total 15 20 110 Total 15 20 75 110 40 males studied both subjects. 52 of the students were male. Complete the two-way table. Page 25 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 25
  26. 26. 50T) Measure this angle. 48° 50S) Measure this angle. Grade D Clip 79 114° 51T) The price of a pair of shoes is £75. £82.50 How much are they after a price increase of 10%? 51S) A new car costs £8000. Grade C Clip 93 £6800 If the price is reduced by 15% what is the new price? 52T) 73.5 ÷ 0.21 350 Grade C Clip 100 52S) 18.02 ÷ 0.34 53 53T) What are the first 5 terms of the number sequence 5 8 11 14 17 with the nth term of 3n + 2? Grade D Clip 65 53S) What are the first 5 terms of the number sequence 1 5 9 13 17 with the nth term of 4n – 3? Page 26 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 26
  27. 27. 54T) Translate triangle A by vector -5 -3 87654321 87654321 87654321 87654321 87654321 87654321 87654321 87654321 Grade D Clip 77 54S) Describe fully the transformation which maps triangle A onto triangle B. Translation by vector -6 1 B .. 3 55T) Change the recurring decimal 0.27 into a fraction in its simplest form. 11 .. 7 55S) Change the recurring decimal 0.63 into a fraction in its simplest form. 11 Grade C Clip 98 Page 27 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 27
  28. 28. 56T) What is the equation of the line? y = 2x + 1 y 5 4 3 2 1 x -3 -2 -1 O 1 2 3 -1 -2 -3 Grade D Clip 114 56S) What is the equation of the line? y = 3x – 2 y 5 4 3 2 1 -3 -2 -1 O 1 2 3 -1 -2 -3 57T) List all of the outcomes if you roll a dice and 1H 2H 3H 4H 5H 6H flip a coin. 1T 2T 3T 4T 5T 6T 57S) List all of the outcomes if you flip three coins. HHH HHT HTH THH TTT TTH THT HTT Grade D Clip 90 Page 28 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 28
  29. 29. 58T) Use a protractor to work out the bearing of A from B. Bearing of A from B is 293° Grade C Clip 131 A A N B B 58S) Use a protractor to work out the bearing of B from A. Bearing of B from A is 046° B N B A A 59T) In the list of fractions, below, which two are equivalent to 4 ? 5 5 8 8 10 16 18 8 16 6 9 10 11 20 24 10 20 59S) In the list of fractions, below, which two are equivalent to 2 ? 3 8 7 6 8 10 14 8 14 12 8 12 14 16 21 12 21 Grade C Clip 47 60T) A map has a scale of 1:100 000. If town A is 5cm away from town B on the map, what is 5km the actual distance between them in kilometres? 60S) A map has a scale of 1:500 000. If town A is 3cm away from town B on the map, what is 15km the actual distance between them in kilometres? Grade C Clip 61 Page 29 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 29
  30. 30. 61T) a) -3 × -4 61S) a) 6 × -3 a) 12 a) -18 b) 7 × -5 b) -10 × -2 b) -35 b) 20 c) -12 ÷ 4 c) 15 ÷ -3 c) -3 c) -5 d) -8 – 6 d) 12 – 18 d) -14 d) -6 e) 9 – -5 e) 2 – -13 e) 14 e) 15 f) 10 + -6 f) 15 + -17 f) 4 f) -2 g) -4 + -5 g) -6 + -8 g) -9 g) -14 Grade C Clip 99 62T) Use the graph to solve the simultaneous equations y = 7 – x and y = 2x – 2 y 8 y = 2x – 2 x = 3 and y = 4 y=7–x 7 6 5 4 3 2 1 0 x 0 1 2 3 4 5 6 7 8 Grade C Clip 115 62S) Use the graph to solve the simultaneous equations y = 8 – 2x and y = ½x + 3 y 8 y = 8 – 2x x = 2 and y = 4 7 y = ½x + 3 6 5 4 3 2 1 0 x 0 1 2 3 4 5 6 7 8 Page 30 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 30
  31. 31. 40 400 37.9 × 417 37.9 × 417 63T) Estimate the answer to 1000 1.94 × 8.03 1.94 × 8.03 2 8 873 × 18 900 20 63S) Estimate the answer to 180 104 873 × 18 104 Grade C Clip 101 100 64T) Point P has coordinates (7, 4, 3) Point T is the intersection of PR and SQ. Work out the coordinates of T. (3.5, 2, 3) y Grade C Clip 120 S . . P . T x R . . Q z 64S) Point P has coordinates (8, 3, 4) a) Work out the coordinates of T. a) (8, 3, 0) b) Work out the coordinates of S. b) (0, 0, 4) y . T . P x S . z 65T) If the probability of passing a driving test is 0.42 what is 0.58 the probability of failing the test? 65S) The probability of a school football team winning a 0.45 football match is 0.34 and the probability of losing is 0.21. What is the probability of the team drawing the match? Grade D Clip 91 Page 31 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 31
  32. 32. 66T) Draw the net of this right-angled triangular prism. 5 squares Grade D 4 squares Clip 82 ares 3 squares 5 squ 66S) Draw the net of this cuboid 3 squares 2 squares 5 squares Page 32 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 32
  33. 33. 67T) Write the following fractions in their simplest forms. a) 16 a) 4 20 5 9 Grade D 3 b) 15 b) Clip 48 5 c) 24 c) 2 60 5 67S) Write the following fractions in their simplest forms. a) 12 a) 2 30 5 b) 7 b) 1 21 3 c) 40 c) 5 64 8 68T) Here are the ingredients needed to make salmon fishcakes for four people. 450g potatoes 900g of salmon 25g butter Grade D 15g dill Clip 62 50g flour 2 eggs 150g breadcrumbs a) What weight of salmon would be needed to use a) 1350g the recipe for six people? b) For seven people, what weight of flour is needed? b) 87.5g 68S) Here are the ingredients needed to make shepherd's pie for five people. 500g potatoes 50g of cheese 150g butter 1 onion 2 carrots 300ml stock 1kg of lamb a) What weight of cheese would be needed to use a) 80g the recipe for eight people? b) For six people, how much stock is needed? b) 360ml c) For nine people, what weight of lamb c) 1.8kg should be used? Page 33 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 33
  34. 34. 69T) Put these fractions in order of size, smallest to largest. 5 7 2 3 7 5 2 3 8 12 3 4 12 8 3 4 69S) Put these fractions in order of size, smallest to largest. 4 9 7 1 9 1 7 4 5 20 10 2 20 2 10 5 Grade D Clip 49 70T) a) What is the square of 6? a) 36 Grade D b) Find the cube of 4. b) 64 c) What is the square root of 49? Clip 46 c) 7 d) What is the cube root of 27? d) 3 e) Evaluate 144 e) 12 70S) a) What is the square of 8? a) 64 b) Find the cube of 2. b) 8 c) What is the square root of 100? c) 10 d) What is the cube root of 125? d) 5 e) Evaluate 169 e) 13 71T) Sara wishes to find out how much pocket money people How much pocket money do you in her class received. receive each week? Design a suitable question she could use Less than £2 on a questionnaire. Between £2.01 and £4 More than £4 You should include some tickboxes. 71S) Fred wants to know which sports are watched by pupils in Sport Tally Frequency his class. Football Design a suitable data collection sheet he can use Cricket to find out. Tennis Athletics Grade D Clip 84 Rugby Grade C Clip 134 Other 72T) Change the following fractions to decimals. a) 4 b) 3 a) 0.8 b) 0.375 5 8 72S) Change the following fractions to decimals. a) 0.6 b) 0.625 a) 6 b) 5 10 8 Grade D Clip 58 Page 34 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 34
  35. 35. Questions 73 to 85 are all calculator questions 73T) Find the length of sides A, B and C giving your answers to one decimal place. 14cm A 13.9cm B 18.2cm A B 12cm 23cm C 5.6cm 7cm Grade C C 3.9cm Clip 118 6.8cm 73S) Find the length of sides A, B and C giving your answers to one decimal place. A 14.4cm 58cm B 111.9cm 17cm A 126cm C 12.7cm 9cm B 9.5cm 8.5cm C 74T) The equation x3 + 2x = 20 has a solution between 2 and 3. x=2 23 + 2 × 2 = 12 Too low x=3 33 + 2 × 3 = 33 Too big Use a trial and improvement method to find this solution. x = 2.4 2.43 + 2 × 2.4 = 18.624 Too low Give your answer to 1 decimal place and show all workings. x = 2.5 2.53 + 2 × 2.5 = 20.625 Too big x = 2.45 2.453 + 2 × 2.45 = 19.60612 Too low x = 2.5 to 1 decimal place. x=4 43 – 4 × 4 = 48 Too low 74S) The equation x3 – 4x = 88 has a solution between 4 and 5. x=5 53 – 4 × 5 = 105 Too big Use a trial and improvement method to find this solution. x = 4.7 4.73 – 4 × 4.7 = 85.023 Too low Give your answer to 1 decimal place and show all workings. x = 4.8 4.83 – 4 × 4.8 = 91.392 Too big x = 4.75 4.753 – 4 × 4.75 = 88.17187 Too big Grade D Clip 110 x = 4.7 to 1 decimal place. Page 35 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 35
  36. 36. 75T) a) 34% of £28.76 = Grade D a) £9.78 b) 76% of 900 = b) 684 Clip 46 c) Reduce £45.50 by 12.5% c) £39.81 75S) a) 29% of £235.60 = a) £68.32 b) 43% of 2400 = b) 1032 c) Reduce £260 by 30% c) £182 76T) If £1 = 1.23 Euros, Grade D a) Change £38 to Euros. Clip 64 a) 46.74 Euros b) Change 650 Euros to pounds (£). b) £528.46 76S) If £1 = 1.27 Euros, a) Change £2000 to Euros. a) 2540 Euros b) Change 923 Euros to pounds (£). b) £726.77 77T) a) Find the area of the following circles. Give both answers to 1 decimal place. (i) (ii) a) (i) 153.9cm2 (ii) 452.4cm2 7cm 24cm b) Find the area of this quarter circle. b) 78.5cm2 Grade D Clip 71 10cm 77S) a) Find the area of the following circles. Give both answers to 1 decimal place. (i) (ii) a) (i) 380.1cm2 (ii) 243.3cm2 11cm 17.6cm b) Find the area of this semicircle. 19cm b) 141.8cm2 Page 36 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 36
  37. 37. 78T) Which is the best value for money 0.55p per gram 500g of sausages for £2.75 or 0.57p per gram 650g of the same type of sausages for £3.70? 500g for £2.75 best value You must show all your working. 78S) Which is the best value for money 0.106p per ml 800ml of orange juice for £0.85 or Grade D 0.13p per ml 350ml of orange juice for £0.46? Clip 50 800ml for £0.85 best value You must show all your working. 79T) a) Find the circumference of the following circles. Give both answers to 1 decimal place. (i) (ii) a) (i) 44.0cm (ii) 75.4cm 7cm 24cm b) Find the perimeter of this b) 35.7cm quarter circle to 1 decimal place. Grade D Clip 72 10cm 79S) a) Find the circumference of the following circles. Give both answers to 1 decimal place. (i) (ii) a) (i) 69.1cm (ii) 55.3cm 11cm 17.6cm b) 48.8cm b) Find the perimeter of this semicircle 19cm to 1 decimal place. Page 37 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 37
  38. 38. 80T) a) Change the following to percentages. Give your answers to 1 decimal place. (i) 17 out of 67 a) (i) 25.4% (ii) 134 out of 386 (ii) 34.7% b) If Sue scores 82 marks out of a possible 120 marks, b) 68.3% what was her score as a percentage? 80S) a) Change the following to percentages. Give your answers to 1 decimal place. (i) 44 out of 78 a) (i) 56.4% (ii) 12.6 out of 59 (ii) 21.4% b) If Sue scores 14 marks out of a possible 75 marks, b) 18.7% what was her score as a percentage? Grade D Clip 53 81T) Find the volume of this cylinder. Give your answer to 1 decimal place. 9cm Volume = 6107.3cm3 Grade D 24cm Clip 122 81S) Find the volume of this cylinder. Give your answer to 1 decimal place. 20cm Volume = 14765.5cm3 47cm 8.23 + 2.32 23.59360083 82T) Evaluate = 0.907097302 (12.4 – 7.3)2 Grade D 26.01 Clip 63 19.62 + 73 + 25 403.5249167 = 3.433767009 82S) Evaluate 117.5166852 3 5 – 56 Page 38 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 38
  39. 39. 83T) Find the length of the line. y 6 5cm Grade C 5 6 Clip 119 5 4 4 3 3 2 2 1 1 x O 1 2 3 4 5 6 O 1 2 3 4 5 6 83S) Find the length of the line to 1 decimal place. y 6 5.4cm 5 6 4 5 4 3 3 2 2 1 1 x O 1 2 3 4 5 6 O 1 2 3 4 5 6 84T) a) A cyclist travels 12 miles in 2 hours. a) 6mph What is the cyclist's speed in mph? Grade C b) Sue walks for 45 minutes at 14mph. b) 10.5 miles How far does she travel? Clip 126 c) A piece of lead has a mass of 340g and a c) 11.3 g/cm3 volume of 30cm3. Work out its density in g/cm3. 84S) a) A cyclist travels at 14.3mph for 4 hours. a) 57.2 miles What distance does he cover? b) Sue drives at an average speed of 57mph and covers b) 4 hours 30 minutes a distance of 256.5 miles. How long does the journey take in hours and minutes? c) A piece of lead has a density of 12g/cm3 and a c) 166.7cm3 mass of 2kg. Work out its volume in cm3. Page 39 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 39
  40. 40. 85T) The two triangles are similar. 37.8cm x y 5cm 8cm 43.2cm a) Work out the size of x. a) x = 27cm b) Work out the size of y. b) y = 7cm 85S) BE is parallel to CD Find the length of BC. Grade C BC = 8cm Clip 123 A 10cm B E 12cm x C D 21.6cm Page 40 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 40
  41. 41. 22 Essential Questions at grade B (A calculator can be used on all questions apart from qu. 13) 1T) Solve these two simultaneous equations 2r + 3s = 6 3r – 2s = 22 Grade B Clip 142 r = 6 and s = –2 1S) Solve these two simultaneous equations h + 3t = –10 h = 2 and t = –4 2h – t = 8 2T) Mary recorded the heights, in centimetres, of the girls in a) LQ = 152 her class. Grade B b) UQ = 177 She put the heights in order. Clip 152 132 144 150 152 160 162 162 167 167 170 172 177 181 182 182 a) Find the lower quartile b) Find the upper quartile c) On the grid, draw a boxplot for this data. 2S) Mary recorded the heights, in centimetres, of the girls in her class. a) LQ = 154 She put the heights in order. b) UQ = 181 131 142 142 150 158 161 165 169 169 169 173 179 183 185 186 188 a) Find the lower quartile b) Find the upper quartile c) On the grid, draw a boxplot for this data. Page 41 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 41
  42. 42. 3T) Work out the lengths or angles indicated by the letters a to d. a = 23.2cm 25cm b a 8cm b = 58.4° c = 61.8cm 13cm 68° d = 64.6° Grade B Clip 153 50cm 42cm 36° c d 18cm 3S) Work out the lengths or angles indicated by the letters e to h. 13cm e e = 56.9° f 15cm f = 24.5cm 23cm 32° g = 21.3cm h = 54.1° h 14° 22cm 19.6cm g 24.2cm Page 42 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 42
  43. 43. 4T) TR and TQ are tangents to the circle a) Explain why angle PQR = 42º a) PQT = 90°(Tangent meets radius at 90°) Grade B 90° – 48° = 42° Clip 150 b) PRQ = 90°(angle in semicircle is 90°) TRQ = 48°(tri. TRQ is isosceles and base angles are equal) PRT = 90° + 48° = 138° b) Find the size of angle PRT giving reasons 4S) TR and TQ are tangents to the circle a) Explain why angle PQR = 35º a) PQT = 90°(Tangent meets radius at 90°) 90° – 55° = 35° b) PRQ = 90°(angle in semicircle is 90°) TRQ = 55°(tri. TRQ is isosceles and base angles are equal) PRT = 90° + 55° = 145° b) Find the size of angle PRT giving reasons a 5T) Find angles a and b a = 85° (opp angles of cyclic 105° quad. add up to 180) b = 75°(opp angles of cyclic Grade B 95° b quad. add up to 180) Clip 150 5S) Find angles a and b b a = 55° (opp angles of cyclic 125° quad. add up to 180°) a b = 117°(opp angles of cyclic 63° quad. add up to 180°) Page 43 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 43
  44. 44. 6T) Find the size of angle x. x = 112° 124 o x Grade B 6S) Find the size of angle y. Clip 150 y = 138° 84 o y 7T) a) John places £13000 in a bank which pays 4.6% a) £1877.79 compound interest per year. How much interest does he earn if he leaves the money in the bank for 3 years? b) Sue buys a new car for £8700. b) £2354.90 Its annual rate of depreciation is 23% per year. How much is it worth after 5 years? Grade B Clip 142 7S) a) Sarah buys a 5-year bond which pays compound a) £10605.19 interest of 5.8% per year. She buys the bond for £8000. How much can she cash the bond in for at the end of the 5 year period? b) Tom buys a house for £145000. b) £135223.35 It will depreciate at the rate of 2.3% per year for the next three years. How much will it then be worth? Page 44 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 44

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