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Level 6 Maths Revision

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Level 6 Maths Revision

  1. 1. Key Stage 3Mathematics Key Facts Level 6
  2. 2. Level 6Number and Algebra
  3. 3. Solve the equation x³ + x = 20Using trial and improvement and give your answer to the nearest tenthGuess Check Too Big/Too Small/Correct
  4. 4. Solve the equation x³ + x = 20Using trial and improvement and give your answer to the nearest tenthGuess Check Too Big/Too Small/Correct 3 3³ + 3 = 30 Too Big
  5. 5. Solve the equation x³ + x = 20Using trial and improvement and give your answer to the nearest tenthGuess Check Too Big/Too Small/Correct 3 3³ + 3 = 30 Too Big 2 2³ + 2 = 10 Too Small
  6. 6. Solve the equation x³ + x = 20Using trial and improvement and give your answer to the nearest tenthGuess Check Too Big/Too Small/Correct 3 3³ + 3 = 30 Too Big 2 2³ + 2 = 10 Too Small 2.5 2.5³ + 2.5 =18.125 Too Small 2.6
  7. 7. Amounts as a %• Fat in a mars bar 28g out of 35g. What percentage is this?Write as a fraction top ÷ bottom converts a fraction to a• =28/35 decimalConvert to a percentage (top ÷ bottom x 100)• 28 ÷ 35 x 100 = 80% Multiply by 100 to make a decimal into a percentage
  8. 8. A percentage is afraction out of 100
  9. 9. The ratio of boys to girls in a class is 3:2Altogether there are 30 students in the class.How many boys are there?
  10. 10. The ratio of boys to girls in a class is 3:2Altogether there are 30 students in the class.How many boys are there? The ratio 3:2 represents 5 parts (add 3 + 2) Divide 30 students by the 5 parts (divide) 30 ÷ 5 = 6 Multiply the relevant part of the ratio by theanswer (multiply) 3 × 6 = 18 boys
  11. 11. A common multiple of 3 and 11 is 33, so change both fractions to equivalent fractions with a denominator of 332 2 22 6 + = +3 11 33 33 28 = 33
  12. 12. A common multiple of 3 and 4 is 12, so change both fractions to equivalent fractions with a denominator of 122 1 8 3 - = -3 4 12 12 5 = 12
  13. 13. Find the nth term of this sequence7 14 21 28 356 13 20 27 34 7 7 7 7 Which times table is this pattern based on? 7 How does it compare to the 7 times table? Each number is 1 less nth term = 7n - 1
  14. 14. Find the nth term of this sequence9 18 27 36 456 15 24 33 42 9 9 9 9 Which times table is this pattern based on? 9 How does it compare to the 9 times table? Each number is 3 less nth term = 9n - 3
  15. 15. - -
  16. 16. 4p + 5 = 75 - 3pSwap Sides, Swap Signs4p + 5 = 75 - 3p4p + = 75 - 7p = 70 p = 10
  17. 17. y axis 6 (3,6) 5 4 (2,4) 3 2 (1,2) 1 x axis -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 -5 (-3,-6) -6The y coordinate is always double the x coordinate y = 2x
  18. 18. Straight Line Graphs y axis y = 4x y = 3x 10 y = 5x y = 2x 8 6 y=x 4 2 y=½x 0 -4 -3 -2 -1 1 2 3 4 x axis -2 -4 y = -x -6 -8 -10
  19. 19. +6 1 x- 2 y axis 2x + 2 -5 10 y = 2x = 2x y= y y= 8 6 4 2 0-4 -3 -2 -1 1 2 3 4 x axis -2 -4 -6 -8 -10
  20. 20. All straight line graphs can be expressed in the form y = mx + cm is the gradient of the line and c is the y interceptThe graph y = 5x + 4 has gradient 5 and cuts they axis at 4
  21. 21. Level 6Shape, Space and Measures
  22. 22. Cube CuboidTriangular Cylinder Prism Hexagonal Prism Square based Cone Pyramid Tetrahedron Sphere
  23. 23. Using Isometric Paper Which Cuboid is the odd one out?
  24. 24. a 50Alternate angles are equal a = 50
  25. 25. b 76Interior angles add up to 180 b = 180 - 76 = 104
  26. 26. c 50Corresponding angles are equal c = 50
  27. 27. 114 dCorresponding angles are equal d = 114
  28. 28. e 112Alternate angles are equal e = 112
  29. 29. f 50Interior angles add up to 180 f = 130
  30. 30. The Sum of the Interior Angles Polygon Sides Sum of Interior Angles (n) Triangle 3 180 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 What is the rule that links the Sum of the Interior Angles to n?
  31. 31. The Sum of the Interior Angles Polygon Sides Sum of Interior Angles (n) Triangle 3 180 Quadrilateral 4 360 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 What is the rule that links the Sum of the Interior Angles to n?
  32. 32. The Sum of the Interior Angles Polygon Sides Sum of Interior Angles (n) Triangle 3 180 Quadrilateral 4 360 Pentagon 5 540 Hexagon 6 Heptagon 7 Octagon 8 What is the rule that links the Sum of the Interior Angles to n?
  33. 33. The Sum of the Interior Angles Polygon Sides Sum of Interior Angles (n) Triangle 3 180 Quadrilateral 4 360 Pentagon 5 540 Hexagon 6 720 Heptagon 7 Octagon 8 What is the rule that links the Sum of the Interior Angles to n?
  34. 34. For a polygon with n sidesSum of the Interior Angles = 180 (n – 2)
  35. 35. A regular polygon has equal sides and equal angles
  36. 36. Regular Polygon Interior Angle (i) Exterior Angle (e)Equilateral Triangle 60 120 Square Regular Pentagon Regular Hexagon Regular Heptagon Regular Octagon If n = number of sides e = 360 ÷ n e + i = 180
  37. 37. Regular Polygon Interior Angle (i) Exterior Angle (e)Equilateral Triangle 60 120 Square 90 90 Regular Pentagon Regular Hexagon Regular Heptagon Regular Octagon If n = number of sides e = 360 ÷ n e + i = 180
  38. 38. Regular Polygon Interior Angle (i) Exterior Angle (e)Equilateral Triangle 60 120 Square 90 90 Regular Pentagon 108 72 Regular Hexagon Regular Heptagon Regular Octagon If n = number of sides e = 360 ÷ n e + i = 180
  39. 39. Regular Polygon Interior Angle (i) Exterior Angle (e)Equilateral Triangle 60 120 Square 90 90 Regular Pentagon 108 72 Regular Hexagon 120 60 Regular Heptagon Regular Octagon If n = number of sides e = 360 ÷ n e + i = 180
  40. 40. Translate the object by () 4 -3
  41. 41. Translate the object by () 4 -3Move eachcorner of theobject 4 squaresacross and 3squares down Image
  42. 42. Rotate by 90 degrees anti-clockwise about c C
  43. 43. Rotate by 90 degrees anti-clockwise about C Image C Remember to ask for tracing paper
  44. 44. We divide by 2 because the area of thetriangle is half that of the rectangle that Trianglesurrounds it Area = base × height ÷ 2 h A = bh/2 b Parallelogram Area = base × height h A = bh b a Trapezium h A = ½ h(a + b) b The formula for the trapezium is given in the front of the SATs paper
  45. 45. The circumferenceof a circle is thedistance around theoutside diameter Circumference = π × diameter Where π = 3.14 (rounded to 2 decimal places)
  46. 46. The radius of a circle is 30m. What is the circumference? r=30, d=60 r = 30 C= πd d = 60 C = 3.14 × 60 C = 18.84 m
  47. 47. Circle Area = πr2
  48. 48. π = 3. 141 592 653 589 793 238 462 643Circumference = π × 20 Need radius = distance = 3.142 × 20 from the centre of a = 62.84 cm circle to the edge 10cm πd πr² 10cmThe distance around Area = π × 100the outside of a circle = 3.142 × 100 = 314.2 cm²Need diameter = distanceacross the middle of a circle
  49. 49. Volume of a cuboidV= length × width × height 10 cm 4 cm 9 cm
  50. 50. Volume of a cuboid V= length × width × heightV= 9 × 4 × 10 10 cm = 360 cm³ 4 cm 9 cm
  51. 51. Level 6Data Handling
  52. 52. Draw a Pie Chart to show the information in the table belowColour FrequencyBlue 5Green 3Yellow 2Purple 2Pink 4Orange 1Red 3 A pie chart to show the favourite colour in our class
  53. 53. Draw a Pie Chart to show the information in the table belowColour FrequencyBlue 5Green 3Yellow 2Purple 2Pink 4Orange 1Red 3TOTAL 20Add the frequencies tofind the total A pie chart to show the favourite colour in our class
  54. 54. Draw a Pie Chart to show the information in the table belowColour FrequencyBlue 5Green 3Yellow 2Purple 2Pink 4Orange 1 DIVIDE 360° byRed 3 the total to find theTOTAL 20 angle for 1 person 360 ÷ 20 = 18Add the frequencies tofind the total A pie chart to show the favourite colour in our class
  55. 55. Draw a Pie Chart to show the information in the table belowColour Frequency AngleBlue 5 5 × 18 = 90 Multiply each frequency by the angleGreen 3 3 × 18 = 54 for 1 personYellow 2 2 × 18 = 36Purple 2 2 × 18 = 36Pink 4 4 × 18 = 72Orange 1 1 × 18 = 18 DIVIDE 360° byRed 3 3 × 18 = 54 the total to find theTOTAL 20 angle for 1 person 360 ÷ 20 = 18Add the frequencies tofind the total A pie chart to show the favourite colour in our class
  56. 56. Draw a Pie Chart to show the information in the table belowColour Frequency AngleBlue 5 5 × 18 = 90 A bar chart to show the favourite colour in our classGreen 3 3 × 18 = 54Yellow 2 2 × 18 = 36 Red BluePurple 2 2 × 18 = 36 OrangePink 4 4 × 18 = 72Orange 1 1 × 18 = 18 Pink GreenRed 3 3 × 18 = 54TOTAL 20 Purple Yellow
  57. 57. Length of FrequencyDraw a frequency polygon to show stringthe information in the table 0 < x ≤ 20 10 20 < x ≤ 40 20 40 < x ≤ 60 45 60 < x ≤ 80 32 80 < x ≤ 100 0
  58. 58. Length of FrequencyDraw a frequency polygon to show string (x)the information in the table 0 < x ≤ 20 10 20 < x ≤ 40 20 40 < x ≤ 60 45 60 < x ≤ 80 32 Plot the point using the 80 < x ≤ 100 0 midpoint of the interval 50 frequency f 40 30 20 10 Use a continuous scale for the x-axis x 10 20 30 40 50 60 70 80 90 100
  59. 59. Length of FrequencyDraw a histogram to show stringthe information in the table 0 < x ≤ 20 10 20 < x ≤ 40 20 40 < x ≤ 60 45 60 < x ≤ 80 32 80 < x ≤ 100 0
  60. 60. Length of FrequencyDraw a histogram to show string (x)the information in the table 0 < x ≤ 20 10 20 < x ≤ 40 20 40 < x ≤ 60 45 60 < x ≤ 80 32 80 < x ≤ 100 0 50 frequency f 40 30 20 10 Use a continuous scale for the x-axis x 10 20 30 40 50 60 70 80 90 100
  61. 61. Describe the correlation between the marks scored in test A and test B A Scatter Diagram to compare the marks of students in 2 maths tests 140 120 100 80 Test B 60 40 20 0 0 20 40 60 80 100 120 140 Test A
  62. 62. Describe the correlation between the marks scored in test A and test B A Scatter Diagram to compare the marks of students in 2 maths tests 160 140 120 100 Test B 80 The correlation is positive because as 60 40 marks in test A increase so do the 20 marks in test B 0 0 20 40 60 80 100 120 140 160 Test A
  63. 63. y Negative Correlation1210 8 6 4 2 x 0 0 2 4 6 8 10 12
  64. 64. The sample or probability space shows all 36 outcomes when you add two normal dice together. Total Probability 1 1 /36 Dice 1 2 1 2 3 4 5 6 3 4 1 2 3 4 5 6 7 5 4 /36 2 3 4 5 6 7 8 6 7 3 4 5 6 7 8 9Dice 2 8 4 5 6 7 8 9 10 9 5 6 7 8 9 10 11 10 11 6 7 8 9 10 11 12 12
  65. 65. The sample space shows all 36 outcomes when you find the difference between the scores of two normal dice. Dice 1 Total Probability 1 2 3 4 5 6 0 1 0 1 2 3 4 5 1 10 /36 2 1 0 1 2 3 4 2 3 2 1 0 1 2 3 3Dice 2 4 3 2 1 0 1 2 4 4 /36 5 4 3 2 1 0 1 5 6 5 4 3 2 1 0
  66. 66. The total probability of all the mutually exclusive outcomes ofan experiment is 1A bag contains 3 colours of beads, red, white and blue.The probability of picking a red bead is 0.14The probability of picking a white bead is 0.2What is the probability of picking a blue bead?
  67. 67. The total probability of all the mutually exclusive outcomes ofan experiment is 1A bag contains 3 colours of beads, red, white and blue.The probability of picking a red bead is 0.14The probability of picking a white bead is 0.2What is the probability of picking a blue bead? 0.14 + 0.2 = 0.34 1 - 0.34 = 0.66
  68. 68. © Dave Cavill

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