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- 1. Key Stage 3Mathematics Key Facts Level 6
- 2. Level 6Number and Algebra
- 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. 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. 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. 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. 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. A percentage is afraction out of 100
- 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. 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. 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. 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. 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. 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. - -
- 16. 4p + 5 = 75 - 3pSwap Sides, Swap Signs4p + 5 = 75 - 3p4p + = 75 - 7p = 70 p = 10
- 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. 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. +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. 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. Level 6Shape, Space and Measures
- 22. Cube CuboidTriangular Cylinder Prism Hexagonal Prism Square based Cone Pyramid Tetrahedron Sphere
- 23. Using Isometric Paper Which Cuboid is the odd one out?
- 24. a 50Alternate angles are equal a = 50
- 25. b 76Interior angles add up to 180 b = 180 - 76 = 104
- 26. c 50Corresponding angles are equal c = 50
- 27. 114 dCorresponding angles are equal d = 114
- 28. e 112Alternate angles are equal e = 112
- 29. f 50Interior angles add up to 180 f = 130
- 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. 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. 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. 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. For a polygon with n sidesSum of the Interior Angles = 180 (n – 2)
- 35. A regular polygon has equal sides and equal angles
- 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. 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. 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. 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. Translate the object by () 4 -3
- 41. Translate the object by () 4 -3Move eachcorner of theobject 4 squaresacross and 3squares down Image
- 42. Rotate by 90 degrees anti-clockwise about c C
- 43. Rotate by 90 degrees anti-clockwise about C Image C Remember to ask for tracing paper
- 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. The circumferenceof a circle is thedistance around theoutside diameter Circumference = π × diameter Where π = 3.14 (rounded to 2 decimal places)
- 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. Circle Area = πr2
- 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. Volume of a cuboidV= length × width × height 10 cm 4 cm 9 cm
- 50. Volume of a cuboid V= length × width × heightV= 9 × 4 × 10 10 cm = 360 cm³ 4 cm 9 cm
- 51. Level 6Data Handling
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. y Negative Correlation1210 8 6 4 2 x 0 0 2 4 6 8 10 12
- 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. 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. 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. 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. © Dave Cavill

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