Key stage 3_mathematics_level_6_revision_

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  • 1. Key Stage 3 Mathematics Key Facts Level 6

2. Level 6Number and Algebra 3. Solve the equation x + x = 20 Using trial and improvement and give your answer to the nearest tenth GuessCheckToo Big/Too Small/Correct 4. Solve the equation x + x = 20 Using trial and improvement and give your answer to the nearest tenth Guess3Check3 + 3 = 30Too Big/Too Small/Correct Too Big 5. Solve the equation x + x = 20 Using trial and improvement and give your answer to the nearest tenth GuessCheck33 + 3 = 3022 + 2 = 10Too Big/Too Small/Correct Too Big Too Small 6. Solve the equation x + x = 20 Using trial and improvement and give your answer to the nearest tenth GuessCheckToo Big/Too Small/Correct Too Big33 + 3 = 3022 + 2 = 10Too Small2.5 + 2.5 =18.125Too Small2.5 2.6 7. Amounts as a % Fat in a mars bar 28g out of 35g. What percentage is this? Write as a fraction =28/35top bottom converts a fraction to a 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 a fraction out of 100 9. The ratio of boys to girls in a class is 3:2 Altogether there are 30 students in the class. How many boys are there? 10. The ratio of boys to girls in a class is 3:2 Altogether 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 30 5 = 6(divide)Multiply the relevant part of the ratio by the answer (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 3+2 11=22 33=28 336 + 33 12. A common multiple of 3 and 4 is 12, so change both fractions to equivalent fractions with a denominator of 122 3-1 4=8 12=5 12-3 12 13. Find the nth term of this sequence 7142128356132027347777Which times table is this pattern based on?7How does it compare to the 7 times table?Each number is 1 lessnth term = 7n - 1 14. Find the nth term of this sequence 9182736456152433429999Which times table is this pattern based on?9How does it compare to the 9 times table?Each number is 3 lessnth term = 9n - 3 15. -- 16. 4p + 5= 75 -3pSwap Sides, Swap Signs4p + 5= 75 - 3p4p += 75 7p= 70p= 10 17. y axis(3,6)6 5(2,4)4 3(1,2)2 1x axis -6-5 -4-3-2 -1-1123456-2 -3 -4 -5(-3,-6)-6The y coordinate is always double the x coordinate y = 2x 18. Straight Line Graphs y = 4x y = 3xy axis10 y = 5xy = 2x8y=x6 4y=x2 -4-3 -2 -10-2 -4 -6 -8 -101234x axisy = -x 19. y axisy=10+6 2x1 x- 2 -5 + 2 2x = 2x y y= y=8 6 4 2 -4-3 -2 -10-2 -4 -6 -8 -101234x axis 20. All straight line graphs can be expressed in the form y = mx + c m is the gradient of the line and c is the y intercept The graph y = 5x + 4 has gradient 5 and cuts the y axis at 4 21. Level 6Shape, Space and Measures 22. CuboidCubeTriangular PrismCylinder Hexagonal PrismSquare based PyramidCone TetrahedronSphere 23. Using Isometric PaperWhich 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. 114dCorresponding 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 PolygonSides (n)Sum of Interior AnglesTriangle3180Quadrilateral4Pentagon5Hexagon6Heptagon7Octagon8What is the rule that links the Sum of the Interior Angles to n? 31. The Sum of the Interior Angles PolygonSides (n)Sum of Interior AnglesTriangle3180Quadrilateral4360Pentagon5Hexagon6Heptagon7Octagon8What is the rule that links the Sum of the Interior Angles to n? 32. The Sum of the Interior Angles PolygonSides (n)Sum of Interior AnglesTriangle3180Quadrilateral4360Pentagon5540Hexagon6Heptagon7Octagon8What is the rule that links the Sum of the Interior Angles to n? 33. The Sum of the Interior Angles PolygonSides (n)Sum of Interior AnglesTriangle3180Quadrilateral4360Pentagon5540Hexagon6720Heptagon7Octagon8What is the rule that links the Sum of the Interior Angles to n? 34. For a polygon with n sides Sum of the Interior Angles = 180 (n 2) 35. A regular polygon has equal sides and equal angles 36. Regular PolygonInterior Angle (i)Exterior Angle (e)Equilateral Triangle60120Square Regular Pentagon Regular Hexagon Regular Heptagon Regular OctagonIf n = number of sides e = 360 n e + i = 180 37. Regular PolygonInterior Angle (i)Exterior Angle (e)Equilateral Triangle60120Square9090Regular Pentagon Regular Hexagon Regular Heptagon Regular OctagonIf n = number of sides e = 360 n e + i = 180 38. Regular PolygonInterior Angle (i)Exterior Angle (e)Equilateral Triangle60120Square9090Regular Pentagon10872Regular Hexagon Regular Heptagon Regular OctagonIf n = number of sides e = 360 n e + i = 180 39. Regular PolygonInterior Angle (i)Exterior Angle (e)Equilateral Triangle60120Square9090Regular Pentagon10872Regular Hexagon12060Regular Heptagon Regular OctagonIf n = number of sides e = 360 n e + i = 180 40. Translate the object by() 4 -3 41. Translate the object by() 4 -3Move each corner of the object 4 squares across and 3 squares down Image 42. Rotate by 90 degrees anti-clockwise about cC 43. Rotate by 90 degrees anti-clockwise about CImage CRemember to ask for tracing paper 44. We divide by 2 because the area of the triangle is half that of the rectangle that surrounds it hTriangle Area = base height 2A = bh/2 bParallelogram Area = base heighth bA = bhaTrapeziumhA = h(a + b)b The formula for the trapezium is given in the front of the SATs paper 45. The circumference of a circle is the distance around the outside diameterCircumference = diameter Where = 3.14 (rounded to 2 decimal places) 46. The radius of a circle is 30m. What is the circumference? r=30, d=60C= d C = 3.14 60 C = 18.84 md = 60r = 30 47. Circle Area = r2 48. = 3. 141 592 653 589 793 238 462 643 Circumference= 20 = 3.142 20 = 62.84 cmNeed radius = distance from the centre of a circle to the edge10cmdr 10cmThe distance around the outside of a circle Need diameter = distance across the middle of a circleArea= 100 = 3.142 100 = 314.2 cm 49. Volume of a cuboid V= length width height10 cm4 cm9 cm 50. Volume of a cuboid V= length width heightV= 9 4 1010 cm= 360 cm4 cm9 cm 51. Level 6Data Handling 52. Draw a Pie Chart to show the information in the table below ColourFrequencyBlue5Green3Yellow2Purple2Pink4Orange1Red3A pie chart to show the favourite colour in our class 53. Draw a Pie Chart to show the information in the table below ColourFrequencyBlue5Green3Yellow2Purple2Pink4Orange1Red3TOTAL20Add the frequencies to find the totalA pie chart to show the favourite colour in our class 54. Draw a Pie Chart to show the information in the table below ColourFrequencyBlue5Green3Yellow2Purple2Pink4Orange1Red3TOTAL20DIVIDE 360 by the total to find the angle for 1 person360 20 = 18 Add the frequencies to find the totalA pie chart to show the favourite colour in our class 55. Draw a Pie Chart to show the information in the table below ColourFrequencyAngleBlue55 18 = 90Green33 18 = 54Yellow22 18 = 36Purple22 18 = 36Pink44 18 = 72Orange11 18 = 18Red33 18 = 54TOTAL20Multiply each frequency by the angle for 1 personDIVIDE 360 by the total to find the angle for 1 person360 20 = 18 Add the frequencies to find the totalA pie chart to show the favourite colour in our class 56. Draw a Pie Chart to show the information in the table belowColourFrequencyAngleBlue55 18 = 90Green33 18 = 54Yellow22 18 = 36Purple22 18 = 36Pink4 11 18 = 18Red3 20Blue3 18 = 54TOTALRed4 18 = 72OrangeA bar chart to show the favourite colour in our classOrangePink GreenPurpleYellow 57. Draw a frequency polygon to showLength of stringFrequencythe information in the table0 < x 201020 < x 402040 < x 604560 < x 803280 < x 1000 58. 301020Plot the point 40 using the 30 50 midpoint of the intervalfrequencyUse a continuous scale for the x-axis4560 < x 80102040 < x 60the information in the table1020 < x 4020Frequency0 < x 20Draw a frequency polygon to showLength of string (x)3280 < x 100 706080900x 100 59. Draw a histogram to showLength of stringFrequencythe information in the table0 < x 201020 < x 402040 < x 604560 < x 803280 < x 1000 60. 30Length of string (x) 0 < x 20101020304050frequencyUse a continuous scale for the x-axis4560 < x 80the information in the table2040 < x 60201020 < x 40Draw a histogram to showFrequency3270 80 < x 1006080900x 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 140120100Test B806040200 020406080 Test A100120140 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 160140120Test B10080The correlation is positive because as marks in test A increase so do the marks in test B6040200 020406080 Test A100120140160 63. Negative Correlationy 12108642x 0 024681012 64. The sample or probability space shows all 36 outcomes when you add two normal dice together. Total 1Dice 1Probability 1/364/3621 12345632345674 52 Dice 23456786345678974567891056789101167891011128 9 10 11 12 65. The sample space shows all 36 outcomes when you find the difference between the scores of two normal dice. Dice 1 Total1345610123452 Dice 2210123423210123343210124543210156543210Probability0 1/36104/36 66. The total probability of all the mutually exclusive outcomes of an experiment is 1 A bag contains 3 colours of beads, red, white and blue. The probability of picking a red bead is 0.14 The probability of picking a white bead is 0.2 What is the probability of picking a blue bead? 67. The total probability of all the mutually exc