# Key Stage 3 Mathematics. Common entrance revision

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1 Key Stage 3 Mathematics Key Facts Common entrance revision

2 Number and Algebra

3 Solve the equation x³ + x = 20 Using trial and improvement and give your answer to the nearest tenth Guess Check Too Big/Too Small/Correct

4 Solve the equation x³ + x = 20 Using trial and improvement and give your answer to the nearest tenth Guess Check Too Big/Too Small/Correct 3 3³ + 3 = 30 Too Big

5 Solve the equation x³ + x = 20 Using trial and improvement and give your answer to the nearest tenth Guess Check Too Big/Too Small/Correct 3 3³ + 3 = 30 Too Big 2 2³ + 2 = 10 Too Small

6 Solve the equation x³ + x = 20 Using trial and improvement and give your answer to the nearest tenth Guess Check Too Big/Too Small/Correct 3 3³ + 3 = 30 Too Big 2 2³ + 2 = 10 Too Small ³ = 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 = 28 / 35 top bottom converts a fraction to a decimal Convert to a percentage (top bottom x 100) x 100 = 80% Multiply by 100 to make a decimal into a percentage

8 A percentage is a fraction out of 100

9

10

11 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?

12 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

13

14 A common multiple of 3 and 11 is 33, so change both fractions to equivalent fractions with a denominator of = = 28 33

15 A common multiple of 3 and 4 is 12, so change both fractions to equivalent fractions with a denominator of = = 5 12

16 Find the nth term of this sequence 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

17 Find the nth term of this sequence 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

18

19 - -

20 4p + 5 = 75-3p Swap Sides, Swap Signs 4p + 5 = 75-3p 4p + = 75-7p = 70 p = 10

21 y axis (3,6) (2,4) (1,2) x axis (-3,-6) -5-6 The y coordinate is always double the x coordinate y = 2x

22 Straight Line Graphs y axis 10 y = 5x 8 6 y = 4x y = 3x y = 2x y = x 4 2 y = ½ x y = -x x axis

23 y axis x axis

24 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

25 Shape, Space and Measures

26 Cube Cuboid Triangular Prism Hexagonal Prism Cylinder Square based Pyramid Tetrahedron Cone Sphere

27 Using Isometric Paper Which Cuboid is the odd one out?

28

29

30 a 50 Alternate angles are equal a = 50

31 b 76 Interior angles add up to 180 b = = 104

32 c 50 Corresponding angles are equal c = 50

33 114 d Corresponding angles are equal d = 114

34 e 112 Alternate angles are equal e = 112

35 50 f Interior angles add up to 180 f = 130

36 The Sum of the Interior Angles Polygon Sides (n) Sum of Interior Angles Triangle Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 What is the rule that links the Sum of the Interior Angles to n?

37 The Sum of the Interior Angles Polygon Sides (n) Sum of Interior Angles Triangle Quadrilateral Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 What is the rule that links the Sum of the Interior Angles to n?

38 The Sum of the Interior Angles Polygon Sides (n) Sum of Interior Angles Triangle Quadrilateral Pentagon Hexagon 6 Heptagon 7 Octagon 8 What is the rule that links the Sum of the Interior Angles to n?

39 The Sum of the Interior Angles Polygon Sides (n) Sum of Interior Angles Triangle Quadrilateral Pentagon Hexagon Heptagon 7 Octagon 8 What is the rule that links the Sum of the Interior Angles to n?

40 For a polygon with n sides Sum of the Interior Angles = 180 (n 2)

41 A regular polygon has equal sides and equal angles

42 Regular Polygon Interior Angle (i) Exterior Angle (e) Equilateral Triangle Square Regular Pentagon Regular Hexagon Regular Heptagon Regular Octagon If n = number of sides e = 360 n e + i = 180

43 Regular Polygon Interior Angle (i) Exterior Angle (e) Equilateral Triangle Square Regular Pentagon Regular Hexagon Regular Heptagon Regular Octagon If n = number of sides e = 360 n e + i = 180

44 Regular Polygon Interior Angle (i) Exterior Angle (e) Equilateral Triangle Square Regular Pentagon Regular Hexagon Regular Heptagon Regular Octagon If n = number of sides e = 360 n e + i = 180

45 Regular Polygon Interior Angle (i) Exterior Angle (e) Equilateral Triangle Square Regular Pentagon Regular Hexagon Regular Heptagon Regular Octagon If n = number of sides e = 360 n e + i = 180

46

47 Translate the object by ( 4) -3

48 Translate the object by ( 4) -3 Move each corner of the object 4 squares across and 3 squares down Image

49 Rotate by 90 degrees anti-clockwise about c C

50 Rotate by 90 degrees anti-clockwise about C Image C Remember to ask for tracing paper

51 We divide by 2 because the area of the triangle is half that of the rectangle that surrounds it b h h a b Triangle Area = base height 2 A = bh / 2 Parallelogram Area = base height A = bh Trapezium h b A = ½ h(a + b) The formula for the trapezium is given in the front of the SATs paper

52 The circumference of a circle is the distance around the outside diameter Circumference = π diameter Where π = 3.14 (rounded to 2 decimal places)

53 The radius of a circle is 30m. What is the circumference? r=30, d=60 C = π d C = C = m d = 60 r = 30

54 Circle Area = πr2

55 π = Circumference = π 20 = = cm Need radius = distance from the centre of a circle to the edge 10cm πd πr² The distance around the outside of a circle Need diameter = distance across the middle of a circle Area = π 100 = = cm² 10cm

56 Volume of a cuboid V= length width height 10 cm 4 cm 9 cm

57 Volume of a cuboid V= length width height V= = 360 cm³ 10 cm 4 cm 9 cm

58

59

60 Data Handling

61 Draw a Pie Chart to show the information in the table below Colour Frequency Blue 5 Green 3 Yellow 2 Purple 2 Pink 4 Orange 1 Red 3 A pie chart to show the favourite colour in our class

62 Draw a Pie Chart to show the information in the table below Colour Frequency Blue 5 Green 3 Yellow 2 Purple 2 Pink 4 Orange 1 Red 3 TOTAL 20 Add the frequencies to find the total A pie chart to show the favourite colour in our class

63 Draw a Pie Chart to show the information in the table below Colour Frequency Blue 5 Green 3 Yellow 2 Purple 2 Pink 4 Orange 1 Red 3 TOTAL 20 DIVIDE 360 by the total to find the angle for 1 person Add the frequencies to find the total = 18 A pie chart to show the favourite colour in our class

64 Draw a Pie Chart to show the information in the table below Colour Frequency Angle Blue = 90 Green = 54 Yellow = 36 Purple = 36 Pink = 72 Orange = 18 Red = 54 TOTAL 20 Multiply each frequency by the angle for 1 person DIVIDE 360 by the total to find the angle for 1 person Add the frequencies to find the total = 18 A pie chart to show the favourite colour in our class

65 Draw a Pie Chart to show the information in the table below Colour Frequency Angle Blue = 90 Green = 54 A bar chart to show the favourite colour in our class Yellow = 36 Purple = 36 Pink = 72 Orange = 18 Red = 54 Orange Pink Red Blue Green TOTAL 20 Purple Yellow

66 Draw a frequency polygon to show the information in the table Length of string Frequency 0 < x < x < x < x < x 100 0

67 Draw a frequency polygon to show the information in the table Plot the point using the midpoint of the interval Length of string (x) Frequency 0 < x < x < x < x < x frequencyf Use a continuous scale for the x-axis x

68 Draw a histogram to show the information in the table Length of string Frequency 0 < x < x < x < x < x 100 0

69 Draw a histogram to show the information in the table Length of string (x) Frequency 0 < x < x < x < x < x frequency Use a continuous scale for the x-axis x

70 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 Test B Test A

71 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 Tes st B The correlation is positive because as marks in test A increase so do the marks in test B Test A

72 y Negative Correlation x

73 The sample or probability space shows all 36 outcomes when you add two normal dice together. Total Probability Dice / / Dice

74 The sample space shows all 36 outcomes when you find the difference between the scores of two normal dice. Dice Total 0 Probability 10 1 / 36 2 Dice /

75 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?

76 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? = = 0.66

77

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