mathsrevision-year 7 maths cambridge.pptx

maths year 7 revision

1. MA THS REVISION

2. simple skills about numbers

3. Square numbers A square number is when you times a number by its self Eg 4 squared is 4 x 4 which equals 16. Use the table below which shows you all the square numbers

4. Multiples Multiples are really just times tables. EG: The multiples of 2 are all the numbers in the 2 times table: 2, 4, 6, 8, 10 and so on. The multiples of 5 are all the numbers in the 5 times table: 5, 10, 15, 20, 25 and so on. Questions: list 5 of these times tables 1. Four Times Tables 2. Six Times Tables 3. Seven Times Tables 4. Eight Times Tables 5. Twelve Times Tables 4, 8, 12, 16, 20 6, 12, 18, 24, 30 7, 14, 21, 28, 35 8, 16, 24, 32, 40 12, 24, 36, 48, 60

5. Common Big and Small Numbers Name Number Trillion 1,000,000,000,000 Billion 1,000,000,000 Million 1,000,000 Thousand 1,000 Hundred 100 ten 10 Unit 1 1 Tenth 0.1 Hundredth 0.01 Thousandth 0.001 Millionth 0.000 001 Billionth 0.000 000 001 Trillionth 0.000 000 000 001

6. Factors Factors are numbers that divide exactly into another number. EG: The factors of 12, are 1, 2, 3, 4, 6 and 12 Questions: 1. The factors of 1 are 2. The factors of 2 are 3. The factors of 3 are 4. The factors of 4 are 5. The factors of 5 are 8. The factors of 8 are 9. The factors of 9 are 10. The factors of 10 are 6. The factors of 6 are 7. The factors of 7 are Answers: 1. One 2. One and two 3. One and three 4. One, two and four 5. One and five 6. One, two, three and six 7. One and seven 8. One, two, four and eight 9. One, three and nine 10. One, two, five and ten

7. Prime Numbers A Prime Number is a number that can be divided evenly only by 1, or itself. And it must be a whole number greater than 1. Example: 5 can only be divided evenly by 1 or 5, so it is a prime number. but 6 can be divided evenly by 1, 2, 3 and 6 so it is NOT a prime number Questions: 1. Is the number 18 prime? no 5. Is the number 97 prime? yes 2. Is the number 45 prime? no 3. Is the number 79 prime? yes 4. Is the number 90 prime? no

8. Algebra

9. Algebra - Substitution "Substitute" means to put in the place of another. Substitution In Algebra "Substitution" means putting numbers where the letters are: If you had x5+12= and you knew that x=2 and if a number and letter together means you’ve got to times them then you know all you have to do is 5x2+12= and then you can work out the answer in this case the answer is 22

10. Nth term Nth term is when you replace some letters for numbers Use this page to help you:

11. Finding the nth term 8,11,14 The common difference is 3, so it must be related to the 3 times table (3n) The 3 times table is 3, 6, 9, ... The sequence is 8, 11, 14, .... Every term in the sequence is 5 more than the corresponding term in the 3 times table, so the nth term is 3n + 5.

12. Finding the nth term for a quadratic sequence

13. Finding nth term of a sequence Eg. 2,5,10,17,26 2. Not a constant difference so we have to fine out the second difference. 3.This second difference is constant at 2.This means the nth term will start with n ². 4. But if you do replace 1 for n it will be 1 ² which is 1 but the first number is 2 the difference between 2 and 1 is 1. If you replace 2 for n it will be 2 ² which is 4 but the second number is 5 the difference between 5 and 4 is 1. We can see here that it the terms in the sequence are 1 number high each time so we write the answer as….. n²+1 1. Find the first difference.

14. Nth term 2 nd differences: 2 = n ² 4 = 2n² 6 = 3n²

15. Mean, median, mode

16. Mean/Average The mean is just the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. Listen to this

17. Median The Median is the "middle number" (in a sorted list of numbers). To find the Median, place the numbers you are given in value order and find the middle number.

18. Mode The mode is simply the number which appears most often. To find the mode, or modal value, first put the numbers in order, then count how many of each number.

19. Range The range means you have to take the small number away from the bigger number to get the range.

20. Modal group If you had a stem and leaf diagram like this for example 1/1,2,6 2/4,4,4,5,7,8,9 3/1,6 4/2 5/4,7 The mode would be the value on the "leaf" that appears most frequently so in this case it would be 24. However, the modal group would be the group from the "stem" that has the most values, so in this case it would focus on the 20's. You would write it from the number on the stem to the highest in the group, like- 20-29.

21. Frequency density = frequency ÷ class width

22. Angles

23. Angles Angles are measured in degrees . The sign for degrees is °. One whole turn is 360° . One quarter turn is 90° or a right angle. One half turn is 180° or a straight line. An angle which is small then 90 Right angle- Straight angle- Obtuse angle- Full rotation angle- Acute angle- Is formed by cutting a circle in quarters. 90 What is: Half a circle. 180 An angle bigger than 90 but less than 180 A whole circle. 360 Angle

24. Draw a line to the correct images: Right angle Straight angle Obtuse angle Full rotation angle Types of angles

25. Circle Theorems This is when there are triangle in a circle and you have to work out missing angles in different triangles. Use this page to help you: Question: 1) 2) 3) 20 17 45 113 54

26. Angles 2 Angles in a triangle 180

27. Angles in parallel lines When you have a: 1. Vertically opposite angles they are equal. Also called the X rule. 2. Corresponding angles they are equal. Also called F rule. 3. Alternate angles they are equal. Also called Z rule. 4. interior angles add up to 180°. Also called C rule. 3. 4. 2. 1.

28. Shapes

29. Nets of 3D shapes There may be several possible nets for one 3D shape. What nets are the following: The net of a 3D shape is what it looks like if it is opened out flat. A net can be folded up to make a 3D shape. 1. 3. 2. 4. 5. cube cuboid Square based pyramid cylinder cone

30. The Pentagram The Pentagram (or Pentangle) is a 5-pointed star. Inside a Pentagram is a Pentagon You can make a pentagram by first drawing a pentagon, then extending the edges. Or by drawing lines from corner to corner inside a pentagon

31. Area Area is the size of a surface! Eg: These shapes all have the same area of 9: You can also find the area by multiplying 2 numbers Eg: Area is the size of a surface! 11cm 5cm 5cm 11cm I will multiply 5 by 11 which is 55 so the area is 55cm squared 55cm squared

32. Perimeter Eg: the perimeter of this rectangle is 7+3+7+3 = 20 The perimeter of a circle is called the circumference Perimeter is the distance around a two-dimensional shape. Questions on perimeter: 1. 12cm 12cm 5cm 5cm 34cm

33. Others

34. Rotation The distance from the centre to any point on the shape stays the same. Every point makes a circle around the centre. Here a triangle is rotated around the point marked with a "+" " Rotation" means turning around a centre

35. Metric system Liquids= millilitres + litres 1 litre = 1,000 millilitres Weight= Grams, Kilograms, Tonnes 1 kilogram = 1,000 grams 1 tonne = 1,000 kilograms Length= Millimetres, Centimetres, Metres, Kilometres 1 centimetre = 10 millimetres 1 metre = 100 centimetres 1 kilometre = 1000 meters Temperature= Celsius, Fahrenheit

36. Symmetry A 2D shape is symmetrical if a line can be drawn through it so that either side of the line looks exactly the same. The line is called a line of symmetry. Shape Lines of symmetry Square 4 Equilateral triangle 3 Parallelogram Isosceles triangle 1 Rectangle 2

37. Negatives When you have+ + together it equals a + When you have - - together it equals a + When you have + - together it equals a - When you have - + together it equals a – Eg: 2 + -5 would be 2 – 5 because a +- together = - so the answer is -3 Questions: 2. 1.

38. Money You have 10p How much change will you get? 7p 3p change Answer 4p 6p change Answer How much change will you get? 1. 2.

39. What is a product? The product is the answer you get when you multiply numbers. For example: If you multiply two times eight, the product (also know as the answer) is sixteen.

40. Multiplying decimals 1 You have to make both the decimal numbers into whole numbers multiply it by 10, 100, 1000 etc then do the sum with whole numbers then divided the answer by the number you multiplied it by. Don’t forget to do divide twice if you have two numbers.

41. Multiplying Decimals 2 1 x 1 = 1 0.75 x 0.75 = 0.5625 O.5 x 0.5 = 0.25 0.25 x 0.25 = 0.0625

42. Multiplying Indices

43. Dividing Indices

44. Bracket Indices

45. Multiplying indices with different numbers

46. Indices Say we had this question 2( x 3 ) I would have to do 2 times which will be 2 then we will put that to the side. Then we will do 2 times 3 which will be 6 . Then we put the answers together to get the answer 2 +6 .

47. fractions

48. Adding like fractions

49. Multiplying mixed number fractions 2 1. Write out the sum 2. Write the mixed number as an improper fraction 3. Cancel by dividing the top and bottom number by the number that equally goes into each number 4.

50. Adding fractions 6 2 8 4

51. Subtracting fractions 1 3 4 6

52. Multiplying fractions 2 5 3 6

53. Dividing fractions 2 1 3 5

54. simplifying Anything times by 0 is 0 Anything times by 1 is itself Multiplying a number by itself is called squaring

55. Volume of cuboid 2 2

56. Volume of a triangular prism 2

57. Volume of a cylinder 2

58. Questions

59. Pi equals  3.14  

60. Perimeter of a circle  D D stands for diameter. Diameter

61. Area of a circle  R ² R stands for radius Radius

62. Circumference of a circle  D OR 2R

63. Properties of a circle Radius Chord Sector

64. Arc length Θ 360 º X  D OR X 2  R Θ 360 º

65. Congruent The word 'Congruent' in maths means that two or more things are exact same size and shape. They should slot together when you place the shapes together.

66. Y=mx+c c C c

67. Gradient/Slope The method to calculate the Gradient is: Divide the change in height by the change in horizontal distance Gradient = Change in Y Change in X Please go to the next slide for some examples of this The Gradient (also called Slope) of a straight line shows how steep a straight line is.

68. Examples The Gradient of this line = 3/3= 1. So the Gradient is equal to 1 The Gradient of this line = 4/2 =2. (The line is steeper, and so the Gradient is larger) The Gradient of this line = 3/5= 0.6. (The line is less steep, and so the Gradient is smaller) Click here for some questions

69. Y Intercept In the above diagram the line crosses the Y axis at 1. So the Y intercept is equal to 1. The Y intercept of a straight line is simply where the line crosses the Y axis. Click here for some questions

70. B-rackets I-ndices D-ivision M-ultiplication A-ddition S-ubtraction

71. Mixed numbers to improper fractions http://www.youtube.com/watch?v=shpf9krdXQQ

72. Percentage to decimal Percent means "per 100", so 50% means 50 per 100, or simply 50/100. If you divide 50 by 100 you get 0.5 (a decimal number). So, to convert from percent to decimal: divide by 100, and remove the "%" sign. The Easy Way: The easy way to divide by 100 is to move the decimal point 2 places to the left, so From Percent To Decimal move the decimal point 2 places to the left, and remove the "%" sign.

73. Cubic function Click here to see a video explaining this.

74. Reciprocal function Click here to see a video explaining this.

75. Pythagoras Theorem A ² + B² = C² √c² A B C? OR

76. Pythagoras Theorem 2 C ² - B² = A² √A² A? B C

77. Angles in a triangle To figure out the angle inside any shape your have to do 180 º(n-2) N stands for the number of sides a shape has. Example: This shape has 6 sides so 6-2=4. Then you have to do 180 ºx4=720º. The interior angles add up to 720. To find each individual angle do 720º / 6 = 120º OR

78. See how many triangles can be formed in the shape. Then times it by 180 º. Example: As you can see we can create 6 triangles from this octagon. We then do 180 ºx6=1080º. We can do the same for each individual angle. 1080º/8=135º

79. Cumulative frequency N always stands for how many numbers there are in the sequence. Lower quartile - ⅛ Median - ⅛ Upper quartile - ⅛ 4 2 4 n N 3n Mode – Most often Range – largest – smallest Median – middle when in order Mean – Total of added numbers / number of numbers

80. 3D shapes Vertices – corners Edges – sides/edges Faces - faces

81. Volume H x w x l H=height W=width L=length

82. Probability I have 2 dice 1 has the numbers 2,4,6,8 on The other dice has the numbers 2,3,4,5 on If I roll both dice and add both number together. What would the probability be that I get an even total? Green=even + 2 4 6 8 2 4 6 8 10 3 5 7 9 11 4 6 8 10 12 5 7 9 11 13 P(Even number)= 8 = 1 16 2

83. Expand the brackets (y+9)(y+2) Answer: Y² + 11y 18

84. Simplify 6y² + 12y You have to think of a number and/or letter that goes into both 6 and 12. In this case it will be 6. Then complete the simplifying. Answer : 6y(y+2)

85. Cumulative frecuency-finding the median and interquartile range for grouped data Watch this video

86. Sine rule – no right angle, a matching pair (angle) 65 10 7.1 θ Sin 65 Sin θ 10 7.1 = = 10Sin θ 7.1Sin 65 Sin θ = 7.1xSin 65 10 θ =   Sin ( ) 7.1xSin 65 10 -1 θ = 40.1

87. Sine rule – no right angle, a matching pair (side)

88. Cosine rule – no right angle, no matching pair a²= b²+ c² - 2bc Cos A

89. 9km 12km x 20 A B C a b c a²=9²+12²-2 x 9 x 12 x Cos 20 a²= 81 + 144 -2 x 9 x 12 x Cos 20 a²= 225 – 202.974 a²= 22.026 a²=√22.026 a=4.7km

90. Interior angles n-2 x 180

91. Exterior angles Always add up to 360˚