How do you know 30 is not a prime. Estimate Estimate 3.9 x 19.4 Do 4 x 20 = about 80 Multiply negatives What is -4 x -3 What is -5 x 4

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1 Factors What are the factors of 20? 1,20, 2,10, 4,5 Primes What are prime numbers between 20 and 30? How do you know 30 is not a prime 23, 29 (they only have 2 factors, 1 and itself) Because 30 is 3 x 10 Estimate Estimate 3.9 x 19.4 Do 4 x 20 = about 80 Multiply negatives What is -4 x -3 What is -5 x 4 12 (two negatives make a positive) -20 Powers, Cubes What is 5 4 What is = 5 x 5 x 5 x 5 = = 10 x 10 x 10 x 10 = Square numbers 3 2 = 3 x 3 = = 4 x 4 = = 5 x 5 = = 6 x 6 = = 7 x 7 = = 8 x 8 = = 9 x 9 = 81 Cube numbers 2 3 = 2 x 2 x 2 = = 3 x 3 x 3 = = 4 x 4 x 4 = = 5 x 5 x 5 = = 6 x 6 x 6 = = 7 x 7 x 7 = 343 Square root is the opposite of square What is = 36 so 36= 6 Cube root is the opposite of cube What is = 343 so 3 343=7 Fractions What is ¾ of x 3 = 60 Percentages What is 27% of 87? x 87, % means 100 Equivalencies Rounding / SF Which is bigger 0.22, 24% or 23/100? Round to 3 dp Round to 2 sf 0.22 = 22/100 24%=24/ (4th decimal number is 7 so round up) 2.4 (2 sf means round to 2 significant figures) Ratio Split 120 into ratio 1:2: = 6 (buckets) Divide 120 by 6 = 20 1x20 : 2x20 : 3x20 = 20:40:60 HCF LCM What is the highest common factor of 20 and 15? What is lowest common multiple of 6 and 4? Factors of 20= 1,20, 2, 10, 4, 5 Factors of 15 = 1, 15, 3, 5 Highest common factor = 5 Multiples of 6 = 6, 12, 18, 24, 30,. Multiples of 4 = 4, 8, 12, 16, 20,. Lowest common multiple = 12

2 Multiply fractions Multiplication 124 x = 9 Just multiply the numbers x x 400 = Multiply out each pair of numbers than add up all the bold numbers in the grid = x 400 = x 400 = x x 5 = x 5 = x 0.5 = 0.4 Division ) BIDMAS Work out 5 2 3x4 Brackets, Indices, Division, Mult, Add, Subtract Prime factors Prime factorisation What are the prime factors of 300? 5 2 3x4 Work out 5 2 first 25 3x4 Now work out 3 x Now subtract = 3 x 5 x 2 x 5 x 2 = 2 2 x 3 x 5 2

3 Travel graphs If the line is flat the person has stopped e.g. 10:30 If the line is steeper the person is travelling fast e.g. at 10:45 If the line is not steep the person is travelling slowly e.g. at 10am. Conversion graphs Plot the points from the table and join then up To convert 30 km to miles draw a line up from 30 km to the line and read across from the miles (about 19 miles) Coordinates P is (2,4) Q is (6,0) R and S have been plotted on the grid.

4 Substitute Y= 4t 10 t =5 y = 4x5 10 y = y = 10 Solve 4g = 20 g = 20 4 ( 4 is opposite of x4) g = 5 Solve 2g 10 = 4 Undo -10 by adding 10 2g = 14 Undo 2x by dividing by 2 g = 14 2 g = 7 Solve 3(x+2) = 60 Undo 3x by dividing by 3 x+2 = 20 Undo + 2 by subtracting 2 x = 18 Simplify 3x + 2y 2x + y + 5 Collect like terms 3x -2x + 2y + y + 5 x + 3y + 5 Multiply brackets 2a (a+3b) 2a x a = 2a 2 2a x 3b = 6ab So 2a (a+3b) = 2a 2 + 6ab Find Nth term 3, 7, 11, 15, 19 Goes up by 4 so Nth term is 4n Trial and improvement Powers Create expressions 4 times table is 4, 8, 12, 16 so subtract 1 4n - 1 X = 8 Guess x=2 Simplify t x t x t x t x t Simplify t 5 t 3 Simplify t 5 t 3 Plot a graph Plot y = 5x + 3 James has 10 bags of sweets and 5 loose sweets. There are T sweets in each bag. How many sweets has he got? Draw y=4 5 is the gradient 3 is the intercept on the Y axis = 9 so too high Guess x= = 7.8 so too low Guess x = = 8.0 t x t x t x t x t = t 5 t 5 t 3 = t 2 (subtract the powers) t 5 t 3 = t 8 (add the powers) 10 T + 5 Create a table X Y Plot them y=4

5 Mean Mean of 10, 12, 5, 7, 6 Add up = = 40 Mode / modal Divide by number of numbers = 40 / 5 = 8 Mode of 10, 12, 12, 5, 7, 6 Most frequent number = 12 Median Median of 10, 12, 5, 7, 6, 12 Write in order = 5, 6, 7, 10, 12, 12 Pick middle number or half way between middle numbers = 8 ½ Range Range of 10, 12, 12, 5, 7, 6 Biggest smallest = 12 5 = 7 Stem Leaf Range = biggest smallest = 56 9 = 47 Mode = most common = 42 Median = middle number = 34 Find the mean Amount Frequency Midpoint Total 0 < x x < x x < x x < x x < x x450 Estimated mean Add up numbers above and divide by total frequency Probability This shows a probability scale 0 is impossible 1 is certain 0.25 is ¼ which is unlikely 0.75 is ¾ which is likely

6 Probability This shows the probability of rolling two four sided dice and adding up the sides The probability that you will get a 7 is 2 = Probabilities are written as fractions Probability Probability Frequency chart The probability that Rovers will win their next match is 0.6. The probability that Rovers will lose their next match is Work out the probability that Rovers will draw their next match. The probability that it will be sunny tomorrow is 0.3. Why is the probability that it will rain NOT 0.7? 50 Total probability = 100% = = 0.25 So probability that they will draw is 0.25 Because it could be cloudy or snowy as well Mrs Spencer Number of journeys (frequency) Scatter Graphs Correlation Mileage ( m miles) Plot the midpoint of the group e.g plot at 45 These show positive strong correlation, then negative weak correlation, then no correlation

7 Scatter graphs Line of best fit Through the middle of the crosses German Two way tables Birmingham French The distance between Leeds and Stoke is 93 miles Leeds Nottingham Peterborough 93 Sheffield Stoke Speed Units Kilo means 1000 A car travels 200 miles in 4 hours What is its speed? Speed = miles per hour ( per means divide ) = 200 miles 4 hours = 50 mph Metric Imperial Estimate 1 kilo gramme = 1000 grammes 2 pounds 1 metre = 100 centi metres = 1000 milli metres About 1 yard Weight of an OJ carton 1 big step 1 kilo metre = 1000 metres About ½ mile 15 minute walk 1 litre = 1000 milli litres 2 pints orange juice carton

8 Shapes Parallelogram... Trapezium... Isosceles triangle... Kite... (f) Pentagon... Hexagon 6... Pentagon 5... Octagon 8 Square based pyramid Cylinder Isometric drawing

9 Nets Shapes which have been unfolded Area... No... yes... No... Yes 8 m 6 m 4 m Area of a triangle 5 m Split it into two shapes and work out area of each 4 x 8 = 32 cm 2 2 x 5 = 10 cm = 42 cm 2 Width x height Then Halve it Area and perimeter Area = count the squares Perimeter = distance around the outside of the shape Volume of a cuboid 3cm 5cm 2cm 3 x 5 x 2 = 30 cm 3 Volume 9 8 cm 3 5 cm 4 2 cm Area of triangle = 3.5 x = 7.35 cm 2 Volume = area of front x 9.8 = cm 3

10 Transformations Reflect Rotate Enlarge y X=4 Translate (move across and then down) x 4 6 Symmetry Octagon has 5 lines of symmetry Rotational symmetry Rotational symmetry of order 4 Circle AO = Radius BE = Diameter CD = Chord Perimeter = circumference Area = Pi x r 2 (pi = 3.142) Angle words Circumference = Pi x diameter Reflex Acute Obtuse

11 Angles on a straight line NOT TO SCALE ADD UP TO 180 p Angles in a quadrilateral (four sided shape) ADD UP TO = NOT TO SCALE 80 r q r = = 70 q = = 110 Angles in a triangle Add up to 180 Isosceles triangle Angles are equal and sides are the same size Angles in parallel lines F Z X angles w y = 50 (Z angle) x = 70 (F angle) w = 70 (X angle)

12 Pythagoras Loci a 2 + b 2 = c 2 (c is the longest side, the hypotenuse) = c = c 2 c 2 = square root of 7225 = 85 The fox can move anywhere that is not in one of the three circles.

13 Bearings The two lines drawn are at angles of 295 o and 242 o from the church and post office. Hangmans hill is where the two lines cross.