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Transcript
PRIME NUMBERS CAN ONLY BE DIVIDED BY THEMSELVES AND 1 EVALUATE- work out CALCULATE – work out EXPRESS – show PRODUCT- multiply SUM/TOTAL- add SIMPLIFY – make easier A number with only 2 factors- 1 and itself 2 3 5 7 11 13 17 19 23 29 31 37 41………… (Note 1 is not a prime number) 2 1 T FACTORS OF 12 1 x 12 = 12 2 x 6 = 12 3 x 4 = 12 A factor is a number that will divide exactly into a larger number Are factors which are also prime numbers The factors of 12 are 1,2,3,4, 6 & 12 They can all divide into 12 And the Factors of 18 are.. 1, 2, 3, 6, 9,and 18 Eg prime factors of 12 are 2×2×3 3 4 The lowest number that 2 or more given numbers can divide into Highest factor common to 2 numbers Eg Factors of 12 12 =2×2×3 and Factors of 16 Factors common to both 12 and 16 16 = 2×2×2×2 Eg 12 Factors of 12= 2×2×3 =2×2 and 16 2×2×2×2 Factors of 16= LCM 2×2×3×2×2 = 48 (ie both 12 and 16 divide into 48) HCF = 2 X 2 = 4 What is a multiple? Multiples are the results of when you multiply - list factors common to both numbers ( 2, 2) and then any additional factors of both numbers (2,2,3) 5 6 2 are numbers multiplied by themselves The multiples of a number are that number’s times table Square numbers are 4. 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 eg 2 2 The multiples of 6 are: 12,18,24,30,36… The multiples of 7 are: 14,21,28,35,42… 2 Eg square of 2 is 4 (2X2) 3 is 9 (3X3) 4 is 16 (4X4) (multiplied by itself 3 times) 2 2x2x2=8 3x3x3=27 2 7 Cube Numbers are 8, 27, 64, 125, 216 8 RULES OF DIVISIBILITY 2 3 4 5 6 7 8 9 10 The answer is a number that has been multiplied by itself Eg Square root of 9 is 3 (3X3=9) 16 is 4 (4X4=16) 25 is 5 (5X5=25) 36 is 6 49 is 7 64 is 8 81 is 9 √ (The square root is the opposite of a Square Number) 9 Index Numbers or Powers (indices) 2 3 33 34 35 = 3x3 = 3x3x3 = 3x3x3x3 = 3x3x3x3x3 The The The The The ÷ last digit is even (0,2,4,6,8) sum of the digits is divisible by 3 last 2 digits are divisible by 4 last digit is 5 or 0 number is divisible by 3 and is even The last 3 digits are divisible by 8 The sum of the digits is divisible by 9 The number ends in 0 10 Brackets 11 Indices Division Multiplication Addition Subtraction 12 Median = Middle value 3,3,3,4,6,7,9 Mode = Most common 3 Mean = Total of items Think of A la mode – in fashion- 367 X 25 Eg 3,6,3,7,4,3,9 MULTIPLY (367 X 20) + (367 X 5) (multiply by 2 and add O) Number of items Multiply by 5 3+3+3+4+6+7+9 = 35 = This is MEAN 13 ! I have to doT the work! 5 7 eg 14 32.138 = 32.1 872.884 = 872.9 = 0.1 0.06 6 630 3 105 35 Add Eg To 1 Decimal Place Divide 630 by the Factors of 18 (6 and 3) Divide answer by 3 13 Look at next number if it is 5 or more the first number will increase by 1 630 ÷ 18 Divide by 6 Multiply by 20 367 X 25 1835 7340 9175 15 IGNORE THE WHOLE NUMBERS- ONLY CONSIDER THE NUMBERS AFTER THE DECIMAL PLACE 16 Look at 4th number- if it is 5 or more the third number will increase by 1 Eg To 3 Significant figures (SF) 657.33 = 65700 432.87 = 43300 2.6582 = 2.66 0.5142 = 0.514 0.0387 = 0.039 Smaller than Eg Note: 0 after the decimal place is significant 9 Bigger than ‹ 12 15 › 13 18 17 PERCENTAGE PROFIT means out of 100 PePercentage Decimal 60 100 = 60% Actual profit(increase in price) X 100 Cost(original) price Decimal – Divide by 100 60% = 0.60 Percentage – Multiply by 100 0.60 = 60% (INCREASE) PERCENTAGE LOSS 19 (DECREASE) Actual loss(decrease in price) X 100 Cost(original) price 21 ADDING & SUBTRACTING MULTIPLICATION & DIVISION when the signs are NOT touching Move up and down the Number line If the signs are the same (both positive or both negative), the answer will be positive. If the signs are different (one positive and one negative), the answer will be negative. 20 ÷ (-4) = -5 (-3) × (-5) = 15 Eg: 2 - 7 = -5 + -1 -5 = -6 When the signs are touching replace the 2 signs with 1 sign - - = + - + = + + = + + - = - (-3) × 4 = - 12 6 –2(x – 3) = –2x + 2 2 25 Eg: 5 - - 6 = 11 26 -4 + - 8 = -12 A MULTIPLY BY 10- Move all numbers 1 place to Left MULTIPLY BY 100- Move all numbers 2 places to Left 6. 274 X 10 = 62.74 6. 274 X 100 = 627.4 1 of 15 = 3 of 15=3 5 A B 3 : 5 parts in total 2 Each part is 3 sweets Each part is 3 sweets D IVIDE BY 100 – Move all numbers 2 places to Right 3. 62÷ 100 = .0362 B Share 15 sweets between 2 children A and B in the ratio 3:2 1 5 DIVIDE BY 10 – Move all numbers 1 place to Right 3. 62 ÷ 10 = .362 i _ 3 of 15 5 sweets 2 5 of 15 sweets 22 9 sweets 6 sweets 23 RULE 2 RULE 1 You can Multiply different and like terms together. Always multiply the numbers together first Then put in letters but leave out multiplication sign 3a x 5b x 2c = 30 abc 3a x 4a = 12 a² 2a x 3b x 3a² = 18 a³b You can only add or subtract LIKE TERMS Eg 4y² + 3y RULE 3 20 abc 4a m and p are not like terms 43 Ratio of With algebra we write division as a fraction Divide the numbers first ( cancel if possible) Cancel the letters where possible 20 abc 4a cannot be added- y² and y are not like terms m + p =m+p 45 5x - 3x = 2x 3m + 2m = 5m Red : Black Black : Red 8 : 12 = 5bc ÷4 8 : 20 12 : 8 ÷4 2 : 3 Red : All ÷4 ÷4 3 : 2 ÷4 ÷4 2: 5 46 24 The length of the distance round a shape The space within a shape (in square units) PeRimeter reminds us of PRison- the guards patrol round the outside 4 cms 5m 2 cms 4m 3m 6m 2m 8m Area = 4X2 =8 square cms (cm²) Perimeter= 5 + 4 + 3 + 2 + 8 + 6 = 28 Metres 29 28 A AREA OF TRIANGLE ½ Base X Perpendicular height 10 cms 15cm 8cm 12cm vertices 10 cms (corners) 8cms 12cms edges 10cm ArArea of Triangle = 5 X 8= 40cm² Area of Triangle 12 X 8 = 48cm 2 30 faces 31 TRIANGLE UNIT Cubic millimetre Cubic centimetres Cubic metre mm3 cm3 m3 You hold a PENcil with 5 fingers PENTAGON (5) SQUARE HEXAGON (6) There is an X in six height width OCTAGON (8) length An Octopus has 8 legs VOLUME= Length x width x height RHOMBUS SQUARE 4 equal sides 4 right angles RECTANGLE (4) (squashed square) 4 sides equal Opposite angles equal 32 33 KITE 2 sets of lines next each other (adjacent) equal Reflection Rotation Enlargement Translation PARALLELOGRAM PARALLELOGRAM Opposite sides sides parallel parallel and equal Opposite and equal RECTANGLE Opposite sides equal 4 right angles Think of a quad bike with 4 wheels TRAPEZIUM 2 sides parallel 34 35 Isosceles Triangle 2 sides equal, 2 angles equal ACUTE less than 90º Equilateral Triangle 3 sides equal, 3 angles equal (60º) OBTUSE between 90º and 180º Scalene triangle REFLEX more than 180º All sides/angles different Right angled triangle RIGHT ANGLE 90º One angle of 90º 37 36 POLYGONS Angles in a triangle add up to 180º Sum of EXTERIOR angles = 360º Angles on a straight line add up to 180º Sum of INTERIOR angles = (n-2) X 180º where n is the number of sides in the polygon Alternate Angles are equal 6 Sides Angles in a circle add up to 360º (n – 2) x 180º (6– 2) x 180º Sum of interior angles= 38 As this is a regular hexagon each angle is 540º ÷ 6 = 120º 4 x 180 = 540º 40 Z Angles equal x F Angles equal x x x This applies to regular and irregular shapes C Angles add up to 180º 41 x x 39 ∏ = 3.14 approx AREA of a circle ∏ X r² (radius ²) CIRCUMFERENCE of a circle ∏ X D (diameter) The Pied (Πd) Piper walks round the town 4a Circumference + b 42 - 2a + + A 3b 4a - 2a + b + 3b EXAMPLE 2a + 4b 6y + 3 - 2y - 6 6y - 2y + 3 - 6 4y - 3 Diameter Radius - + O R 44 R Fraction . Divide top by bottom 1 whole Fraction Decimal Multiply by 100 Percentage 1.0 100% ½ 0.5 50% ¼ 0.25 25% /3 0.33 33% ⅛ 0.125 12.5% Over 10/ 100/ 1000 & cancel down Decimal Divide by 100 We are on the hunt for common factors in both numbers and letters 7a +28 59 (7 is the only common factor) 7(a + 4) 10b + 15bc ( 5 and b are common factors) 5b(2 + 3c) Percentage 4b² + 5b (b is the only common factor) Favourite Football team Supporters b(4b + 5) Degrees Arsenal 15 15 x 10 = 150º Man United 12 12 X 10 = 120º Liverpool 8 8 x 10 = 80 º Burton Albion 1 1 x 10 = 10 º Construct a pie chart to shown this information. A full circle is 360º 36 people have been surveyed (15 + 12 + 8 + 1). If they shared the Pie chart equally each supporter would get 360º = 10º 36 27 49