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) PRIME NUMBERS CAN ONLY BE DIVIDED BY THEMSELVES AND 1 1 2 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 FACTORS OF 12 1 x 12 = 12 2 x 6 = 12 3 x 4 = 12 And the Factors of 18 are.. 1, 2, 3, 6, 9,and 18 3 Eg prime factors of 12 are 2 2 3 4
Highest factor common to 2 numbers Eg 12 and 16 actors of 12 =2 2 3 Factors of 16 = 2 2 2 2 The lowest number that 2 or more given numbers can divide into Eg 12 and 16 Factors of 12= 2 2 3 Factors of 16= 2 2 2 2 Factors common to both 12 and 16 =2 2 HCF = 2 X 2 = 4 5 LCM 2 2 3 2 2 = 48 (ie both 12 and 16 divide into 48) - list factors common to both numbers ( 2, 2) and then any additional factors of both numbers (2,2,3) 6 What is a multiple? Multiples are the results of when you multiply The multiples of a number are that number s times table The multiples of 6 are: 12,18,24,30,36 The multiples of 7 are: 14,21,28,35,42 7 are numbers multiplied by themselves Eg square of 2 is 4 (2X2) 3 is 9 (3X3) 4 is 16 (4X4) Square numbers are 4. 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 2 2 eg 2x2x2=8 (multiplied by itself 3 times) 2 3x3x3=27 Cube Numbers are 8, 27, 64, 125, 216 2 2 2 8
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 RULES OF DIVISIBILITY 2 The last digit is even (0,2,4,6,8) 3 The sum of the digits is divisible by 3 4 The last 2 digits are divisible by 4 5 The last digit is 5 or 0 6 The number is divisible by 3 and is even 7 8 The last 3 digits are divisible by 8 9 The sum of the digits is divisible by 9 10 10 The number ends in 0 Index Numbers or Powers (indices) 3 2 = 3x3 3 3 = 3x3x3 3 4 = 3x3x3x3 3 5 = 3x3x3x3x3 11 Brackets Indices Division Multiplication Addition Subtraction 12
Think of A la mode in fashion- 3,6,3,7,4,3,9 Median = Middle value 3,3,3,4,6,7,9 Mode = Most common 3 Mean = Total of items Number of items This is MEAN! 13 3+3+3+4+6+7+9 = 35 = 5 I have to do 7 13 Add 9175 14 the work! Eg 367 X 25 MULTIPLY (367 X 20) + (367 X 5) (multiply by 2 and add O) 367 X 25 Multiply by 5 1835 Multiply by 20 7340 eg 630 18 Divide 630 by the Factors of 18 (6 and 3) Eg To 1 Decimal Place Look at next number - if it is 5 or more the first number will increase by 1 Divide by 6 6 630 Divide answer by 3 3 105 35 15 32.138 = 32.1 872.884 = 872.9 0.06 = 0.1 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 2.6582 = 2.66 432.87 = 43300 0.5142 = 0.514 0.0387 = 0.039 17 Smaller than Bigger than Eg 9 12 15 13 Note: 0 after the decimal place is significant 18 PERCENTAGE PROFIT (INCREASE) means out of 100 60 = 60% 100 Percentage Decimal Divide by 100 60% = 0.60 Decimal Percentage Multiply by 100 0.60 = 60% 19 Actual profit(increase in price) X 100 Cost(original) price PERCENTAGE LOSS (DECREASE) Actual loss(decrease in price) X 100 Cost(original) price 21
MULTIPLICATION & DIVISION 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 (-3) 4 = - 12 2 2 ADDING & SUBTRACTING when the signs are NOT touching Move up and down the Number line Eg: 2-7 = -5-1 -5 = -6 When the signs are touching replace the 2 signs with 1 sign - - = + - + = - + + = + + - = - 2(x 3) = 2x + 6 25 26 Eg: 5 - - 6 = 11-4 + - 8 = -12 + _ 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 DIVIDE BY 10 Move all numbers 1 place to Right D IVIDE BY 100 Move all numbers 2 places to Right A B Share 15 sweets between 2 children A and B i in the ratio 3:2 1 of 15 = 3 1 of 15=3 5 5 Each part is 3 sweets Each part is 3 sweets A B 3 : 2 5 parts in total 3 of 15 sweets 2 of 15 sweets 5 5 3. 62 10 =.362 3. 62 100 =.0362 22 9 sweets 6 sweets 23
RULE 2 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 45 RULE 1 You can only add or subtract LIKE TERMS Eg 3m + 2m = 5m 5x - 3x = 2x 4y² + 3y cannot be added- y² and y are not like terms m + p = m + p m and p are not like terms 43 RULE 3 With algebra we write division as a fraction Divide the numbers first ( cancel if possible) Cancel the letters where possible Ratio of Red : Black Black : Red Red : All 20 abc 20 abc = 5bc 4 a 4 a 46 8 : 12 12 : 8 8 : 20 4 4 4 4 4 4 2 : 3 3 : 2 2 : 5 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 6m 5m 4 m 3 m 2 cms 4 cms 8m 2m Area = 4X2 =8 square cms (cm²) Perimeter= 5 + 4 + 3 + 2 + 8 + 6 = 28 Metres 28 29 A AREA OF TRIANGLE ½ Base X Perpendicular height 15cm 8cm 10 cms 10 cms 8cms vertices (corners) 12cm 12cms edges 10cm rarea of Triangle 5 X 8= 40cm² Area of Triangle 12 X 8 = 48cm 2 30 faces 31
TRIANGLE SQUARE height UNIT Cubic millimetre mm 3 Cubic centimetres cm 3 Cubic metre m 3 You hold a PENcil with 5 fingers PENTAGON (5) HEXAGON (6) There is an X in six length width VOLUME= Length x width x height An Octopus has 8 legs OCTAGON (8) RECTANGLE (4) 32 33 SQUARE 4 equal sides 4 right angles RHOMBUS (squashed square) 4 sides equal Opposite angles equal KITE 2 sets of lines next each other (adjacent) equal PARALLELOGRAM Opposite posite sides sides parallel and equal and equal Think of a quad bike with 4 wheels Reflection Rotation RECTANGLE Opposite sides equal 4 right angles TRAPEZIUM 2 sides parallel 34 Enlargement Translation 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 All sides/angles different REFLEX more than 180º Right angled triangle One angle of 90º 36 RIGHT ANGLE 90º 37 Angles in a triangle add up to 180º POLYGONS Angles on a straight line add up to 180º Alternate Angles are equal Angles in a circle add up to 360º 38 Sum of EXTERIOR angles = 360º Sum of INTERIOR angles = (n-2) X where n is the number of sides in the polygon 6 Sides (n 2) x 180º (6 2) x 180º Sum of interior angles= 4 x 180 = 540º 180º As this is a regular hexagon each angle is 540º 6 = 120º 40
Z Angles equal x x F Angles equal x This applies to regular and irregular shapes 41 C Angles add up to 180º x 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 Circumference Diameter Radius + - + 4a + b - 2a + 3b 4a - 2a + b + 3b 2a + 4b EXAMPLE 6y + 3-2y - 6 6y - 2y + 3-6 4y - 3 42 44 A O R R
Divide top Multiply by.fraction Decimal Percentage by bottom 100 1 whole 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 Divide by 100 Fraction down Decimal Percentage 59 We are on the hunt for common factors in both numbers and letters 7a +28 (7 is the only common factor) 7(a + 4) 10b + 15bc ( 5 and b are common factors) 5b(2 + 3c) 4b² + 5b (b is the only common factor) b(4b + 5) 49 Favourite Football team Supporters 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