Maths revision What maths can be used in the question? What strategies will help? What working do I need to show? Is the answer down to maths?

Number Integers = whole numbers Prime numbers = cannot be ÷ by any number except itself (2, 3, 5, 7, 11, etc) Multiple = in that numbers times table Factor = a number that ÷ into it Square number = the result of a number x itself (1, 4, 9, 16, etc) Square root is the opposite of square

Approximations Sometimes an answer is too precise and needs rounding off. e.g pence would make more sense to be written as 8p Basically if the number is 5 or larger the previous number rounds up. E.g could be written as 7 or 6.5 or 6.55

Decimal places and significant figures These are instructions into how precise the answer must be. Decimal places start from the point. E.g = to 1 decimal place or = to 2 decimal places Significant figures start at the first number E.g = 200 to 1 significant figure or = 240 to 2 significant figures

Multiplication

Decimals 0.2 = 2/10 = 1/5 (20p) 0.02 = 2/100 = 1/50 (2p) If 3 x 4 = 12 Then 0.3 x 4 = 1.2 And 30.0 x 0.4 = 12 And 0.3 x 0.4 = 0.12 etc.

Fractions 2 ¼ = 9/4 (4 x = 9 quarters) 3 4 = 34 ( 3 x = 34 tenths ) = 6 = 2 ( cancel by other numbers than 2)

Fractions 2 The method for + and – is the same (think 3 x 4) X 4 X 3 9 – 8 = 1 12 Include the red arrow

Fractions 3 Multiply is easy 2 x 4 = Divide is easy if you turn the 2 nd upside down 2 ÷ 4 becomes 2 x 5 = 10 =

Fractions 4 To find three quarters (3/4) of a number (32) 132 ÷ 4 = 8 28 x 3 = 24 Three quarters of 32 is 24.

Percentages With a calculator 1÷ by 100 2X by the % e.g. find 22% of ÷ 100 = 6 6 x 22 = 132

Percentages Without a calculator 1Find 10% move the decimal point 1 place 2Find 1% move the decimal point 2 places 3Use these to get to the answer e.g. find 22% of % = 60.0 and 1% = 6.00 So 22% = = 132

Writing as a percentage First write as a fraction Then x by 100 E.g. A car is bought for £10,000 and sold for £8,000. what is the percentage loss? loss = 2,000 x 100 = 2000 = 20% 10,

Fractions/Decimals/Percentages To compare change them all to % E.g. Arrange 0.61, 3/5, 59%, in order 0.61 = 61 out of 100 = 61% 3/5 of 100 = 60% is 59 and a bit out of 100 = 59.9% So 59% then 0.599, then 3/5, then 0.61

Negative numbers Go up and down a ladder = -6, = = = 4 BUT if there are 2 signs next to each other = = = = 14 Simplify the signs BEFORE using a ladder

Negative numbers Multiplying/dividing/brackets involve the signs coming together -3 x -3 is 3 x 3 and - - = +9 5 x -2 is 5 x 2 and + - = = +212 = (-5) = +15(-4)² = -4 x -4 = +16

Angles Use the rules F z x

Ratios Bill and Ben share £30 in the ratio of 3:2 This means that the money is being shared 5 ways The key is to find the value of 1 share £30 ÷ 5 = £6 = 1 share Bill gets £6 x 3 = £18 Ben gets £6 x 2 = £12

Area (cm²) (Base x vertical height) halved Remember to halve

Area Split into several sections

Area Base x vertical height

Circles

Volume (cm³) Volume = area of A x length l A A A l l l

Probability Probabilities are expressed in decimals or fractions. Probabilities lie between 0 (not possible) and 1 (must happen) What is the probability of choosing an 8 in a pack of cards Answer 4 in 52 or 1/13

Relative frequency Relative frequency is the number of times that the event is likely to happen e.g. a RF of 0.2 means it will happen one fifth of the time. How many times will the red counter appear in 200 goes if the relative frequency is 0.3 Answer 0.3 x 200 = 60 The relative frequency can be found by experimenting but to be reasonably accurate must be found after numerous goes.

Algebra - simplifying Similar terms can be added or subtracted. a + 3a = 4a5y – 2y = 3a BUT 3y – 2a cannot be simplified Simplify 3a – 4y + 2y – 5a + 8y Answer -2a + 6y or 6y – 2a

Algebra - simplifying Multiplying 2a x 3b = 6ab 2a x -4a x 3c = -24a²c Dividing 6a ÷ 3a = 210a ÷ 5c = 2a/c 10a²bd = 2ad 5ab Think number/letter/sign

Algebra - solving Get rid of brackets Isolate the unknowns on one side Find the value of the unknown 5(a – 2) = 3(a + 6) don’t forget the number 5a – 10 = 3a a – 3a = change the signs 2a = 28 find the value of 1 a = 14