Maths revision What maths can be used in

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. 7. 88889934 pence would make more sense to be written as 8 p Basically if the number is 5 or larger the previous number rounds up. E. g. 6. 547 could be written as 7 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. 237. 664 = 237. 7 to 1 decimal place or = 237. 66 to 2 decimal places Significant figures start at the first number E. g. 237. 664 = 200 to 1 significant figure or = 240 to 2 significant figures

Multiplication 3 6 9 1 1 7 2 3 4 2 4 6 2 4 4 7 8 8 2 7 1 2

Decimals • 0. 2 = 2/10 = 1/5 (20 p) • 0. 02 = 2/100 = 1/50 (2 p) • 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 2 + 1 = 9 quarters) • 3 4 = 34 (3 x 10 + 4 = 34 tenths) 10 10 • 12 = 6 = 2 ( cancel by other numbers than 2) 18 9 3

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

Fractions 3 • Multiply is easy • 2 x 4 = 8 • 3 5 15 • Divide is easy if you turn the 2 nd upside down • 2 ÷ 4 becomes 2 x 5 = 10 = 5 3 5 3 4 12 6

Fractions 4 To find three quarters (3/4) of a number (32) 1 32 ÷ 4 = 8 2 8 x 3 = 24 Three quarters of 32 is 24.

Percentages • With a calculator 1 ÷ by 100 2 X by the % e. g. find 22% of 600 ÷ 100 = 6 6 x 22 = 132

Percentages • 1 2 3 Without a calculator Find 10% move the decimal point 1 place Find 1% move the decimal point 2 places Use these to get to the answer e. g. find 22% of 600 10% = 60. 0 and 1% = 6. 00 So 22% = 60 + 6 + 6 = 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 = 20% 10, 000 100

Fractions/Decimals/Percentages • To compare change them all to % E. g. Arrange 0. 61, 3/5, 59%, 0. 599 in order 0. 61 = 61 out of 100 = 61% 3/5 of 100 = 60% 0. 599 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 -3 -3 = -6, -3 +2 -2 = -3 7 -4 -5 = -2 7 -4 +1 = 4 BUT if there are 2 signs next to each other. -3 - -3 = -3 +3 = 0 7 + -2 + +4 - -5 = 7 -2 +4 +5 = 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 + - = -10 = +2 -5 12 = -2 -6 -3(-5) = +15 (-4)² = -4 x -4 = +16

Angles • Use the rules 180 360 F 360 180 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 l l A 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 + 3 a = 4 a 5 y – 2 y = 3 a BUT 3 y – 2 a cannot be simplified Simplify 3 a – 4 y + 2 y – 5 a + 8 y Answer -2 a + 6 y or 6 y – 2 a

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

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 5 a – 10 = 3 a + 18 5 a – 3 a = +18 +10 change the signs 2 a = 28 find the value of 1 a = 14