Year 9 Higher – Number revision Use this revision list ALONGSIDE the presumed knowledge topics….. Recurring Decimals Recurring decimals to fractions Prime Factorisation Writing a number as a product of primes HCF and LCM from prime factorisation Fractional and Negative Indices Fractional Indices Negative Indices I can change a fraction (eg 6/11) into a recurring decimal by using “bus-shelter” division I know how to spot whether a fraction will terminate or recur when written as a decimal I can use an algebraic argument to change a recurring decimal into a fraction (in its simplest form) I can write a number as a product of its prime factors (possibly using a factor tree) I can use prime factorisation to find the HCF of a pair (or more) of numbers I can use prime factorisation to find the LCM of a pair (or more) of numbers I understand that a fractional power represents a “root” I understand that a negative power represents “one over” I can work out complicated powers like 5 2 or  Standard Form Standard form Addition and subtraction Multiplication Division Surds Intro, rules and simplifying Expanding brackets Bounds and errors Largest and smallest values Reciprocals Reciprocals Multiplication and division of decimals Long multiplication – traditional Long multiplication – grid method Multiplying decimals Division (bus shelter) Division of decimals Using proportional reasoning to solve problems Not many videos about for this – just one on Recipes Repeated percentage change Multipliers Compound Interest and depreciation Reverse percentages 1 2 64 I understand what it means to write a number in standard form I can change between standard form and “normal” I can add and subtract numbers in standard form I can multiply and divide numbers in standard form I understand what a surd is I can simplify a surd I can expand brackets involving surds I understand what we mean by the upper and lower bound for a number that has been rounded I can use inequality symbols to represent bounds for a number I can find the reciprocal of an integer, a simple fraction, a mixed number and a decimal I can multiply ANY two decimal numbers together (your favourite method!) I can divide ANY two decimal numbers I understand what is meant by a proportional relationship between two variables I can solve problems involving proportional reasoning I understand how to use a multiplier to effect percentage change I can solve problems involving compound interest and depreciation I can solve “reverse percentage” questions Questions Recurring Decimals 1) Write 4 as a recurring decimal. 7 2) Determine which of the following fractions terminate and which ones recur when written as decimals. Explain your reasoning. 5 , 8 1 , 3 11 20 2 , 7 3) Write 0.34 as a fraction in its simplest form. 4) Write 0.512 as a fraction in its simplest form. Prime Factorisation 1) Write 300 and 252 as products of prime numbers. Use your answer to work out the Highest Common Factor of 300 and 252. 2) Write 220 and 462 as products of prime numbers. Use your answer to work out the Lowest Common Multiple of 220 and 462. Give your answer as a product of primes (no need to work out its actual value). Fractional and Negative Indices Work out the following – give your answers as simply as possible. 1) 4-1 2) 3-2 3) 16 ½ 4) 8 ⅓ Standard Form 1) Write the following numbers in standard form a) 3400000 b) 25200 c) 0.023 d) 0.000045 c) 3.01 x 10-1 d) 9.876 x 10-5 2) Write the following numbers normally a) 1.2 x 103 b) 5.62 x 105 3) If a = 1.2 x 106 and b = 6 x 104, work out the following, giving your answers in standard form a) a + b b) ab c) a ÷ b Surds 1) Simplify the following surds a) 50 2) Expand and simplify a) (1 + 2 )(3 - 2 ) b) 48 b) (3 + 3 )(5 - 3 ) Bounds and Errors Use inequality symbols to represent the bounds of the following rounded numbers a) w = 5 (nearest whole number) b) x = 1.2 (1 decimal place) c) y = 3.45 (2 decimal places) d) z = 550 (two significant figures) Reciprocals Write down the reciprocal of each of the following values a) 3 b) 1 6 c) 3 4 d) 2 1 2 e) 0.8 Multiplication and division of decimals Showing a clear method, work out the following: 1) 23 x 576 2) 5.4 x 0.0298 3) 4505 ÷ 17 4) 151.06 ÷ 0.26 Proportional Reasoning 1) A recipe for 24 cupcakes requires 200g of flour and 150g of sugar (as well as other ingredients) a) How much flour and sugar would be required for (i) 12 cupcakes? (ii) 30 cupcakes? b) If I have 300g of flour and 200g of sugar, what is the MAXIMUM number of cupcakes that I would be able to make? 2) It takes 4 people 3 hours to put 3000 cards into envelopes. How long would it take… (i) 6 people to put 6000 cards into envelopes? (ii) 10 people to put 20000 cards into envelopes? Write down any assumptions that you are making in your answer. Repeated Percentage Change 1) I invest £3000 into a bank account paying COMPOUND INTEREST at 2% per annum. (i) How much is it worth after 1 year? (ii) How much is it worth after 5 years? (iii) How much interest will I earn in the first 10 years of investment? (iv) Write down an expression for how much it is worth after n years. 2) I buy a car for £6500. Every year it depreciates in value by 20%. (i) How much is it worth after 1 year? (ii) How much is it worth after 5 years? (iii) Write down an expression for how much it is worth after n years. 3) In a shop sale ALL prices are reduced by 15%. I buy a tumble dryer IN THE SALE for £136. How much is it normally worth (ie BEFORE the sale)?