GCSE Mathematics AQA 8300 Programme of Study Learning Outcomes (Updated April 2017) AQA 8300 Subject content with learning outcomes for Programme of Study Page 1 The Fernwood School GCSE MATHEMATICS SUBJECT CONTENT FOR AQA 8300 AND FULL LEARNING OUTCOMES FOR PROGRAMME OF LEARNING Subject content from Specification (May 2014) TOPIC: 1.1 THE NUMBER SYSTEM Basic foundation Additional foundation Higher Only I can read and write numbers given in figures. N1 I can read and write numbers given in words. order positive and negative integers, I can recognise positive and negative numbers. decimals and fractions I can recognise odd and even numbers. I know the place values for whole numbers. N1 I can recall the multiplication tables for numbers up to 12 X 12 use the symbols =, ≠, <, >, ≤, ≥ I can add and subtract large numbers. I can multiply and divide large numbers. Notes: including the use of a number line. I know the place value for decimal numbers. See also A22 I can order decimal numbers. I can add and subtract negative numbers using a number line. N2 I can use BODMAS for calculations. apply the four operations, including formal I know how to apply inverse operations to reverse a calculation written methods, to integers, decimals and I can use and know how to interpret a calculator correctly simple fractions (proper and improper), and I can add and subtract decimal numbers mixed numbers – all positive and negative I can multiply and divide decimals by 10, 100 and 1000. I know the rules for negative numbers when adding, subtracting, N2 dividing and multiplying. understand and use place value (eg when working with very large or very small I can add, subtract, multiply and divide negative numbers such numbers, and when calculating with as decimals) (-3) – (-4) or -3 x (-4) I can multiply decimals such as 2.4 x 3.6 Notes: including questions set in context. Knowledge and understanding of terms used in household finance, for example profit, loss, cost price, selling price, debit, credit, balance, income tax, VAT and interest rate. See also R9 N3 recognise and use relationships between operations, including inverse operation (eg cancellation to simplify calculations and expressions) N3 use conventional notation for priority of operations, including brackets, powers, roots and reciprocals AQA 8300 Subject content with learning outcomes for Programme of Study Page 2 The Fernwood School Subject content from Specification (May 2014) TOPIC: 1.2 ROUNDING, APPROXIMATING AND ESTIMATIONS Basic foundation Additional foundation Higher Only N14 I can round numbers to the nearest integer – knowing that this estimate answers means to the nearest unit or nearest whole number. I can round numbers to the nearest 10, 100 or 1000. check calculations using approximation and I can find estimates for square roots by using a list of square estimation, including answers obtained numbers. using technology I can round numbers to 1 decimal place. I can round numbers to any number of decimal places. Notes: including evaluation of results I can round numbers to 1 significant figure. obtained. See also N15 I know that when finding an estimate this means that the exact answer is not needed. I can estimate answers to calculations such as N15 (22.6 x 18.7) ÷ 5.2 Round numbers and measures to an by rounding each part to 1 significant figure. appropriate degree of accuracy (eg to a I know what happens to numbers when they are divided by specified number of decimal places or decimal numbers less than 1. significant figures) I know what happens to numbers when they are multiplied by decimal numbers less than 1. use inequality notation to specify simple I can estimate answers to calculations such as error intervals due to truncating or rounding (22.6 x 18.7) ÷ 0.52. I can make decisions on which numbers to round to any number Notes: including appropriate rounding for of significant figures for complex problems. questions set in context. I can find minimum and maximum values for numbers which Students should know not to round values have been rounded. during intermediate steps of a calculation. I can represent these minimum and maximum values as an See also N14 error interval using inequality notation. I can find the upper and lower bounds of simple calculations involving quantities to a particular degree of accuracy. N16 I can find the upper and lower bounds of more difficult apply and interpret limits of accuracy calculations involving decisions of when to use the maximum or minimum values as part of the calculations. including upper and lower bounds AQA 8300 Subject content with learning outcomes for Programme of Study Page 3 The Fernwood School Subject content from Specification (May 2014) TOPIC: 1.3 NUMBER PROPERTIES Basic foundation Additional foundation Higher Only I can find the factors of a number. N4 I can calculate squares and square roots of numbers both with use the concepts and vocabulary of prime and without the use of a calculator. numbers, factors (divisors), multiples, I can write down the multiples of numbers. common factors, common multiples, I can write down common factors and multiples for two or more highest common factor, lowest common numbers. multiple, prime factorisation including using I can calculate cubes and cube roots of numbers both with and product notation and the unique without the use of a calculator. factorisation theorem I can use index notation for squares and cubes. I can use the power, square root and cube root keys on my Notes: prime factor decomposition calculator. including product of prime factors written in I can recall the squares from 2 x 2 up to 15 x 15. index form. I can recall the cubes of 2, 3, 4, 5 and 10. I understand that numbers can have a positive and negative square root. N5 I can estimate powers and roots of any given positive number apply systematic listing strategies I can complete calculations that involve roots and powers without using a calculator. Including use of the product rule for I can recognise and recall prime numbers. counting I can find the reciprocal of any number. I can write any number as a product of its prime factors. Notes: including using lists, tables and I can use the prime products to work out the highest common diagrams. factor and lowest common multiple of two or more numbers. N6 use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 estimate powers and roots of any given positive number Notes: including square numbers up to 15 x 15. Students should now that 1000 = 103 and 1 million = 106 N7 calculate with roots, and with integer indices AQA 8300 Subject content with learning outcomes for Programme of Study Page 4 The Fernwood School Subject content from Specification (May 2014) TOPIC: 1.4 FRACTIONS AND FRACTION ARITHMETIC Basic foundation Additional foundation Higher Only I can recognise and find half, quarter or three-quarters of an N2 amount given as a diagram or quantity. apply the four operations, including formal I can name the parts of a fraction using the terms numerator written methods, to integers, decimals and and denominator. simple fractions (proper and improper), and I can arrange fractions with different denominators in order of mixed numbers – all positive and negative size when 1 is the numerator. I can simplify simple fractions such as 24/ 36 N8 I can convert between mixed numbers and improper fractions. Calculate exactly with fractions I can convert fractions into equivalent ones. Notes: see also G17 and G18 I can order fractions with other numerators and different denominators. R3 I can convert fractions into decimals. Express one quantity as a fraction of I can covert fractions into percentages. another, where the fraction is less than 1 or I can order a set of numbers containing a mixture of fractions, greater than 1 decimals and percentages. I can find one number as a fraction of another numbers. N10 I can work out fractions of quantities. Work interchangeably with terminating I can add and subtract fractions. decimals and their corresponding fractions I can convert decimals into fractions. 7 3 (such as 3.5 and or 0.375 and ) 2 8 I can do calculations with simple fractions involving division and multiplication Change recurring decimals into their 2 2 I know that ‘of’ means to multiply eg 𝑜𝑓 30 𝑚𝑒𝑎𝑛𝑠 𝑥 30 corresponding fractions and vice versa 5 5 I can do calculations with mixed numbers. Notes: including ordering I can identify recurring and terminating decimals. I can convert recurring decimals to fractions and fractions to recurring decimals AQA 8300 Subject content with learning outcomes for Programme of Study Page 5 The Fernwood School Subject content from Specification (May 2014) TOPIC: 1.5 PERCENTAGES AND WORKING WITH PERCENTAGES Basic foundation Additional foundation Higher Only I can recognise the percentage notation - % N12 I know that percentage means ‘out of 100’. Interpret fractions and percentages as I can write down the shaded region of a shape as a percentage. operators I can change a percentage into a fraction or decimal and vice versa. Notes: including interpreting percentage I can express one quantity as a percentage of another number. problems using a multiplier. See also R9. I can find 10%, 1%, 50% and 20% of a quantity without using a calculator. I can recognise the multiplier when trying to find a percentage of R9 an amount. Define percentage as ‘number of parts per I can find any percentage of a quantity using a calculator. hundred’ I can increase or decrease a quantity by a given percentage. I can recognise the multiplier when increasing or decreasing a Interpret percentages and percentage quantity by a percentage. changes as a fraction or a decimal, and I can calculate simple interest using the same percentage each interpret these multiplicatively time on the original amount. I can calculate compound interest when using percentage Express one quantity as a percentage of increase repeatedly on successive amounts. another I can work out a percentage change. For example ‘percentage loss or percentage profit’ Compare two quantities using percentages I can represent percentage change as a decimal or fraction e.g. 112 Work with percentages greater that 100% 12% 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 ≡𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑦𝑖𝑛𝑔 𝑏𝑦 1.12 ≡𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑦𝑖𝑛𝑔 𝑏𝑦 100 I can work out reverse percentage problems. Solve problems involving percentage change including percentage increase/decrease problems, and simple interest including in financial mathematics Notes: see also N2 and N12 AQA 8300 Subject content with learning outcomes for Programme of Study Page 6 The Fernwood School Subject content from Specification (May 2014) TOPIC: 2.1 Algebra Notation and Rules for Basic foundation Indices Additional foundation Higher Only I can use symbols to represent numbers in expressions A1 I can tell the difference between expressions, identities, Use and interpret algebraic notation, formulas, equations and inequalities. including: I can recognise and use the symbols =, ≠, <, >, ≤, ≥,   ab in place of a x b I know what the abbreviations mean when interpreting or using  3y in place of y + y + y and 3 x y algebraic expressions.  a2 in place of a x a, a3 in place of a x a I know that when I am simplifying or writing expressions in a x a, a2b in place of a x a x b different form that I should use the identity, , symbol. 𝑎  in place of a ÷ b I can use very simple formulas given in words and symbols. 𝑏  Coefficients written as fractions rather I can use simple flow charts representing formulas than as decimals I can use the rules for indices when expressions are being  Brackets multiplied. I can use the rules for indices when expressions are being Notes: it is expected that answers will be divided. given in their simplest form without an I can use the rules for indices when expressions contain more explicit instruction to do so. than one letter. A3 Understand and use the concepts and vocabulary of expressions, equations, formulae, inequalities, terms and factors. to include identities Notes: this will be implicitly and explicitly assessed. AQA 8300 Subject content with learning outcomes for Programme of Study Page 7 The Fernwood School Subject content from Specification (May 2014) TOPIC: 2.2 Manipulating Expressions Basic foundation Additional foundation Higher Only I can simplify expressions that contain the same letter. A4 I can simplify expressions that contain more than one letter. Simplify and manipulate algebraic I can simplify expressions that contain letters given in index expressions by: form.  collecting like terms I can multiply out expressions like 3(x + 2)  multiplying a single term over a bracket I can factorise expressions like 6a + 8  taking out common factors I can factorise expressions like x2 – 3x  simplifying expressions involving sums, I can expand and simplify expressions like products and powers, including the x(x2 -5) and 3(x + 2) – 5(2x -1) laws of indices I can expand and simplify expressions like A4 (x + 4)(x – 2), (2x + y)(3x – 2y) and (x + 2)2 Simplify and manipulate algebraic I can expand and simplify expressions like expressions (including those involving (√𝑥+4)(√𝑥−3) surds) by: expanding products of two binomials Subject content from Specification (May 2014) TOPIC: 2.3 FORMULAE AND Basic foundation SUBSTITUTION Additional foundation Higher Only I know that a formula can contain more than one letter and that A2 these can represent variables. Substitute numerical values into formulae I know what the dependent and independent variables are in a and expressions, including scientific formula. formulae I can use a simple formula written in words such as Cost = 20 x distance Notes: unfamiliar formulae will be given in I can put numbers into a formula and know that this is what the question. substitution means. See the appendix for a full list of the I can use simple formula written using symbols such as prescribed formulae. See also A5. T = 10d Or C = a + b to find values by substitution remembering to apply the correct A5 order of operations. Understand and use standard I can use formulae such as P = 2L + 2W and find values by mathematical formulae substitution of positive numbers only. I can find values for formulae by substituting positive and Notes: including use of formulae from other negative numbers subjects in words and using symbols I can read a problem and work out the expression for it. For example ‘5 more than x’ will have the expression 5 + x I can substitute numbers into more complex formulae such as (𝐴+1)𝐷 𝐶 = 9 I can substitute numbers into formulae that contain powers and roots such as; 𝑣 =𝑢+𝑎𝑡 𝑠 =𝑢𝑡+1𝑎𝑡2 𝑣2 = 𝑢2+2𝑎𝑠 2 AQA 8300 Subject content with learning outcomes for Programme of Study Page 8 The Fernwood School Subject content from Specification (May 2014) TOPIC: 2.4 LINEAR EQUATIONS AND INEQUALTIES Basic foundation Additional foundation Higher Only I can complete a question when I see the word ‘solve’ or the A17 words ‘find the solution’. Solve linear equations in one unknown I can solve simple linear expressions that contain only one algebraically operation, such as 3x = 12 or x + 5 = 9. I can solve simple linear expressions that contain division, such Find appropriate solutions using a graph 𝑥 as =7. 2 I can solve equations that involve more than one operation such Including those with the unknown on both as 3x -1 = 9. sides of the equation I am able to find solutions that are positive or negative. Notes: including the use of brackets I am able to find solutions that are fractions or decimals. I can solve equations that contain brackets such as 2(5x +1) = 28. A21 I can solve equations where the unknown occurs on both sides Translate simple situations or procedures of the equal sign such as 3x - 4 = 5 + x into algebraic expressions or formulae I can solve equations that contain brackets and the unknown occurring on both sides of the equal sign such as Derive an equations (or two simultaneous 3x - 12 = 2(x - 5). equations), solve the equation(s) and I can solve harder equations that contain more than one interpret the solution operation such as 7−𝑥=3 3 Notes: including the solution of geometrical I can form an equation for a situation. problems and problems set in context. I can solve an equation that I have formed. A22 Solve linear inequalities in one variable I can solve equations that require fraction arithmetic such as 2𝑥 𝑥 − =5. 3 4 Represent the solution set on a number line. I can recognise and use the symbols for inequalities <, >, ,  Notes: students should know the I know that solving inequalities means that the solution is a set conventions of an open circle on a number of numbers line for a strict inequality and a closed circle I can represent the solution set of an inequality on a number line for an included boundary. including using open and closed circles. I can solve simple inequalities such as 3x < 9 I can solve inequalities such as 12  3n  20 I can solve inequalities such as 4x – 3 < 10 and 4x < 2x + 7 I can solve inequalities such as x + 3 > 5x – 3 I know how to represent the solution set of an inequality using set notation e.g. -3 ≤ x ≤ 2 is given by 𝑥 ∈ {−3,−2,−1,0,0,1,2} AQA 8300 Subject content with learning outcomes for Programme of Study Page 9 The Fernwood School Subject content from Specification (May 2014) TOPIC: 3.1 Collecting Data Basic foundation Additional foundation Higher Only S1 I can collect information and record it using a tally chart Infer properties of populations or I can collect information and record it into a frequency table distributions from a sample, whilst knowing I can tell whether a data set is a discrete set of information the limitations of sampling I can tell whether a data set is from a continuous set of numbers I know and understand the difference between quantitative and Notes: students should know and qualitative data understand the terms: primary data, I know and understand the difference between primary and secondary data, discrete data and secondary continuous data. I can design and use a two-way table I can use a variety of sampling methods I know and understand the limitations of sampling methods I can tell whether bias is affecting a data collection exercise NB. This is an exceptionally small part of the New GCSE, time allocated to teaching this should be minimal. Subject content from Draft Specification (May 2014) TOPIC: 3.2 Statistical Measures Basic foundation Additional foundation Higher Only I can find the mode and median for a small set of numbers. S4 I can work out the range for a set of numbers Interpret, analyse and compare the I can work out the mode and range from a graph distributions of data sets from univariate I can calculate the mean for a small set of numbers. empirical distributions through: I can complete a frequency table for grouped data  appropriate measures of central I can work out the ‘fx’ column for a frequency table and use this tendency (median, men, mode and to calculate the mean. modal class) and spread (range, I can make a comment about two sets of data by comparing an including consideration of outliers) average and the range. I can work out the effect of very large or very small values on Notes: students should know and each type of averages and the range of a data set. understand the terms: primary data, I can work out the modal class from a grouped frequency table. secondary data, discrete data and I can calculate a mean estimate for data given in a grouped continuous data. frequency table NB. The vast majority of students should not need to be S5 retaught this, the main focus should be frequency tables Apply statistics to describe a population and problem solving with averages and range. AQA 8300 Subject content with learning outcomes for Programme of Study Page 10 The Fernwood School