AQA GCSE Maths Schemes of Work Writing Brief D R a F T

Longman AQA GCSE Maths 1-Year LINEAR Scheme of Work – Middle Sets taking Foundation

OVERVIEW

Notes: 1. Assumes 3 hours of guided teaching per week. 2. Assumes a minimum of 3 hours of personal study per week. 3. Assumes the Autumn term is based on an early September start. 4. Assumes the June exams are at the beginning of June. 5. The scheme assumes teaching is on a topic basis as indicated by the Chapter/Chapter groupings. The assigned hours per topic should be flexibly implemented. 6. Blue type shows content that will only be examined at Higher Tier GCSE.

Chapter Guided Grades AQA Linear specification reference learning hours

M 9. Number skills 3 [F] E, D, C Working with numbers and the number system: N1.2, N1.4, N1.4h R

E 13. Decimals 3 [F] E, D, C, B Working with numbers and the number system: N1.1, N1.2 T Fractions, Decimals and Percentages: N2.3, N2.4 N

M 11. Basic rules of algebra 3 [F] E, D, C, B The Language of Algebra: N4.1

U Expressions and Equations: N5.1, N5.1h T

U 21. Angles 3 [F] E, D, C Properties of angles and shapes: G1.1, G1.2 A Measures and Construction: G3.1, G3.6 1. Data collection 3 [F] E, D, C The Data Handling Cycle: S1 Data Collection: S2.1, S2.2, S2.3, S2.4, S2.5 Data presentation and analysis: S3.1 22. Measurement 1 3 [F] E, C Working with numbers and the number system: N1.3 Measures and Construction: G3.1, G3.3, G3.4 14. Equations and inequalities 3 [F] E, D, C, B Expressions and Equations: N5.4, N5.4h, N5.7, N5.7h

2. Fractions, decimals and 3 [F] E, D, C Working with numbers and the number system: N1.14 percentages Fractions, Decimals and Percentages: N2.6, N2.7 7. Ratio and proportion 3 [F] E, D, C, B Ratio and Proportion: N3.1, N3.2, N3.3 23. Triangles and 3 [F] E, D, C Properties of angles and shapes: G1.1, G1.2, G1.8 constructions Measures and Construction: G3.9, G3.10 24. Equations, formulae and 3 [F] D, C, B The Language of Algebra: N4.2 proof Expressions and Equations: N5.1, N5.4, N5.6, N5.8 Geometrical reasoning and calculation: G2.3, G2.3h 26. Perimeter, area and 3 [F] E, D, C Mensuration: G4.1, G4.4 volume

3. Interpreting and 3 [F] E, D, C Data presentation and analysis: S3.2 representing data Data Interpretation: S4.2, S4.3 12. Fractions 3 [F] E, D, C, B Working with numbers and the number system: N1.2, N1.3, N1.5 Fractions, Decimals and Percentages: N2.1, N2.2, N2.7 15. Indices and formulae 3 [F] E, D, C, B Working with numbers and the number system: N1.9 The Language of Algebra: N4.2 Expressions and Equations: N5.6 4. Range and averages 3 [F] E, D, C Data presentation and analysis: S3.3 Data Interpretation: S4.1 17. Sequences and proof 3 [F] E, D, C Expressions and Equations: N5.9 Sequences, Functions and Graphs: N6.1, N6.2 28. Reflection, translation and 3 [F] E, D, C Properties of angles and shapes: G1.6, G1.7 rotation Vectors: G5.1 31. Enlargement and similarity 3 [F] E, D, C, B Properties of angles and shapes: G1.7, G1.7h, G1.8 Measures and Construction: G3.2 20. Number skills revisited REVISION Working with numbers and the number system: N1.3, N1.4, N1.14 THROUGH Fractions, decimals and Percentages: N2.1, N2.5, N2.7 PERSONAL Ratio and Proportion: N3.1 STUDY 16. Percentages 3 [F] E, D, C, B Fractions, Decimals and Percentages: N2.5, N2.7, N2.7h

M 8. Complex calculations 3 [F] C, B Working with numbers and the number system: N1.10h R

E Fractions, Decimals and Percentages: N2.7h T 25. Quadrilaterals and other 3 [F] E, D, C Expressions and Equations: N5.4 G

N polygons Sequences, Functions and Graphs: N6.3 I

R 27. 3-D objects Properties of angles and shapes: G1.2, G1.3, G1.4 P

S Geometrical reasoning and calculation: G2.4 5. Probability 3 [F] E, D, C, B Data presentation and analysis: S3.1 Probability: S5.1, S5.2, S5.3, S5.4, S5.5h, S5.6h, S5.7, S5.8, S5.9 18. Linear graphs 3 [F] E, D, C, B Expressions and Equations: N5.4h, N5.7h Sequences, Functions and Graphs: N6.3, N6.4, N6.5h, N6.6h, N6.11, N6.12 10. Factors, powers and 3 [F] E, D, C, B Working with numbers and the number system: N1.6, N1.7, N1.8, N1.9, standard form N1.9h, N1.10h 6. Cumulative frequency 0 [F] B Data presentation and analysis: S3.2h, S3.3h Data Interpretation: S4.4 29. Circles and cylinders 3 [F] D, C Properties of angles and shapes: G1.5 Geometrical reasoning and calculation: G2.4 Mensuration: G4.1, G4.3, G4.4 30. Measurement 2 3 [F] D, C, B Measures and Construction: G3.4, G3.7

19. Quadratic equations 0 [F] B Expressions and Equations: N5.2h, N5.5h 32. Non-linear graphs 3 [F] D, C, B Expressions and Equations: N5.2h, N5.5h Sequences, Functions and Graphs: N6.7h, N6.8h, N6.11h, N6.13

M 34. Pythagoras’ theorem 3 [F] C Geometrical reasoning and calculation: G2.1 R

E 33. Constructions and loci 3 [F] C Measures and Construction: G3.8, G3.10, G3.11 T 35. Trigonometry 0 [F] B Working with numbers and the number system: N1.14h R

E Geometrical reasoning and calculation: G2.2h M Measures and Construction: G3.6 M

U 36. Circle theorems 0 [F] B Properties of angles and shapes: G1.5h S REVISION: 9 GUIDED HOURS JUNE EXAMS

DETAIL

Chapter 9 Number skills GLH: 3 hours [F]

N1.2 Add, subtract, multiply and divide any number. N1.4 Approximate to a given power of 10, up to three decimal places and one significant figure. N1.4h Approximate to specified or appropriate degrees of accuracy, including a given number of decimal places and significant figures.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide Number skills: adding and subtracting (N1.2); multiplying and dividing (N1.2) N1.2, N1.4 Multiply whole E, D Section 9.1 Forgetting to add the numbers to find the final GPW Section numbers using answer when using the grid method. 9.1 9.1 written methods Forgetting the zero when multiplying by tens when Use repeated using the standard method. subtraction for Writing 3.6 to represent 3 remainder 6. division of whole Not giving an answer in the context of the problem. numbers Round up or down in context N1.4, N1.4h Check and estimate E, D, C Section 9.2 Finding an approximate value independent of the Section answers to problems context in which it is set. 9.2 Estimate answers to Working out the actual answer instead of an problems involving approximation. decimals Make estimates and approximations of calculations N1.2 Multiply and divide E Section 9.3 Applying the ‘general rules’ (the signs are different, Section negative numbers so the answer is negative; the signs are the same, 9.3

so the answer is positive) without constraint. Applying the rules for multiplying/dividing negative numbers to adding/subtracting negative numbers.

Chapter 13 Decimals GLH: 3 hours [F]

N1.1 Understand integers and place value to deal with arbitrarily large positive numbers. N1.2 Add, subtract, multiply and divide any number. N2.3 Use decimal notation and recognise that each terminating decimal is a fraction. N2.4 Recognise that recurring decimals are exact fractions, and that some exact fractions are recurring decimals.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide N1.1, N1.2 Add and subtract E Section 13.1 Not lining up the decimal points. GPW Section decimal numbers Not recording the ‘carry over’ and forgetting to add 13.1 13.1 it on. Not reducing a number during an exchange. N2.3 Convert decimals to D Section 13.2 Working with the incorrect power of 10. GPW Section fractions Not giving answers in the simplest form. 13.2 13.2 N1.2 Multiply and divide D, C Section 13.3 Working out the equivalent whole-number GPW Section decimal numbers multiplication but forgetting to return to the decimal 13.3 13.3 calculation at the end. Confusing multiplication with the rules for addition, writing a long multiplication with decimal points underneath each other. N2.3, N2.4 Convert fractions to D, C, B Section 13.4 Confusing 0.3 with . GPW Section decimals Not understanding that recurring decimals are a 13.4 13.4 Recognise recurring form of exact maths and therefore rounding decimals answers. Understand how recurring decimals relate to fractions

Chapter 11 Basic rules of algebra GLH: 3 hours [F]

N4.1 Distinguish the different roles played by letter symbols in algebra, using the correct notation. N5.1 Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors. N5.1h Multiply two linear expressions.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide Algebra skills: writing and simplifying expressions (N4.1, N5.1) N4.1, N5.1 Simplify algebraic E Section 11.1 Failing to comprehend that x = 1x. Section expressions by Combining unlike terms. 11.1 collecting like terms N5.1 Multiply together two E Section 11.2 Treating terms in m2 and in m as like terms (e.g. Section simple algebraic simplifying 3m2 + m wrongly to 4m2). 11.2 expressions N5.1 Multiply terms in a D Section 11.3 Forgetting to multiply the second term in the GPW Section bracket by a number bracket by the term outside (e.g. expanding 2(x + 11.3 11.3 outside the bracket 3) as 2x + 3), or ignoring minus signs (e.g. writing Multiply terms in a 3(m – 2) as 3m + 6). bracket by a term that includes a letter N5.1 Simplify expressions D, C Section 11.4 Forgetting to multiply the second term in the Section involving brackets bracket by the term outside. 11.4 Getting the wrong signs when multiplying negative values. N5.1 Recognise factors of D Section 11.5 Not realising that x is a factor of x and x2. GPW Section algebraic terms Not taking out the highest common factor. 11.5 11.5 Simplify algebraic expressions by taking out common

factors N5.1h Multiply together two C, B Section 11.6 Forgetting to multiply pairs of terms. GPW Section algebraic 11.6 11.6 expressions with brackets Square a linear expression

Chapter 21 Angles GLH: 3 hours [F]

G1.1 Recall and use properties of angles at a point, angles at a point on a straight line (including right angles), perpendicular lines, and opposite angles at a vertex. G1.2 Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals. G3.1 Use and interpret maps and scale drawings. G3.6 Understand and use bearings.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide Geometry skills: angles (G1.1) G1.1 Calculate angles E Section 21.1 Measuring rather than calculating angles. Section around a point 21.1 Recognise vertically opposite angles G1.2 Recognise D Section 21.2 Confusing alternate and corresponding angles. GPW Section corresponding and 21.2 21.2 alternate angles Calculate angles in diagrams with parallel lines G3.1, G3.6 Use three-figure E, D, C Section 21.3 Confusing which angles need to be found. GPW Section bearing notation Not realising that some of the angles asked for can 21.3 21.3 Measure the bearing simply be read off the diagram. from one place to another Plot a bearing Calculate bearings for return journeys Draw and interpret

scale diagrams to represent journeys

Chapter 1 Data collection GLH: 3 hours [F]]

S1 Understand and use the statistical problem solving process which involves  specifying the problem and planning  collecting data  processing and presenting the data  interpreting and discussing the results. S2.1 Types of data: qualitative, discrete, continuous. Use of grouped and ungrouped data. S2.2 Identify possible sources of bias. S2.3 Design an experiment or survey. S2.4 Design data collection sheets distinguishing between different types of data. S2.5 Extract data from printed tables and lists. S3.1 Design and use two-way tables for grouped and ungrouped data.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide S1 Learn about the data D Section 1.1 Formulating a hypothesis that cannot be tested. Section handling cycle Thinking that a hypothesis is not valuable if it is 1.1 Know how to write a eventually proved false. hypothesis S2.3, S2.4 Know where to look D Section 1.2 Not realising that data collected by a third party Section for information (even if the results of a survey or experiment) is 1.2 classed as secondary data. S2.1 Be able to identify D Section 1.3 Not appreciating that some data can be treated as Section different types of either discrete or continuous depending on the 1.3 data context (e.g. age – this is really continuous, but is often treated as discrete, such as when buying child or adult tickets). S2.4 Work out methods E Section 1.4 Using shortcuts in the tallying process – counting Section for gathering data up the items in each class, rather than tallying 1.4

efficiently items one by one.

S2.4, S2.5 Work out methods D Section 1.5 Using overlapping class intervals. Section for gathering data Recording data which is on the boundary of a class 1.5 that can take a wide interval in the wrong class. range of values S2.5, S3.1 Work out methods D Section 1.6 Not checking that the totals in two-way tables add Section for recording related up. 1.6 data S2.3, S2.4 Learn how to write C Section 1.7 Using overlapping classes, or gaps between Section good questions to classes, for response options. 1.7 find out information S2.2, S2.3, Know the techniques C Section 1.8 Mistaking biased samples for random samples. Section S2.4 to use to get a 1.8 reliable sample

Chapter 22 Measurement 1 GLH: 3 hours [F]

N1.3 Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations. G3.1 Use and interpret maps and scale drawings. G3.3 Interpret scales on a range of measuring instruments and recognise the inaccuracy of measurements. G3.4 Convert measurements from one unit to another.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide N1.3 Solve problems E Section 22.1 Confusing the decimal parts of an hour with hours GPW Section involving times, and minutes (e.g. writing 1.25 hours as 1 hour 25 22.1 22.1 dates and timetables minutes) and vice versa. G3.4 Know and use E Section 22.2 Not considering the relative size of units when GPW Section approximate metric deciding whether to multiply or divide. 22.2 22.2 equivalents of pounds, feet, miles, pints and gallons G3.1 Use and interpret E Section 22.3 Missing out steps when converting between (for Section maps and scale example) km and cm. 22.3 drawings Not making allowances when measurements are given in a variety of units. G3.3 Recognise that C Section 22.4 Difficulty comprehending the definition of the upper Section measurements given bound, since, for example, 146.5 rounds to 147. 22.4 to the nearest whole unit may be inaccurate by up to one half unit in either direction

Chapter 14 Equations and inequalities GLH: 3 hours [F]

N5.4 Set up and solve simple linear equations. N5.4h Including simultaneous equations in two unknowns. N5.7 Solve linear inequalities in one variable and represent the solution set on a number line. N5.7h Solve linear inequalities in two variables, and represent the solution set on a suitable diagram.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide N5.4 Solve two-step E, D Section 14.1 Not appreciating that an equation can be written in GPW Section equations like 2x – 1 different but equivalent formats (e.g. 2a + 7 = 9 → 14.1a- 14.1 = 11 7 + 2a = 9 → 9 = 2a + 7). 14.4a GPW 14.1b- 14.4b N5.4 Write and solve E, D Section 14.2 Not following a question carefully when writing an GPW Section equations equation to represent a problem. 14.1a- 14.2 14.4a GPW 14.1b- 14.4b N5.4 Solve equations D, C Section 14.3 Forgetting to multiply the second term in the GPW Section involving brackets bracket by the term outside. 14.1a- 14.3 Getting the wrong signs when multiplying negative 14.4a numbers. GPW Incorrectly simplifying after expanding the bracket. 14.1b- 14.4b N5.4 Solve equations with D, C Section 14.4 Introducing errors when there are a negative GPW Section an unknown on both number of unknowns on either side of the equation. 14.1a- 14.4 sides 14.4a

GPW 14.1b- 14.4b N5.4 Solve equations C, B Section 14.5 Incorrectly cancelling after multiplying by the LCM. Section involving fractions x + 2 14.5 Solving out of order (e.g. = 8 : trying to do −2 4 first). N5.7, N5.7h Represent E, D, Section 14.6 Not reversing the sign when multiplying or dividing Section inequalities on a C, B by a negative. 14.6 number line Confusing the convention of an open circle for a Write down whole- strict inequality and a closed circle for an included number values for boundary. unknowns in an inequality Solve inequalities N5.4h Solve a pair of B Section 14.7 Adding equations when they should be subtracted, Section simultaneous and vice versa. 14.7 equations

Chapter 2 Fractions, decimals and percentages GLH: 3 hours [F]

N1.14 Use calculators effectively and efficiently, including statistical functions. N2.6 Interpret fractions, decimals and percentages as operators. N2.7 Calculate with fractions, decimals and percentages.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide N2.7 Find a fraction of an E, D Section 2.1 Incorrectly inputting numbers on the calculator. GPW Section amount with a Being unsure of what to work out when a fraction 2.1 2.1 calculator calculation is set in context. Find a fraction of an amount with a calculator in more complex situations N2.7 Write one quantity as D Section 2.2 Not making the denominator the total in questions GPW Section a fraction of another involving a number of quantities. 2.2 2.2 Working with quantities in different units. Incorrectly cancelling down. N1.14 Use the fraction key E, D Section 2.3 Not recognising or know how to use the fraction Section on a calculator key on a calculator. 2.3 Use the fraction key Misinterpreting a mixed number on a calculator on a calculator with display. mixed numbers N2.7 Find a percentage of E, D Section 2.4 Thinking that percentages over 100% cannot exist. Section an amount with a Treating a percentage such as 0.05% as though it 2.4 calculator were 5%. Find percentages of Adding the percentage to the cost when finding a amounts in more percentage increase (e.g. £315 + 15% VAT = complex situations £330).

N2.7 Write one quantity as D, C Section 2.5 Not using the original amount as the denominator, Section a percentage of when finding a percentage difference. 2.5 another Working with quantities in different units. Write one quantity as a percentage of another in more complex situations N2.6, N2.7 Calculate a D Section 2.6 Giving the actual increase/decrease as the answer Section percentage increase when the amount after the increase/decrease is 2.6 or decrease what is required. Using the multiplier as 1.5 rather than 1.05 for an increase of 5%. N2.7 Understand and use D, C Section 2.7 Using a previously found price instead of the base GPW Section a retail prices index year price. 2.7 2.7 Understand and use a retail prices index in more complex situations

Chapter 7 Ratio and proportion GLH: 3 hours [F]

N3.1 Use ratio notation, including reduction to its simplest form and its various links to fraction notation. N3.2 Divide a quantity in a given ratio. N3.3 Solve problems involving ratio and proportion, including the unitary method of solution.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide N3.1, N3.2 Simplify a ratio to its E, D Section 7.1 Swapping over the numbers in the ratio (e.g. 2 : 5 GPW Section lowest terms becomes 5 : 2). 7.1a, b 7.1 Use a ratio in Simplifying ratios without ensuring the quantities practical situations are in the same units. N3.1, N3.3 Write a ratio as a D, C Section 7.2 Turning a ratio into a fraction (e.g. the ratio 4 : 5 GPW Section fraction becomes ). 7.2 7.2 Use a ratio to find Failing to find the value of the unit fraction in more one quantity when complex problems. the other is known N3.3 Write a ratio in the C Section 7.3 Ignoring different units in a ratio (e.g. simplifying 2 GPW Section form 1 : n or n : 1 days : 15 hours to 1 : 7½) . 7.3 7.3 N3.3 Share a quantity in a D, C Section 7.4 Forgetting to work out the total number of parts GPW Section given ratio first. 7.4 7.4 Using a ratio as a fraction. N3.3 Solve word problems C Section 7.5 Not multiplying both sides of the ratio by the same Section involving ratio number. 7.5 Giving an answer without considering the context. N3.3 Understand direct D Section 7.6 Not always seeing the relationships between Section proportion numbers (e.g. if the cost of 4 items is given, and 7.6 Solve proportion the price of 8 is asked for). problems, including using the unitary

method N3.3 Work out which D Section 7.7 Not making the units the same for each item. GPW Section product is the better Comparing unlike unit rates (e.g. price per gram for 7.7 7.7 buy one item but amount for 1p for the other). N3.3 Solve word problems D, C, B Section 7.8 Dividing by the wrong quantity in conversion GPW Section involving direct and problems. 7.8 7.8 inverse proportion Understand inverse proportion

Chapter 23 Triangles and constructions GLH: 3 hours [F]

G1.1 Recall and use properties of angles at a point, angles at a point on a straight line (including right angles), perpendicular lines, and opposite angles at a vertex. G1.2 Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals. G1.8 Understand congruence and similarity. G3.9 Draw triangles and other 2D shapes using a ruler and protractor. G3.10 Use straight edge and a pair of compasses to do constructions.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide G1.1, G1.2 Solve angle E, D Section 23.1 Not realising when a triangle is isosceles and GPW Section problems in triangles thinking that the problem cannot be solved. 23.1 23.1 Solve angle Trying to do too many steps in one go when problems in triangles answering algebra-based questions. involving algebra G3.9, G3.10 Draw triangles E, D Section 23.2 Inaccurately using a protractor or compasses. Section accurately when Not completing the triangle by drawing the third 23.2 given the length of all side. three sides Rubbing out construction lines. Draw triangles accurately when at least one angle is given G1.8 Recognise and C Section 23.3 Thinking that two triangles are congruent when Section explain how triangles they are not (due to the relative positions of side 23.3 are congruent lengths or angles being in different positions). Incorrectly assuming that by showing that the three sets of angles are the same in both triangles congruency is proved.

Chapter 24 Equations, formulae and proof GLH: 3 hours [F]

N4.2 Distinguish in meaning between the words ‘equation’, ‘formula’, and ‘expression’. N5.1 Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors. N5.4 Set up and solve simple linear equations. N5.6 Derive a formula, substitute numbers into a formula. N5.8 Use systematic trail and improvement to find approximate solutions of equations where there is no simple analytical method of solving them. G2.3 Justify simple geometrical properties. G2.3h Simple geometrical proofs.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide Algebra skills: expressions (N4.2, N5.1); brackets (N5.1); solving equations (N5.4); formulae (N5.6) N5.4, N5.6 Write your own D, C, B Section 24.1 Failing to consider the different terms of an GPW Section formulae and expression when changing the subject of a formula 24.1 24.1 equations (e.g. W = 1 x + 3 2W = x + 3). Substitute into a 2 formula to solve Not using brackets or a clear division (e.g. rewriting problems c = 2a + 5 as a = c − 5 ÷ 2). Set up and solve Not using the inverse operation (e.g. x + y = z equations becomes x = z + y). Change the subject of a formula G2.3, G2.3h Prove simple results C Section 24.2 Not laying out answers in an organised way. Section from geometry Not providing reasons for each stage of the 24.2 working. N5.8 Use trial and C Section 24.3 Not checking the mid-point to determine which of GPW Section improvement to find two values is correct (e.g. choosing between x = 24.3 24.3 solutions to 3.3 and x = 3.4 based on the value of the function equations and the desired output).

Using the value of the equation as the answer rather than the value of the variable.

Chapter 26 Perimeter, area and volume GLH: 3 hours [F]

G4.1 Calculate perimeters and areas of shapes made from triangles and rectangles. G4.4 Calculate volumes of right prisms and of shapes made from cubes and cuboids.

Chapter 3 Interpreting and representing data GLH: 3 hours [F]

S3.2 Produce charts and diagrams for various data types. Scatter graphs, stem-and-leaf, tally charts, pictograms, bar charts, dual bar charts, pie charts, line graphs, frequency polygons, histograms with equal class intervals. S4.2 Look at data to find patterns and exceptions. S4.3 Recognise correlation and draw and/or use lines of best fit by eye, understanding what they represent.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide S3.2 Draw a pie chart E Section 3.1 Not drawing the angles in the pie chart accurately GPW Section or using the appropriate scale on the protractor. 3.1 3.1 Measuring each angle from the same starting point. S3.2 Draw stem-and-leaf D Section 3.2 Forgetting to put a key and order the leaves. Section diagrams Forgetting to recombine the stem and leaf and just 3.2 giving the leaf as the value. S3.2, S4.2 Draw a scatter D Section 3.3 Assuming that all the plotted points must be joined Section diagram on a given with a line. 3.3 grid Drawing the diagram without spending time Interpret points on a working out the best scale. scatter diagram S4.3 Draw a line of best fit D, C Section 3.4 Trying to make the line of best fit go through the Section on a scatter diagram origin, rather than drawing it appropriately. 3.4 Describe types of Not appreciating correlation in terms of ‘positive’ correlation and ‘negative’. Use the line of best fit S3.2 Draw frequency D Section 3.5 Using grouped labels on the data axes (e.g. 15–20, Section diagrams for rather than the ends of the bar being clearly 3.5 grouped data marked with a 15 at one end and a 20 at the other end).

S3.2 Draw frequency C Section 3.6 Using a grouped label on the horizontal axis rather GPW Section polygons for grouped than a continuous scale. 3.6 3.6 data Plotting the upper bound instead of the mid-point.

Chapter 12 Fractions GLH: 3 hours [F]

N1.2 Add, subtract, multiply and divide any number. N1.3 Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations. N1.5 Order rational numbers. N2.1 Understand equivalent fractions, simplifying a fraction by cancelling all common factors. N2.2 Add and subtract fractions. N2.7 Calculate with fractions, decimals and percentages.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide N1.5, N2.1 Compare fractions E, D Section 12.1 Multiplying the denominator but not the numerator GPW Section with different when finding equivalent fractions. 12.1 12.1 denominators N2.2 Add and subtract E, D Section 12.2 Adding/subtracting the denominators as well as the Section fractions when one numerators. 12.2 denominator is a multiple of the other Not converting to equivalent fractions to make the Add and subtract denominators the same. fractions when both denominators have to be changed N2.2 Add and subtract C Section 12.3 Incorrectly converting a mixed number to an GPW Section mixed numbers improper fraction. 12.3 12.3 Not converting the final answer back to a mixed number. N1.2 Multiply a fraction by E Section 12.4 Multiplying diagonally as though ‘cross-multiplying’ Section a fraction is being done (e.g. × = ). 12.4 N2.7 Multiply a whole D, C, B Section 12.5 Multiplying both the numerator and the Section number by a mixed denominator by the whole number (e.g. 3 × = ). 12.5

number Multiply a fraction by a mixed number Multiply a mixed number by a mixed number N1.3 Find the reciprocal of C Section 12.6 Leaving denominators as decimal numbers. GPW Section a whole number, a Not simplifying answers when asked to do so. 12.6 12.6 decimal or a fraction N1.2 Divide a whole D, C, B Section 12.7 Finding the reciprocal of the wrong fraction, or Section number or a fraction finding the reciprocal of both fractions. 12.7 by a fraction Divide mixed numbers or fractions by whole numbers Divide mixed numbers by mixed numbers

Chapter 15 Indices and formulae GLH: 3 hours [F]

N1.9 Index laws for multiplication and division of integer powers. N4.2 Distinguish in meaning between the words ‘equation’, ‘formula’, and ‘expression’. N5.6 Derive a formula, substitute numbers into a formula and change the subject of a formula.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide N1.9 Use index notation in E, D, C Section 15.1 Not realising that x means x1, or that a number Section algebra divided by 1 equals the number (e.g. 6 ÷ 1 = 6). 15.1 Use index notation when multiplying or dividing algebraic terms N1.9 Use index laws to C, B Section 15.2 Confusing unit and zero powers (e.g. stating that x GPW Section multiply and divide means x 0, or that x 0 = 0). 15.2 15.2 powers in algebra Raise a number or variable to the power of 1 or 0 Use index laws for raising a power to another power N4.2 Use algebra to write E, D Section 15.3 Not seeing the ‘general’ case. Section formulae in different 15.3 situations N4.2, N5.6 Substitute numbers E, D, C Section 15.4 Incorrectly substituting values into expressions Section to work out the value (e.g. substituting a = 6 into the expression 4a, 15.4 of simple algebraic writing 46 and assuming it is forty-six). expressions Ignoring BIDMAS.

Substitute numbers into expressions involving brackets and powers N4.2, N5.6 Substitute numbers E, D Section 15.5 Not realising that means n ÷ 10, or that × 6 means GPW Section into a variety of of 6 = 3. 15.5 15.5 formulae N5.6 Rearrange a formula C, B Section 15.6 Not using brackets or a clear division (e.g. rewriting GPW Section to make a different c = 2a + 5 as a = c − 5 ÷ 2). 15.6 15.6 variable the subject Not using the inverse operation (e.g. x + y = z of the formula becomes x = z + y).

Chapter 4 Range and averages GLH: 3 hours [F]

S3.3 Calculate median, mean, range, mode and modal class. S4.1 Interpret a wide range of graphs and diagrams and draw conclusions.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide S3.3, S4.1 Find the mean, E, D Section 4.1 Omitting units when writing averages or range. GPW Section median and range Forgetting to include the stem when reading the 4.1 4.1 from a set of data, median from a stem and leaf diagram. including data given in a stem and leaf diagram S3.3, S4.1 Calculate the mode, E Section 4.2 Confusing the frequencies and the data values. Section median and range 4.2 from an ungrouped frequency table S3.3, S4.1 Calculate the mean D, C Section 4.3 Dividing by the number of rows in the frequency Section from an ungrouped table (i.e. the number of different data values), not 4.3 frequency table by the sum of the frequencies. S3.3, S4.1 Find the modal class D, C Section 4.4 Not appreciating that the statistics calculated from GPW Section from a grouped grouped frequency tables are estimates. 4.4/4.5 4.4 frequency table Not understanding that the estimate for the range is Estimate the range an upper limit. from a grouped frequency table Work out the class interval which contains the median from data given in a

grouped frequency table S3.3, S4.1 Estimate the mean of C Section 4.5 Incorrectly calculating the mid-points of class GPW Section data given in a intervals for grouped discrete data (e.g. the mid- 4.4/4.5 4.5 grouped frequency point of the class interval 10–19 is 14.5, not 15). table Interpreting ‘find an estimate for the mean’ as ‘guess the mean’.

Chapter 17 Sequences and proof GLH: 3 hours [F]

N5.9 Use algebra to support and construct arguments. N6.1 Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence. N6.2 Use linear expressions to describe the nth term of an arithmetic sequence.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide N6.1 Find the next term in E, D Section 17.1 Expecting all sequences to have common Section a sequence differences. 17.1 Describe the rule for Looking at the first two numbers and assuming that continuing a the rest follow this pattern. sequence N6.2 Find any term of a E, C Section 17.2 Mistaking x2 for 2x. GPW Section sequence given a 17.2a, b 17.2 formula for the nth term Find the nth term of a linear sequence N6.2 Find the nth term of C Section 17.3 Not comprehending that when finding the 50th term Section a linear sequence it is not necessary to find all the terms up to that 17.3 Use the nth term to term. find terms in a sequence N6.2 Find the next few E, C Section 17.4 Not writing down the sequence and trying to do it Section terms in a sequence all mentally. 17.4 of patterns Not making the connection between the structure Find the nth term for of the physical pattern and the form the nth term a sequence of takes. diagrams

N6.1 Find the first few D Section 17.5 Mistaking x2 for 2x. Section terms of a quadratic 17.5 sequence by using the nth term Find the next few terms of a quadratic sequence by looking at differences N6.1 Find the nth term of C Section 17.6 Thinking that (3x)2 = 3x2. Section a simple quadratic Not checking whether the derived quadratic rule 17.6 sequence works. N5.9 Show step-by-step E, D, C Section 17.7 Not appreciating that a proof shows something GPW Section deduction when works for all values. 17.7 17.7 proving results N5.9 Show something is C Section 17.8 Assuming that ‘number’ means positive whole GPW Section false by using a number. 17.8 17.8 counter-example Not identifying an appropriate counter-example.

Chapter 28 Reflection, translation and rotation GLH: 3 hours [F]

G1.6 Recognise reflection and rotation symmetry of 2D shapes. G1.7 Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that are preserved under particular transformations. G5.1 Understand and use vector notation for translations.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide G1.7 Draw reflections on a E, D, C Section 28.1 Drawing the image a different distance from the GPW Section coordinate grid mirror line than the object. 28.1 28.1 Describe reflections Incorrectly identifying mirror lines parallel to the x- on a coordinate grid or y-axis. G1.7, G5.1 Translate a shape on D, C Section 28.2 Forgetting what the two values in the column vector Section a grid mean. 28.2 Use column vectors Using coordinate notation instead of vector to describe notation. translations Confusing the terms ‘transformation’ and ‘translation’. G1.6, G1.7 Draw the position of D, C Section 28.3 Working out the angle of rotation incorrectly. GPW Section a shape after rotation Turning in the wrong direction. 28.3 28.3 about a centre Ignoring the centre of rotation when it is outside the Describe a rotation shape. fully giving the size and direction of turn and the centre of rotation G1.7 Transform shapes C Section 28.4 Not appreciating that two transformations, one Section using more than one followed by another, may be equivalent to a single 28.4 transformation transformation.

Describe combined Not understanding that for ‘general’ questions transformations of where no shape is given, transformations can be shapes on a grid carried out on different shapes to investigate what happens.

Chapter 31 Enlargement and similarity GLH: 3 hours [F]

G1.7 Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that are preserved under particular transformations. G1.7h Use positive fractional and negative scale factors. G1.8 Understand congruence and similarity. G3.2 Understand the effect of enlargement for perimeter, area and volume of shapes and solids.

Chapter 20 Number skills revisited PERSONAL STUDY

N1.3 Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations. N1.4 Approximate to a given power of 10, up to three decimal places and one significant figure. N1.14 Use calculators effectively and efficiently. N2.1 Understand equivalent fractions, simplifying a fraction by cancelling all common factors. N2.5 Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions. N2.7 Calculate with fractions, decimals and percentages. N3.1 Use ratio notation, including reduction to its simplest form and its various links to fraction notation.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide N1.3, N1.4, Understand Chapter 20 Forgetting to multiply/divide both the numerator and Chapter N1.14, N2.1, equivalent fractions denominator when finding equivalent fractions and 20 N2.5, N2.7, Simplify a fraction by N3.1 cancelling all simplifying fractions. common factors Applying an incorrect understanding of ‘reciprocal’. Recognise that each terminating decimal Writing the ratio in the incorrect order. is a fraction Forgetting to use BIDMAS when using calculators Convert simple to perform calculations. fractions to percentages and Not giving an answer in the context of the problem. vice versa Treating the digits each side of the decimal point as Use percentages to separate whole numbers , so that 0.95 rounded to compare proportions Understand 1 d.p. = 0.1. ‘reciprocal’ as Dropping zeros when rounding to a number of multiplicative inverse significant figures (e.g. 5840 = 6 to 1 s.f.). Use ratio notation

Use brackets and the hierarchy of operations Add, subtract, multiply and divide integers Use calculators effectively and efficiently; use function keys for squares Use inverse operations Round to the nearest integer, to one significant figure and to one, two or three decimal places Give solutions in the context of the problem to an appropriate degree of accuracy

Chapter 16 Percentages GLH: 3 hours [F]

N2.5 Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions. N2.7 Calculate with fractions, decimals and percentages. N2.7h Including reverse percentage calculations.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide Number skills: fractions, decimals and percentages (N2.7); using percentages in calculations (N2.7) N2.7 Calculate a D Section 16.1 Giving the actual increase/decrease as the answer GPW Section percentage increase when the amount after the increase/decrease is 16.1 16.1 or decrease what is required. Using the multiplier as 1.5 rather than 1.05 for an increase of 5%. Writing ‘=’ between quantities that are not equal, because the ‘=’ sign is used as a shorthand for ‘then I do this’. N2.5, N2.7 Perform calculations E, D Section 16.2 Not seeing that 17.5% = 10% + 5% + 2.5%. GPW Section involving VAT Forgetting to add on the initial deposit in credit 16.2a, b 16.2 Perform calculations calculations. involving credit Perform simple interest calculations N2.7 Calculate a C Section 16.3 Confusing cost price and selling price. GPW Section percentage profit or 16.3 16.3 loss N2.7 Perform calculations C Section 16.4 Not understanding when the multiplier should be GPW Section involving repeated greater than or less than 1. 16.4 16.4 percentage changes Using the multiplier as 1.5 rather than 1.05 for an increase of 5%.

N2.7h Perform calculations B Section 16.5 Not recognising that the problem is not a GPW Section involving finding the straightforward percentage increase/decrease 16.5 16.5 original quantity question. Not using the correct multiplier.

Chapter 8 Complex calculations GLH: 3 hours [F]

N1.10h Interpret, order and calculate numbers written in standard index form. N2.7h Including reverse percentage calculations.

Chapter 25 Quadrilaterals and other polygons GLH: 3 hours [F]

N5.4 Set up and solve simple linear equations. N6.3 Use the conventions for coordinates in the plane and plot points in all four quadrants, including geometric information. G1.2 Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals. G1.3 Calculate and use the sums of the interior and exterior angles of polygons. G1.4 Recall the properties and definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and rhombus.

Chapter 27 3-D objects

G2.4 Use 2D representations of 3D shapes.

Solve more complex angle problems involving exterior and interior angles of a polygon N6.3 Plot all points of a E Section 25.4 Plotting the numbers on the x- and y-axes the Section quadrilateral given wrong way round. 25.4 geometric Not recognising, or be able to name, some of the information less common quadrilaterals (e.g. the kite and Find the mid-point of trapezium). a line plotted on the Averaging only the x- or y-coordinate and not both coordinate axes when finding the mid-point. G2.4 Make a drawing of a E, D Section 27.1 Missing out hidden cubes when converting from a Section 3-D object on 3-D view to a plan or elevation. 27.1 isometric paper Using isometric paper in landscape not in portrait. Draw plans and elevations of 3-D objects Identify planes of symmetry of 3-D objects

Chapter 5 Probability GLH: 3 hours [F]

S3.1 Design and use two-way tables for grouped and ungrouped data. S5.1 Understand and use the vocabulary of probability and the probability scale. S5.2 Understand and use estimates or measures of probability from theoretical models (including equally likely outcomes), or from relative frequency. S5.3 List all outcomes for single events, and for two successive events, in a systematic way and derive related probabilities. S5.4 Identify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1. S5.5h Know when to add or multiply two probabilities: if A and B are mutually exclusive, then the probability of A or B occurring is P(A) + P(B), whereas if A and B are independent events, the probability of A and B occurring is P(A) × P(B). S5.6h Use tree diagrams to represent outcomes of compound events, recognising when events are independent. S5.7 Compare experimental data and theoretical probabilities. S5.8 Understand that if an experiment is repeated, this may – and usually will – result in different outcomes. S5.9 Understand that increasing sample size generally leads to better estimates of probability and population characteristics.

number of successful Not cancelling a fraction to its simplest form. 5.4 5.4 events given the probability of any outcome and the number of trials or experiments S5.2, S5.7, Estimate C Section 5.5 Trying to plot decimals worked out to three decimal Section S5.8, S5.9 probabilities from places or more. 5.5 experimental data Comparing theoretical probability with relative frequency without taking into account the number of trials carried out. S5.5h Calculate the C Section 5.6 Not recognising when a question involves GPW Section probability of two independent events and so adding rather than 5.6 5.6 independent events multiplying the fractions. happening at the same time S5.6h Use and understand B Section 5.7 Adding probabilities along the branch rather than Section tree diagrams in multiplying. 5.7 simple contexts

Chapter 18 Linear graphs GLH: 3 hours [F]

N5.4h Including simultaneous equations in two unknowns. N5.7h Solve linear inequalities in two variables, and represent the solution set on a suitable diagram. N6.3 Use the conventions for coordinates in the plane and plot points in all four quadrants, including using geometric information. N6.4 Recognise and plot equations that correspond to straight-line graphs in the coordinate plane, including finding their gradients. N6.5h Understand that the form y = mx + c represents a straight line and that m is the gradient of the line and c is the value of the y-intercept. N6.6h Understand the gradients of parallel lines. N6.11 Construct linear functions from real-life problems and plot their corresponding graphs. N6.12 Discuss, plot and interpret graphs (which may be non-linear) modelling real situations.

in the equation y = mx + c Find the equation of a line N6.11 Plot and use E Section 18.4 Inaccurately reading from one value on a Section conversion graphs conversion graph to find another value. 18.4 N6.11, N6.12 Draw, read and E, D, C Section 18.5 Drawing and labelling axes before working out the Section interpret distance– axes range appropriate to the problem. 18.5 time graphs Sketch and interpret real-life graphs N5.4h Use a graphical B Section 18.6 Forgetting to ensure that the individual lines are GPW Section method to solve drawn accurately. 18.6 18.6 simultaneous Not appreciating that the graphical solutions to equations simultaneous equations are only approximate. N5.7h Solve inequalities B Section 18.7 Mixing up whether the lines should be dotted or Section graphically solid. 18.7 Shading the incorrect area.

Chapter 10 Factors, powers and standard form GLH: 3 hours [F]

N1.6 The concepts and vocabulary of factor (divisor), multiple, common factor, highest common factor, least common multiple, prime number and prime factor decomposition. N1.7 The terms square, positive and negative square root, cube and cube root. N1.8 Index notation for squares, cubes and powers of 10. N1.9 Index laws for multiplication and division of integer powers. N1.9h Fractional and negative powers. N1.10h Interpret, order and calculate numbers written in standard index form.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide N1.6 Solve problems E, C Section 10.1 Confusing factors and multiples. GPW Section involving multiples Multiplying numbers with a common factor when 10.1/10.2 10.1 Find lowest common attempting to find the LCM. multiples N1.6 Solve problems E, C Section 10.2 Confusing factors and multiples. GPW Section involving factors Missing out 1 as a factor. 10.1/10.2 10.2 Recognise two-digit Forgetting whether it is the highest or lowest prime numbers common factor that needs to be found. Find highest Thinking that 1 is a prime number. common factors N1.7, N1.8 Calculate squares E, D, C Section 10.3 Multiplying by 2 instead of squaring. Section and cubes Writing = –6 or = ±6 when finding the negative 10.3 Calculate square square root. roots and cube roots Understand the difference between positive and negative square roots

Evaluate expressions involving squares, cubes and roots N1.8, N1.9h Understand and use E, B Section 10.4 Not being able to describe numbers written with GPW Section index notation in powers. 10.4/10.6 10.4 calculations Working out 45 as 4 × 5. Understand and use negative powers and numbers to the power of 1 or 0 N1.6 Write a number as a C Section 10.5 Not identifying the prime factors that appear in the GPW Section product of prime decompositions of both numbers when finding the 10.5 10.5 factors using index HCF. notation Use prime factors to find HCFs and LCMs N1.9, N1.9h, Use laws of indices C, B Section 10.6 Not converting the answers to calculations back GPW Section N1.10h to multiply and divide into standard form (e.g. 32 × 10–4 3.2 × 10–3). 10.4/10.6 10.6 numbers written in index notation Carry out calculations with numbers given in standard form

Chapter 6 Cumulative frequency GLH: 0 hours [F]

S3.2h Histograms with equal or unequal class intervals, box plots, cumulative frequency diagrams, relative frequency diagrams. S3.3h Quartiles and inter-quartile range. S4.4 Compare distributions and make inferences.

Chapter 29 Circles and cylinders GLH: 3 hours [F]

G1.5 Distinguish between centre, radius, chord, diameter, circumference, tangent, arc, sector and segment. G2.4 Use 2D representations of 3D shapes. G4.1 Calculate perimeters and areas of shapes made from triangles and rectangles. G4.3 Calculate circumferences and areas of circles. G4.4 Calculate volumes of right prisms and of shapes made from cubes and cuboids.

Chapter 30 Measurement 2 GLH: 3 hours [F]

G3.4 Convert measurements from one unit to another. G3.7 Understand and use compound measures.

Chapter 19 Quadratic equations GLH: 0 hours [F]

N5.2h Factorise quadratic expressions, including the difference of two squares. N5.5h Solve quadratic equations.

Chapter 32 Non-linear graphs GLH: 3 hours [F]

N5.2h Factorise quadratic expressions, including the difference of two squares. N5.5h Solve quadratic equations. N6.7h Find the intersection points of the graphs of a linear and quadratic function, knowing that these are the approximate solutions of the corresponding simultaneous equations representing the linear and quadratic functions. N6.8h Draw, sketch, recognise graphs of simple cubic functions, the reciprocal function y = 1/x with x ≠ 0, the function y = kx for integer values of x and simple positive values of k, the circular functions y = sin x and y = cos x. N6.11h Construct quadratic and other functions from real life problems and plot their corresponding graphs. N6.13 Generate points and plot graphs of simple quadratic functions, and use these to find approximate solutions.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide Algebra skills: quadratic expressions (N5.2h, N5.5h) N6.11h, N6.13 Draw quadratic D, C Section 32.1 Drawing the bottom of the graph flat when a graph GPW Section graphs has its vertex between two plotted points. 32.1 32.1 Identify the line of symmetry of a quadratic graph Draw and interpret quadratic graphs in real-life contexts N6.7h Use a graph to solve C Section 32.2 Forgetting to write down all the solutions. Section quadratic equations 32.2 N6.8h Draw cubic graphs B Section 32.3 Incorrectly finding the cube of a negative number. Section Use a graph to solve Forgetting to write down all the solutions. 32.3 cubic equations

Chapter 34 Pythagoras’ theorem GLH: 3 hours [F]

G2.1 Use Pythagoras’ theorem.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide G2.1 Understand C Section 34.1 Forgetting that x2 means x × x, not x × 2. Section Pythagoras’ theorem 34.1 G2.1 Calculate the C Section 34.2 Forgetting to take the square root to find the final Section hypotenuse of a answer. 34.2 right-angled triangle Not correctly identifying the hypotenuse. Solve problems Forgetting that Pythagoras’ theorem only applies to using Pythagoras’ right-angled triangles. theorem G2.1 Calculate the length C Section 34.3 Not correctly identifying the hypotenuse. Section of a shorter side in a Forgetting to take the square root to find the final 34.3 right-angled triangle answer. Solve problems Forgetting that Pythagoras’ theorem only applies to using Pythagoras’ right-angled triangles. theorem Not identifying the appropriate information when problems are set in context. Not being able to identify the position of the right angle. G2.1 Calculate the length C Section 34.4 Subtracting instead of adding the two pairs of Section of a line segment AB coordinates. 34.4

Chapter 33 Constructions and loci GLH: 3 hours [F]

G3.8 Measure and draw lines and angles. G3.10 Use straight edge and a pair of compasses to do constructions. G3.11 Construct loci.

Chapter 35 Trigonometry GLH: 0 hours [F]

N1.14h Including trigonometrical functions. G2.2h Use the trigonometrical ratios and the sine and cosine rules to solve 2D and 3D problems. G3.6 Understand and use bearings.

Learning objectives Grade Resource Common mistakes and misconceptions Support and homework AQA GCSE Maths Middle Middle AQA Linear Middle sets sets sets specification Student Book; Teacher Practice reference Middle sets Guide Book Teacher Guide G2.2h, N1.14h Understand and B Section 35.1 Forgetting that the sine, cosine and tangent ratios Section recall trigonometric only apply to right-angled triangles. 35.1 ratios in right-angled Incorrectly using the trigonometric function keys on triangles a calculator. Know how to enter the trigonometric functions on a calculator G2.2h Use trigonometric B Section 35.2 Forgetting that the sine, cosine and tangent ratios GPW Section ratios to find lengths only apply to right-angled triangles. 35.2 35.2 in right-angled Not correctly identifying the opposite, adjacent and triangles hypotenuse. Incorrectly using the trigonometric function keys on a calculator. G2.2h Use trigonometric B Section 35.3 NOTE: Although sin-1 has been introduced, it is not GPW Section ratios to find the required at GCSE; therefore, it can be simply said 35.3 35.3 angles in right- that the inverse is being found. angled triangles Incorrectly using the trigonometric function keys on a calculator. G2.2h, G3.6 Use trigonometric B Section 35.4 Not identifying the appropriate information when Section ratios and problems are set in context. 35.4 Pythagoras’ theorem Drawing a diagram that incorrectly represents the

to solve problems, problem. including the use of Rounding off values during the intermediate steps bearings of a calculation. G2.2h Solve problems B Section 35.5 Not identifying the appropriate information when Section using an angle of problems are set in context. 35.5 elevation or an angle Drawing a diagram that incorrectly represents the of depression problem. Rounding off values during the intermediate steps of a calculation.

Chapter 36 Circle theorems GLH: 0 hours [F]

G1.5h Know and use circle theorems.