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GCSE HIGHER SCHEME OF WORK Target TIME Grades Previous Module Homework SumBooks Sheet Module Stage 1 Number 1 8 hours C/B/A 2 Substitution and formulae 1 C 3 3D shape, volume and surface area 1 4 Data Handling 1 6 hours 5 hours 8 hours 5 Powers and Standard Index Form 1 C/B/A/A* 1,2 6 Pythagoras’ Theorem 1 C/B/A 1,2,5 7 Algebraic expressions, and fractions 1 6 hours 3 hours 6 hours C/B/A 5 8 Percentages 1 B/C 1 9 Geometry and trigonometry 1 8 hours 6 hours C/B 6 10 Algebraic equations, and rearranging formulae 1 7 hours C/B 1,2,7 1 C/B/A C/B/A 1. Estimation and Calculations 3. Rational and Irrational Numbers Ex 1 5. Prime Factors 12. Number Sequences 13. Substitution 51. Volume 53. Degree of Accuracy 62. Questionnaires 68. Histograms 1 69. Histograms 2 70. Histograms 3 75. Cumulative Frequency 1 76. Cumulative Frequency 2 91. Moving Averages 92. Box Plots 2. Standard Form 9. Indices Ex 1, 3 55. Pythagoras Theorem 8. Fractions 9. Indices Ex 2, 4 10. Simplifying Ex 1 14. Factorising Ex 1 6. Percentages 35. Regular Polygons 56. Sine, Cosine and Tangent Ratios 61. Three Dimensional Trigonometry 11. Rearranging Formulae 15. Trial and Improvement 18. Solving Equations 1 Ex 1 20. Writing Simple Equations W Robertson GCSE HIGHER SCHEME OF WORK Target TIME Grades Previous Module Homework SumBooks Sheet Module Stage 11 Transformations 1 5 hours C/B/A 12 Handling data 2 1 6 hours C/B 4 13 Algebraic graphs 1/2 6 hours C/B 10 14 Ratio and proportion 1/2 C/A 1,7 15 Circles 1/2 4 hours 7 hours C/B/A/A* 3,5,10 16 Quadratics 2 9 hours C/B/A 7,10 17 Vectors 2 A* 18 Simultaneous equations and inequalities 2 5 hours 6 hours A 7,10 19 Congruence and transformations 2 4 hours C/B/A 11,17 46. Transformations 1 47. Transformations 2 83. Enlargements with a Negative Scale Factor 1 84. Enlargements with a Negative Scale Factor 2 64. Scatter Diagrams 71. Mean 72. Mean, Median and Mode 7. Conversion Graphs 23. Straight Line Graphs 27. Recognising Graphs 32. Distance - Time Diagrams 33. Velocity - Time Diagrams 17. Direct and Inverse Proportion 52. Ratios and Scales 37. Geometry of a Circle 1 38. Geometry of a Circle 2 50. Area and Perimeter 10. Simplifying Ex 2 14. Factorising Ex 2, 3, 4 18. Solving Equations 1 Ex 2 19. Solving Equations 2 22. Writing Quadratic Equations 28. Graphs 1 (solving quadratic eqns) 39. Vectors 1 40. Vectors 2 21. Simultaneous Equations 24. Inequalities 25. Linear Inequalities 29. Graphs 2 (solving sim eqns) 36. Congruent Triangles 41. Similar Shapes 42. Similarity W Robertson GCSE HIGHER SCHEME OF WORK Target TIME Grades Previous Module Homework SumBooks Sheet Module Stage 20 Probability 2 7 hours C/B/A/A* 21 Powers and Surds 2 B/A/A* 22 Constructions 2 23 Area and Volume 3 24 Sine rule, cosine rule and 3-D 3 8 hours 5 hours 6 hours 6 hours 25 Proportion and algebraic graphs 3 4 hours A/A* 13,14 26 Graphical solutions of equations 3 A/A* 10,13,16, 18 27 Graphs of functions 3 28 Circle Theorems 3 29 Using a calculator 3 4 hours 4 hours 5 hours 3 hours 5 C C/B/A/A* 3,5,11,19 A/A* A/A* B 15 77. Probability 1 78. Probability 2 79. Relative Probability 80. Tree Diagrams 4. Surds 31. Growth and Decay 44. Constructions 45. Loci 54. Formulae 43. Bearings 57. Sine and Cosine Rules 58. Areas of Triangles 59. Trigonometry - Mixed Exercise 89. Three Dimensional Co-ordinates 1 90. Three Dimensional Co-ordinates 2 85. Equation of a Circle 86. Simultaneous Equations 2 (with circles and straight lines) 48. Transformations of Graphs 60. Graphs of Sines, Cosines and Tangents 37. Geometry of a Circle 1 38. Geometry of a Circle 2 A/A* W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE ONE) MODULE 1 Number TIME: 8 hours TARGET GRADE: C/B/A PRIOR KNOWLEDGE/ STARTER OBJECTIVES Basic number bonds and multiplication/division facts. Awareness of position of numbers on number lines. Ability to recognise basic number patterns. CONTENT Recognise triangular, square and cube numbers NA2b (INT ) Recalling integer squares and corresponding square roots to 15 15 NA3g Recalling the cubes of 2, 3, 4, 5 and 10 NA3g MAIN OBJECTIVES Recognise the different types of numbers, and find multiples and factors. Calculate squares and cubes, and recall the relevant facts. Find square and cube roots of numbers. Y10 TEXT 17-19 55-59 More needed! Finding multiples, factors, primes and prime factors NA2a Finding prime factor composition of positive integers NA2a Using prime factors to find HCFs and LCMs NA2a Rounding to the nearest integer, to decimal places and to significant figures NA3h Selecting and justifying appropriate degrees of accuracy* NA4b Checking and estimating answers to problems NA4b Write numbers in terms of their prime factors and use prime factors to find the HCF, and LCM. 71 More needed! Round any number to a specified accuracy, or justify their own choice of accuracy e.g. nearest integer, significant figures or decimal places. Use rounding methods to estimate answers to complex expressions. 77-79 More needed! Recognising the limitations on the accuracy of measurement* NA4b Terminating and recurring decimals NA2c Finding a fraction equivalent to a recurring decimal NA2c Calculate upper and lower bounds of measurements or rounded numbers. Change between fractions and decimals, including those that recur. Multiply and divide multiples of powers of ten and decimals. 109-114 104-107 DIFFERENTIATION / EXTENSION / HOMEWORK Further work on indices to include powers, with negative and/or fractional indices. Trial and improvement for roots of integers. H/W SumBooks 5 It is essential to ensure that pupils are absolutely clear about the difference between significant figures and decimal places and take note of the required degree of accuracy for questions. H/W SumBooks 1 H/W SumBooks 3 Ex 1 101-3 W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE ONE) MODULE 2 Substitution and formulae TIME: 6 hours TARGET GRADE: C PRIOR KNOWLEDGE/ STARTER OBJECTIVES Module 1 CONTENT The ability to: commutative, associative and distributive laws Apply rules for the order NA4a of operations for Four rules with negative numbers NA3a Using the order of operations, and the MAIN OBJECTIVES 119-120 more Recognise descending needed Substituting into algebraic formulae NA5g DIFFERENTIATION / EXTENSION / HOMEWORK 72 numbers. and ascending number patterns. Confidently use order of operations commutative, associative and distributive laws for positive and negative numbers. Y10 TEXT 68-70, Substitute numbers into any expression or formula. 153-4 Estimate answers before attempting complex substitutions. H/W SumBooks 13 Extend finding the nth term to expressions involving second differences and terms in n squared. H/W SumBooks 12 Need an Use the four rules for exercise negative numbers. with negative numbers Generating a formula NA5g Generating common number sequences NA6a Generating number sequences using term-toterm and position-to-term definitions NA6a Finding the nth term (linear expressions) Derive a formula from given information. Find a designated term of a sequence given a pattern or a formula. Find the nth term of a linear expression. 7-12 NA6a Use function notation NA5a W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE ONE) MODULE 3 3D shape, volume and surface area TIME: 5 hours TARGET GRADE: C/B/A PRIOR KNOWLEDGE/ STARTER OBJECTIVES Names and properties of 2D and 3D shapes. Nets of simple solids. Experience of finding areas of shapes from formulae. Ability to give answers to a degree of accuracy. CONTENT Finding areas of plane shapes using formulae SSM4d MAIN OBJECTIVES Find the perimeter and area of simple shapes, such as rectangles squares, triangles, parallelograms, trapezia, kites, and composites of rectangles and triangles. Know the formulae for area of the shapes mentioned. Y11 TEXT 239-257 DIFFERENTIATION / EXTENSION / HOMEWORK Fencing problems. Additional work using symbolic expressions. Finding upper and lower bound of areas or volumes. Nets of simple solids SSM2k Finding surface area of solids with triangular and rectangular faces SSM4d Developing, knowing and using the formula for the volume of a cuboid SSM4d Finding volume of solids made from cuboids SSM4d Finding volume of prisms SSM4d Work confidently with 3-D shapes and be able to calculate the volume of cuboids, prisms, pyramids, cones, spheres, and solids made from cuboids. Calculate the surface area of solids with triangular and rectangular faces. Find how many boxes of a given size fit into a larger box. Know the formulae for area of the shapes mentioned. 258-263 Finding upper and lower bound of areas or volumes. H/W SumBooks 53 H/W SumBooks 51 Investigate the different nets that can be used to make certain 3-D shapes given a particular area of card. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE ONE) MODULE 4 Data Handling TIME: 8 hours TARGET GRADE: C/B/A PRIOR KNOWLEDGE/ STARTER OBJECTIVES Experience of displaying data. An understanding of the concept of an average. Experience of reading from graphs. Some concept of a ‘running total’. CONTENT Designing questionnaires and criticise methods of using questionnaires HD3a (INT ) Understanding frequency density* HD5d Constructing histograms for grouped continuous data HD4a Calculating a mean from simple data HD4E Calculating a moving average HD4f Completing cumulative frequency tables HD4a Plotting cumulative frequency diagrams HD4a Using cumulative frequency to find the median HD4e Using cumulative frequency to find quartiles and interquartile range HD4e Drawing Box plots HD4a MAIN OBJECTIVES Y10 TEXT 213-8 DIFFERENTIATION / EXTENSION / HOMEWORK H/W SumBooks 62 Use frequency density to construct a histogram. 236-238 Extend work on histograms to unequal intervals. Calculate means, and moving averages making predictions. 179 H/W SumBooks 68, 69, 70 H/W SumBooks 91 Investigate what effects, if any, to (i) the median, (ii) the interquartile range if you (a) + 10, (b) - 10 (c) * 10, (d) / 10, to all the data. Collect, analyse and display own data in a cumulative frequency diagram and then compare the distribution with others in the class. (E.g. the number of minutes spent doing homework daily during a particular month)... what general conclusions can be made for the subgroups within the class? H/W SumBooks 75,76,92 Design and complete a cumulative frequency table, identifying class boundaries where necessary. Plot a cumulative frequency curve using upper class boundaries. Solve problems using a cumulative frequency curve (e.g. How many____ were more than…). Use a cumulative frequency curve to estimate the median, lower quartile, upper quartile, and interquartile range. Construct box plots. 224-229 Use moving averages to make seasonal predictions. *For 1388 this is not assessed until Stage 2. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE ONE) MODULE 5 Powers and Standard Index Form TIME: 6 hours TARGET GRADE: C/B/A/A* PRIOR KNOWLEDGE/ STARTER OBJECTIVES Modules 1, 2. An ability to multiply and divide by powers of 10. CONTENT Using index notation NA2b Using indices in expressions NA5d Using index laws for multiplication and division (integer powers)* NA2b STAGE ONE Using standard index form NA2b Converting between ordinary and standard index form representations NA3h Using standard index form to make estimates* NA3h Calculating with standard index form* NA3m Using a calculator for standard index form NA3r Experience of using powers of numbers. MAIN OBJECTIVES Know and use the rules of indices (adding, subtracting and multiplying indices). Evaluate fractional and negative indices. Recognise that some numbers are too large or too small to be represented normally on a calculator. Represent standard form as a number between 1 and 10 multiplied by a positive or negative power of ten. Convert between standard form and ‘normal’ numbers. Solve problems involving standard form, using the correct calculator method and making estimates. Interpret a calculator display showing a number in standard form. Y10 61-64 (the algebra side is in Module 7 too) 81-88 DIFFERENTIATION / EXTENSION / HOMEWORK Simplify expressions involving complex indices. Solve equations involving indices. H/W SumBooks 9 H/W SumBooks 2 NOTES There is now a greater emphasis on manipulative algebra at Key Stage 4, particularly at this tier. *For 1388 this is not assessed until Stage 1. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE ONE) MODULE 6 Pythagoras’ Theorem TIME: 3 hours TARGET GRADE: C/B/A PRIOR KNOWLEDGE/ STARTER OBJECTIVES Modules 1, 2, 5 The ability to square integers, with and without a calculator and use a calculator to find square roots. The ability to manipulate equations. Rounding an answer to a given number of decimal points or significant figures. Plotting points given their co-ordinates. Knowledge of simple bearings. CONTENT Using Pythagoras’ Theorem to find the Hypotenuse SSM2f Using Pythagoras’ Theorem to find the shorter sides SSM2f Using Pythagoras’ Theorem to solve problems SSM2f Calculating lengths of lines on a grid SSM3e MAIN OBJECTIVES Identify the hypotenuse of a rightangled triangle. Recall Pythagoras’ theorem. Pick out right-angled triangles from diagrams, (e.g. circles, isosceles triangles). Use Pythagoras’ theorem to find the length of any side of a right angled triangle. Use Pythagoras’ theorem to solve problems such as bearings, areas of triangles, diagonals of rectangles etc. Y10 287-298 DIFFERENTIATION / EXTENSION / HOMEWORK Use Pythagoras’ theorem to find the area of isosceles and equilateral triangles whose sides are known. Prove Pythagoras’ theorem for shapes (other than squares) on the sides of right-angled triangles. Investigate Pythagorean triples, looking for a general case. Find a formula for the area, A cm2, of a right-angled isosceles triangle with hypotenuse x cm. Investigate how to draw a line of exactly 5 cm. Further work can be developed on applying Pythagoras’ theorem in three-dimensional problems. H/W SumBooks 55 NOTES Consult GCSE papers for types of questions, depending on the orientation of the triangle and whether or not the hypotenuse or shorter side is required. Emphasise:- (i) hypotenuse (opposite the right angle) is the longest side; (ii) the length of the hypotenuse < the sum of the lengths of the other two sides. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE ONE) MODULE 7 Algebraic expressions, and fractions TIME: 6 hours TARGET GRADE: C/B/A PRIOR KNOWLEDGE/ STARTER OBJECTIVES Module 5 Four rules with negative numbers. Understand the concept of a factor. CONTENT MAIN OBJECTIVES Collecting like terms NA5b Removing a single pair of brackets NA5b Simplifying expressions using the rules of indices NA5d Factorising with a single pair of brackets NA5b Simplify expressions involving algebraic fractions NA5b Understanding the term ‘identity’ NA5c Understanding the term ‘identity’. Adding and subtracting fractions NA3c Multiplying and dividing fractions NA3d Use the four rules with fractions (including mixed numbers). Experience of the four rules for simple fractions. Simplify algebra by collecting like terms – answers may involve negative coefficients. Simplify algebraic expressions using the rules of indices. Remove and factorise a single pair of brackets – including cases where variables are removed as part of the factor. Simplify any algebraic expression involving fractions. Y10 128-9, 132 DIFFERENTIATION / EXTENSION / HOMEWORK H/W SumBooks 10 Ex1 H/W SumBooks 9 Ex2 and 4 161 H/W SumBooks 14 Ex1 factorising 62,63,64 Y11 208-213 More complicated expressions which involve a combination of brackets and fractions Use the tools learned in this module to prove identities. 89-100 H/W SumBooks 8 includes algebraic fractions NOTES At this stage it is important to develop a logical way to set out their algebraic manipulation. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE ONE) MODULE 8 Percentages TIME: 8 hours TARGET GRADE: B/C PRIOR KNOWLEDGE/ STARTER OBJECTIVES Module 1. A basic understanding of the concept of a percentage. An understanding of the ideas behind VAT, taxation and interest. CONTENT Interchanging between percentages, fractions and decimals NA3e Finding percentages and percentage changes NA3j Finding VAT, a percentage profit or loss NA3j Using simple interest NA3j Multiplying by a number between 0 and 1 NA3a Understanding the multiplicative nature of percentages as operators NA3e Finding 100% when another amount is known NA3e Solving percentage problems NA3e Solving reverse percentage problems NA3e Solving problems involving compound interest NA3k MAIN OBJECTIVES Change between percentages, fractions and decimals. Find percentages of quantities using both mental mathematics and calculator method, and solve percentage problems. Increase and decrease quantities by a percentage, including within contexts of VAT, profit and loss. Find one quantity as a percentage of another, and calculate the percentage when an actual profit or loss is given. Calculate simple and compound interest. Solve problems using percentages e.g. taxation, bills. Recognise that an increase of e.g. 15% leads to 115% and a decrease of e.g. 15% leads to 85%. Find the original amount e.g. price before a sale, price before VAT. Write down a decimal multiplier that is equivalent to an increase or decrease in percentage. Use multipliers to solve reverse percentage and compound interest problems. DIFFERENTIATION / EXTENSION / HOMEWORK Problems which lead to the necessity of rounding to the nearest penny (eg real-life contexts). Calculate original price before compound interest. Combine multipliers to simplify a series of percentage changes. Independent research into the many uses made of percentages e.g. in the media, VAT, in shops. H/W SumBooks 6 NOTES Amounts of money should always be rounded to the nearest penny where necessary, except where such rounding is premature (e.g. in successive calculations like in compound interest). Pupils typically answer compound interest questions incorrectly, either by using simple interest or by calculating over the wrong number of years. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE ONE) Module 9 Geometry and trigonometry TIME: 6 hours TARGET GRADE: C/B PRIOR KNOWLEDGE/ STARTER OBJECTIVES Module 6 Knowledge of Pythagoras’ theorem. Ability to use a calculator to change fractions to decimals. Knowledge of basic concepts of ratio. CONTENT MAIN OBJECTIVES Y10/11 Angles in polygons SSM2d (INT ) Solve problems involving interior/exterior angles of polygons (regular and irregular), and understand the concept and limitations of tessellation. Y11 226-9 Tangent, sine and cosine ratios. SSM2g Uses of the three ratios. SSM2g Angles of elevation and depression. SSM2g Bearings and trigonometry SSM2g Identify appropriately the various sides of a right-angled triangle as the Hypotenuse, Opposite and Adjacent. Recall the ratios for sine, cosine, and tangent and identify which are required to solve a problem. Use information given to find angles using the appropriate ratio. Use the appropriate ratio to find the lengths of sides in a rightangled triangle. Find angles of elevation and depression using the appropriate ratio. Apply trigonometric ratios and Pythagoras’ Theorem to solve assorted problems, including those involving bearings. Y10 299-316 Y11 1827 DIFFERENTIATION / EXTENSION / HOMEWORK H/W SumBooks 35 Further work can be developed on applying the ratios in threedimensional problems. Work on the sine and cosine rules could be developed. Given two properties of a rightangled triangle find the others. H/W SumBooks 56 H/W SumBooks 61 3D NOTES For some students this work is found difficult simply because they cannot identify which sides to use or which ratio can be used. The labelling of sides can be confused when both angles are labelled. Emphasise the importance that a calculator is in ‘Degree mode’, and that scale drawings will score 0 marks for this type of question. *Not assessed until Stage 3. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE ONE) Module 10 Algebraic equations, and rearranging formulae Time: 7 hours TARGET GRADE: C/B PRIOR KNOWLEDGE/ STARTER OBJECTIVES Module 1, 2, 7. A knowledge and understanding of pairs of inverse operations. Experience of solving simple linear equations. CONTENT MAIN OBJECTIVES Using inverse operations to solve equations NA5e Linear equations with integer or fractional coefficients NA5f Equations combining operations NA5e Solving equations with the unknown on both sides NA5f Solving equations using brackets and negative solutions NA5f Set up simple equations NA5e Using algebraic equations to solve problems NA5e Using trial and improvement to solve non-linear equations NA5m Use inverse operations to rearrange formulae NA5g Solve linear equations including those with an unknown on both sides, those that require prior simplification (e.g. brackets), fractional equations, and those where the answers are either negative or a fraction. Derive algebraic expressions from information given and extend this to derive equations, solving problems. Find square and cube roots of numbers including decimals, and solve non-linear equations using trial and improvement. Rearrange formulae, including those where the potential subject occurs more than once. Y10 135-149 DIFFERENTIATION / EXTENSION / HOMEWORK Derive equations from practical situations (such as angle calculations). Solve equations where more manipulation of fractions is required. H/W SumBooks 18 Ex 1 H/W SumBooks 20 171-2 H/W SumBooks 15 155-160 H/W SumBooks 11 NOTES Pupils can leave their answers in fractional form where appropriate. In ‘trial and improvement’ emphasise the need to justify the final answer by considering the half way value. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE ONE) Module 11 Transformations Time: 5 hours TARGET GRADE: C/B/A PRIOR KNOWLEDGE/ STARTER OBJECTIVES Plotting co-ordinates An understanding of the concepts of congruency, similarity and enlargement. CONTENT Reflecting 2D shapes SSM2a Rotating shapes through various angles and about various centres of rotation SSM2a Using translations that are specified by a vector SSM2a MAIN OBJECTIVES Enlarging assorted shapes using various centres of enlargement and integer scale factors SSM3c Enlarging assorted shapes using noninteger scale factors SSM3c Enlargement calculations SSM3d Reflect shapes and identify equations of mirror-lines, including diagonal lines (y = x, y = x). Rotate 2-D shapes following instruction and describe a rotation in full. Recognise translations as sliding movements, and translate simple 2-D shapes within a plane using words or vector notation. Understand which are the invariant properties of enlargements. Enlarge shapes using a variety of positive, negative, integer and non-integer scale factors. Use scale factors to solve problems involving similar shapes. Work on tasks involving these transformations. Use scale to interpret maps and complete scale drawings. Y11 DIFFERENTIATION / EXTENSION / HOMEWORK 267-272 273-5 The tasks set can be extended to include combinations of transformations, including those from other modules. Investigation into different ways of transforming an object into a particular image. H/W SumBooks 46, 47 H/W SumBooks 83, 84 Negative S.F. NOTES Emphasis needs to be placed on ensuring that students do describe the given transformation fully. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE ONE) Module 12 Handling data 2 Time: 6 hours TARGET GRADE: C/B PRIOR KNOWLEDGE/ STARTER OBJECTIVES Module 4 The ability to plot points given their co-ordinates (in all four quadrants). An ability to read from graphs. Knowledge of the terms mean, median, mode and inequality signs. An understanding of the concept of a variable. Recognition that a change in one variable can affect another. CONTENT Identifying trends in time series HD5b Comparing shapes of distributions HD5d Comparing distributions using measures of average and spread HD5d Using a calculator for statistical calculations HD4j Plotting and interpreting scatter diagrams HD4a Describing correlation from a scatter graph HD5f Drawing and using a line of best fit HD4i MAIN OBJECTIVES Y10 DIFFERENTIATION / EXTENSION / HOMEWORK Make predictions based on trends of a graph. 199-202 Use averages and range to compare two distributions. Evaluate mean, median, mode and range from simple and grouped data, justifying the choice of a particular average. (Calculator and non-calculator). Plot and use a scatter graph to describe correlation in terms of the two variables, and as positive, weak, negative, or strong. Draw a line of best fit where possible “by eye”, and use this to make predictions. 203212, 181 239-40 H/W SumBooks 71, 72 219-223 Vary the axes required on a scatter graph to suit the ability of the class H/W SumBooks 64 NOTES When plotting points or reading off where a graph crosses the x-axis, check the scale on the axes carefully. If possible in exam questions choose an easy scale for each axis. Students should check that their answers for mean, median and mode lie within the given range of data. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE ONE/TWO) Module 13 Algebraic graphs TIME: 6 hours TARGET GRADE: C/B PRIOR KNOWLEDGE/ STARTER OBJECTIVES Module 10. The ability to plot points that follow a simple rule (in four quadrants). The ability to substitute positive and negative values into a non-linear formula. CONTENT Plotting graphs of functions where y is expressed in terms of x, leading to a straight line NA6b Calculating gradients of straight lines, and exploring gradients of parallel lines* NA6c Recognising the y-intercept of a straight line* NA6c Exploring graphs of the form y = mx + c* NA6c Plotting linear graphs from real-life problems NA6d Plotting the graph of a quadratic function NA6e Plotting graphs of cubic, reciprocal and exponential functions* NA6f Interpret graphs representing real-life situations NA6d (time-distance etc) Recognising characteristics of graphs* NA6f MAIN OBJECTIVES Plot a straight-line graph from a given set of values. Realise that an equation of the type y = mx + c represents a straight line graph, and plot this graph. Understand the relevance of m and c in the above equation. From a given graph, find the gradient and yintercept and hence the equation of the graph. Draw a straight-line graph without plotting points. Y10 251-262 DIFFERENTIATION / EXTENSION / HOMEWORK Extend to identifying regions relating to straight line graphs. Having drawn the graph of type y = ax + bx +cx, investigate how it can be used to solve equations of the type ax + bx + cx + k = 0, where a, b, c and k are constants. Use of a graphic calculator. Find gradients at a point of a curve. H/W SumBooks 23 3 2 3 2 263 Evaluate exponential functions. Plot curves from given quadratic, cubic, reciprocal and exponential functions. Interpret travel graphs, and calculate with speed, distance and time (including decimal divisions of an hour). Interpret and plot real-life graphs such as conversion graphs and distance/time graphs. Recognise graphs e.g. filling different shaped containers. Understand compound measures such as density or rate of flow, and interpret this from a graph. 267-273 Exponen tials in Y11 131140 Y11 1159 H/W SumBooks 31 Growth and Decay H/W SumBooks 7 Conversion Graphs H/W SumBooks 27 Real life graphs H/W SumBooks 32 Distancetime H/W SumBooks 33 Velocity Time NOTES Links with the Science department could yield many experiments that would give rise to straight line relationships. *For 1388 this is not assessed until Stage 2 W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE ONE/TWO) Module 14 Ratio and proportion TIME: 4 hours TARGET GRADE: C/A PRIOR KNOWLEDGE/ STARTER OBJECTIVES Module 1, 7. Basic number skills and ability to recognise common factors. Calculator skills. CONTENT Simplifying ratios NA2f Relating ratio form to fractions NA2f Dividing in a given ratio NA3f Unitary method* NA3n (FDN ) MAIN OBJECTIVES Using direct proportion* NA3l & NA5h Using inverse proportion* NA3l & NA5h DIFFERENTIATION / EXTENSION / HOMEWORK H/W SumBooks 52 Ratios and Recognise a ratio as a way of showing the relationship between two numbers. Relate a ratio to a fraction. Simplify a ratio by dividing both its numbers by a common factor and recognise when it is in its lowest terms. Recognise when two variables are in direct proportion or inverse proportion. Use the unitary method as a way of solving ratio and proportion problems (e.g. recipes). Divide a quantity into a given ratio (in two or three parts). Use the unitary method as a way of solving ratio and proportion problems (e.g. recipes). Y10 116 Scales H/W SumBooks 17 direct and indirect proportion Currency calculations using current exchange rates. NOTES Candidates often fall down when dividing into a 3-part ratio. *For 1388 this is not assessed until Stage 2. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE ONE/TWO) Module 15 Circles Time: 7 hours TARGET GRADE: C/B/A/A* PRIOR KNOWLEDGE/ STARTER OBJECTIVES Modules 3, 5, 10. Knowledge of basic circle vocabulary, and the ability to construct a circle. CONTENT Recalling terms relating to a circle SSM2h Understanding and using right angles between tangent and radius SSM2h Understanding and using tangents of equal length SSM2h Explaining why the perpendicular from the centre of a chord bisects the chord* SSM2h Calculating circumferences* SSM4d (INT ) Calculating lengths of arcs * SSM4d Calculating areas of circles* SSM4d (INT ) Recalling formulae for areas of circles* SSM4d (INT ) Calculating areas of sectors* SSM4d Using pi in exact calculations* NA3n (INT ) MAIN OBJECTIVES Y11 Use the vocabulary of a circle (circumference, radius, diameter, sector, segment, chord, and tangent). Calculate angles within circles using rules relating to tangents and radii. Explain why the perpendicular from the centre of a chord bisects the chord. This section is missing from the text!! See Y11 Int 208 Recall and apply the formulae for the area and circumference of a circle given either the radius or diameter, using various approximations to or leaving as part of an irrational answer. Find the length of an arc, the area and perimeter of a sector, and the area of a segment. Find the area of compound shapes or shaded areas that include part of a circle. Y11 250257 DIFFERENTIATION / EXTENSION / HOMEWORK H/W SumBooks 37, 38 Find the area of an annulus, or volume of a prism with a crosssection that is part of a circle. H/W SumBooks 50 NOTES can be 3 or 3.14 or 22/7 depending on accuracy or style of answer required. Answers on a non-calculator paper can be irrational (i.e. in terms of ). * For 1388 this is not assessed until Stage 2. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE TWO) Module 16 Quadratics Time: 9 hours TARGET GRADE: C/B/A PRIOR KNOWLEDGE/ STARTER OBJECTIVES Modules 7, 10. Removing and factorising with one pair of brackets. An appreciation that if the product of two numbers is zero then one of the numbers must be zero. Confidence with the four rules for directed numbers. Drawing quadratic graphs. Use BODMAS for complicated examples, and substitute values into a complex formula. CONTENT Expanding brackets – the product of two linear expressions NA5b Factorising of quadratic expressions. NA5b Finding the difference of two squares NA5b Solving quadratic equations by factorising NA5k Solving quadratic equations by using the difference of two squares NA5k MAIN OBJECTIVES Make efficient use of techniques covering signs, products and sums. Expand and simplify two pairs of linear brackets, e.g. (x + 2)(x – 4), (3x + 2y)(4x + y), (x + p)(a + g) etc. Expand the square of a linear expression. Factorise a trinomial Use a factorised trinomial in one variable to solve a quadratic equation. Y10 129-131, Ex C&D 133-4 DIFFERENTIATION / EXTENSION / HOMEWORK Set up quadratics from practical situations (e.g. area of a rectangle with both edges expressed in terms of x). H/W SumBooks 10 Ex 2 162-168 Factorise using the difference of two squares and use this to solve quadratic equations. H/W SumBooks 14 Ex 3, 4 Factorising H/W SumBooks 18 Ex 2 solving equations (including completing square) Apply difference of two squares to Pythagoras’ Theorem. Evaluation of calculations e.g. 98 – 2. 2 2 Solving quadratic equations using the quadratic formula NA5k Use the formula to solve quadratic equations. Simplify expressions by cancelling common factors NA5b Finding approximate solutions to quadratics using graphs NA6e Finding approximate solutions to problems using graphs of complex functions NA6f Use factorising methods to simplify algebraic fractions. Solve quadratic and cubic equations using a given graph or where one has to be drawn. Use terms like ‘minimum point’, ‘maximum point’, ‘quadratic function’. Use graphical methods to find the maximum or minimum of a quadratic function. Solve problems using cubic or exponential graphs. 280-283 H/W SumBooks 14 Ex 2 Factorising H/W SumBooks 22 Significance of whether discriminant is positive, negative or zero. H/W SumBooks 19, 22 Use graphical calculators to enable pupils to get through examples more rapidly. H/W SumBooks 28 W Robertson GCSE HIGHER SCHEME OF WORK DIFFERENTIATION & EXTENSION Area of an annulus. NOTES There may be a need to remove the HCF (numerical) of a trinomial before factorising to make the factorisation more obvious. Students should be reminded that factorisation should be tried before the formula is used. In problem-solving, one of the solutions to a quadratic may not be appropriate. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE TWO) Module 17 Vectors Time: 5 hours TARGET GRADE: A* PRIOR KNOWLEDGE/ STARTER OBJECTIVES The ability to use the four rules confidently with fractions and negative numbers. CONTENT Understanding and using vector notation SSM3f Calculating the sum and difference of two vectors SSM3f Calculating a scalar multiple of a vector SSM3f Calculating the resultant of two vectors SSM3f Representing graphically the sum and difference of two vectors SSM3f Representing graphically a scalar multiple of a vector SSM3f Solving simple geometrical problems in 2-D using vector methods SSM3f MAIN OBJECTIVES Understand the content of the module Y11 296-304 DIFFERENTIATION / EXTENSION / HOMEWORK Find the modulus of a vector, or its angle to the horizontal H/W SumBooks 39, 40 NOTES Pupils often find the pictorial representation of vectors more difficult than the manipulation of column vectors. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE TWO) MODULE 18 Simultaneous equations and inequalities TIME: 6 hours TARGET GRADE: A PRIOR KNOWLEDGE/ STARTER OBJECTIVES Modules 7, 10. The ability to solve linear equations. Understanding of LCM. Understanding of the concept of an inequality. Ability to construct straight line graphs. CONTENT MAIN OBJECTIVES Solving simultaneous equations using elimination NA5i Solve linear simultaneous equations by eliminating a variable, using them to solve problems. Y10 and 11 121-125 Y11 1558 Solving linear inequalities in one variable NA5j Solve linear inequalities through both algebraic methods and listing possible integer values. Solve simple inequalities involving squares. 150-152 Y11 9798 Use regions on a graph to solve inequality problems in two variables. Y11 99103 Solve linear simultaneous equations by graphical methods, using them to solve problems. 274-279 Solving linear inequalities in two variables and finding the solution set NA5j Solving simultaneous equations using a graphical method NA5i DIFFERENTIATION / EXTENSION / HOMEWORK Simultaneous equations that need rearranging before one of the methods can be used. Most able: Solve simultaneous equations in 3 variables. H/W SumBooks 21 H/W SumBooks 24 Use graphical calculators to enable pupils to get through examples more rapidly. Use gradient and intercept to draw lines. H/W SumBooks 25 Graphical Inequalities H/W SumBooks 29 Sim.Eqns graphically NOTES Inaccurate graphs could lead to incorrect solutions. Could lead to investigations such as Car hire, Mobile Phones. Many pupils find locating regions difficult – it is often useful to choose a particular point on one side of the line to check if it fits the inequality. All working should be clearly presented and show how coefficients are matched and eliminated. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE TWO) MODULE 19 Congruence and transformations TIME: 4 hours TARGET GRADE: C/B/A PRIOR KNOWLEDGE/ STARTER OBJECTIVES Modules 11, 17. Understanding of reflection, rotation, translation and enlargement and an ability to describe each transformation in full. CONTENT MAIN OBJECTIVES Understand similarity and congruence SSM2e Prove the congruence of triangles using formal arguments SSM2e Transforming 2-D shapes using a combination of transformations SSM3b Recognising properties which are preserved under transformations SSM3b Recognise combinations of transformations and describe them in full. Recognise properties that are preserved, and those that are changed under transformations. Calculate missing sides of triangles and other shapes (e.g. regular polygons) using similarity. Prove the congruence of triangles using formal arguments. Y11 278-287 288These pages missing from the book!! 276-7 DIFFERENTIATION / EXTENSION / HOMEWORK H/W SumBooks 41, 42 H/W SumBooks 36 W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE TWO) MODULE 20 Probability TIME: 7 hours TARGET GRADE: C/B/A/A* PRIOR KNOWLEDGE/ STARTER OBJECTIVES Writing probabilities as fractions, decimals or percentages. Probability of an event happening or not happening. CONTENT MAIN OBJECTIVES Estimating probability from theoretical models HD4b Using relative frequency HD4b Using the vocabulary of probability to interpret results HD5g Using probability estimates to compare results HD5h (INT ) Selecting and justifying a method of sampling* HD2d Understanding the effect of sample size on probability estimates HD5i (INT) Understanding the concepts of mutual exclusivity and independent events HD4g Knowing when to add or multiply probabilities HD4g Know when to use the P(A) + P(B) ‘OR’ rule, and the P(A) (B) ‘AND’ rule. Using tree diagrams to represent outcomes of compound events HD4h Probability of an event happening or not happening. Use the result P(not n) = 1 – P(n) for consecutive events. Complete tree diagrams as a means of showing outcomes for two successive events and related probabilities, and use them to solve probability problems. Writing probabilities as fractions, decimals or percentages. Estimate probabilities and use relative frequencies to make predictions or test for bias. Probability of an event happening or not happening. Use the result P(not n) = 1 – P(n) for consecutive events. Understand sampling techniques, and justify their choice. Appreciate that a larger sample size will give a more accurate estimate, and question the reliability of results. Analyse experimental data and compare this to theoretical results. DIFFERENTIATION / EXTENSION / HOMEWORK Use the fraction button of a calculator to work with harder fractions. Use Venn diagrams to solve probability questions. Make predictions of outcomes for probability games and then test the predictions. Consider the rules of a probability game where the first player is favourite to win and change the rules to make the game fair. Use spreadsheets to generate random dice throws etc. to consider large numbers of trials – look at effects as n becomes large, plot graphs …. This could lead to asymptotes. H/W SumBooks 77 H/W SumBooks 78 H/W SumBooks 79 Relative Prob H/W SumBooks 80 Tree diagrams OBJECTIVES Use the ideas of conditional probability to solve problems. NOTES Pupils can often lose marks at probability due to inability to manipulate fractions. Pupils do not always appreciate that some descriptions of probabilities cover more than one outcome e.g. tossing 2 coins and obtaining ‘one of each’. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE TWO) MODULE 21 Powers and Surds TIME: 8 hours TARGET GRADE: B/A/A* PRIOR KNOWLEDGE/ STARTER OBJECTIVES Module 5. Evaluating powers, and the rules of indices. Some understanding that a surd is more accurate than a rounded answer. CONTENT Understanding and using reciprocals NA3a Fractional and negative powers NA3a Recognising the relationships between fractional powers and roots NA3g Recalling the zero power NA3g Using index laws for multiplication and division of integer, fractional and negative powers NA3a Using surds and in exact calculations NA3n Rationalising a denominator – simple cases only* NA3n Using powers to explore exponential growth and decay NA3t MAIN OBJECTIVES Evaluate integer, fractional negative and zero powers with or without a calculator. Understand the term reciprocal, and use this in calculations involving powers. Use the rules of indices on all types of powers of numeric and algebraic terms. Understand the concept of a root being an irrational number, and leave answers to problems in surd form. Simplify numeric calculations by manipulating surds. Rationalise a denominator. Understand exponential growth and decay, and use it to make predictions. DIFFERENTIATION / EXTENSION / HOMEWORK Investigate the constant e. Estimating answers of complex calculations involving surds, or powers. H/W SumBooks 4 Surds H/W SumBooks 31 Growth and Decay NOTES Where appropriate, pupils will need to be able to move between power and surd or power and reciprocal forms. * For 1388 this is not assessed until Stage 3. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE TWO) MODULE 22 Constructions TIME: 5 hours TARGET GRADE: C PRIOR KNOWLEDGE/ STARTER OBJECTIVES An ability to use a pair of compasses. Understanding of the term’s perpendicular, bisecting and parallel. CONTENT Constructing triangles SSM4c Constructing a perpendicular bisector and finding the midpoint of a line segment SSM4c Construct perpendiculars to a line SSM4c Bisecting an angle SSM4c Finding Loci SSM4e Constructing graphs of simple loci NA6h (INT ) MAIN OBJECTIVES Construct shapes from given information using only compasses and a ruler. Construct perpendicular bisectors, and angle bisectors using only compasses and a ruler. Construct LOCI in terms of distance from a point, equidistance from two points, distance from a line, equidistance from two lines and line of sight. Shade regions using LOCI to solve problems e.g. vicinity to lighthouse/ port. DIFFERENTIATION / EXTENSION / HOMEWORK Solve LOCI problems that require a combination of LOCI. Past GCSE questions. H/W SumBooks 44 Constructions H/W SumBooks 45 Loci NOTES All working should be presented clearly, and accurately. A sturdy pair of compasses is essential. Work on LOCI particularly lends itself to practical activities. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE THREE) MODULE 23 Area and Volume TIME: 6 hours TARGET GRADE: C/B/A/A* PRIOR KNOWLEDGE/ STARTER OBJECTIVES Modules 3, 5, 11, 19. Formulae for finding areas of plane shapes, and volumes of cuboids and prisms. CONTENT Solving problems involving surface areas of more complex solids* SSM2i Solving problems involving volumes of more complex solids * SSM2i Solving problems involving more complex shapes and solids SSM2i Understanding the dimensions of formulae for perimeter, area and volume SSM3d Understanding the effect of enlargement on areas and volumes SSM3d Converting between area and volume measures SSM4d MAIN OBJECTIVES Solve problems involving surface areas of prisms, cylinders, pyramids, and spheres. Find the surface area of a cone from a given net. Solve problems involving volumes of prisms, cylinders, pyramids, cones and spheres. Recognise whether a formula represents a length, area or volume by considering its dimensions. Understand the effect an enlargement has on the area and volume of a shape, by considering scale factors. Convert between units of area and volume e.g. square metres to square centimetres. DIFFERENTIATION / EXTENSION / HOMEWORK Use trigonometry calculations to solve problems of volume and surface area. The scale factor for mass/weights of similar solids. H/W SumBooks 54 Dimensions of Formulae NOTES The notion of approximate similarity can be discussed, for example between infants and adults. For 1388 this is assessed in Stage 2. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE THREE) MODULE 24 Sine rule, cosine rule and 3-D TIME: 6 hours TARGET GRADE: A/A* PRIOR KNOWLEDGE/ STARTER OBJECTIVES Names and properties of 3-D shapes. The three trigonometric ratios. Pythagoras’ theorem. Ability to substitute and rearrange complex formulae. CONTENT MAIN OBJECTIVES Y11 DIFFERENTIATION / EXTENSION / HOMEWORK Find a side using the cosine rule, when the quadratic formula is required. The ambiguous case for sine rule. H/W SumBooks 57 Cosine and Using the cosine rule SSM2g Use the cosine rule to find the size of an angle or side in a non-right-angled triangle. 49-50 Using the sine rule SSM2g Use the sine rule to find the size of an angle or side in a non-right-angled triangle. 51-53 Area of a triangle using sin C * SSM2g STAGE TWO Using Pythagoras’ theorem in 3-D problems SSM2f Using trigonometric relationships in 3-D problems SSM2g Find the area of a triangle using sin C. Sine H/W SumBooks 58 Solve problems (including those involving bearings) using the sine and cosine rules. Use Pythagoras’ theorem, trigonometric ratios, sine rule and cosine rule to solve problems in 3D. H/W SumBooks 43 H/W SumBooks 89, 90 3D problems H/W SumBooks 61 3D problems H/W SumBooks 59 Mixed trig exercise Angle between a line and a plane SSM2g 35-36 37-9 NOTES Pupils may need to be reminded that the sine rule and cosine rule should not be used on right-angled triangles. Reminders of simple geometrical facts may be helpful, e.g. angle sum of a triangle, the smallest side is opposite the smallest angle. Pupils find the cosine rule more difficult for obtuse angles. * For 1388 this is assessed in Stage 2. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE THREE) MODULE 25 Proportion and algebraic graphs TIME 4 hours TARGET GRADE: A/A* PRIOR KNOWLEDGE/ STARTER OBJECTIVES Modules 13, 14. The concept of proportion. Ability to plot curves. Pythagoras’ theorem. CONTENT Setting up equations involving proportion NA5h Graphical representations of equations involving proportion NA5h Constructing the graphs of simple loci, including the circle x2 + y2 = r2 NA6h MAIN OBJECTIVES Define inverse or direct proportion in terms of a formula, finding the constant using given information. Y11 175-180 DIFFERENTIATION / EXTENSION / HOMEWORK Use of three variables in proportion questions e.g. y is directly proportional to the square of x and x is directly proportional to the cube of z; write a statement to show the proportionality between y and z. For the most able: Investigation based on the cylinder e.g. A closed cylinder, half filled with water, is placed with its curved surface in contact with a horizontal table. Mark on the circular end of the cylinder the position of the water level. Repeat the problem for when the cylinder is a quarter full. Generalise for any fraction. 181-185 Express a circle of radius r, and centre (0,0) in algebraic form. H/W SumBooks 85, 86 W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE THREE) MODULE 26 Graphical solutions of equations TIME: 4 hours TARGET GRADE: A/A* PRIOR KNOWLEDGE/ STARTER OBJECTIVES Modules 10, 13, 16, 18. The ability to solve linear simultaneous equations algebraically and graphically. The ability to draw straight-line graphs, quadratics graphs and the graphical representation of a circle. The ability to manipulate algebraic expressions confidently. CONTENT Solving by substitution a pair of simultaneous equations (one non-linear) NA5l Use simultaneous equations to calculate where a straightline graph meets a circle NA5l Using graphs to solve a pair of simultaneous equations (one non-linear) NA6e Using graphs to show where a straight-line graph intersects a circle NA6h MAIN OBJECTIVES Solve by substitution a pair of simultaneous equations (one non-linear). Use simultaneous equations to calculate where a straight-line graph meets a circle. Use graphs to solve a pair of simultaneous equations (one non-linear). Use graphs to show where a straight-line graph intersects a circle. DIFFERENTIATION / EXTENSION / HOMEWORK Circles with a centre other than the origin. H/W SumBooks 86 Circles with a centre other than the origin. Intersections of two curves. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE THREE) MODULE 27 Graphs of functions TIME: 4 hours TARGET GRADE: A/A* PRIOR KNOWLEDGE/ STARTER OBJECTIVES Knowledge of sin, cos and tan. Experience of substituting values into a function. CONTENT Drawing, sketching and describing the graphs of trigonometric functions SSM2g Applying transformations to the function y = f(x) : y = f(x) + a y = f(ax) y = f(x + a) NA6g y = af(x) (for linear, quadratic, sine and cosine functions) MAIN OBJECTIVES Y10/11 Sketch the curves y = sin x, y = cos x and y = tan x. 40-44 Draw such graphs as y = a + b sin x. Use graphs to aid the solution of equations such as a + b cos x = 1, for angles between 0 and 360. Given the graph of y = f(x), be able to sketch the graphs of y = f(x) + a, y = f(ax), y = f(x + a), and y = af(x) by applying transformations. Investiga tive task 141-4 DIFFERENTIATION / EXTENSION / HOMEWORK Use a graphical calculator to investigate the effects the above factors have on the graph of a function. The study of such curves as y = a + b sin (cx + d). Quadratic graphs and completing the square. Investigation of curves which are unaffected by particular transformations. H/W SumBooks 48 functions with x2 and x3 H/W SumBooks 60 NOTES Investigation of simple relationships such as sin (180 – x) = sin x, and sin (90 – x) = cos x can help. W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE THREE) MODULE 28 Circle Theorems TIME: 5 hours TARGET GRADE: B PRIOR KNOWLEDGE/ STARTER OBJECTIVES Module 15. Angle facts for triangles, quadrilaterals, interior/exterior angles of polygons, parallel lines, angles on a straight line, and angles at a point. Nomenclature of a circle. CONTENT Prove and use circle theorems SSM2h The angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference SSM2h Angles in the same segment are equal SSM2h The angle subtended at the circumference by a semicircle is a right angle. SSM2h Opposite angles of a cyclic quadrilateral add up to 180 degrees SSM2h Explain why the perpendicular from the centre of a chord bisects the chord SSM2h Prove and use the alternate segment theorem SSM2h MAIN OBJECTIVES Y11 Int text DIFFERENTIATION / EXTENSION / HOMEWORK Theorem 1 205-6 H/W SumBooks 60 Understand and use the properties to solve problems. Theorem 2 205-6 Theorem 4 207 Theorem 3 207 NOTES LOCI questions may be used to introduce circle theorems, e.g. page 137 of Edexcel GCSE Higher (old edition). W Robertson GCSE HIGHER SCHEME OF WORK 1387/1388 (STAGE THREE) MODULE 29 Using a calculator TIME: 3 hours TARGET GRADE: A/A* PRIOR KNOWLEDGE/ STARTER OBJECTIVES CONTENT Using a calculator effectively and efficiently for complex calculations NA3o Using an extended range of calculator function keys NA3o MAIN OBJECTIVES DIFFERENTIATION / EXTENSION / HOMEWORK Understand the content of the module. W Robertson