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PETERHOUSE SCHOOL DEPARTMENT OF MATHEMATICS 2013/14 IGCSE SCHEME OF WORK Text: Extended Mathematics for Cambridge IGCSE - David Raynor (New Edition) Syllabus Topic B Block Lent Term 8,9. Estimation & Limits of Accuracy Week Work to be covered (Objectives) Reference text 1 6. Standard Form 2 10, 15. Ratio and Proportion/Money 3, 4 4. Vulgar and decimal fractions and percentages 4, 5 10. Ratio, Proportion, Rate 12. Calculator 6 6 Rounding numbers to a given number of significant figures or decimal places Stating or finding upper and lower bounds of quantities Estimating results of calculations by rounding numbers to 1 s.f. Expressing given numbers in standard form (+ve and –ve indices) Calculations in standard form Sharing in given ratio; Equating ratios Solving problems pertaining to direct and inverse proportion Converting to foreign currency Finding distances and areas on maps and on the ground Changing between fractions and percentages; calculating percentages percentage increase/decrease Simple Interest; Compound Interest Converting between speed units; Average speed The four operations; Powers, roots and reciprocals Memory The four operations with directed numbers Substitution in formulae 9 10-12 12 13 14 15-16 17 18 19-21 22-24 25 26 29-32 34 Collecting like terms and removing brackets Multiplying and squaring brackets Solving simple, bracketed and fractional equations Formulating and solving equations Solving a pair of simultaneous equation by substitution and by elimination Solving word problems resulting in simultaneous equations Direct factorisation, grouping Three term expressions, difference of two squares Solving by factorisation, formula and completing the square (not in text) Solving word problems resulting in quadratic equations 51 51-52 53-57 58-61 63,65 66-67 68-69 69-71 71-74 76-77 3. Directed numbers 7 20. Algebraic representation and 8 formulae 21. Algebraic manipulation 9 24. Solutions of equations and inequalities 10 21. Algebraic manipulation 11 24. Solutions of equations and inequalities 11, 12 44-46 46-50 Syllabus Topic B Block Trinity Term 32. Trigonometry Week Work to be covered (Objectives) Reference text 1-3 31. Mensuration 4 Solving right-angled triangles using Pythagoras’ Theorem Finding sides of right-angled triangles using the three ratios Finding unknown angles Solving bearing and 3-D problems relating to right-angled triangles Areas of trapezium, triangle and kite Sine formulae for areas of triangle and parallelogram Perimeter and area of shapes containing circular arcs; shaded areas; cutting out discs Finding arc length and area of sector/segment Calculating the volume of a prism, sphere, cone and composites Finding surface areas of cylinders, spheres and cones Sum of angles on a straight line Sum of angles at a point Sum of angles in a triangle/quadrilateral Sum of interior/exterior angles of any polygon Angles related to parallel lines Line symmetry and rotational symmetry Finding lengths in similar triangles and rectangles Areas of similar shapes Volumes of similar objects 120-121 184-187 188-189 191-196 83 85-86 88-91 Reference text 5 31. Mensuration 5,6 7, 8 29. Angle Properties 9 28. Symmetry 26. Geometrical terms and relationships 10 10 Syllabus Topic B Block Michaelmas Term 29. Angle properties Week Work to be covered (Objectives) 1,2 Using the four circle theorems: Angle at the centre is double angle at the circumference Angles in the same segment Angles in cyclic quadrilaterals Angle in the semi-circle Tangents to circles and angle in the alternate segment Constructing perpendicular bisector, angle bisector, 45°, 60°, 90° angles Construction of the four loci: Points equidistant from a given point Points equidistant from a given line Points equidistant from two given points Points equidistant from two intersecting straight lines 27. Geometrical constructions 30. Locus 3,4 93-96 98-104 105-107 115 117-118 119 123-124 125-126 129 132 135-136 135-136 137-138 138 139-141 142-143 144-145 26. Geometrical terms and relationships 21. Algebraic manipulation 4 Drawing, identifying and finding lengths of sides of nets 145-146 5 Expressing fractions in lowest terms by factorising Expressing as a single fraction Change of subject: - Only one term with the required letter - Two terms with required letter - Expressions with square roots and squares Direct Variation Inverse Variation The three rules of indices Negative indices and roots Bracketed expressions Solving index equations Comparing quantities Solving linear inequalities for a range/set of values Graphing inequalities in two variables Using the two forms of the sine rule to solve triangles Using the two forms of the cosine rule to solve triangles Bearing questions involving sine and cosine rules 154 155 20. Algebraic representation and 6,7 formulae 156-157 160-161 159-161 163-164 165-167 168 168-169 169 170 170-171 171-172 173 199-201 203-204 204-205 10. Ratio, Proportion, Rate 7,8 23. Indices 9 24. Solutions of equations and inequalities 10 32. Trigonometry 11-12 Syllabus Topic A Block Lent Term 18. Graphs of functions Week Work to be covered (Objectives) Reference text 1 Drawing linear graphs Calculating gradient from coordinates Sketching curves using information from y = mx + c Finding the equation of a straight line given two points or point and gradient Plotting parabolas Plotting other non-linear curves Using graphs to solve equations Drawing and interpreting distance-time graphs Calculating distance and acceleration from speed-time graphs Sketching speed-time graphs Set and set-builder notation; complement of a set Union and intersection 212 214 215 216 218 219 226 230 232 234 242 244 2 3 17. Graphs in practical situations 4 1. Number, set notation and language 5, 6 35. Vectors in two dimensions 7, 8 22. Functions 9 25. Linear Programming 10 Syllabus Topic A Block Trinity Term 36. Matrices Week 37. Transformations 2 1 Week Work to be covered (Objectives) Reference text 1-2 Continuing number sequences Finding nth term or term number 5-6; 352 5 6 7 Syllabus Topic A Block Trinity Term 1. Number, set notation and language Reference text 279-280 282-284 285 287 291 293-297 298 299 309 312 316 322 325 329 332 333 4 34. Probability 247 251 253 257 260 262 265 268 269 175 Order of a matrix; Operations with matrices Finding the inverse of a matrix Reflection in given mirror line; Finding equation of mirror line Rotation about a given centre; describing rotations Translation Enlargement using a given centre and scale; describing enlargements Combined and repeated transformations Using matrices to transform Use base vectors to describe transformations Stretch and shear Using bar and pie charts to display data Drawing histograms Averages: Mean, median and mode in grouped and raw data Drawing scatter graphs and lines of best fit Drawing cumulative frequency curve and finding quartiles and IQR Simple probability: equally likely outcomes Finding probabilities of independent and exclusive events Evaluating probabilities using tree diagrams 3 33. Statistics Logical problems Adding vectors and multiplying by scalar Expressing vectors in terms of given bases Operations with column vectors; parallel vectors Finding the modulus of a vector Vector geometry Using flow diagrams to represent functions Composite of functions Using flow diagrams to find the inverse function Obtaining required area from given equations Finding values to minimise/maximise given equation Work to be covered (Objectives) 8 9 - 11