Download IGCSE Extended Scheme 2013

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