Download IGCSE Core Schemes 2013

Mathematics Core Syllabus
Text: Core Mathematics for Cambridge IGCSE - David Raynor
Syllabus Topic
Timing
Work to be Covered
Ref Text
Page
B Block
27. Geometrical constructions
Lent week
1
1
26. Geometrical terms and relationships
29. Angle properties
2
3:4
28. Symmetry
5
31. Mensuration
31. Mensuration
6
7
Measure lines and angles;
construct a triangle given the three sides using ruler and pair of compasses
only
construct other simple geometrical figures from given data using
protractors and set squares as necessary;
Use and interpret the geometrical terms: point,line, parallel,
right angle, acute, obtuse and reflex angles,
perpendicular, similarity, congruence; use and interpret vocabulary of triangles
quadrilaterals, circles, polygons and simple solid figures including nets
Calculate unknown angles using the following geometrical properties
(a) angles at a point
(b) angles at a point on a straight line and intersecting straight lines
(c) angles formed within parallel lines
(d) angle properties of triangles and quadrilaterals
(e) angle properties of regular polygons
(f) angle in a semi-circle
(g) angle between tangent and radius of a circle
Recognise rotational and line symmetry (including order of rotational
symmetry) in two dimensions
properties of triangles, quadrilaterals and circles related to their symmetries
The circumference and area of a circle,
Carry out calculations involving the perimeter and area of
a rectangle and triangle,
1
2
4
4
4
6
5
10
13
13
14
17
26
31. Mensuration
7
8
27. Geometrical constructions
1. Number, set notation and language
9
10
20. Algebraic representation and formulae
20. Algebraic representation and formulae
11
12
24. Solutions of equations and inequalities
12
17. Graphs in practical situations
17. Graphs in practical situations
18. Graphs of functions
18. Graphs of functions
19. Straight line graphs
13. Measures
7. The four rules
1. Number, set notation and language
5. Ordering
The area of a parallelorgram and a trapezium,
The volume of a cuboid, prism and cylinder
the surface area of a cuboid and a cylinder.
Read and make scale drawings.
Continue a given number sequence
recognise patterns in sequences
and relationships between different sequences,
Construct simple expressions and set up simple equations
Use letters to express generalised numbers and express basic arithmetic
processes algebraically,
Solve simple linear equations in one unknown;
Trinity Week
1
Demonstrate familiarity with Cartesian co-ordinates in two dimensions
2
Draw graphs from given data.
3
Construct tables of values for functions of the form ax + b, ±x² + ax + b,
a/x (x ≠ 0) where a and b are integral constants;
draw and interpret such graphs;
4
solve linear and quadratic equations approximately by grapical methods
find the gradient of a straight line graph;
5
Interpret, obtain the equation of a straight line graph in the form y = mx + c
determine the equation of a straight line parallel to a given line.
6
Use current units of mass, length, area, volume and capacity in
practical situations ,express quantities in terms of larger or smaller unit
7
Use the four rules for calculations with whole numbers,
decimal fractions and vulgar (and mixed) fractions,
including correct ordering of operations and use of brackets.
7
Identify and use natural numbers, integers (positive, negative and zero)
prime numbers, square numbers
common factors and common multiples,
real numbers, rational and irrational numbers(e.g. π , √2 )
8
Order quantities by magnitude and demonstrate familiarity
28
30
35
44
46
47
48
53
55
55
57
58
67
81
81
82
82
85
86
14. Time
9
16. Personal and household finance
11. Percentages
10
10
16. Personal and household finance
11
16. Personal and household finance
11
10. Ratio, proportion, rate
12
15. Money
Michaelmas
Week
1
Calculate using money and convert from one currency to another
10. Ratio, proportion, rate
8. Estimation
1
2
33. Statistics
3
33. Statistics
4
33. Statistics
5;6
37. Transformations
with the symbols =, ≠ , <.>, ,≤ , ≥
Calculate times in terms of the 24-hour and 12-hour clock;
read clocks, dials and timetables.
Discount, profit and loss; extract data from tables and charts.
Calculate a given percentage of a quantity;
express one quantity as a percentage of another;
Use given data to solve problems on personaland household finance
involving earnings
Simple interest and compound interest (knowledge of compound interest
formula is not required)
Demonstrate an understanding of the elementary ideas and
notation of ratio, direct and inverse proportion and
7
Calculate average speed.
Give approximations to specified numbers of sig fig, decimal places
round off answers to reasonable accuracy in the context
of a given problem.
Collect, classify and tabulate statistical data;
read, interpret,draw simple inferences from tables and statistical diagram
Construct and use bar charts, pie charts, pictograms,
simple frequency distributions,
histograms with equal intervals
Scatter diagrams (including drawing a line of best fit by eye);
understand what is meant by positive, negative and zero correlation
Calculate the mean, median and mode for individual and discrete data
and distinguish between the purposes for which they are used
calculate the range.
Reflect simple plane figures in horizontal or vertical lines
88
95
95
98
99
102
104
107
108
110
128
130
own
resources
138
139
152
166
37. Transformations
8
37. Transformations
9
35. Vectors in two dimensions
10
32. Trigonometry
30. Locus
11
12
A Block
27. Geometrical constructions
32. Trigonometry
Lent Week
1
2;3
1. Number, set notation and language
24. Solutions of equations and inequalities
17. Graphs in practical situations
4
5
6
21. Algebraic manipulation
20. Algebraic representation and formulae
11. Percentages
4. Vulgar, decimal fractions and
percentages
7
8
9
10. Ratio, proportion, rate
10
11;12
Rotate simple plane figures about the origin, vertices or midpoints of edges
of the figures, through multiples of 90°
Construct given translations and enlargements of simple plane figures
recognise and describe reflections, rotations, translations and enlargements
Describe a translation by using a vector represented by e.g. column vector or
AB or a
Add and subtract vectors; multiply a vector by a scalar
Interpret and use three-figure bearings measured clockwise from the North
Use the following loci and the method of intersecting loci for sets of points
in two dimensions:
(a) which are at a given distance from a given point
(b) which are at a given distance from a given straight line
(c) which are equidistant from two given points
(d) which are equidistant from two given intersecting straight lines
169
172
179
188
193
Construct angle bisectors and perpendicular bisectors using straight edges
and a pair of compasses only
Pythagoras’ theorem
Generalise to simple algebraic statements (including expressions for the nth
term)
solve simultaneous linear equations in two unknowns.
Interpret and use graphs in practical situations including travel graphs and
conversion graphs
Manipulate directed numbers; use brackets and extract common factors.
Transform simple formulae
Calculate percentage increase or decrease.
193
Use the language and notation of simple vulgar and decimal fractions
and percentages in appropriate contexts
recognise equivalence and convert between these forms.
Common measures of rate; divide a quantity in a given ratio;
use scales in practical situations;
241
196
209
214
219
228
229
238
241
8. Estimation
9. Limits of accuracy
12. Use of an electronic calculator
34. Probability
Trinity Week
1
Make estimates of numbers, quantities and lengths,
2
Give appropriate upper and lower bounds for data given to a specified
accuracy (e.g. measured lengths)
3
Use an electronic calculator efficiently; apply approp checks of accuracy.
4;5
32. Trigonometry
23. Indices
2. Squares and cubes
6. Standard form
6;7;8
9
9
10
3. Directed numbers
11
20. Algebraic representation and formulae
12
Michaelmas
Probability of a single event as either a fraction or a decimal (not a ratio)
understand and use the probability scale from 0 to 1;
the probability of an event occurring = 1 – the probability of the event not
occurring;
understand probability in practice, e.g. relative frequency.
The sine, cosine tanent for acute angles
Use and interpret positive, negative and zero indices
Calculate squares, square roots, cubes and cube roots
Use the standard form A × 10 ^n where n is a
positive or negative integer, and 1 ≤ A < 10
Use directed numbers in practical situations
(e.g. temperature change, flood levels).
Substitute numbers for words and letters in formulae;
Revision
243
247
261
276
292
304
305
309
313
317