IGCSE Mathematics Scheme of Work - Cambridge

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Week
Syllabus topic
Suggested Activities or Lesson Plan Outlines
Resources
Oxford – Core
Oxford –
Extended
Cambridge
Hodder
Past Papers
C1: Number
C1.1
Identify and use natural
numbers, integers
(positive, negative and
zero), prime numbers,
square numbers, common
factors and common
multiples, rational and
irrational numbers, real
numbers.
A useful starting point would be to revise positive and negative numbers using a number line and
explain the difference between natural numbers and integers.
Learners would find it useful to have a definition of the terms (e.g. factor, multiple, square
number) which can be found on the maths revision website. (I)
A fun activity would be to allocate a number to each learner in the class and ask them to stand up
if they are, for example, “a multiple of 4”, “a factor of 18” etc. Use this to show interesting facts
such as prime numbers will have 2 people standing up (emphasises 1 is not prime); square
numbers will have an odd number of people standing up. See which are common factors/common
multiples for pairs of numbers. This could be extended to HCF and LCM.
A follow-on activity would be for learners to identify a number from a description of its
properties. For example, say to the class “which number less than 50 has 3 and 5 as factors and is
a multiple of 9?” Learners could then make up their own descriptions and test one another.
Another interesting task is to look a Fermat’s discovery that some prime numbers are the sum of
two squares, e.g. 29 = 25 + 4 = 5P2P + 2P2P. Learners could see what primes they can form in
this way, and any they can’t form in this way. Learners can look for a rule which tests whether or
not a prime can be made like this. (I)
Move on to looking at how to write any integer as a product of primes. One method that can be
used is the factor tree approach. After demonstrating, ask learners to practise using the method to
write other numbers as products of primes. Then ask learners to look at finding the product of
primes of other numbers, for example 60, 450, 42, 315, but this time they can be encouraged to
look for alternative methods, for example by researching on the internet. Another useful method
is the repeated division method. (I)
Learners would find it useful to have a definition of the terms rational, irrational and real
numbers which can be found on the Maths is Fun website. On the website there are questions on
rational and irrational numbers for learners to try. These start simple and soon become more
challenging. (I) (F)
http://www.mathsrevision.net/content/numbers
http://www.mathsisfun.com/irrational-numbers.html
File: crossword
puzzle:
837841_U1_1_
crossnumber
72–74, 88–92
Software:
NVLM for
factor trees
7—9
Chapter 1
Using simple examples illustrate squares, square roots, cubes and cube roots of integers.
- Extend the task by asking more able learners to square and cube fractions and decimals
without a calculator, it may be worth doing topic 1.8 first to help with this.
C1.3
C1.4
C1.5
C1.6
Calculate squares, square roots,
cubes and cube roots of
numbers.
Use directed numbers in
practical situations.
Use the language and
notation of simple
vulgar and decimal
fractions and
percentages in
appropriate contexts.
Recognise
equivalence and
convert between
these forms.
Order quantities by
magnitude and demonstrate
familiarity with the
symbols =, ≠, >, <, ⩾, ⩽
An interesting activity is to look at finding the square root of an integer by repeated
subtraction of consecutive odd numbers until you reach zero. For example, for 25
subtract in turn 1, 3, 5, 7, and then 9 to get to 0. Five odd numbers have been
subtracted so the square root of 25 is 5. Ask learners to investigate this method for
other, larger, square numbers. (I)
-
Another interesting challenge is to look at the palindromic square number 121.
(Palindromic means when the digits are reversed it is the same number). Ask learners to
find all the palindromic square numbers less than 1000. (I)
-
Ask learners to try the past paper question. (F)
328–333
Chapter 1
339–343
Chapter 1
102–103, 257–258
Chapter 5
78, 92–94, 337
Paper 32, June 2012, Q3
Paper 12, June 2013,
Q17
Week Syllabus topic
C1.7
Understand the meaning
and rules of indices.
Use the standard form A ×
10n where n is a positive
or negative integer, and
1⩽A<10.
Use the four rules for
calculations with whole
numbers, decimals and
C1.8
vulgar (and mixed)
fractions, including correct
ordering of operations and
use of brackets.
Make estimates of numbers,
quantities and lengths, give
approximations to specified
numbers of significant
C1.9
figures and decimal places and
round off answers to
reasonable accuracy in the
context of a given problem.
Give appropriate upper
and lower bounds for
C1.10
data given to a
specified accuracy.
Demonstrate an
understanding of ratio
and proportion. Use
C1.11
common measures
of rate. Calculate
average speed.
Calculate a given percentage of
a quantity. Express one quantity
C1.12 as a percentage of another.
Calculate percentage increase
or decrease.
Use a calculator efficiently.
C1.13 Apply appropriate checks of
accuracy.
Calculate times in terms of
the 24-hour and 12-hour
C1.14 clock.
Read clocks, dials and
timetables.
Calculate using money and
C1.15 convert from one currency to
another.
Use given data to solve
problems on personal and
household finance involving
C1.16 earnings, simple interest and
compound interest.
Extract data from tables and
charts.
C2: Algebra and graphs
Use letters to express
generalised numbers and
express basic arithmetic
processes algebraically.
C2.1
Substitute numbers for words
and letters in formulae.
Transform simple formulae.
Construct simple expressions
and set up simple equations.
Suggested Activities or Lesson Plan Outlines
Resources
Oxford – Core
Oxford –
Extended
Cambridge
Hodder
Past Papers
331–336
Paper 33, June 2012, Q1
(b)(c)
Paper 12, Nov 2012, Q16
C1.6
Paper
Week Syllabus topic
Manipulatedirected numbers.
Usebrackets and extract common
factors.
Use and interpret positive,
C2.4
negative and zero indices.
Use the rules of indices.
Solve simple linear equations in
one unknown.
C2.5
Solve simultaneous linear
equations in two unknowns.
Continue a given number
sequence.
Recognise patterns in sequences
and relationships between
C2.7
different sequences.
Find the nth term of sequences
(including simple quadratic
and cubic sequences).
Interpret and use graphs in
practical situations including
C2.9
travel graphs and conversion
graphs.
Draw graphs from given data.
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.
C2.10 Draw and interpret such
graphs.
Solve linear and quadratic
equations approximately
by graphical methods.
C3: Geometry
Use and interpret the
geometrical terms: point, line,
parallel, bearing, right angle,
acute, obtuse and reflex angles,
perpendicular, similarity and
C3.1
congruence.
Use and interpret vocabulary of
triangles,
quadrilaterals, circles, polygons
and simple solid figures including
nets.
Measure lines and angles.
Construct a triangle given the
three sides using ruler and pair
of compasses only. Construct
other simple geometrical
C3.2
figures from given data using
ruler and protractor as necessary.
Construct angle bisectors and
perpendicular bisectors using
straight edge and pair of
compasses only.
Read and make scale
C3.3
drawings.
C2.2
C3.4
Calculate lengths of similar
figures.
C3.5
Recognise rotational and line
symmetry (including order of
rotational symmetry) in two
dimensions.
Suggested Activities or Lesson Plan Outlines
Resources
Oxford – Core
Oxford –
Extended
Cambridge
Hodder
Past Papers
Paper 21, June 2013, Q6
Paper 22, June 2013,
Q10
Paper 22, June 2013, Q3
Paper 11, June 2012,
Q12
Paper 41, June 2013,
Q8(d)
Paper 42, June 2013,
Q11
Week Syllabus topic
C3.6
Calculate unknown angles using
the following geometrical
properties:
• angles at a point
• angles at a point on a straight
line and intersecting straight
lines
• angles formed within
parallel lines
• angle properties of triangles
and quadrilaterals
• angle properties of regular
polygons
• angle in a semi-circle
• angle between tangent and
radius of a circle.
Use the following loci and the
method of intersecting loci for
sets of points in two
dimensions which are:
• at a given distance from a
given point
C3.7
• at a given distance from a
Suggested Activities or Lesson Plan Outlines
Resources
Oxford – Core
Oxford –
Extended
Cambridge
Hodder
Past Papers
Paper 12, Nov 2012,
Q15, 20
Paper 21, Nov 2012, Q6
Paper 43, June 2013,
Q2(a)
given straight line
• equidistant from two given
points
• equidistant from two given
intersecting straight lines.
C4: Mensuration
Use current units of
mass, length, area,
volume and capacity in
C4.1
practical situations and
express quantities in
terms of larger or
smaller units.
Carry out calculations
involving the perimeter
and area of a rectangle,
C4.2
triangle, parallelogram and
trapezium and compound
shapes derived from
these.
Carry out calculations involving
C4.3
the circumference and area of a
circle.
Carry out calculations
involving the volume of a
C4.4
cuboid, prism and cylinder
and the surface area of a
cuboid and a cylinder.
C4.5
Carry out calculations involving
the areas and volumes of
compound shapes.
C5: Coordinate geometry
Demonstrate familiarity with
C5.1
Cartesian coordinates in two
dimensions.
Find the gradient of a straight
C5.2
line.
Paper 23, Nov 2012, Q15
Paper 11, June 2013,
Q14
Paper 21, June 2013,
Q15
Paper 31, June 2013,
Q11
Paper 43, June 2012, Q5
Paper 42, June 2012
Q11
Week Syllabus topic
Interpret and obtain the equation
of a straight-line graph in the
form y = mx + c.
Determine the equation of a
C5.5
straight line parallel to a given
line.
C6: Trigonometry
Interpret and use three-figure
C6.1
bearings.
Apply Pythagoras’ theorem
and the sine, cosine and
tangent ratios for acute
C6.2
angles to the calculation of
a side or of an angle of a
right-angled triangle.
C7: Matrices and transformations
Suggested Activities or Lesson Plan Outlines
Resources
Oxford – Core
Oxford –
Extended
Cambridge
Hodder
Past Papers
C5.4
Describe a translation by using a

vector represented by e.g. ()
C7.1
⃗⃗⃗⃗⃗
  a. Add and subtract
vectors. Multiply a vector by a
scalar.
Reflect simple plane figures
in horizontal or vertical lines.
Rotate simple plane figures
about the origin, vertices or
midpoints of edges of the
figures, through multiples of
C7.2
90°. Construct given
translations and enlargements
of simple plane figures.
Recognise and describe
reflections, rotations,
translations and
enlargements.
C8: Probability
Calculate the
probability of a single
C8.1
event as either a
fraction, decimal or
percentage.
Understand and use the
C8.2
probability scale from 0 to 1.
Understand that the probability
of an event occurring = 1 − the
C8.3
probability of the event not
occurring.
Understand relative
C8.4
frequency as an estimate of
probability.
C9: Statistics
Collect, classify and tabulate
statistical data. Read, interpret
C9.1
and draw simple inferences
from tables and statistical
diagrams.
Construct and read bar
charts, pie charts, pictograms,
C9.2
simple frequency distributions,
histograms with equal intervals
and scatter diagrams.
Paper 11, November
2012, Q18
Paper 13, Nov 2012,
Q20b
Paper 21, Nov 2012,
Q18a
Paper 12, June 2013, Q9
Paper 33, June 2013, Q6a
Paper 12, June 2013, Q6
Paper 41, June 2013,
Q5(c)
Week Syllabus topic
C9.3
C9.6
C9.7
Calculate the mean, median,
mode and range for
individual and discrete data
and distinguish between the
purposes for which they are
used.
Understand what is meant by
positive, negative and zero
correlation with reference to a
scatter diagram.
Draw a straight line of best fit
by eye.
Suggested Activities or Lesson Plan Outlines
Resources
Oxford – Core
Oxford –
Extended
Cambridge
Hodder
Past Papers
Paper 31, Nov 2012,
Q3(a)
Paper 13, June 2013,
Q18
Paper 22, June 2013,
Q17
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