Download IGCSE Mathematics Revision checklist 2015.

IGCSE Mathematics
Revision checklist 2015.
Syllabus
number
1
Topic
Numbers, set
notation and
language
Lesson
number
1.1
1.2
2.1
8.1
1
Sequences
1.2
2
Squares and
cubes
Directed numbers
Fractions and
percentages
1.2
5
Ordering
6
7
Standard form
The four rules
1.1
5.5
1.4
1.1
2.4
8
Estimation
1.3
8
Approximations
and rounding
1.3
9
Limits of accuracy
1.3
10
Ratio
1.5
3
4
2.2
1.1
Core
content
Identify and use:
Extended
content
- natural numbers
- prime numbers
- square numbers
- common factors; find HCF
- common multiples; find LCM
- rational numbers
- irrational numbers
- real numbers
- Continue a number sequence
- Find the nth term of linear/quadratic/cubic sequence
Calculate:
- squares / square roots
- cubes / cube roots
- Use directed numbers in practical situations
- Use the language and notation of simple vulgar and
decimal fractions
- convert between simple vulgar and decimal fractions
- ordering quantities by magnitude
- know and use symbols =, ≠, <, >, ≤, ≥
- Use the standard form A x 10n
- Use the four rules for calculations
including:
- ordering of operations
- use of brackets
Makes estimates of:
- numbers
- quantities
- lengths
- Give approximations to specified number of:
- significant figures
- decimal places
- Give appropriate upper and lower bounds of data
given to a specified accuracy (e. g. measured length)
- Understand elementary idea and notation of ratio
- Divide a quantity in a given ratio
Find the HCF and LCM of two or more numbers
Represent sets using
- language
- Venn diagrams
- set notation
,, , U , , , , , 
- number of elements
- complement
- Exponential sequences
- Simple combinations of sequences
- Convert reccuring decimals to fractions
- Obtain appropriate upper and lower bouds to
solutions of simple problems (area, perimeter)
1
Syllabus
number
Topic
Lesson
number
10
Proportion, rate
1.5
5.3
11
Percentages
1.6
12
1.8
13
Use of a
calculator
Measures
14
Time
1.7
15
Money
1.5
16
Personal and
household
finance
1.6
17
Graphs in
practical
situations
7.1
7.7
7.8
18
Linear functions
7.2
7.3
7.4
7.6
3.1
3.5
Core
content
Extended
content
- Understand: - direct proportion
- inverse proportion
- common measures of rate
- map scales
- Calculate average speed
- Calculate percentage of a quantity
- Express one quantity as a percentage of another
- Calculate percentage increase/ decrease
- Use an electronic calculator efficiently
- apply appropriate checks of accuracy
Use (in practical situations) units of
- mass
- length
- area
- volume
- capacity
Express quantities in terms of larger or smaller units
Calculate times in terms of the
- 24-hour clock
- 12-hour clock
Read - clocks; - dials
- timetables
- Calculate using money
- Convert from one currency to another
- Express, in algebraic terms:
- direct variation
- inverse variation
- Increase/ decrease a quantity by a given ratio
- simple interest
- compound interest
- discount
- profit and loss
- Cartesian co-ordinates
- travel graphs
- conversion graphs
- drawing graphs from given data
- construct tables of values
- draw graphs
- interpret graphs
- find the gradient of a straight line graph
- solve linear equations approximately by graphical
method
- reverse percentages
(finding the cost price given the selling price and
percentage profit)
2
- Compound interest formula
- Exponential growth and decay in relation to
population and finance
- distance-time graphs
- speed-time graphs
- acceleration
- deceleration
- distance travelled (as an area under a graph)
Syllabus
number
Topic
Lesson
number
18
Quadratic
functions
7.1
7.5
2.10
2.11
18
Exponential
functions
5.4
7.1
7.5
Core
content
Extended
content
- construct tables of values
- draw graphs
- interpret graphs
- solve quadratic equations approximately by graphical
method
19
Straight line
graphs
7.3
7.4
- 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
20
Algebraic
representation
Formulae
- use letters to express generalised numbers
- express basic arithmetic processes algebraically
- substitute numbers for words and letters in formulae
21
Algebraic
manipulation
22
Functions
2.3
2.4
2.3
5.2
2.4
2.9
5.1
5.2
8.6
23
Indices
5.4
Use and interpret
24
Solutions of
equations and
inequalities
2.5
2.6
2.7
2.8
Solve
Linear
programming
5.6
20
25
- manipulate directed numbers
- use brackets
- extract common factors
- positive indices
- negative indices
- zero indices
- simple linear equations
- simultaneous equations (two unknowns)
- construct tables of values and draw graphs for
functions
axn, aєR, n є {−2, −1, 0, 1, 2, 3}
- draw tangent to estimate gradient of curve
- solve associated equations approximately by
graphical method
- calculate the gradient from the 2 points on a
straight line
- calculate the length of a segment
- calculate the co-ordinates of midpoints
- find the gradient of parallel and perpendicular lines
Construct and transform more complicated
equations
Construct and transform more complicated formulae
- expand products of algebraic expressions
- factorise more complicated expressions
- manipulate algebraic fractions
- factorise and simplify expressions
- Use function notation
- describe inverse function
- form composite functions
- The meaning and rules of indices
- Use and interpret fractional indices
- Solve simple exponential equation
Solve quadratic equations by:
- factorisation
- completing the square
- use of the formula
Solve simple linear inequalities
Represent inequalities graphically
Solve simple linear programming problems
- broken line for strict inequalities
- shading unwanted region
3
Syllabus
number
Topic
Lesson
number
Core
content
Extended
content
- relationships between:
- areas of similar triangles
- areas of similar figures
- surface areas of similar solids
- volumes of similar solids
- lengths of similar figures
26
Geometrical
terms and
relationships
4.1
4.4
Use and interpret terms:
- point
- line
- parallel
- bearing
26
Geometrical
terms and
relationships
4.1
3.1
4.7
27
Geometrical
constructions
4.6
28
Symmetry
4.3
Use and interpret terms:
- right/ acute/ obtuse angle
- reflex angle
- perpendicular
- similarity
Vocabulary of
- triangles
- quadrilaterals
- circles
- polygons
- simple solid figures (and nets)
Measure
- lines
- angles
Construct simple geometrical figures using:
- ruler
- pair of compasses
- protractor
Construct
- angle bisectors
- perpendicular bisectors
Read and make scale drawings
Recognise symmetry in two dimensions:
- rotational symmetry (including its order)
- line symmetry
4
Recognise symmetry properties of prism (including
cylinder)
Use the symmetry properties of circle:
- equal chords are equidistant from the
centre
- perpendicular bisector of a chord passes
through centre
- tangents from an external point are equal
in length
Syllabus
number
29
Topic
Angle properties
Lesson
number
4.1
4.5
30
Locus
4.6
31
Mensuration
3.1
3.2
3.3
3.4
3.5
3.6
32
Trigonometry
35
Vectors
4.2
6.1
6.2
6.3
6.4
6.5
6.6
8.3
8.4
8.5
Core
content
Extended
content
Calculate unknown angles using angle(s):
- at a point
- at a point on a straight line and intersecting
lines
- formed within parallel lines
- properties of - triangles
- quadrilaterals
- polygons
- in a semi-circle
- between tangent and radius
Using the following loci:
- at a given distance from
- a given point
- a given straight line
- equidistant from
- 2 given points
- 2 intersecting lines
Calculating the perimeter and area of
- triangle
- rectangle
- parallelogram
- trapezium
- circle (circumference)
Calculating the volume and surface area of a:
- cuboid
- prism
- cylinder
- Pythagoras’ theorem
- Calculate the side or an angle using ratios for acute
angles:
- sine
- cosine
- tangent
(angles in degrees and decimals to 1 dp)
Describe a translation by using vector
- add and subtract vectors
- multiply a vector by a scalar
Use the following geometrical properties:
- Angle properties of irregular polygons
- Angle at the centre of a circle is twice the angle at
the circumference
- Angles in the same segment are equal
- Angles in opposite segments are supplementary
- Cyclic quadrilaterals
5
Solve problems involving
- the arc length
- sector area
- surface area and volume of a
- sphere
- pyramid
- cone
Solving problems that include:
- angles of elevation
- angles of depression
- sine rule
- cosine rule
- formula for the area of a triangle
- 3D: angle between a line and a plane
- calculate the magnitude
- represent vectors by directed line segments
- use position vectors
- use the sum and difference of 2 vectors to express
given vectors
Syllabus
number
33
Topic
Statistics
34
Probability
36
Matrices
37
Transformations
Lesson
number
10.1
10.2
10.3
10.4
10.5
10.6
9.1
9.2
9.3
9.4
9.5
Core
content
Extended
content
- Collect, classify and tabulate data
- Read, interpret and draw simple inferences from
tables and diagrams
- Construct and use:
- bar charts
- pie charts
- pictograms
- frequency distribution
- histograms (equal intervals)
- scatter graphs (line of best fit)
Understand correlation
Calculate the: - mean
- median
- mode
- range
Calculate the probability of a single event
Use the probability scale from 0 to 1
Probability of an event not happening
Construct and read
- histograms with
- equal intervals
- unequal intervals
- cumulative frequency diagrams
Estimate and interpret:
- the median
- percentiles
- quartiles
- inter-quartile range
- mean of the - grouped data
- continuous data
Identify the modal class from a grouped frequency
distribution
Reflect simple plane figures in
- horizontal line
- vertical line
Rotate simple plane figures
-about: - the origin
- vertices
- midpoints of edges
- through multiples of 90o
Construct given
- translations
- enlargements
Calculate the probability of combined events using:
- possibility diagrams
- tree diagrams
- display information in a form of a matrix
Calculate
- the sum of two matrices
- the product of two matrices
- the product of a matrix and a scalar
- the determinant
- the inverse matrix
Use the following transformations of a plane:
- reflection (M)
- rotation (R)
- translation (T)
- enlargement (E)
- and their combinations
Identify and give precise description of
transformations connecting given figures
Describe transformations using:
- coordinates
- matrices
6