(This is an on demand course. Once there are sufficient number of free registrations indicating the need of this course, detailed course material for each month will be published at a rate of US$19.00 per month for interested participants. Group registration discounts are available. Please contact us at [email protected])

1: Numbers and the number system

1.1 Integers

A understand and use integers (positive,negative and zero)
B understand place value
C use directed numbers in practical situations
D order integers
E use the four rules of addition, subtraction, multiplication and division
F use brackets and the hierarchy of operations
G use the terms ‘odd’, ‘even’, ’prime numbers’,‘factors’ and ‘multiples’
H identify prime factors, common factors and common multiples

1.2 Fractions

A understand and use equivalent fractions, simplifying a fraction by cancelling common factors
B understand and use mixed numbers and vulgar fractions
C identify common denominators
D order fractions and calculate a given fraction of a given quantity
E express a given number as a fraction of another number
F use common denominators to add and subtract fractions and mixed numbers
G convert a fraction to a decimal or a percentage
H understand and use unit fractions as multiplicative inverses
I multiply and divide fractions and mixed numbers

1.3 Decimals

A use decimal notation
B understand place value
C order decimals
D convert a decimal to a fraction or a percentage
E recognise that a terminating decimal is a fraction

1.4 Powers and roots

A identify square numbers and cube numbers
B calculate squares, square roots, cubes and cube roots
C use index notation and index laws for multiplication and division of positive and negative integer powers including zero
D express integers as a product of powers of prime factors
E find highest common factors (HCF) and lowest common multiples (LCM)

1.5 Set language and notation

A understand the definition of a set
B use the set notation ∪, ∩ and ∈ and ∉
C understand the concept of the universal set and the empty set and the symbols for these sets
D understand and use the complement of a set
E use Venn diagrams to represent sets

1.6 Percentages

A understand that ‘percentage’ means ‘number of parts per 100’
B express a given number as a percentage of another number
C express a percentage as a fraction and as a decimal
D understand the multiplicative nature of percentages as operators
E solve simple percentage problems, including percentage increase and decrease
F use reverse percentages
G use compound interest and depreciation

1.7 Ratio and proportion

A use ratio notation, including reduction to its simplest form and its various links to fraction notation
B divide a quantity in a given ratio or ratios
C use the process of proportionality to evaluate unknown quantities
D calculate an unknown quantity from quantities that vary in direct proportion
E solve word problems about ratio and proportion

1.8 Degree of accuracy

A round integers to a given power of 10
B round to a given number of significant figures or decimal places
C identify upper and lower bounds where values are given to a degree of accuracy
D use estimation to evaluate approximations to numerical calculations

1.9 Standard form

A calculate with and interpret numbers in the form a × 10^n where n is an integer
and 1 <= a < 10

1.10 Applying number

A use and apply number in everyday personal, domestic or community life
B carry out calculations using standard units of mass, length, area, volume and capacity
C understand and carry out calculations using time, and carry out calculations using money, including converting between currencies

1.11 Electronic calculators

A use a scientific electronic calculator to determine numerical results

2: Equations, formulae and identities
3: Sequences, functions and graphs
4: Geometry and trigonometry
5: Vectors and transformation geometry
6: Statistics and probability