1. Number and Calculation
1.1 Irrational Numbers
●​ Differentiate between rational and irrational numbers by checking if a number cannot
be written as a fraction.
●​ Estimate square/cube roots using approximation techniques.
1.2 Standard Form
●​ Convert numbers into the form a × 10ⁿ by adjusting the decimal point.
1.3 Indices
●​ Apply index laws:
○​ Multiplication: aᵐ × aⁿ = aᵐ⁺ⁿ
○​ Division: aᵐ ÷ aⁿ = aᵐ⁻ⁿ
○​ Power of a Power: (aᵐ)ⁿ = aᵐˣⁿ
○​ Zero Index: a⁰ = 1
○​ Negative Index: a⁻ⁿ = 1 / aⁿ
2. Expressions and Formulae
2.1 Substituting into Expressions
●​ Replace variables with given values and follow BIDMAS (Brackets, Indices,
Division/Multiplication, Addition/Subtraction).
2.2 Constructing Expressions
●​ Write algebraic expressions using variables based on given situations or word
problems.
2.3 Expressions and Indices
●​ Simplify expressions containing indices using exponent laws.
2.4 Expanding the Product of Two Linear Expressions
●​ Use the distributive property:​
(a + b)(c + d) = ac + ad + bc + bd
2.5 Simplifying Algebraic Fractions
●​ Factorise numerators and denominators, then cancel out common terms.