Forming and evaluating expressions
Algebraic terms and operations
Expanding brackets and binomials
Factorising common factors
Algebraic fraction products
Algebraic fraction sums
Index laws: products and quotients
Index laws and zero powers
Negative and combined indices
Scientific notation and significant figures
Exponential growth, decay and interest
Applied logarithmic scales
Algorithms and data structures
Identify the terms, constant term and coefficients of an algebraic expression Translate a word statement into an algebraic expression with the correct operation, order and grouping Evaluate an algebraic expression by substituting exact values Signed numbers Substitute known values into a formula and evaluate it correctly Order of operations with integers Recognise like terms by matching pronumeral factors and powers exactly Collect like terms by adding or subtracting their signed coefficients Multiply and divide algebraic terms, combining coefficients and pronumeral powers separately Multiplication and division Simplify a fraction Expand a single bracket by the distributive law, preserving every sign Remove brackets in an expression and collect like terms Expand a product of two binomials by distributing both terms and collecting like terms Factorise by removing the highest common numerical and algebraic factor from every term Factorise by taking out a repeated binomial factor from two term groups Highest common factor Simplify an algebraic fraction by factorising and cancelling common factors only Multiply and divide algebraic fractions, cancelling common factors and using the reciprocal for division Multiply and divide fractions Add and subtract algebraic fractions by forming the lowest common denominator and collecting like terms Add and subtract fractions and mixed numbers Write repeated multiplication in index form and evaluate small positive integer powers Simplify products and quotients of powers with the same base by adding or subtracting indices Powers and roots of perfect powers Apply index laws 3 to 5: power of a power, of a product and of a quotient, distributing the outer index Evaluate the zero power of a nonzero base and distinguish c × a⁰ from (c × a)⁰ Rewrite negative indices as reciprocals with positive indices, without moving factors that do not carry the negative index Simplify a product, quotient or power combining index laws 1 to 5, the zero power and negative indices to a positive-index form Write a large or small number as a × 10ⁿ with 1 ≤ a < 10 Round to a stated number of significant figures Rounding Decimal place value Form a growth or decay rule A = A₀(1 ± r/100)^n from a described situation Substitute a whole-number period into an exponential rule and compute the amount, rounding once at the stated precision Use systematic trial and error on an exponential rule to find the period at which a quantity reaches a stated target Compound interest using A = P(1 + r/100)^n Percentage change as a multiplier Interpret positive quantities and equal ratios on logarithmic scales; compare small and large quantities and changes in applied contexts Implement, trace, test and explain algorithms using ordered lists