Grade 9

Extend the laws of exponents to include negative (integer) exponents, write very small numbers in scientific notation using negative powers of 10, and solve calculations and real-life problems using all the laws of exponents.

Revise calculations with integers including squares, cubes, square roots and cube roots, apply commutative, associative and distributive properties, identify additive and multiplicative inverses, and solve multi-step real-life integer problems.

Apply all four operations with fractions and mixed numbers in multi-step problems, calculate squares, cubes, square roots and cube roots of common fractions, and solve real-life problems combining fractions, mixed numbers and percentages.

Apply multiple operations with decimal fractions using BODMAS, calculate squares, cubes and roots of decimal fractions in combined calculations, and solve multi-step real-life problems involving decimal fractions with appropriate rounding.

Solve direct and inverse proportion problems using equal ratios and constant products, calculate commission and rental costs, and apply compound interest to multi-year financial scenarios.

Investigate and extend numeric and geometric patterns represented algebraically, move between diagram, table and algebraic forms, and justify general rules using multi-step verification.

Determine input and output values using equations, interpret equivalent forms of a relationship expressed verbally, in tables, by equations and as graphs on the Cartesian plane, and generate tables of ordered pairs using substitution.

Multiply monomials by polynomials using the distributive law, divide polynomials by integers or monomials, and multiply two binomials using FOIL including the square of a binomial and the difference of two squares.

Factorise expressions using the highest common factor, apply the difference of two squares identity, factorise trinomials of the form ax² + bx + c, and simplify algebraic fractions by factorising the numerator and denominator.

Solve quadratic equations by factorisation, apply the zero product property to equations given in factorised form, and rearrange equations using common factor, difference of squares and trinomial factorisation methods.

Determine x-intercepts, y-intercepts and gradients of linear graphs, draw straight-line graphs from given equations using intercepts or a table of values, and determine the equation of a linear graph in the form y = mx + c.

Investigate minimum conditions for congruent triangles (SSS, SAS, AAS, RHS) and similar triangles (AA, SSS proportionality), and solve geometric problems involving unknown sides and angles using these conditions.

Identify and describe the properties of the five Platonic solids, verify Euler's formula (F + V − E = 2) for polyhedra, and classify and compare 3D objects including prisms, pyramids, cylinders, cones and spheres.

Revise and apply angle relationships including vertically opposite, supplementary and complementary angles, solve multi-step problems involving parallel lines cut by a transversal using corresponding, alternate and co-interior angle theorems, and justify angle calculations with geometric reasons.

Reflect points and figures in the line y=x, identify transformations from given image coordinates, and investigate coordinates of vertices after enlargement or reduction by a scale factor from the origin.

Investigate the exterior angle theorem by construction, explore the properties of diagonals in quadrilaterals, and confirm the sum of interior angles formula for any polygon by dividing it into triangles.

Solve problems using appropriate formulae and unit conversions for polygons and circles, investigate how doubling dimensions affects perimeter and area, and apply scale factor reasoning to real-life enlargement and reduction problems.

Calculate the volume and surface area of cylinders using formulae, solve real-life capacity problems with SI unit conversions, and investigate how scaling dimensions by a factor affects the volume of prisms and cylinders.

Apply the Theorem of Pythagoras to find unknown sides in right-angled triangles within geometric figures, solve multi-step real-life problems and use algebraic methods to find unknown lengths.

Organise data by multiple criteria, interpret and draw scatter plots to identify positive, negative and no correlation, and critically compare two data sets by analysing their central tendency and spread.

Use two-way tables and tree diagrams for compound events, calculate probability of combined outcomes, predict relative frequency and compare with theoretical probability to explain differences.