Grade 10

Apply the laws of exponents to integral exponents, simplify surds, show that square roots of non-perfect squares are irrational, and round irrational numbers to a given degree of accuracy.

Identify rational and irrational numbers, convert recurring decimals to fractions, recognise equations with no real solutions, and investigate linear number patterns to find general terms.

Solve linear equations and inequalities, quadratic equations by factorisation, and literal equations, applying inverse operations and algebraic reasoning to find unknown values.

Apply SOHCAHTOA to find missing sides and angles in right-angled triangles, extend trig functions to all four quadrants, interpret graphs of sin, cos and tan, and solve real-life 2D problems.

Understand the concept of a function, sketch and interpret linear, quadratic, hyperbolic and exponential functions, identify key features such as gradients, turning points and asymptotes, and solve problems using prescribed function types.

Revise similarity and congruence of triangles, investigate properties of special quadrilaterals, explore alternative definitions of polygons, and prove or disprove geometric conjectures using counter-examples and formal proofs.

Use the distance, gradient and midpoint formulae to find lengths, slopes and midpoints on the Cartesian plane, and apply these to prove properties of geometric figures.

Apply simple and compound interest formulae, solve for n using trial and improvement, explore simple decay, and calculate the implications of fluctuating foreign exchange rates.

Find the approximate mean and modal interval of grouped data, use a Casio fx-82 calculator for statistics, identify outliers, draw frequency polygons, and calculate range, quartiles and the interquartile range.

Find the volume and surface area of cylinders, cones, spheres and pyramids, calculate dimensions of combined solids, and solve problems involving missing dimensions by rearranging formulae.

Use relative frequency and theoretical probability, solve Venn diagram problems, apply mutually exclusive and complementary event rules, and use the general addition rule for combined probabilities.