Mathematics

Assessment

Year 12 HALF TERM 1 • Expand brackets (single, double, triple) • Collect like terms • Factorise linear, quadratic and simple cubic expressions • Laws of indices • Rules of surds • rationalise • solve quadratics • factorise • complete the square • quadratic formula • curve sketching • turning point • discriminant • modelling quadratics • simultaneous equations, linear and quadratics • inequalities, linear and quadratics HALF TERM 2 • sketch cubic, quartic, reciprocal • solve equations • translate, stretch, transform graphs • gradient • y = mx + c • points of intersection • parallel and perpendicular gradients • length and area problems • modelling HALF TERM 3 • midpoint • perpendicular bisector • equation of a circle • straight lines and circles • circle properties • angle in a semicircle • algebraic fractions • algebraic long division • algebraic proof • proof by exhaustion and disproof by counterexample • Pascal’s triangle • combinations and factorial notation • binomial expansion • approximations using the binomial expansion • cosine rule • sine rule • area of a triangle • graphs of the sine, cosine and tangent functions • Sketch simple transformations of these graphs HALF TERM 4 • Sin, cos, tan • exact trigonometric ratios for 30°, 45° and 60° • relationships tan θ = sinθ/cos θ and sin2θ + cos2θ = 1 • Solve simple trigonometric equations • sin (θ +- α) = k • 2D vectors • Column vectors • Magnitude and direction • Position vectors • Vector problems • vectors in speedand distance calculations • f’(x) or dy/dx • gradients, tangents and normal • increasing and decreasing functions • f ‘’(x) or d 2y/dx2 • stationary points • gradient function • modelling HALF TERM 5 • integrate term by term • definite integrals • bounded area • sketch and transform y = ax , y = ex • Differentiate ekx • laws of logarithms • solve equations using logs • natural logs • modelling Year 13 HALF TERM 1 • proof by contradiction • add, subtract, times, divide algebraic fractions • partial fractions with linear factors, repeated factors in denominator • algebraic long division • improper fractions • modulus function • mappings and functions • domain and range • composite function • inverse of a function • graphs of the modulus function 𝑦 = |𝑓(𝑥)| and 𝑦 = 𝑓(|𝑥|) • two (or more) transformations to the same curve • N-th term of an arithmetic and geometric • Sn • Sum to infinity • sigma notation • recurrence relations • Model HALF TERM 2 • (1 + 𝑥) 𝑛 • (𝑎 +𝑏𝑥) 𝑛 • Use partial fractions • Use radians, with trig graphs and their transformations • Exact values eg 30 = 𝜋 6 • Arc length • Sector area • Solve trig equations with radians • Trig approximations when Ɵ is small • Use sec, cosec, cot, and their graphs • Prove identities with sec, cosec, cot • Prove and use sec2 𝑥 ≡ 1 + tan2 𝑥 and cosec2 𝑥 ≡ 1 +cot2 𝑥 • inverse trigonometric functions and their domain and ranges • addition formulae • double-angle formulae • Solve trigonometric equations using the doubleangle and addition formulae • 𝑅 cos(𝜃 ±𝑎), 𝑅 sin(𝜃 ± 𝑎) • Prove trigonometric identities • Use trigonometric functions to model real-life situations HALF TERM 3 • parametric equations into Cartesian • parametric equations into Cartesian form using trigonometric identities • use parametric equations of curves • sketch parametric curves • Solve coordinate geometry problems • modelling Differentiation of/using • trigonometric functions • exponentials and logarithms • using the chain, product and quotient rules • parametric equations • implicit • second derivative connected rates of change differential equations HALF TERM 4 • Locate roots • Iteration • Newton Raphson • Numerical methods Integrate: • Trig functions • Exponentials • Using reverse chain rule • Using trig identities • By substitution • By parts • Using partial fractions • To find area under a curve Trapezium rule Solve differential equations, and model • 3D coordinates • Vectors in 3D • Solve problems with vectors • 3D motion