## Order of topics

Autumn term 1Functions and equations- Terminology: mapping, domain, range, image, natural numbers, integers, rational numbers and real numbers. - Composite function - Inverse function Transformation of graphs- Translation - Stretch - Reflections in the axes - Composite transformations The quadratic function- The properties of the graph of a quadratic - Solving quadratics, including factorising, completing the square and the quadratic formula - Discriminant Rational functions- Reciprocal - The graph of a rational function - Asymptotes Trigonometry- Sine and cosine rules - Area of a triangle using sine - Straight lines through the origin Spring term 1Algebra- Arithmetic sequences and series - Sum of finite arithmetic series - Geometric sequences and series - Sum of finite geometric series - Sigma notation. - Sum of infinite geometric series. Calculus- Limit and convergence. - Limit notation - Differentiation from first principles - Gradient function and as rate of change. - Finding equations of tangents and normals. - Differentiate x^n, e^x, lnx and trigonometric functions - The second derivative - Chain, Product and Quotient Rules - Nature of stationary points - Applications of calculus including Kinematics problems Summer term 1Statistics- Population sample, random sample and frequency distribution of discrete and continuous data. - Frequency tables & diagrams, frequency histograms with equal class intervals, box & whisker plots, stem & leaf - Outliers - Grouped data; mid- interval values; interval width; upper and lower interval boundaries. - Frequency histograms - Central tendancy: mean, median, mode, quartiles, percentiles. - Range; interquartile range, variance; standard deviation - Cumulative frequency |
Autumn term 2Radians - Radian measure of angles - Length of an arc - Area of a sector Circular functions- sine and cosine of an angle in terms of the unit circle - Defining tan in terms of sine and cosine - Special angles values of sine, cosine and tan - Double angle formulae - Trigonometric identities - Period and amplitude of sinx, cosx and tanx Spring term 1Trigonometry- Double-angle formulae - Solving trigonometric equations, including quadratics in trigonometric funtions Algebra- Binomial expansion Summer term 1Probability- Trial and outcome - The probability of an event - The complementary events A and A’ (not A ) - Probabilities add to 1 - Combined events - Mutually exclusive events - Conditional probability - Independent events - Venn diagrams - Tree diagrams Calculus- Integration as the reverse of differentiation- Definite integrals. |