# St Paul's School for Girls

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### Pure Mathematics

 Unit Title Estimated lessons Algebra and functions a Algebraic expressions – basic algebraic manipulation, indices and surds 3 b Quadratic functions – factorising, solving, graphs and the discriminants 4 c Equations – quadratic/linear simultaneous 4 d Inequalities – linear and quadratic (including graphical solutions) 5 e Graphs – cubic, quartic and reciprocal 5 f Transformations – transforming graphs – f(x) notation 5 2 Coordinate geometry in the (x, y) plane a Straight-line graphs, parallel/perpendicular, length and area problems 6 b Circles – equation of a circle, geometric problems on a grid 7 3 Further algebra a Algebraic division, factor theorem and proof 8 b The binomial expansion 7 4 Trigonometry a Trigonometric ratios and graphs 6 b Trigonometric identities and equations 10 5 Vectors (2D) a Definitions, magnitude/direction, addition and scalar multiplication 7 b Position vectors, distance between two points, geometric problems 7 6 Differentiation a Definition, differentiating polynomials, second derivatives 6 b Gradients, tangents, normals, maxima and minima 6 7 Integration a Definition as opposite of differentiation, indefinite integrals of xn 6 b Definite integrals and areas under curves 5 8 Exponentials and logarithms: Exponential functions and natural logarithms 12 120 hours

### Applied Mathematics - Mechanics and Statistics

 Unit Title Estimated hours Section A – Statistics 1 Statistical sampling a Introduction to sampling terminology; Advantages and disadvantages of sampling 1 b Understand and use sampling techniques; Compare sampling techniques in context 2 2 Data presentation and interpretation a Calculation and interpretation of measures of location; Calculation and interpretation of measures of variation; Understand and use coding 4 b Interpret diagrams for single-variable data; Interpret scatter diagrams and regression lines; Recognise and interpret outliers; Draw simple conclusions from statistical problems 8 3 Probability: Mutually exclusive events; Independent events 3 4 Statistical distributions: Use discrete distributions to model real-world situations; Identify the discrete uniform distribution; Calculate probabilities using the binomial distribution (calculator use expected) 5 5 Statistical hypothesis testing a Language of hypothesis testing; Significance levels 2 b Carry out hypothesis tests involving the binomial distribution 5 30 hours Section B – Mechanics 6 Quantities and units in mechanics a Introduction to mathematical modelling and standard S.I. units of length, time and mass 1 b Definitions of force, velocity, speed, acceleration and weight and displacement; Vector and scalar quantities 2 7 Kinematics 1 (constant acceleration) a Graphical representation of velocity, acceleration and displacement 4 b Motion in a straight line under constant acceleration; suvat formulae for constant acceleration; Vertical motion under gravity 6 8 Forces & Newton’s laws a Newton’s first law, force diagrams, equilibrium, introduction to i, j system 4 b Newton’s second law, ‘F = ma’, connected particles (no resolving forces or use of F = μR); Newton’s third law: equilibrium, problems involving smooth pulleys 6 9 Kinematics 2 (variable acceleration) a Variable force; Calculus to determine rates of change for kinematics 4 b Use of integration for kinematics problems i.e. 3 30 hours