Summary wk/ Term Teacher A Maths Teacher B Maths Teacher C & D Further Maths (Each teacher deliveries core pure + 1 applied component) [Students study all core pure + both applied components] (Each teacher delivers core pure + 1 option) [Students study all core pure + 2 options] Y532 Stats Y533 Mech Y534 Discrete Y535 Add Pure 1/T1 2.02 a 1.02 a, b, c, d, e P & C 5.01 a Dim Analysis 6.01 a, b, d Graphs 7.02 a, b, c, g Number Theory 8.02 a, b, c, d 2/T1 2.01 a, b, c, d 1.01 a, b, c Applications of P & C 5.01 b Dim Analysis 6.01 c, e Graphs 7.02 d, e, p, q, r Number Theory 8.02 e, f, i, j, k 3/T1 1.03 a 1.04 a Proof by Induction 4.01 a The language of complex numbers 4.02 a, b, c 4/T1 1.03 b, c 1.02 m, n, o The language of Matrices 4.03 a, b, c Basic Operations with complex numbers (Radians) 4.02 e, f 5/T1 1.03 d, e, f 3.01 a, b 3.02 a, b Determinants and Inverses 4.03 h, j, l, m, n, o, p Solutions of equations 4.02 g, h, i, j 6/T1 1.10 a, c, d 3.02 c solutions of simultaneous equations 4.03 r Argand Diagrams and Loci 4.02 k, l, o, p
7/T1 1.10 e, f, g 3.02 d Chi Squared Contingency Tables 5.06 a Energy 6.02 d, e Mathematical Preliminaries 7.01 a, b, c Groups 8.03 a, b 8/T1 1.04 b, 2.03 a, b 1.07 a, b Fitting distributions 5.06 b, d (ratio and proportion) Energy 6.02 i Mathematical Preliminaries 7.01 d, e, f, g, I, k Groups 8.03 c, d 9/T1 2.04 a, b, c 1.07 c, d, e Probability Distributions 5.02 a, b, c Momentum 6.03 a, b Algorithms 7.03 a, b, c Groups 8.03 e, f 10/T1 1.02 p, q, r, w 1.07 g, i Binomial, Uniform and Geometric distributions 5.02 d, e, f, g, h Restitution 6.03 i, j Algorithms 7.03 j, l Groups 8.03 g, h 11/T1 1.02 f, j 1.07 m Linear Transformations using matrices 4.03 d, e, f Vectors 4.04 a, c, e, g 12/T1 1.02 g, h, i 1.07 n, o Invariance and scale factors 4.03 g, i, k, q Roots of equations 4.05 a, b
1/T2 2.02 b 3.03 a, f, g Fitting distributions 5.06 b, d (Bin, U and Geo) Resolving forces (preliminary work) Graphs 7.02 j, k Properties of groups 8.03 i 2/T2 2.02 c, d, e s 3.03 b, c, d, h Dependent and Independent Variables 5.09 a Impulse 6.03 e, f Network Algorithms 7.04 a Properties of sequences 8.01 a, b, h 3/T2 2.02 f, g 3.03 I, j, r Linear regression 5.09 b, c, d, e Restitution 6.03 i, j, k Network Algorithms 7.04 b, f Properties of sequences 8.01 c, d 4/T2 2.02 j Particles 3.03 k, n PMCC 5.08 a, b, c Work, Energy and Power 6.02 a, b, (i) Critical Path Analysis 7.05 a Fibonnaci and Solving relations 8.01 e, f 5/T2 1.06 a, b, c 1.05 a, b, c SRC 5.08 e, g Work, Energy and Power 6.02k, l, (i) Critical Path Analysis 7.05 b, c Vector product and scalar triple product 8.04 a, b, c, d
5/T3 1.03 g 3.01 c, 3.04 a, b Proof 4.01 b Exponential form of complex numbers and geometric effects 4.02 d, m 6/T3 1.03 h 3.04 c Solutions of equations and intersection of planes 4.03 s, t Euler’s formula and de Moivre’s theorem 4.02 n, q, r, s 7/T3 2.04 e, f 1.07 t Continous random variables 5.03 a Centre of Mass of symmetric lamina 6.04 a, b Arrangement and Selection problems 7.01 h, j Groups 8.03 j, k, l 8/T3 2.04 d, g, h 1.08 k Probability density functions 5.03 b, c, d Composite Rigid bodies 6.04 c principle 7.01 l Groups 8.03 m
1/T4 1.02 k, y 1.01 d Summation of series 4.06 a Further Vectors 4.04 b, d, f 2/T4 1.02 l, s, t 1.10 b Method of differences 4.06 b Further Vectors 4.04 h, i, j 3/T4 1.04 c 1.10 h, 3.02 e Cumulative distribution functions 5.03 e, f, Work in 2-D 6.02 c Efficiency and complexity of Algorithms 7.03 h, i, Scalar Vector 8.04 e 4/T4 Normal and Hypothesis 2.05 d 3.03 e, l Cumulative distribution functions 5.03 g Energy 6.02 f Strategies 7.03 k, m Surfaces 8.05 b 5/T4 2.05 e 3.03 m, o Random Variables 5.04 a Conservation of Energy 6.02 j Critical Path Analysis 7.05 d, e Stationary points 8.05 f 6/T4 1.07 f, p 3.03 p, q, s, t, u Normal Random Variables 5.04 b Power 6.02 m Critical Path Analysis 7.05 d, e Tangent planes 8.05 g
7/T4 1.07 q 1.08 f Polar Coordinates 4.09 a, b Hyperbolic functions 4.07 a, b 8/T4 1.07 r 1.08 g 1.09 f Area enclosed by polar curve 4.09 c Hyperbolic functions 4.07 c, d 9/T4 1.05 k. l, m 1.08 h 5.06 Chi Squared Tests 5.06 c Statics of solids 6.04 d, e Game Theory 7.08 d, f Second Order Recurrence Relation 8.01 g, i 10/T4 1.05 n, o, p, q two dimensions 3.02 e, h, i Differential Equations 4.10 a, c Volumes of solids of revolution 4.08 d 11/T4 1.09 g 3.02 i 2nd order homogeneous differential equations 4.10 d (real) Volumes of solids of revolution defined parametrically 4.08 d
Term 1 (AS and A Level) Week Ref Teacher A Ref Teacher B 1/T1 Prior knowledge GCSE review 12.03a Prior knowledge GCSE review 3.01c, 3.03b, 6.01f, 6.03b, 6.03c, 6.03d 2.02 a Large data Set and Sampling Be able to interpret tables and diagrams for single-variable data. 1.02 a 1.02 b 1.02 c 1.02 d 1.02 e Algebra and Functions Understand and be able to use the laws of indices for all rational exponents. Be able to use and manipulate surds, including rationalising the denominator. Be able to solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation. Be able to work with quadratic functions and their graphs, and the discriminant (D or) of a quadratic function, including the conditions for real and repeated roots. Be able to complete the square of the quadratic polynomial . Resource links Resource links
1.03 d 1.03 e 1.03 f Equations of Circles Understand and be able to use the coordinate geometry of a circle including using the equation of a circle in the form . Be able to complete the square to find the centre and radius of a circle. Be able to use the following circle properties in the context of problems in coordinate geometry: 1. the angle in a semicircle is a right angle, 2. the perpendicular from the centre of a circle to a chord bisects the chord, 3. the radius of a circle at a given point on its circumference is perpendicular to the tangent to the circle at that point. 3.01 a 3.01 b 3.02 a 3.02 b Units and Kinematics Understand and be able to use the fundamental quantities and units in the S.I. system: length (in metres), time (in seconds), mass (in kilograms). Understand and be able to use derived quantities and units: velocity (m/s or ms-1), acceleration (m/s2 or ms-2), force (N), weight (N). Understand and be able to use the language of kinematics: position, displacement, distance, distance travelled, velocity, speed, acceleration, equation of motion. Understand, use and interpret graphs in kinematics for motion in a straight line. Resource links Resource links 6/T1 Prior knowledge GCSE review 9.03a, 9.03b Prior knowledge GCSE review 7.04b, 7.04c
1.10 e 1.10 f 1.10 g Vectors 2 Understand and be able to use position vectors. Be able to calculate the distance between two points represented by position vectors. Be able to use vectors to solve problems in pure mathematics and in context, including forces. 3.02 d Suvat Understand, use and derive the formulae for constant acceleration for motion in a straight line: Resource links Resource links 8/T1 Prior knowledge GCSE review 11.01d, 11.02a, 11.02c, 11.02d, 11.02e Prior knowledge GCSE review 7.02a, 7.02b, 7.04b
1.02 h 1.02 i inequalities graphically, including inequalities with brackets and fractions. Be able to express solutions through correct use of ‘and’ and ‘or’, or through set notation. Be able to represent linear and quadratic inequalities such as and graphically. 1.07 o Be able to identify where functions are increasing or decreasing. Resource links Resource links
2/T2 Prior knowledge GCSE review 12.03c Statistical Sampling 2.01 a Prior knowledge Suvat 3.02 d 2.02 c 2.02 d 2.02 e Bivariate Data Be able to interpret scatter diagrams and regression lines for bivariate data, including recognition of scatter diagrams which include distinct sections of the population. Be able to understand informal interpretation of correlation. Be able to understand that correlation does not imply causation. 3.03 b 3.03 c 3.03 d 3.03 h Newton’s Laws Understand and be able to use Newton’s first law. Understand and be able to use Newton’s second law () for motion in a straight line for bodies of constant mass moving under the action of constant forces. Understand and be able to use Newton’s second law () in simple cases of forces given as two dimensional vectors. Understand and be able to use Newton’s third law. Resource links Resource links
3/T2 Prior knowledge GCSE review 12.03a, b, d Prior knowledge Forces 3.03 f, g 2.02 f 2.02 g 2.02 h 2.02 i Average, spread and outliers Be able to calculate and interpret measures of central tendency and variation, including mean, median, mode, percentile, quartile, interquartile range, standard deviation and variance Be able to calculate mean and standard deviation from a list of data, from summary statistics or from a frequency distribution, using calculator statistical functions. Recognise and be able to interpret possible outliers in data sets and statistical diagrams. Be able to select or critique data presentation techniques in the context of a statistical problem. 3.03 i 3.03 j 3.03 r Equilibrium Understand and be able to use the concept of a normal reaction force. Be able to use the model of a ‘smooth’ contact and understand the limitations of the model. Understand the concept of a frictional force and be able to apply it in contexts where the force is given in vector or component form, or the magnitude and direction of the force are given Resource links Resource links
5/T2 Prior knowledge GCSE review 7.01d Indices 1.02 a Prior knowledge GCSE review 6.02d, 10.05b, 10.05d, 10.05e, 10.03a Surds 1.02 b 1.06 a 1.06 b 1.06 c Exponentials and Logarithms Know and use the function ax and its graph, where a is positive. Know and use the function ex and its graph. Know that the gradient of is equal to and hence understand why the exponential model is suitable in many applications. Know and use the definition of (for ) as the inverse of (for all ), where is positive. 1.05 a 1.05 b 1.05 c Trigonometry (in degrees) Understand and be able to use the definitions of sine, cosine and tangent for all arguments. Understand and be able to use the sine and cosine rules. Understand and be able to use the area of a triangle in the form . Resource links Resource links
10/T2 Prior knowledge Binomial Hypothesis Testing 2.05 b, c Prior knowledge Constant Acceleration 3.02 d 2.05 c Inference Understand that a sample is being used to make an inference about the population and appreciate that the significance level is the probability of incorrectly rejecting the null hypothesis. 3.02 d 3.02 f Variable Acceleration derive the constant acceleration formulae using a variety of calculus techniques: by integration, e.g. . Be able to use differentiation and integration with respect to time in one dimension to solve simple problems concerning the displacement, velocity and acceleration of a particle Resource links Resource links
2/T3 Prior knowledge Algebra and Functions 1.02 j, w Differentiation 1.07 a, d Integration 1.08 a Prior knowledge Trigonometry 1.05 f, j 1.02 u 1.02 v 1.02 x Algebra and functions Understand and be able to use the definition of a function. Understand and be able to use inverse functions and their graphs, and composite functions. Know the condition for the inverse function to exist and be able to find the inverse of a function either graphically, by reflection in the line , or algebraically. Understand the effect of combinations of transformations on the graph of including sketching associated graphs, describing transformations and finding relevant equations. 1.05 g 1.05 h 1.05 i 1.05 k 1.05 o Radians and Trigonometry Know and be able to use exact values of and for and multiples thereof, and exact values of for and multiples thereof. Understand and be able to use the definitions of secant (), cosecant () and cotangent () and of , and and their relationships to , and respectively. Understand the graphs of the functions given in 1.05h, their ranges and domains. Understand and be able to use and . Be able to solve simple trigonometric equations in a given interval, including quadratic equations in , and and equations involving multiples of the unknown angle. Resource links Resource links 3/T3 Prior knowledge Prior knowledge
Binomial Expansion 1.04 a GCSE review 6.03e Polynomials 1.02 j, q 1.04 c 1.04 d 1.04 e 1.04 f 1.04 g Series and Sequences Be able to extend the binomial expansion of to any rational , including its use for approximation. Know that the expansion is valid for . Be able to work with sequences including those given by a formula for the term and those generated by a simple relation of the form . Understand the meaning of and work with increasing sequences, decreasing sequences and periodic sequences. Understand and be able to use sigma notation for sums of series. 1.09 a 1.09 b 1.09 c Numerical Methods Be able to locate roots of by considering changes of sign of in an interval of on which is sufficiently well-behaved. Understand how change of sign methods can fail. Be able to solve equations approximately using simple iterative methods and be able to draw associated cobweb and staircase diagrams. Resource links Resource links 4/T3 Prior knowledge Series and Sequences 1.04 e, f, g Prior knowledge Polynomials 1.02 q
Forces 3.03 b, 3.03 h 1.03 g Parametric form Understand and be able to use the parametric equations of curves and be able to convert between cartesian and parametric forms. 3.01 c 3.04 a 3.04 b Moments Understand and be able to use the unit for moment (N m). Be able to calculate the moment of a force about an axis through a point in the plane of the body. Understand that when a rigid body is in equilibrium the resultant moment is zero and the resultant force is zero. Resource links Resource links 6/T3 Prior knowledge Parametric form 1.03 g Prior knowledge Moments 3.04 a, b
1/T4 Prior knowledge Polynomials 1.02 j Prior knowledge Proof 1.01 a 1.02 k 1.02 y Partial Fractions Be able to simplify rational expressions. Be able to decompose rational functions into partial fractions (denominators not more complicated than squared linear terms and with no more than 3 terms, numerators constant or linear). 1.01 d Proof by contradiction Understand and be able to use proof by contradiction. Resource links Resource links 2/T4 Prior knowledge Proof 1.01 b Prior knowledge Vectors 1.10 a
Constant Acceleration 3.02 d 1.04 c Binomial Expansion Be able to extend the binomial expansion of to any rational n, including its use for approximation 1.10 h 3.02 e Further Vectors and Kinematics Be able to use vectors to solve problems in kinematics. Be able to extend the constant acceleration formulae to motion in two dimensions using vectors. Resource links Resource links 4/T4 Prior knowledge Measures of average and spread 2.02 f Prior knowledge Newton’s second law 3.03 c, d
Differentiation 1.07 i, j, k, l, q Definite Integrals 1.08 d 1.07 r Chain Rule Be able to differentiate using the chain rule, including problems involving connected rates of change and inverse functions. 1.08 g 1.09 f Integration as a limit of a sum Understand and be able to use integration as the limit of a sum. Understand and be able to use numerical integration of functions, including the use of the trapezium rule, and estimating the approximate area under a curve and the limits that it must lie between. Resource links Resource links 9/T4 Prior knowledge Trigonometry Identities 1.05 j Prior knowledge Chain Rule 1.07 r
Vectors 1.10 c 1.05 n 1.05 o 1.05 p 1.05 q Trigonometry Identities Understand and be able to use expressions for in the equivalent forms of or . Extend their knowledge of trigonometric equations to include radians and the trigonometric identities in Stage 2. Be able to construct proofs involving trigonometric functions and identities. Be able to use trigonometric functions to solve problems in context, including problems involving vectors, kinematics and forces. 3.02 e 3.02 h 3.02 i Motion in two dimensions Be able to extend the constant acceleration formulae to motion in two dimensions using vectors. Be able to model motion under gravity in a vertical plane using vectors where or . Be able to model the motion of a projectile as a particle moving with constant acceleration and understand the limitation of this model. Resource links Resource links 11/T4 Prior knowledge Numerical Methods 1.09 a, b, c, d, e, f Prior knowledge Constant acceleration 3.02 d
2/T5 Prior knowledge Language of Hypothesis Testing 2.05 a Pearson Product Moment Correlation 2.05 f Prior knowledge Graphs of Trigonometric functions 1.05 f, g Differentiation from first principles 1.07 g 2.05 g Hypothesis Testing and Correlation Use and be able to interpret Pearson's correlation coefficient in hypothesis tests, using either a given critical value or a and a table of critical values. When using Pearson's coefficient in an hypothesis test, the data may be assumed to come from a bivariate normal distribution. 1.07 h 1.07 k (1.07 q) (1.07 r) Trigonometrical Calculus Be able to show differentiation from first principles for and . Be able to differentiate , , and related sums, differences and constant multiples. Differentiate trigonometric functions using the product rule and the quotient rule. Differentiate trigonometric functions using the chain rule. Resource links Resource links
4/T5 Prior knowledge Parametric equations 1.03 g Prior knowledge Frictional forces 3.03 r, s, t, u, v 1.08 f Integration of parametric functions Be able to use a definite integral to find the area between two curves defined parametrically 3.03 v Further Kinematics Understand and be able to solve problems regarding the motion of a body on a rough surface. Resource links Resource links
6/T5 Prior knowledge Differentiation 1.07 i Integration 1.08 d Prior knowledge Polynomials 1.02 j 1.07 t 1.08 k 1.08 l Further Differential equations Be able to construct simple differential equations in pure mathematics and in context (contexts may include kinematics, population growth and modelling the relationship between price and demand) Be able to evaluate the analytical solution of simple first order differential equations with separable variables, including finding particular solutions. Be able to interpret the solution of a differential equation in the context of solving a problem, including identifying limitations of the solution. 1.03 g 1.03 h 1.07 s 1.08 f Further Parametrics Understand and be able to use the parametric equations of curves and be able to convert between cartesian and parametric forms. Be able to use parametric equations in modelling in a variety of contexts. Be able to differentiate simple functions and relations defined implicitly or parametrically for the first derivative only. Be able to use a definite integral to find the area between two curves. Resource links Resource links