Pre U A level Course
Outline (Year 12)
TERM 1A / Teacher A (3 lessons)Wk / No. / Topic / Content /
T
1 / 2 / Algebra / 1 /Indices
/
2 / 2 /Polynomials Add, subtract, times and divide
2 / 3 / Factor and Remainder Theorem / 1 / Factor Theorem2 / Remainder Theorem /
4 / 6 / Sequences and Series / 1 / Summation Notation
2 / Recurrence relations
3 / APs /
4 / GPs /
6 / 6 / Coordinate Geometry / 1 / Line segments
2 / The equation of a straight line /
3 / The equation of a circle /
H/T / Revision Task – Half Term Assessment
(all topics from term 1A)
TERM 1A / Teacher B (2 lessons)
Wk / No. / Topic / Content /
T
1 / 1 / Notation and Surds / 1 /Notation (Reals etc)
1 / 2 / Surds / 2 / Quadratics / 3 / Graphing, completing the square, factorising and using the formula to determine roots and properties
1 / 4 / Quadratic inequalities
2 / 4 / b2 – 4ac and determination of roots /
4 / 2 / Algebraic Fractions / 1 / Add, Subtract, Times and Divide /
5 / 2 / Simultaneous equations / 1 / Linear and quadratic, relationship to graphical solutions /
7 / 3 / Permutations and Combinations / 1 / Arrangements, factorial notation
2 / nPr
3 / nCr /
TERM 1B / Teacher A (3 lessons)
Wk / No. / Topic / Content /
T
1 / 3 / Partial Fractions / 1 /Linear, quadratic and repeated linear
/
1 / 2 / Binomial Expansion / 1 /Positive Integer Powers
/ 2 / 1 / Differentiation I / 1 / Idea of a limiting sequence
1 / 2 / Differentiation from 1st principles – Newton’s rule
1 / 3 / Differentiation of sums, products and quotients by expansion
2 / 4 / Equations of tangents and normals /
2 / 5 / Locating of Maxima and Minima
1 / 6 / Idea of 2nd derivative /
5 / 1 / Integration I / 1 / As reverse of differentiation
1 / 2 / Definite and Indefinite integrals
2 / 3 / As Area under a curve/between curves /
7 /
TEST (2 lessons) All term 1 topics but not Trig II
TERM 1B / Teacher B (2 lessons)Wk / No. / Topic / Content / T
1 / 1 / Functions and Graphs / 1 /
Definition of a function
1 / 2 / Find the inverse function1 / 3 / Graph transformations
1 / 4 / Relationship between graphs of f and f-1 /
3 / 1 / Trigonometry I / 1 / Definitions of sin, cos, tan, sec, cosec, cot and associated graphs
1 / 2 / Exact values
3 / Definitions of inverse trig functions and graphs
2 / 4 / Sine and cosine rule, ½ absin C
2 / 5 / Solve trig equations of the nature sin(2x + 45) = ½ (linear in nature)
6 / 2 / 1 / Identities
2 / 2 / Solving equations in more than 1 trig function by using identities /
TERM 2A / Teacher A (3 lessons)
Wk / No. / Topic / Content /
T
1 / 1 / Exponentials and Logarithms / 1 /Understand that
ab = c loga c = b
2 / 2 / Understand the rules of log algebra and be able to solveax = b or ax < b
2 / 3 / Use logarithms to transform appropriate relationships into a linear form /
3 / 2 / Vectors / 1 /
Notation and geometric representation
3 / 2 / Vector equation of a line2 / 3 / Dot Product /
TERM 2A / Teacher B (2 lessons)
Wk / No. / Topic / Content / T
1 / 1 / Radians measure / 1 /
Definition
2 / 1 / Arc length and sector area formulae1 / 1 / Solving equations in radians /
3 / 2 / Differentiation II / 1 / Chain rule for polynomials
2 / 2 / Product rule for polynomials
2 / 3 / Quotient rule for polynomials
2 / 4 / Applications to max and min /
H/T / Revision Task – Half Term Assessment
(all topics from term 2A and Trig I from term 1b)
TERM 2B / Teacher A (3 lessons)
Wk / No. / Topic / Content /
T
1 / 1 / Kinematics and Motion / 1 / Vector and scalar quantities2 / 2 / Sketch and interpret s/t and v/t graphs
2 / 3 / ‘suvat’ equations for constant acceleration /
3 / 4 / Differentiation for non constant acceleration /
4 / 2 / Projectiles / 1 /
Model a particle under constant acceleration, understanding the limitations of the model
2 / 2 / Solve problems involving finding the velocity, maximum height and range2 / 3 / Derive and use a trajectory equation in Cartesian form to model a projectile /
6 / TEST (2 lessons) - all term 2 topics
TERM 2B / Teacher B (2 lessons)
Wk / No. / Topic / Content / T
1 / 1 / Trigonometry II / 1 / Derive the formulae for Sin(A±B) Cos(A±B) and Tan(A±B)
1 / 2 / Application to finding exact values for sin(135)
2 / 3 / Derivation of double angle formula for Cos2A, Sin2A and Tan2A and application to finding trigonometric identities and solving equations
2 / 4 / Use for solving writing Asinx + Bcosx in the form Rcos(x +a) or Rsin(x + a) and applications /
4 / 1 / ex and ln x / Introduce ex by using the property that
Look at graphs and properties of ex and ln x /
5 / 2 / Differentiation III / 2 / Differentiating trigonometric Functions: sinx, cosx and tanx.
Tie in with chain rule, product rule and quotient rule
2 / Differentiate ex and ln x using chain rule, product rule and quotient rule /
TERM 3A / Teacher A (3 lessons)
Wk / No. / Topic / Content /
T
3 / 3 / Forces and equilibrium / 1 / Understand the vector nature of a force and identify the different types of force that can be applied to a particle2 / 2 / Find and use force components to find the resultant of a system
3 / 3 / Solve problems for particles in equilibrium without friction a consideration /
4 / 2 / Integration II / eax+b, sin(ax+b), cos(ax+b) and sec2(ax+b) by inspection and reverse differentiation
2 / Substitution method introduced for things like (sin x)(cos2x) or
2 / Substitution method for things like /
TERM 3B / Teacher A (3 lessons)
Wk / No. / Topic / Content
1 / 6 / Revision
3 / TEST – Pure and Mechanics 2 lessons (all of Year 12)
TERM 3A / Teacher B (2 lessons)
Wk / No. / Topic / Content / T
1 / 1 / Differentiation IV / Relationship between
2 / Related rates of change /
2/3 / 1 / Analysis of Data / 1 /
Measures of central tendency: Mean, mode, median for all types of data
1 / 2 / Measures of spread: interquartile range and standard deviation for all types of data1 / 3 / Identify outliers using 1.5×IQR and skewness /
2 / 4 / Find linear regression lines for bivariate data
2 / 5 / Find product moment correlation for bivariate data /
TERM 3B / Teacher B (2 lessons)
Wk / No. / Topic / Content
1 / 6 / Revision
3 / TEST – Pure and Statistics 2 lessons (all of Year 12)
Pre U A level Course
Outline (Year 13)
TERM 4A / Teacher A (3 lessons)Wk / No. / Topic / Content /
T
1 / 1 / Friction / 1 /Understand that
2 / 2 /Be able to use friction in problems relating to equilibrium
2 / 3 / Be able to solve problems relating to limiting equilibrium / 3 / 2 / Newton’s Laws of Motion / 1 / Know that “RF = ma” and understand the implications of Newton’s 2nd law
2 / 2 / Solve Problems relating to constant acceleration that may or may not include friction on a flat surface or on a slope
2 / 3 / Solve Problems relating to connected particles being accelerated
1 / 4 / Look at “RF = ma” relates to movement in a lift /
H/T / Pre Mock Revision Paper
TERM 4A / Teacher B (2 lessons)
Wk / No. / Topic / Content /
T
1 / 1 / Probability / 1 / Single event2 / 2 / Tree diagrams for more than one event /
1 / 3 / Conditional Probability
2 / 3 / P(AB) = P(A) + P(B) – P(AB)
P(AB) = P(A)P(BA)
2 / 4 / Understand independent and mutually exclusive events /
5 / 1 / Complex Numbers / 1 / Definition and arithmetic
1 / 2 / Recognise that complex numbers have a unique real and imaginary part and plot them on an Argand Diagram
1 / 3 / Know the Fundamental Thm of Algebra
2 / 4 / Be able to solve quadratics and cubics with real coefficients /
H/T / Pre Mock Revision Paper
TERM 4B / Teacher A (3 lessons)
Wk / No. / Topic / Content /
T
1 / 1 / Momentum and Impulse / 1 /Be able to find the momentum of an object
2 / 2 / Use conservation of momentum to solve problems with 2 or 3 particles colliding2 / 3 / Use restitution to solve problems where energy is lost
1 / 4 / Impulse /
2 / Integration III / Revise Integration II
2 / Double angle formulae for integrating sin2x and other powers of trig functions
2 / Integration using
Partial Fractions
2 / Volume of Revolution /
6 /
MOCK EXAM
TERM 4B / Teacher B (2 lessons)Wk / No. / Topic / Content / T
1 / 1 / Modulus Function /
Know that:
1 /Be able to sketch graphs of functions containing a modulus sign
1 / Solve equations involving a modulus sign by considering graphs or by squaring / 2 / Discrete Random Variables /
Know what a Discrete Random Variable is and how to calculate E(X) and Var(X)
3 / Recognise a Binomial Distribution. Know E(X), Var(X) and be able to find probabilities including cumulative probabilities from a table / 2 / Recognise a Geometric Distribution. Know E(X), Var(X) and be able to find probabilities. /
MOCK EXAM
TERM 5A / Teacher A (3 lessons)
Wk / No. / Topic / Content /
T
1 / 2 / Implicit Equations / 1 /Understand that some equations are written implicitly and be able to sketch them
2 / 2 / Differentiate an equation written implicitly to find 1st and 2nd derivitives / 2/3 / 1 / Parametric Equations / 1 /
Understand what a parametric equation is and be able to sketch them
1 / 2 / Be able to convert between parametric and Cartesian forms2 / 3 / Differentiate a parametric equation to find 1st and 2nd derivitives /
4/5 / 2 / Differential Equations / 1 / Understand how to formulate a differential equation
2 / 2 / Be able to solve a differential equation by separating variables (and using initial conditions)
2 / 3 / Interpret the solution of a differential equation into a real life context. /
TERM 5A / Teacher B (2 lessons)
Wk / No. / Topic / Content / T
1 / 1 / Normal Distribution / 1 /
Understand the properties of a Normal distribution
2 / 2 / Calculate probabilities from a generalised Normal Distribution2 / 3 / Calculate the mean and/or sd of a Normal distribution given probabilities by working backwards /
4 / 1 / Numerical Methods / 1 / Understand how to use sign change on f(x) to locate an approximate solution to f(x) = 0
2 / 2 / Use x = g(X) and direct iteration to solve an equation. Interpret with cobweb diagrams and recognise that rate of convergence is related to gradient
2 / 3 / Understand and Apply-Newton Raphson
1 / 4 / Understand what is meant by the rate of convergence. /
TERM 5B / Teacher A (3 lessons)
Wk / No. / Topic / Content /
T
1 / 3 / Binomial Expansion for negative or fractional indices / 1 /Expansions
2 / ValidityRange / REVISION
TERM 5B / Teacher B (2 lessons)
Wk / No. / Topic / Content / T
REVISION
TERM 6A / Teacher A (3 lessons)
Wk / No. / Topic / Content /
T
REVISIONTERM 6A / Teacher B (2 lessons)
Wk / No. / Topic / Content / T
REVISION