Content

Term 1 Topic and Content:

Bridging the gap

This is a week intervention session focused on improving algebra skills from GCSE. It is an opportunity to set expectations and standards for an A Level class.

Sequences and Series

Working to generate sequences and decipher general expressions of sequences. Also, students will learn mathematical notations some the sum of a series. Finally, students will investigate convergent and divergent sequences and use the modulus function.

Data Collection

Students will be introduced to the large data set which will be tested on their final exam. Students will be able to understand the different forms and data collection and know the advantages and disadvantages.  

Data Processing, Presentation and Interpretation

Students now will be develop the skills to analyse data collected, through a variety of diagrams.  Students will have to know all key features of the diagrams used. Students will be expected to make comments on real world data.

Surds and Indices

Students will be able to use the laws of indices for all rational components. Students will be manipulating surds as well as rationalising.

Quadratic Functions

Students will be able to sketch quadratics, highlighting key points. Students will be using the discriminant including real and repeated roots. Students will be able to complete the square with values of a greater than 1 and be able to identity turning points.

Graphs and transformations

Students will be able to understand and sketch simple polynomials as well as transforming them using function notation.

Trigonometry

To be able to understand the definitions of sine, cosine and tangent. Using radian measure to calculate area of sectors and arc lengths. Understand the use of the trigonometric functions graphs, symmetries and periodicity. To know the exact values sine, cosine and tangent for 0, 30, 45, 60, 90.

Understand basic trigonometric identities. Solving trigonometric equations within a given range.

Equations and Inequalities

Solving pairs of simultaneous equations including when one is a quadratic. To be able solve inequalities putting the correct range in the set notation.

Polynomials

Manipulate polynomials algebraically, using factor theorem to simplify.

Term 2 Topic and Content:

The Binomial Expansion

Students will be able to use the binomial expansion 〖(a+bx)〗^n for positive integers of n; the notations n! and n∁r. 

Probability

Students will be able to understand the use of mutually exclusive and independent events when calculating probabilities. Students will be able to use conditional probabilities, including tree and Venn diagrams.

The binomial Distribution

Students will be able to understand and use the binomial distribution model to calculate probabilities for cumulative and probability distributions.

Coordinate Geometry

Students will understand the use of the equation of a straight line, including the forms y-y_1=m(x-x_1) and ax+by+c=0. To also know the gradient conditions for perpendicular and parallel lines.
Students will be able to use the equation of a circle 〖(x-a)〗^2+〖(y-b)〗^2=r

Differentiation

Students will understand the use of the derivative of f(x)as the gradient of the tangent to the graph of y = f(x) at a general point. Students will be able to interpret the rate of change; sketching the gradient function for a given curve; second derivatives; differentiating from first principle. Students will be able to apply differentiation to find gradients, tangents and normal, maxima and minim and stationary points.

Kinematics

Students will be introduced to the language of kinematics: position; displacement; distance travelled; velocity; speed; acceleration. Students will interpret kinematic graphs and derive the constant acceleration formulae.

Vectors

Students will use vectors in two and three dimensions. Students will be able to calculate the magnitude and direction of a vector and be adept at representing vectors in a variety of forms.
 
Forces and Laws of Motion

Students will be able to understand and use Newton’s first, second and third laws.

Term 3 Topic and Content:

Functions

Students will be able to understand composite and inverse functions.

Integration

Students will know and use the fundamental theorem of Calculus. Integrate x^n(excluding n = -1) and related sums. Evaluate definite integrals to find areas under a curve.

Statistical Hypothesis Testing

Students will be able to understand and apply the language of hypothesis testing through a binomial model; 1-tail test; 2 tail-test, critical value; critical region; acceptance region, p-value. Students will also conduct and interpret hypothesis tests.

Exponentials and Logarithms

To know the gradient e^kxis equal to 〖ke〗^kxand explain why the model has many suitable applications. To know the laws of logarithms. To be able to understand and use exponential growth and decay in modelling.
 
Variable Acceleration

To use calculus to solve problems of a particle travelling on a straight line.

Proof

To be able to know the structure of a proof with a worded conclusion. To know the following proofs:

•  Exhaustion
•  Contradiction
•  Algebraic

Term 1 Topic and Content:

Trigonometry

Students need to know the exact values of sine, cosine and tangent for {0,π/6,π/4,π/3,π/2,π}. To understand the small angle approximation.

Trigonometric Functions

Students will understand the definitions of secant, cosecant and cotangent and arcsine, arccosine and arctangent; identifying their graphs; their ranges and domains.

Trigonometric Identities

Students will understand and use the double angle formulae; use of formulae for sin(a±b),cos(a±b), tan (a±b). As well as constructing trigonometric proofs.

Probability

Students will understand the use conditional probabilities P(A│B)=  (P(A∩B))/(P(B)) as well as modelling and critiquing assumptions.

Probability Distributions

Understand and use the normal distribution as a model and find probabilities using the distribution. Select an appropriate probability distribution for a context, with appropriate reasoning, distinguishing between Normal and Binomial.

Algebra

Students will be able simplify rational expressions including by factorising and cancelling. Decompose rational functions into partial fractions.

Differentiation

Students can apply differentiation to find the points of inflection. Use differentiation using product, quotient and chain rule.

Further Differentiation

Students will be able to differentiate functions and relations defined implicitly for the first derivative.
 
Vectors

Use vectors in three dimensions and use the vectors to solve problems in kinematics.

Kinematics

Students use calculus in kinematics for motion in a straight line using 2D.
v=  dr/dt,a=  dv/dt=(d^2 r)/(dt^2 ),r=∫▒vdt,v=∫▒adt
Projectiles

Students will model motion under gravity in a vertical plane using vectors.

Term 2 Topic and Content:

Integration

Students will be able to integrate e^kx,1/x,sin⁡(kx),cos⁡(kx) and related sums, differences and constant multipliers. Use integration as the limit of a sum. Use integration by substitution and integration by parts.

Hypothesis Testing

Students will be able to conduct a statistical hypothesis test for a mean of a Normal distributions with known, given or assumed variance and interpret and results in context.

Forces and Motion

Students will understand and use Newton’s second law for motion in a straight line; also where forces need to be resolved. Students will solve problems involving smooth pulley.

Moments

Students will use moments in simple static contexts as.

Differential Equations

Students will be able to construct differential equations. Students will be able to evaluate the analytical solution. To be able to interpret the solution with any given context.

Friction

Students will need to understand and use Fr = µR  for rough surfaces and limiting surfaces.

Term 3 Topic and Content:

Parametric Equations

Students will use parametric equations of curves and conversion between Cartesian and parametric equations. Differentiate simple functions and relations defined parametrically.

Numerical Methods

Locate roots of f(x) = 0 by considering a change of sign and being able to understand how the methods fail. Solve using Newton-Raphson method and other recurrence relationship. To be able to use the trapezium rule and estimating the approximate area under a curve and the limits that lie between.