**Surds and Indices **

Students will understand and use the laws of indices for all rational exponents; use and manipulate surds, including rationalising the denominator. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.

**Algebra and Functions **

Students will learn about quadratic functions and their graphs including the discriminant of a quadratic function, completing the square; solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation; solve linear and quadratic inequalities in a single variable and interpret such inequalities graphically; manipulate polynomials algebraically, including expanding brackets and collecting like terms, factorisation and simple algebraic division; use of the factor theorem. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.

**Graph Transformations **

Students will understand the effect of simple transformations on the graph of y = f(x) including sketching associated graphs: y = af(x), y = f(x) + a, y = f(x + a) and y = f(ax). Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.

**Differentiation **

Students will understand and use the derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a general point (x, y); the gradient of the tangent as a limit; interpretation as a rate of change; sketching the gradient function for a given curve; differentiation from first principles for small positive integer powers of x; understand and use the second derivative as the rate of change of gradient; differentiate constant multiples, sums and differences, apply differentiation to find gradients, tangents and normals, maxima and minima and stationary points and identify where functions are increasing or decreasing. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.

**Binomial Expansion**

Students will understand and use the binomial expansion of (a + bx)^n for positive integer n; the notations n! and nCr; link to binomial probabilities. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.

**Statistics and Probability **

Students will use samples to make informal inferences about the population; understand and use sampling techniques; interpret diagrams for single-variable data; interpret scatter diagrams and regression lines for bivariate data; interpret measures of central tendency and variation; be able to calculate standard deviation; understand and use mutually exclusive and independent events when calculating probabilities and link to discrete and continuous distributions; understand and use simple, discrete probability distributions including the binomial distribution; calculate probabilities using the binomial distribution; understand and apply the language of statistical hypothesis testing, null hypothesis, alternative hypothesis, significance level, test statistic, 1-tail test, 2-tail test, critical value, critical region, acceptance region, p-value; conduct a statistical hypothesis test for the proportion in the binomial distribution and interpret the results in context and 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. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.

**Proof **

Students will understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof, including proof by deduction, proof by exhaustion and disproof by counter example; proof by contradiction (including proof of the irrationality of surds and the infinity of primes, and application to unfamiliar proofs). Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.

**Binomial Expansion **

Students will be familiar with, and be able to use, the binomial expansion of (1 + x)^n. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.

**Sequences and Series **

Students will work with sequences including those given by a formula for the nth term, increasing sequences, decreasing sequences, periodic sequences; understand and use sigma notation for sums of series; understand and work with arithmetic sequences and series, including the formulae for nth term and the sum to n terms; understand and work with geometric sequences and series including the formulae for the nth term and the sum of a finite geometric series; the sum to infinity of a convergent geometric series, including the use of |r| < 1; modulus notation and use sequences and series in modelling. Assessment will be via continuous scrutiny of class and homework, coupled with an end of module test.