Algebra and Functions

Indices and Surds

be able to use and manipulate surds, including rationalising the denominator · understand and use the laws of indices for all rational exponents · be able to evaluate expressions involving surds and rational indices without a calculator

Quadratic Functions

be able to solve quadratic equations by factorising, by completing the square and by using the quadratic formula · be able to complete the square of a quadratic expression and use the result to sketch the graph and identify the vertex and line of symmetry · understand and use the discriminant b^2 - 4ac to determine the nature of the roots of a quadratic equation · be able to solve equations that can be reduced to a quadratic in a function of x (e.g. quadratic in x^2 or in sqrt(x))

Simultaneous Equations and InequalitiesSign up

be able to solve simultaneous equations in two unknowns (linear-linear and linear-quadratic) algebraically and graphically · be able to solve linear and quadratic inequalities, expressing solution sets using inequality and interval notation · understand how to represent linear and quadratic inequalities graphically, including regions defined by multiple inequalities

Polynomials and Algebraic ManipulationSign up

be able to manipulate polynomials algebraically, including expanding brackets, collecting like terms and simplifying rational expressions · be able to factorise quadratic and cubic polynomials, recognising standard forms such as the difference of two squares

Graphs and TransformationsSign up

be able to sketch graphs of quadratic, cubic, reciprocal and simple rational functions, identifying key features (intercepts, asymptotes, turning points) · understand the effect of the transformations y = f(x) + a, y = f(x + a), y = af(x) and y = f(ax) on the graph of y = f(x), and apply these to sketch transformed curves