Algebra and Functions

Recognise and use expressions in expanded or factorised form.
Understand the process of expanding products of algebraic expressions, including multinomial products (like (a + b) (c + d)).
Apply understanding of indices to simplify and calculate the value of numerical expressions involving powers.
Apply the laws of indices for all rational exponents.
Use the concept of a function to express quantities varying one in terms of another.

Solve quadratic equations by factorising, completing the square and using the formula.
Factorise quadratic expressions, both simple and harder forms.
Interpret the solution(s) of a quadratic equation as the x-coordinate(s) of the point(s) of intersection of the graph y = ax^2 + bx + c and the x-axis.
Understand the quadratic formula and the discriminant ∆.
Know that if ∆ < 0 there are no real roots, if ∆ = 0 there is one real root - a double root, and if ∆ > 0 there are two real roots.

Understand the effect of modifications of a function’s graph y = f(x) to y = f(x) + a, y = af(x), y = f(x + a) and y = f(ax).
Draw the graph of a function from the function’s rule.
Determine the range of a function from its graph.
Understand that any point on a logarithmic graph satisfies the equation y = loga x and that changing the base of a logarithm changes the scale used on the corresponding axis.
Interpret real-world contexts in terms of functions and their graphs.

Simplify rational expressions by factorising and cancelling, and by combining expressions by addition and subtraction.
Use fractional expressions including numerical and algebraic examples.
Be aware of the non-permissibility of zero in the denominator.

Solve linear, quadratic and simultaneous equations.
Solve linear and quadratic inequalities in one variable and interpret such inequalities graphically.
Express solutions of inequalities in interval notation.