# Algebra: Indices, linear and quadratic functions

AS Level

• Understand and use the laws of indices for all rational exponents
• Use and manipulate surds, including rationalising the denominator
• Work with quadratic functions and their graphs; the discriminant of a quadratic function, including the conditions for real and repeated roots; completing the square; solution of quadratic equations including solving quadratic equations in a function of the unknown
• 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, including inequalities with brackets and fractions
• Express solutions through correct use of ‘and’ and ‘or’, or through set notation]
• Represent linear and quadratic inequalities such as y >x+1 and y>ax2+bx+c graphically
• Manipulate polynomials algebraically, including expanding brackets and collecting like terms, factorisation and simple algebraic division; use of the factor theorem

A Level

• Simplify rational expressions including by factorising and cancelling, and algebraic division (by linear expressions only)