Pure Mathematics exam tips

Exam tips

• Proof exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to a1 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 and proof by exhaustion; use disproof by counter example; use proof by contradiction including proof of the irrationality of sqrt(2), the infinity of primes and application to unfamiliar proofs..

  This keeps the answer actionable and aligned to Proof, rather than giving generic revision advice.

• Laws of indices exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to b1 Understand and use the laws of indices for all rational exponents..

  This keeps the answer actionable and aligned to Laws of indices, rather than giving generic revision advice.

• Surds exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to b2 Use and manipulate surds, including rationalising the denominator..

  This keeps the answer actionable and aligned to Surds, rather than giving generic revision advice.

• Quadratic functions exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to b3 Work with quadratic functions and their graphs; use the discriminant including the conditions for real and repeated roots; complete the square; solve quadratic equations including solving quadratic equations in a function of the unknown..

  This keeps the answer actionable and aligned to Quadratic functions, rather than giving generic revision advice.

• Simultaneous equations exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to b4 Solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation..

  This keeps the answer actionable and aligned to Simultaneous equations, rather than giving generic revision advice.

• Inequalities exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to b5 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 graphically..

  This keeps the answer actionable and aligned to Inequalities, rather than giving generic revision advice.

• Polynomial and rational expression manipulation exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to b6 Manipulate polynomials algebraically, including expanding brackets and collecting like terms, factorisation and simple algebraic division; use the factor theorem; simplify rational expressions including by factorising and cancelling, and algebraic division by linear expressions only..

  This keeps the answer actionable and aligned to Polynomial and rational expression manipulation, rather than giving generic revision advice.

• Graphs of functions exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to b7 Understand and use graphs of functions; sketch curves defined by simple equations including polynomials, the modulus of a linear function, y = a/x and y = a/x^2 including their vertical and horizontal asymptotes; interpret algebraic solution of equations graphically; use intersection points of graphs to solve equations; understand and use proportional relationships and their graphs..

  This keeps the answer actionable and aligned to Graphs of functions, rather than giving generic revision advice.

• Composite and inverse functions exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to b8 Understand and use composite functions, inverse functions and their graphs..

  This keeps the answer actionable and aligned to Composite and inverse functions, rather than giving generic revision advice.

• Transformations of function graphs exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to b9 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), y = f(ax), and combinations of these transformations..

  This keeps the answer actionable and aligned to Transformations of function graphs, rather than giving generic revision advice.