Pure Mathematics common mistakes

Common mistakes

• Proof common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: 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..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Proof.

• Laws of indices common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: B1 Understand and use the laws of indices for all rational exponents..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Laws of indices.

• Surds common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: B2 Use and manipulate surds, including rationalising the denominator..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Surds.

• Quadratic functions common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: 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..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Quadratic functions.

• Simultaneous equations common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: B4 Solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Simultaneous equations.

• Inequalities common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: 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..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Inequalities.

• Polynomial and rational expression manipulation common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: 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..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Polynomial and rational expression manipulation.

• Graphs of functions common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: 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..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Graphs of functions.

• Composite and inverse functions common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: B8 Understand and use composite functions, inverse functions and their graphs..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Composite and inverse functions.

• Transformations of function graphs common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: 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..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Transformations of function graphs.