Pure Mathematics common mistakes

Common mistakes

• Partial fractions common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: B10 Decompose rational functions into partial fractions, with denominators not more complicated than squared linear terms and with no more than three terms, and numerators constant or linear..

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

• Functions in modelling common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: B11 Use functions in modelling, including consideration of limitations and refinements of the models..

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

• Straight line coordinate geometry common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: C1 Understand and use the equation of a straight line, including the forms y - y1 = m(x - x1) and ax + by + c = 0; use gradient conditions for two straight lines to be parallel or perpendicular; use straight line models in a variety of contexts..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Straight line coordinate geometry.

• Circle coordinate geometry common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: C2 Understand and use the coordinate geometry of the circle including the equation of a circle in the form (x - a)^2 + (y - b)^2 = r^2; complete the square to find the centre and radius; use circle properties including the angle in a semicircle, the perpendicular from the centre to a chord, and the radius perpendicular to a tangent..

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

• Parametric equations common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: C3 Understand and use the parametric equations of curves and conversion between Cartesian and parametric forms..

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

• Parametric modelling common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: C4 Use parametric equations in modelling in a variety of contexts..

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

• Binomial expansion common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: D1 Understand and use the binomial expansion of (a + bx)^n for positive integer n; use the notations n!, nCr and binomial coefficients; link to binomial probabilities; extend to any rational n including use for approximation; be aware that the expansion is valid for |bx/a| < 1, with proof not required..

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

• Sequences common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: D2 Work with sequences including those given by a formula for the nth term and those generated by a simple relation of the form x_(n+1) = f(x_n); work with increasing, decreasing and periodic sequences..

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

• Sigma notation common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: D3 Understand and use sigma notation for sums of series..

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

• Arithmetic sequences and series common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: D4 Understand and work with arithmetic sequences and series, including the formulae for nth term and the sum to n terms..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Arithmetic sequences and series.