Pure Mathematics common mistakes

Common mistakes

• Geometric sequences and series common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: D5 Understand and work with geometric sequences and series, including formulae for the nth term and the sum of a finite geometric series; use the sum to infinity of a convergent geometric series, including the use of |r| < 1 and modulus notation..

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

• Sequences and series in modelling common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: D6 Use sequences and series in modelling..

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

• Trigonometric definitions and radians common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: E1 Understand and use the definitions of sine, cosine and tangent for all arguments; use the sine and cosine rules; use the area of a triangle in the form 1/2 ab sin C; work with radian measure, including use for arc length and area of sector..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Trigonometric definitions and radians.

• Small angle approximations common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: E2 Understand and use the standard small angle approximations of sine, cosine and tangent, including sin theta approximately theta, cos theta approximately 1 - theta^2/2, and tan theta approximately theta where theta is in radians..

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

• Trigonometric functions and exact values common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: E3 Understand and use the sine, cosine and tangent functions, their graphs, symmetries and periodicity; know and use exact values of sin and cos for 0, pi/6, pi/4, pi/3, pi/2, pi and multiples thereof, and exact values of tan for 0, pi/6, pi/4, pi/3, pi and multiples thereof..

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

• Reciprocal and inverse trigonometric functions common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: E4 Understand and use the definitions of secant, cosecant and cotangent and of arcsin, arccos and arctan; understand their relationships to sine, cosine and tangent, their graphs, ranges and domains..

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

• Trigonometric identities common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: E5 Understand and use tan theta = sin theta / cos theta; understand and use sin^2 theta + cos^2 theta = 1, sec^2 theta = 1 + tan^2 theta, and cosec^2 theta = 1 + cot^2 theta..

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

• Compound and double angle formulae common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: E6 Understand and use double angle formulae; use formulae for sin(A +/- B), cos(A +/- B) and tan(A +/- B); understand geometrical proofs of these formulae; understand and use expressions for a cos theta + b sin theta in equivalent forms r cos(theta +/- alpha) or r sin(theta +/- alpha)..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Compound and double angle formulae.

• Trigonometric equations common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: E7 Solve simple trigonometric equations in a given interval, including quadratic equations in sin, cos and tan and equations involving multiples of the unknown angle..

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

• Trigonometric proofs common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: E8 Construct proofs involving trigonometric functions and identities..

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