Pure Mathematics exam tips

Exam tips

• Geometric sequences and series exam tip 1

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

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

• Sequences and series in modelling exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to d6 Use sequences and series in modelling..

  This keeps the answer actionable and aligned to Sequences and series in modelling, rather than giving generic revision advice.

• Trigonometric definitions and radians exam tip 1

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

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

• Small angle approximations exam tip 1

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

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

• Trigonometric functions and exact values exam tip 1

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

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

• Reciprocal and inverse trigonometric functions exam tip 1

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

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

• Trigonometric identities exam tip 1

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

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

• Compound and double angle formulae exam tip 1

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

  This keeps the answer actionable and aligned to Compound and double angle formulae, rather than giving generic revision advice.

• Trigonometric equations exam tip 1

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

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

• Trigonometric proofs exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to e8 Construct proofs involving trigonometric functions and identities..

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