Pure Mathematics exam tips

Exam tips

• Trigonometry in context exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to e9 Use trigonometric functions to solve problems in context, including problems involving vectors, kinematics and forces..

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

• Exponential functions exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to f1 Know and use the function a^x and its graph, where a is positive; know and use the function e^x and its graph..

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

• Exponential gradient and modelling exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to f2 Know that the gradient of e^(kx) is equal to ke^(kx) and hence understand why the exponential model is suitable in many applications..

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

• Logarithmic functions exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to f3 Know and use the definition of log_a x as the inverse of a^x, where a is positive and x >= 0; know and use the function ln x and its graph; know and use ln x as the inverse function of e^x..

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

• Laws of logarithms exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to f4 Understand and use the laws of logarithms, including log_a x + log_a y = log_a(xy), log_a x - log_a y = log_a(x/y), and k log_a x = log_a(x^k), including cases such as k = -1 and k = -1/2..

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

• Exponential equations exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to f5 Solve equations of the form a^x = b..

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

• Logarithmic graphs exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to f6 Use logarithmic graphs to estimate parameters in relationships of the form y = ax^n and y = kb^x, given data for x and y..

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

• Exponential growth and decay exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to f7 Understand and use exponential growth and decay; use exponential models in contexts such as continuous compound interest, radioactive decay, drug concentration decay and population growth; consider limitations and refinements of exponential models..

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

• Derivative concept exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to g1 Understand and use the derivative of f(x) as the gradient of the tangent to y = f(x) at a general point; understand the gradient of the tangent as a limit and as a rate of change; sketch the gradient function for a given curve; understand second derivatives; differentiate from first principles for small positive integer powers of x and for sin x and cos x; understand and use the second derivative as the rate of change of gradient, including links to convex and concave sections and points of inflection..

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

• Differentiation techniques exam tip 1

  Write the method before the answer so the examiner can follow each step. Apply this to g2 Differentiate x^n for rational values of n and related constant multiples, sums and differences; differentiate e^(kx), a^(kx), sin kx, cos kx, tan kx and related sums, differences and constant multiples; understand and use the derivative of ln x..

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