Pure Mathematics common mistakes

Common mistakes

• Trigonometry in context common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: E9 Use trigonometric functions to solve problems in context, including problems involving vectors, kinematics and forces..

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

• Exponential functions common mistake 1

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

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

• Exponential gradient and modelling common mistake 1

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

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

• Logarithmic functions common mistake 1

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

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

• Laws of logarithms common mistake 1

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

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

• Exponential equations common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: F5 Solve equations of the form a^x = b..

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

• Logarithmic graphs common mistake 1

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

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

• Exponential growth and decay common mistake 1

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

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Exponential growth and decay.

• Derivative concept common mistake 1

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

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

• Differentiation techniques common mistake 1

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

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