Pure Mathematics common mistakes

Common mistakes

• Applications of differentiation common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: G3 Apply differentiation to find gradients, tangents and normals, maxima and minima, stationary points and points of inflection; identify where functions are increasing or decreasing..

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

• Product, quotient and chain rules common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: G4 Differentiate using the product rule, quotient rule and chain rule, including problems involving connected rates of change and inverse functions..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Product, quotient and chain rules.

• Implicit and parametric differentiation common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: G5 Differentiate simple functions and relations defined implicitly or parametrically, for first derivative only..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Implicit and parametric differentiation.

• Differential equation construction common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: G6 Construct simple differential equations in pure mathematics and in context, including contexts such as kinematics, population growth and modelling the relationship between price and demand..

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

• Fundamental Theorem of Calculus common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: H1 Know and use the Fundamental Theorem of Calculus..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Fundamental Theorem of Calculus.

• Integration techniques common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: H2 Integrate x^n excluding n = -1 and related sums, differences and constant multiples; integrate e^(kx), 1/x, sin kx, cos kx and related sums, differences and constant multiples..

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

• Definite integration and areas common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: H3 Evaluate definite integrals; use a definite integral to find the area under a curve and the area between two curves..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Definite integration and areas.

• Integration as limit of a sum common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: H4 Understand and use integration as the limit of a sum..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Integration as limit of a sum.

• Integration by substitution and parts common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: H5 Carry out simple cases of integration by substitution and integration by parts; understand these methods as inverse processes of the chain and product rules respectively, with substitution limited to cases where one substitution leads to an integrable function and integration by parts excluding reduction formulae..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Integration by substitution and parts.

• Integration using partial fractions common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: H6 Integrate using partial fractions that are linear in the denominator..

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