Pure Mathematics common mistakes

Common mistakes

• First order differential equations common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: H7 Evaluate the analytical solution of simple first order differential equations with separable variables, including finding particular solutions, where separation of variables may require factorisation involving a common factor..

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

• Differential equation interpretation common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: H8 Interpret the solution of a differential equation in the context of solving a problem, including identifying limitations of the solution and links to kinematics..

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

• Root location common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: I1 Locate roots of f(x) = 0 by considering changes of sign of f(x) in an interval of x on which f(x) is sufficiently well behaved; understand how change of sign methods can fail..

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

• Iterative methods and Newton-Raphson common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: I2 Solve equations approximately using simple iterative methods; draw associated cobweb and staircase diagrams; solve equations using the Newton-Raphson method and other recurrence relations of the form x_(n+1) = g(x_n); understand how such methods can fail..

  Fix itShow the method first, then give the final answer in the required form. Apply this directly to Iterative methods and Newton-Raphson.

• Numerical integration common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: I3 Understand and use numerical integration of functions, including the trapezium rule and estimating the approximate area under a curve and limits that it must lie between..

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

• Numerical methods in context common mistake 1

  Writing a final answer without showing the method that justifies it. This can weaken answers for: I4 Use numerical methods to solve problems in context..

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