Edexcel IGCSE Further Pure Mathematics Past Papers

Common mistake: Many students assume a triangle is right-angled, isosceles, or equilateral when it is not specified in the question, often incorrectly applying Pythagoras’ Theorem or the tangent ratio.

How to solve it: Draw a sketch. Teachers repeatedly note that students who sketch the problem are far more successful. Only use Pythagoras or right-angled trigonometry if you have explicitly proven a 90° angle exists; otherwise, stick to the general Sine and Cosine rules

Common mistake: Common errors include writing ln(x+3) as lnx+ln3, misplacing powers (e.g., 3log4 as (log4)3), or failing to correctly raise a right-hand side as a power of e.

How to solve it: : Practice the fundamental laws of logs religiously. When substituting to solve a log quadratic, choose a letter other than x (like u or y) to avoid confusion with the original variables in the question.

Common mistake: Students often divide both sides of a trigonometric equation by a function like cosθ or sin7θ. This effectively cancels out valid solutions where that function would equal zero. Additionally, many forget the "ambiguous case" of the sine rule, failing to provide the second obtuse/acute angle when required.

How to solve it: Never divide through by a trigonometric function; rearrange and factorise instead. Always check the specified range (e.g., 0<θ<360) and ensure you have found all possible solutions within it.

Common mistake: When solving quadratic inequalities, students often find the correct "critical values" but struggle to identify the correct "inside" or "outside" region for the final answer. A recurring error is failing to flip the inequality sign when dividing or multiplying by a negative number.

How to solve it: Always draw a quick sketch of the parabola to see if you need the region above or below the x-axis. Be extremely careful when dividing by terms like −log0.25, as these are negative and require a sign reversal.

Common mistake: Forgetting the +C in indefinite integration is a standard error that simplifies the problem's demand and caps your marks. In definite integration, students often omit the step showing the limits substituted into the expression.

How to solve it: Make it a habit to add +C the moment you integrate an expression without limits. For definite integrals, show the full substitution of your upper and lower limits before calculating the final value; this ensures you get method marks even if your final arithmetic is wrong.

Common mistake: In kinematics, students frequently treat distance and displacement as the same. They may give a negative displacement when asked for distance, or fail to integrate separate sections of motion where the particle changes direction

How to solve it: Remember that distance is a scalar and must always be positive. If a particle changes direction within your integration limits, find the time it is at rest (v=0), integrate each section separately, and add the absolute values (modulus) of the results.