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27/08/2026

Think proof questions are just about writing down algebra neatly? This IAL P2 question is a good example of why proof can be difficult at A-level, especially when inequalities and counterexamples are involved.

In this video, we work through Pearson Edexcel International A-level Pure Mathematics 2, June 2022, Question 5, step by step. We look at how to structure the algebraic proof, use the inequality carefully, and then deal with the counterexample in part (b).

This is excellent practice for A-level Maths students because examiners reported that most candidates could not score more than 3 out of the 6 marks available. The question tests not only algebra, but also whether you can write a convincing argument and recognise when a statement is not always true.

A really useful revision example for anyone preparing for IAL P2 and wanting more confidence with proof, inequalities, counterexamples, and the kind of reasoning that often separates stronger answers from incomplete ones.

26/08/2026

Think inverse functions are straightforward until the function is piecewise? This IAL P2 question is a strong example of how functions can become much more demanding when domains, inequalities, composites, and one-to-one restrictions all appear together.

In this video, we work through Pearson Edexcel International A-level Mathematics Pure Mathematics 2, Question 6, step by step. We look at how to handle piecewise functions, form composite functions, solve the inequalities involved, and decide when an inverse function is valid.

This is excellent practice for A-level Maths students because the question separates students who only know the notation from those who really understand what functions are doing. You need to track the domain carefully, recognise many-to-one versus one-to-one behaviour, and present your reasoning clearly.

A really useful revision example for anyone preparing for IAL P2 and wanting more confidence with piecewise functions, inverse functions, composite functions, and harder function questions.

25/08/2026

Think quadratic and cubic graphs are straightforward until you have to find exactly where they intersect? This IAL P1 question is a strong example of how familiar topics can become much harder when algebra, graph interpretation, and problem-solving are combined.

In this video, we work through Pearson Edexcel International A-level Pure Mathematics 1, October 2024, Question 4, step by step. We look at how to handle quadratic and cubic graphs, find their intersections, and avoid the mistakes that led to so many blank or nearly blank solutions.

This is excellent practice for A-level Maths students because very few candidates managed to score full marks, and this question produced more blank or nearly blank responses than any other question on the paper.

A really useful revision example for anyone preparing for IAL P1 and wanting more confidence with quadratics, cubics, graph intersections, and exam-style algebraic problem-solving.

20/08/2026

Think trigonometric graph transformations are straightforward until the question asks you to describe the changes precisely? This IAL P1 question is a strong example of how quickly marks can disappear when students are not confident with the shape, movement, and interpretation of trig graphs.

In this video, we work through Pearson Edexcel International A-level Pure Mathematics 1, October 2021, Question 4, step by step. We look at how to approach trigonometric graphs, identify the transformations clearly, and avoid the mistakes that led many students to leave part (b) completely blank.

This is excellent practice for A-level Maths students because graph transformation questions test more than just recognition. You need to understand how the graph changes, describe the transformation accurately, and connect the visual information to the algebra.

A really useful revision example for anyone preparing for IAL P1 and wanting more confidence with trigonometric graphs, transformations, and exam questions where many students failed to score any marks.

19/08/2026

Think differentiation is straightforward until the question asks for vertical tangents? This IAL P3 question is a good example of how students can lose marks when they know the quotient rule but are less confident about what the derivative is telling them geometrically.

In this video, we work through Pearson Edexcel International A-level Pure Mathematics 3, June 2023, Question 10, step by step. We look at how to differentiate using the quotient rule, then use the result to find the equations of the vertical tangents to the curve.

This is excellent practice for IAL Maths students because it brings together calculus, algebraic accuracy, and graphical interpretation. You need to apply the quotient rule carefully, understand the condition for a vertical tangent, and present the final equations clearly.

A really useful revision example for anyone preparing for IAL P3 and wanting more confidence with differentiation, quotient rule questions, and the link between gradients and tangents.

18/08/2026

Think differentiation is straightforward until the question asks you to work the other way round? This IAL P3 question is a strong example of how quickly students can lose marks when trigonometry, implicit differentiation, and gradient all appear together.

In this video, we work through Pearson Edexcel International A-level Pure Mathematics 3, January 2025, Question 10, step by step. We look at how to handle differentiation involving trigonometric functions, use identities carefully, and interpret the gradient correctly.

This is excellent practice for IAL Maths students because only a small proportion of the very best candidates were able to score full marks. The question demands accurate calculus, controlled algebra, and a clear understanding of what the derivative actually represents.

A really useful revision example for anyone preparing for IAL P3 and wanting more confidence with trigonometric differentiation, implicit methods, gradients, and tougher calculus exam questions.

13/08/2026

Think integration by inspection is just about spotting a pattern? This IAL P3 question shows how easily students can get stuck when the structure is not immediately obvious.

In this video, we work through Pearson Edexcel International A-level Pure Mathematics 3, January 2021, Question 9, step by step. We look at how to recognise when the reverse chain rule is needed and how to set out the integration clearly.

This is excellent practice for A-level Maths students because many candidates failed to score any marks at all on this question. It is a strong reminder that integration is not only about knowing methods, but also about recognising which method fits the expression in front of you.

A really useful revision example for anyone preparing for IAL P3 and wanting more confidence with integration by inspection, reverse chain rule, and tricky calculus exam questions.

12/08/2026

Think trig identities are fine until you have to use them in a proof and then solve an equation? This IAL P3 question is a strong example of how quickly a trigonometry problem can become difficult when several skills are tested together.

In this video, we work through International A-level Maths Pure Mathematics 3, June 2022, Question 9, step by step. We look at how to approach the trigonometric proof, use the identities carefully, and then solve the trig equation without losing control of the algebra.

This is excellent practice for IAL Maths students because the question was a major discriminator. The most common score was zero, with a quarter of students scoring no marks at all, while only the strongest candidates were able to secure full marks.

A really useful revision example for anyone preparing for IAL P3 and wanting more confidence with trig identities, proof, solving trigonometric equations, and longer exam-style questions.

11/08/2026

Think polar calculus has to be complicated? This January 2025 IAL Further Pure Mathematics F2 question is a good example of where students can overthink the method and make the question harder than it needs to be.

In this video, we work through Question 5 step by step, looking at how to use polar differentiation to find tangents parallel to an initial tangent, before using integration to find the area swept out by a polar curve.

This is excellent practice for Further Maths students because polar questions test several skills at once. You need to understand the geometry of the curve, handle the calculus accurately, and keep the method clean rather than getting pulled into unnecessary algebra.

A really useful revision example for anyone preparing for IAL Further Maths and wanting more confidence with polar coordinates, tangents, and polar area questions.

06/08/2026

Think vectors are manageable until planes, intersecting lines, and direction cosines all appear in the same question? This 2024 Further Pure Mathematics 1 question was one of the hardest on the paper, with many students leaving the second part completely blank, even some top A* candidates.

In this video, we work through Question 9 step by step, looking at how to find the intersection of two straight lines, form the equation of a plane containing given lines, and deal with lines through the origin making specified angles with the coordinate axes.

This is excellent practice for Further Maths students because it tests far more than standard vector notation. You need to understand the geometry, choose the right vector form, and keep your algebra controlled through a demanding multi-part question.

A really useful revision example for anyone preparing for Further Maths and wanting more confidence with vectors, planes, direction cosines, and the sort of question that separates strong answers from incomplete ones.

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