Trapezium Rule & Logs (Q5 A2 P2 Edexcel 2022)

In this video, Lee Guffick takes you through a beautifully structured A-Level Maths question combining the Trapezium Rule with logarithms.

You’ll see exactly how to:
✔️ Apply the trapezium rule correctly using all y-values in the table
✔️ Work with log to the base 3 and apply log laws efficiently
✔️ Manipulate integrals using constants and log identities
✔️ Build part B using the answer from part A (a common Edexcel pattern!)

Lee breaks the question into simple, exam-ready steps — ideal revision for any Year 13 student aiming for top marks.

In this video, Lee Guffick explains how to estimate the integral of log to the base three of 2x using the trapezium rule, and then how to use this value to evaluate related integrals involving powers and logarithmic transformations.

⏱️ TIMESTAMPS:

00:00 Introduction to the question
00:20 Understanding the table and strip width
00:50 Setting up the trapezium rule formula
01:40 Substituting all y-values correctly
02:30 Final estimated area for the first integral
03:00 Using log laws to bring powers forward
04:00 Building the second integral using the answer to part A
05:00 Splitting products inside logarithms using the log laws
06:20 Evaluating the constant term in part B
07:00 Final answers and exam-style reasoning

✏️ TOPICS COVERED:

Trapezium Rule / Numerical Integration

Logarithms with base three

Using log laws (power law, product law)

Splitting and simplifying integrals

Constants inside integrals

Edexcel A-Level Paper 2 techniques

Combining numerical and algebraic methods

💯 EXAM TIPS:

Always identify the strip width h before applying the trapezium rule.

Check you have included:
– first y value
– last y value
– two times the middle values

When logs involve powers, bring the power down first — it often saves huge amounts of work.

If an integral looks complicated, try rewriting the expression using the product or quotient laws.

When Edexcel says “use your answer to part A,” they are signalling an efficient shortcut — don’t re-integrate!

📚 ABOUT GUFFICK TUITION:
Lee Guffick is a former Head of Mathematics and A-Level Examiner helping students achieve A*/A grades and secure places at leading universities including Oxford, Cambridge, and the Ivy League.

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