Edexcel IGCSE Further Pure Mathematics Tuition Online (4PM1)
Pearson Edexcel Further Pure Mathematics: logarithms, series, vectors, calculus and trigonometry, a step towards A Level.
Founder & Head of School, Afterkelas
Afterkelas teaches Pearson Edexcel International GCSE Further Pure Mathematics (4PM1) online to students at international and private schools in Malaysia. Tutors matched to the specification teach live in English, 1-to-1 or in small groups, across all ten topics and both papers.
What Edexcel IGCSE Further Pure Mathematics covers
The ten topics of the 4PM1 specification. Several of them, calculus and the binomial series among them, are the opening topics of A Level Mathematics.
Topics (4PM1)
10 topics- Logarithmic functions and indices
- The quadratic function
- Identities and inequalities
- Graphs
- Series
- The binomial series
- Scalar and vector quantities
- Rectangular Cartesian coordinates
- Calculus
- Trigonometry
Who should take Further Pure Mathematics
Further Pure Mathematics suits students who are comfortable in Mathematics A and are heading for A Level Mathematics, Further Mathematics, physics or engineering. It covers ground that A Level starts with, so students who take it usually find the first year of A Level far smoother.
It is a demanding qualification on top of Mathematics A, and the timing matters. Tutors map which 4PM1 topics the school has covered, then work on the ones still to come, with most practice going to the topics that need the strongest algebra: logarithms, series and calculus.
Where students lose marks
Algebra under pressure is the main leak. The questions are longer than in Mathematics A and chain several topics, so a sign error early in a calculus question can cost the whole answer. Students practise setting out every step and checking intermediate results, especially with logarithms and indices.
"Show that" questions give the answer and mark the route to it. Every line has to follow from the one before, and skipping a step to reach the given answer loses marks even when the mathematics is understood.
Who teaches Further Pure Mathematics
Tutors are university students and graduates, screened before they teach, and matched to the 4PM1 specification and exam series. An academic advisor asks for the student's latest Mathematics A result and which topics the school has covered.
A question, worked through
A 4PM1-style question on the roots of a quadratic equation. Using the sum and product of the roots avoids solving the equation at all.
Question
The roots of 2x² − 6x + 3 = 0 are α and β. (a) Find the value of α² + β². (b) Find a quadratic equation, with integer coefficients, whose roots are α² and β².
- From the equation, α + β = −(−6) ÷ 2 = 3 and αβ = 3 ÷ 2 = 3/2.
- Use the identity α² + β² = (α + β)² − 2αβ = 3² − 2 × 3/2 = 9 − 3 = 6.
- For the new equation, the sum of the roots is α² + β² = 6 and the product is α²β² = (αβ)² = 9/4.
- An equation with that sum and product is x² − 6x + 9/4 = 0; multiplying by 4 gives integer coefficients.
Answer (a) 6. (b) 4x² − 24x + 9 = 0.
Frequently asked questions
Is Further Pure Mathematics worth taking?
For students heading to A Level Mathematics, Further Mathematics, physics or engineering, usually yes. It goes further than Mathematics A in algebra, calculus and trigonometry, and students who take it start A Level with much of the first year familiar.
How is it different from Cambridge Additional Mathematics?
The content is similar in spirit, but the papers differ: 4PM1 has two two-hour papers graded 9 to 1, while Cambridge 0606 has its own papers, including one without a calculator, graded A* to E. Tutors prepare for the qualification on the student's entry.
When should my child start?
Alongside Mathematics A in Year 10, or as soon as the school offers it. Students who start late can still succeed with a plan that covers the remaining topics before moving to past papers.
How much does Edexcel IGCSE Further Pure Mathematics tuition cost?
The fee depends on the format (1-to-1 or a small group), how many classes a week and the tutor, so there is no single figure. Send an academic advisor the exam series, the latest Mathematics A result and the topics covered so far on WhatsApp, and you will get the current packages and a quote, usually within one working day.