EDEXCEL · IGCSE · 4PM1 · Opens 10 January 2027

Edexcel International GCSE Further Pure Mathematics, method mark by method mark.

Every topic of 4PM1, from logarithms and surds to calculus and trigonometric equations, taught in Pearson's order. Then real Paper 1 and 2 questions on each, worked against the mark scheme, method mark by method mark.

Taught by Rashin Shareef · Mathematics · 15 years

Hold a placeBDT 5,500Watch the demo

The course opens on 10 January 2027. You pay once for your sitting.

Course demo · 2 min

433
real past-paper questions
15
papers, every one practisable

2019 to 2024

Rashin Shareef
your tutor

Students ask

  1. 01

    I got the right answer. Why did I only get half the marks?

  2. 02

    Alpha and beta questions: how do I form the new equation without expanding everything?

  3. 03

    How do I justify that a stationary point is a maximum, the way the mark scheme wants?

  4. 04

    Trigonometric equations: how do I find every solution in the interval without missing one?

  5. 05

    Two hours a paper. How do I stop spending forty minutes on one question?

The loop

01

Learn

Each part of the 4PM1 specification taught in Pearson's order, with every line of working written out the way the mark scheme gives marks for it.

01 · Learn
02

Check

A short check at the end of each section, so a method that did not stick shows up before the next section builds on it.

02 · Check
03

Drill

Real 4PM1 questions on one topic at a time, from the sittings in the bank. Write the working, then see the mark scheme and tick each method and accuracy mark you earned.

433 questions
03 · Drill

By syllabus section

423 questions

  • 9Calculus93
  • 10Trigonometry90
  • 5Series51
  • 2The quadratic function40
  • 3Identities and inequalities35
  • 4Graphs33
  • 8Rectangular Cartesian coordinates27
  • 7Scalar and vector quantities24
Open the past papers
04

Exam desk

The ruler, the protractor and the calculator you get in the hall, on screen. Mark the diagram itself; a stroke along the ruler comes out straight.

04 · Exam desk

Try the desk · drawn to scale, AB = 6 cm

ABC6 cm0306090120150180012345678cm

Start a stroke against the ruler edge. Drag the tools by their bodies; turn them by the knobs.

RulerProtractor
06

Revisit

Green, yellow, red. Red is yours to clear: say you still do not understand and the topic stays on your revisit list until you do.

06 · Revisit
  • All correct
  • Some mistakes
  • Still not clear

October/November 2024 · Paper 1

Some mistakes

The syllabus, 4PM1

10 sections.

10 sections and 43 sub-topics, in the board's own order. Open any section to see what it covers. Practice is open on every section.

Most practised in the bank: Arithmetic and geometric series, Applications to simple linear kinematics and to determination of areas and volumes, Applications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes), Simple examples involving functions of the roots of a quadratic equation, The use of the basic addition formulae of trigonometry.

Open the past papers
  1. 01Logarithmic functions and indices15 questions in the bank
    • 1.AThe functions $a^x$ and $\log_b x$ (where $b$ is a natural number greater than one)1
    • 1.BUse and properties of indices and logarithms, including change of base12
    • 1.CSimple manipulation of surds1
    • 1.DRationalising the denominator1
  2. 02The quadratic function40 questions in the bank
    • 2.AThe manipulation of quadratic expressions13
    • 2.BThe roots of a quadratic equation4
    • 2.CSimple examples involving functions of the roots of a quadratic equation23
  3. 03Identities and inequalities35 questions in the bank
    • 3.ASimple algebraic division
    • 3.BThe factor and remainder theorems8
    • 3.CSolutions of equations, extended to include the simultaneous solution of one linear and one quadratic equation in two variables10
    • 3.DSimple inequalities, linear and quadratic8
    • 3.EThe graphical representation of linear inequalities in two variables8
  4. 04Graphs33 questions in the bank
    • 4.AGraphs of polynomials and rational functions with linear denominators22
    • 4.BThe solution of equations and transcendental functions by graphical methods11
  5. 05Series51 questions in the bank
    • 5.AUse of the $\sum$ notation4
    • 5.BArithmetic and geometric series47
  6. 06The binomial series15 questions in the bank
    • 6.AUse of the binomial series $(1 + x)^n$15
  7. 07Scalar and vector quantities24 questions in the bank
    • 7.AThe addition and subtraction of coplanar vectors and the multiplication of a vector by a scalar3
    • 7.BComponents and resolved parts of a vector
    • 7.CMagnitude of a vector3
    • 7.DPosition vector1
    • 7.EUnit vector5
    • 7.FUse of vectors to establish simple properties of geometrical figures12
  8. 08Rectangular Cartesian coordinates27 questions in the bank
    • 8.AThe distance between two points7
    • 8.BThe point dividing a line in a given ratio3
    • 8.CGradient of a straight line joining two points
    • 8.DThe straight line and its equation7
    • 8.EThe condition for two lines to be parallel or to be perpendicular7
  9. 09Calculus93 questions in the bank
    • 9.ADifferentiation and integration of sums of multiples of powers of $x$ (excluding integration of $\frac{1}{x}$), $\sin ax$, $\cos ax$, $e^{ax}$7
    • 9.BDifferentiation of a product, quotient and simple cases of a function of a function11
    • 9.CApplications to simple linear kinematics and to determination of areas and volumes32
    • 9.DStationary points and turning points6
    • 9.EMaxima and minima11
    • 9.FThe equations of tangents and normals to the curve $y = f(x)$12
    • 9.GApplication of calculus to rates of change and connected rates of change12
  10. 10Trigonometry90 questions in the bank
    • 10.ARadian measure, including use for arc length and area of sector12
    • 10.BThe three basic trigonometric ratios of angles of any magnitude (in degrees or radians) and their graphs
    • 10.CApplications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes)30
    • 10.DUse of the sine and cosine formulae13
    • 10.EThe identity $\cos^2 \theta + \sin^2 \theta = 1$
    • 10.FUse of the identity $\tan \theta = \frac{\sin \theta}{\cos \theta}$1
    • 10.GThe use of the basic addition formulae of trigonometry23
    • 10.HSolution of simple trigonometric equations for a given interval10

The papers you will sit, 4PM1

  • Paper 1

    2 hours · 100 marks · 50%

    Written paper of questions worth varying marks. A calculator may be used.

    Every topic taught, then real Paper 1 questions on it, each with the mark scheme to tick your working against, method mark by method mark.

    171 questions from real papers in the bank

  • Paper 2

    2 hours · 100 marks · 50%

    Written paper of questions worth varying marks. A calculator may be used.

    Real Paper 2 questions by topic with their mark schemes, and whole papers on the real clock.

    262 questions from real papers in the bank

Past papers

Practise the real papers.

Every paper on the shelf is sat online: timed for multiple choice, self-marked against the real mark scheme for written work. Pick one up.

15

papers · 2019 to 2024

About

About this course.

This is the Edexcel International GCSE Further Pure Mathematics course, written against specification 4PM1 for the 2027 and 2028 examinations.

It follows the specification in Pearson's order: logarithms, indices and surds; the quadratic function and the roots of a quadratic; identities and inequalities, with the factor and remainder theorems; graphs; arithmetic and geometric series; the binomial series; vectors; coordinate geometry; calculus, from differentiation and integration to kinematics, areas, volumes and rates of change; and trigonometry, from radians to the addition formulae and trigonometric equations. Each section is taught, checked, then practised on questions from real 4PM1 papers.

You sit two papers of 2 hours each, with a calculator allowed on both. The question bank holds real Paper 1 and Paper 2 questions. There is no multiple choice: you write the working, then see the mark scheme and tick each method and accuracy mark you earned.

The course is recorded. It has no live classes and no messaging a teacher.

Access runs to the date printed against your sitting.

Outcomes

What this course leaves you with.

What you’ll be able to do

  1. Use the sum and product of the roots of a quadratic to form new equations

  2. Solve logarithmic and exponential equations, including a change of base

  3. Sum arithmetic and geometric series, including to infinity when the series converges

  4. Differentiate and integrate for tangents, maxima and minima, kinematics, areas and volumes

  5. Solve trigonometric equations in a given interval, in degrees and in radians

  6. Set out every line of working so method marks are earned even when an answer slips

Before you decide

01

Is it only practice, or is the method taught?

Both, in that order. Each part of the specification is taught first, with the working set out line by line. At the end of each section comes a short check, then real 4PM1 questions on that topic, a full paper on the real clock, and a revisit list built from what your child says still does not make sense. In Further Pure the working earns most of the marks, so the course treats the method as the thing being learned, not only the answer.

02

How are the answers marked when there is no multiple choice?

Your child writes the full working, as in the exam hall, then sees the real mark scheme for that question and ticks each mark earned: the method marks for the right approach and the accuracy marks for the right result. Writing clear and accurate solutions carries 35 to 50% of the 4PM1 marks, so learning to read a mark scheme this way is part of the preparation, not a shortcut.

03

How do we know whether it is actually working?

Open your child's account with them. Every paper they sit carries a light. Green means everything correct. Yellow means marks lost, with the mark scheme there to show which step. Red is the one they set themselves: when a question still does not make sense after checking the working, they mark it, and that topic stays on their revisit list until they clear it. That list is the useful part. It names the topics still not clear, in the specification's own words.

04

My child already has a tutor. Why this as well?

Keep the tutor. A tutor has a few hours a week. This is open at every other hour: real 4PM1 questions on any topic, such as series or connected rates of change, with the mark scheme for each. The revisit list, the topics your child has said still do not make sense, is a good thing to bring to the next session.

05

What exactly are we paying for, and what if it does not suit us?

A place on the course for the sitting you choose, with access to the date printed against it. That one payment is the whole cost; there are no further charges. The question bank and past papers are open from 10 January 2027, and lessons are added section by section. Seven days from the day you pay, the full amount back, no questions asked. If you pay before the course opens on 10 January 2027, you can have the full amount back until 17 January 2027. Ask from your Account page, or email support@eudikalearn.com. Pay with bKash, Nagad, Rocket or a card.

Faculty file

Rashin ShareefTutor

Rashin Shareef

Mathematics · 15 years

Every lesson is guided by patience, clarity and excellence, with a focus on building strong mathematical understanding, developing problem-solving skills, and helping every student learn confidently and achieve their full potential.

Rashin Shareef has taught mathematics privately since 2011, specialising in O Level, IGCSE, IB and Cambridge International mathematics, including Cambridge O Level Mathematics (4024) and Additional Mathematics (4037) and Pearson Edexcel International GCSE Mathematics B (4MB1). He has worked with students of different abilities and learning styles, building a strong foundation and preparing them for school and Cambridge examinations, with the focus on understanding rather than memorised procedures. His teaching is patient, structured and student-centred. He breaks hard topics into manageable steps and encourages students to explain their reasoning, not just give an answer. After each concept come targeted practice, past-paper questions and exam-style problems. He goes through mistakes carefully, so a student understands what went wrong, why, and how not to repeat it. For the exam, he works on time management, setting out working, choosing the right method, and reading mark schemes and common question patterns. His aim is to make mathematics less intimidating and more logical. Whether a student needs to strengthen the basics or is aiming for higher grades, the lessons are fitted to their needs and pace.

  • Surds, indices and logarithms

    The laws of indices and logarithms, surds and change of base for Edexcel International GCSE Further Pure Mathematics (4PM1), with exam-style questions on each.

  • Differentiation and integration

    The rules of differentiation and integration and how they are used: gradients, rates of change, stationary points and areas, with guided practice on questions like the exam’s.

  • Vectors

    Vector notation, magnitude and vector geometry, from the basic operations to the longer questions that combine them.

  • Teaching mathematics privately since 2011
  • Teaching Cambridge O Level Mathematics (4024) and Additional Mathematics (4037)
  • Teaching Cambridge IGCSE Mathematics (0580)
  • Teaching Pearson Edexcel International GCSE Mathematics A (4MA1) and B (4MB1)
  • Teaching Cambridge International AS and A Level Mathematics (9709)
  • Teaching IB mathematics: Primary Years, Middle Years and Diploma programmes, Standard and Higher Level
  • MBA, North South University
  • BBA, City University

Choose your plan

One subject, or every course.

Pay once for the sitting you are working towards. Access runs to the end of the exam window and a month beyond it.

Practice bank

01 · Practice only · every subject

Practice bank only

Every subject's past-paper bank and virtual practicals for your sitting, without the lessons.

Choose your sitting

BDT1,500pay once

Access until 30 Jul 2027

  • Every paper on the site, every subject
  • Every virtual practical, at no extra cost
  • Marked against the real mark scheme
  • The exam desk: ruler, protractor, calculator
Arrange with the team
This course

02 · One subject · one sitting

Further Pure Mathematics

The whole course for this subject, through the sitting you choose.

Choose your sitting

BDT5,500pay once

Access until 30 Jul 2027

  • Every lesson, check and drill
  • This subject's full past-paper bank
  • Access until a month after the exam
Hold my place
All Access

03 · Every subject · one sitting

All Access

Every course on sale for the sitting, plus the whole practice bank and every practical.

Choose your sitting

BDT12,500pay once

Access until 30 Jul 2027

  • Every subject on sale for your sitting
  • Every subject's practice bank and practicals
  • One payment for the sitting
Arrange with the team

7-day refund window. Pay with bKash, Nagad, Rocket or card.

FAQ

Questions parents ask.

Is this the right course for my syllabus code?

This is Edexcel International GCSE Further Pure Mathematics, specification 4PM1. Check the code on the statement of entry. In Bangladesh, Edexcel International GCSE is often called Edexcel O Level; it is the same qualification. Edexcel Mathematics A (4MA1), Mathematics B (4MB1) and Cambridge O Level Additional Mathematics (4037) are different qualifications with different papers.

Which papers are in the question bank?

Paper 1 and Paper 2 of 4PM1, from sittings between 2019 and 2024. The newest is October/November 2024, and there are no 2021, 2022 or 2025 papers in the bank yet. Under The papers you will sit, each paper shows how many of its questions are in the bank. Every one was set on the current 4PM1 specification.

How long does access last?

Until the date printed against each sitting under Choose your plan, which falls after the exam for that sitting. You see the date before you pay.

Is there any multiple choice?

No. Both 4PM1 papers are written working, so the practice is too. You write each step, then see the real mark scheme for that question and tick the method and accuracy marks you earned, the way an examiner would.

Can we try it before paying?

Yes. Create a free account, with no card, and you get three free attempts in Further Pure Mathematics (4PM1). A whole question paper counts as one attempt.

Is there a live teacher?

No. The course is recorded, with no live classes and no messaging a teacher. The worked lessons, the checks and the mark schemes show where the marks went; they do not answer your child's questions. If your child needs someone to explain, keep the tutor for that, and take the revisit list to them.

What if it is not right for us?

Seven days from the day you pay, the full amount back, no questions asked. If you pay before the course opens on 10 January 2027, you can have the full amount back until 17 January 2027. Ask from your Account page, or email support@eudikalearn.com. Pay with bKash, Nagad, Rocket or a card.

Hold a place. The course opens on 10 January 2027.

Pick your sitting. One payment for the whole run to the exam, and the price shown is the price you pay.

BDT 5,500 for the May/Jun 2027 session · 7-day refund window

Hold a place