WJECAS/A Level21 resources

WJEC AS/A Level Further Mathematics Past Papers & Mark Schemes

Free WJEC A Level Further Mathematics past papers & mark schemes. Units 4–6 covering Further Pure, Statistics, and Mechanics. 22 resources.

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21 of 21 resources

Summer 2023

6 files
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AS/A Level Further Mathematics – Unit 4: Written: Further Pure Mathematics B – Past Paper – Summer 2023

Past Paper
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AS/A Level Further Mathematics – Unit 5: Written: Further Statistics B – Past Paper – Summer 2023

Past Paper
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AS/A Level Further Mathematics – Unit 6: Written: Further Mechanics B – Past Paper – Summer 2023

Past Paper

AS/A Level Further Mathematics – Unit 4: Written: Further Pure Mathematics B – Mark Scheme – Summer 2023

Mark Scheme

AS/A Level Further Mathematics – Unit 5: Written: Further Statistics B – Mark Scheme – Summer 2023

Mark Scheme

AS/A Level Further Mathematics – Unit 6: Written: Further Mechanics B – Mark Scheme – Summer 2023

Mark Scheme

Summer 2022

6 files
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AS/A Level Further Mathematics – Unit 4: Written: Further Pure Mathematics B – Past Paper – Summer 2022

Past Paper
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AS/A Level Further Mathematics – Unit 5: Written: Further Statistics B – Past Paper – Summer 2022

Past Paper
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AS/A Level Further Mathematics – Unit 6: Written: Further Mechanics B – Past Paper – Summer 2022

Past Paper

AS/A Level Further Mathematics – Unit 4: Written: Further Pure Mathematics B – Mark Scheme – Summer 2022

Mark Scheme

AS/A Level Further Mathematics – Unit 5: Written: Further Statistics B – Mark Scheme – Summer 2022

Mark Scheme

AS/A Level Further Mathematics – Unit 6: Written: Further Mechanics B – Mark Scheme – Summer 2022

Mark Scheme

Summer 2019

9 files
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AS/A Level Further Mathematics – Unit 4: Written: Further Pure Mathematics B – Past Paper – Summer 2019

Past Paper
📄

AS/A Level Further Mathematics – Unit 5: Written: Further Statistics B – Past Paper – Summer 2019

Past Paper
📄

AS/A Level Further Mathematics – Unit 6: Written: Further Mechanics B – Past Paper – Summer 2019

Past Paper

AS/A Level Further Mathematics – Unit 4: Written: Further Pure Mathematics B – Mark Scheme – Summer 2019

Mark Scheme

AS/A Level Further Mathematics – Unit 5: Written: Further Statistics B – Mark Scheme – Summer 2019

Mark Scheme

AS/A Level Further Mathematics – Unit 6: Written: Further Mechanics B – Mark Scheme – Summer 2019

Mark Scheme

AS/A Level Further Mathematics – Unit 4: Written: Further Pure Mathematics B – Mark Scheme – Summer 2019

Mark Scheme

AS/A Level Further Mathematics – Unit 5: Written: Further Statistics B – Mark Scheme – Summer 2019

Mark Scheme

AS/A Level Further Mathematics – Unit 6: Written: Further Mechanics B – Mark Scheme – Summer 2019

Mark Scheme

WJEC Further Mathematics: Advanced Pure, Statistics, and Mechanics Beyond the Standard A Level

WJEC A Level Further Mathematics extends the mathematical content of the standard A Level into more abstract and demanding territory. The qualification builds upon Units 1–4 of A Level Mathematics, adding three further units: Unit 4 (Further Pure Mathematics B), Unit 5 (Further Statistics B), and Unit 6 (Further Mechanics B). Candidates must hold or be co-entering for A Level Mathematics. Further Pure Mathematics B covers complex numbers, matrices, proof by induction, hyperbolic functions, polar coordinates, and differential equations. Further Statistics B extends into continuous probability distributions, estimation, and chi-squared tests. Further Mechanics B introduces circular motion, simple harmonic motion, and centres of mass. Each unit carries 120 marks across a 2-hour-30-minute written examination. The A Level grade is determined by the combined performance across the three further units. WJEC provides papers in both English and Welsh. The 22 available resources represent a focused but sufficient collection for candidates preparing for this demanding qualification.

Exam Paper Structure

Unit 4

Further Pure Mathematics B

2 hours 30 minutes🎯 120 marks📊 % of grade
Complex numbersMatricesProof by inductionHyperbolic functionsPolar coordinatesDifferential equations
Unit 5

Further Statistics B

2 hours 30 minutes🎯 120 marks📊 % of grade
Continuous distributionsEstimation and confidence intervalsChi-squared testsCorrelation and regression
Unit 6

Further Mechanics B

2 hours 30 minutes🎯 120 marks📊 % of grade
Circular motionSimple harmonic motionCentres of massFurther dynamics

Key Information

Exam BoardWJEC
Specification CodeWJEC A Level Further Maths
QualificationAS/A Level
Grading ScaleA*–E
Assessment Type3 written exams (plus A Level Maths units)
TiersNone
Number Of Papers3 further units
Exam Duration2 hours 30 minutes per unit
Total Marks360 (120 per unit)
Calculator StatusCalculator permitted
Total Resources22

Key Topics in Further Mathematics

Topics you need to know

Complex numbers and Argand diagramsMatrix algebra and transformationsProof by inductionDifferential equations — first and second orderChi-squared tests and confidence intervalsCircular motion and simple harmonic motion

Exam Command Words

Command wordWhat the examiner expects
Prove by inductionUse the base case, inductive hypothesis, and inductive step to prove the result for all positive integers
FindCalculate or determine using appropriate mathematical methods
Show thatDemonstrate the given result using clear working
ExpressWrite in the specified mathematical form

Typical Grade Boundaries

GradeApproximate mark needed
A*80–90%
A70–79%
B60–69%
C50–59%
D40–49%
E30–39%

⚠️ Boundaries vary by session. Check WJEC’s website for exact figures.

Complex Numbers, Induction Proofs, and Circular Motion: Tackling WJEC Further Maths

Further Pure Mathematics B is the backbone of this qualification. Complex number arithmetic, Argand diagrams, and De Moivre’s theorem appear in almost every session. Practise converting between Cartesian and polar form until the process is automatic, then focus on using De Moivre’s theorem to find roots of unity and solve polynomial equations. Proof by induction follows a rigid structure: base case, inductive hypothesis, inductive step, conclusion. WJEC examiners penalise candidates who skip the conclusion or fail to state the inductive hypothesis explicitly. Write out the full structure for every induction question, even when the algebra feels straightforward. Further Mechanics B introduces circular motion — a topic that catches many candidates because it requires resolving forces radially and tangentially rather than horizontally and vertically. Draw a clear force diagram for every problem, label the centre of the circular path, and resolve forces towards that centre. With only 22 papers available, each one is valuable. Work through every paper under timed conditions, then review the mark scheme meticulously — WJEC mark schemes often reveal the specific algebraic steps that earn method marks, which can teach you efficient solution strategies.

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