WJEC A-Level Mathematics
Explore your course, one topic at a time.
Course overview
The WJEC A-Level Mathematics specification covers 41 topics with 615 learning objectives (603/1977/X). Use the topic browser below to explore subtopics, exam tips, common mistakes, and key terminology for each area of the course.
- 41 topics
- 6 study pages
- 615 learning objectives
Ofqual Regulated: 603/1977/XOfficial specification (opens in a new tab)
Course version · 603/1977/XVersion from Sept 2017Change version
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Official Regulatory Specification
Regulated by the Office of Qualifications and Examinations Regulation (Ofqual) in England
- Qualification Number (QN)
- 603/1977/X
- Awarding Organisation
- WJEC
- Regulatory Type
- GCE A Level
- National Level & Units
- A-Level • 204 units
Sector Subject Area: Mathematics and statistics
This qualification is officially accredited under the national framework. Credits and certified outcomes are recognised by employers, further education colleges, and training providers throughout the UK.
- 612
- practice questions
- 204
- teaching notes
- 41
- topics
- 10
- audio lessons
Your exams
| Paper | Time | Marks | Weight |
|---|---|---|---|
| Unit 1: Pure Mathematics A | 150 min | 120 | 25% |
| Unit 2: Applied Mathematics A | 105 min | 75 | 15% |
| Unit 3: Pure Mathematics B | 150 min | 120 | 35% |
| Unit 4: Applied Mathematics B | 105 min | 80 | 25% |
Explore your topics
41 topics
Overarching themes4 topics
- Overarching themes - Mathematical argument, language and proof6 specification points covering Construct and present mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction;…18 objectives · 1 study page
- Overarching themes - Mathematical problem solving7 specification points covering Recognise the underlying mathematical structure in a situation and simplify and abstract appropriately to enable problems to…21 objectives · 1 study page
- Overarching themes - Mathematical modelling5 specification points covering Translate a situation in context into a mathematical model, making simplifying assumptions, Use a mathematical model with…15 objectives
- Use of data in statistics2 specification points covering This specification requires learners, during the course of their study, to: • develop skills relevant to exploring and…6 objectives
Unit 1: Pure Mathematics A9 topics
- Proof (AS Unit 1: Pure Mathematics A)Mathematical proof establishes universal truth from initial axioms through a deductive chain.3 objectives
- Algebra and Functions (AS Unit 1: Pure Mathematics A)17 specification points covering Understand and use the laws of indices for all rational exponents., Use and manipulate surds, including rationalising the…51 objectives
- Coordinate geometry in the (x, y) plane (AS Unit 1: Pure Mathematics A)4 specification points covering Understand and use the equation of a straight line, including the forms y = mx + c, y − y₁ = m(x − x₁) and ax + by+ c = 0;…12 objectives
- Sequences and Series - The Binomial Theorem (AS Unit 1: Pure Mathematics A)3 specification points covering Understand and use the binomial expansion of (a + bx)ⁿ for positive integer n ., The notations n!, (n choose r) and nCr.,…9 objectives
- Trigonometry (AS Unit 1: Pure Mathematics A)7 specification points covering Understand and use the definitions of sine, cosine and tangent for all arguments., Understand and use the sine and cosine…21 objectives
- Exponentials and logarithms (AS Unit 1: Pure Mathematics A)13 specification points covering Know and use the function aˣ and its graph, where a is positive., Know and use the function eˣ and its graph., Know that…39 objectives
- Differentiation (AS Unit 1: Pure Mathematics A)6 specification points covering Understand and use the derivative of f (x) as the gradient of the tangent to the graph of y = f (x) at a general point (x,…18 objectives · 1 study page
- Integration (AS Unit 1: Pure Mathematics A)4 specification points covering Know and use the Fundamental Theorem of Calculus., Integrate xⁿ (excluding n = − 1) and related sums, differences and…12 objectives
- Vectors (AS Unit 1: Pure Mathematics A)4 specification points covering Use vectors in two dimensions., Add vectors diagrammatically and perform the algebraic operations of vector addition and…12 objectives
Unit 2: Applied Mathematics A9 topics
- Statistical Sampling (AS Unit 2: Applied Mathematics A)4 specification points covering Understand and use the terms 'population' and 'sample'., Use samples to make informal inferences about the population.,…12 objectives
- Data presentation and interpretation (AS Unit 2: Applied Mathematics A)11 specification points covering Interpret diagrams for single-variable data, including understanding that area in a histogram represents frequency.,…33 objectives
- Probability (AS Unit 2: Applied Mathematics A)3 specification points covering Understand and use mutually exclusive and independent events when calculating probabilities., Link to discrete and…9 objectives
- Statistical distributions (AS Unit 2: Applied Mathematics A)4 specification points covering Understand and use simple, discrete probability distributions., Understand and use, • the binomial distribution, as a model…13 objectives
- Statistical hypothesis testing (AS Unit 2: Applied Mathematics A)4 specification points covering Understand and apply the language of statistical hypothesis testing, developed through a binomial model: null hypothesis,…12 objectives
- Quantities and units in mechanics (AS Unit 2: Applied Mathematics A)2 specification points covering Understand and use fundamental quantities and units in the S.I.6 objectives
- Kinematics (AS Unit 2: Applied Mathematics A)4 specification points covering Understand and use the language of kinematics: position, displacement, distance travelled, velocity, speed, acceleration.,…12 objectives
- Forces and Newton’s laws (AS Unit 2: Applied Mathematics A)8 specification points covering Understand the concept of a force., Understand and use Newton’s first law., Understand and use Newton’s second law for…24 objectives
- Vectors (AS Unit 2: Applied Mathematics A)2 specification points covering Calculate the magnitude and direction of a vector and convert between component form and magnitude/direction form., Use…6 objectives
Unit 3: Pure Mathematics B8 topics
- Proof (A2 Unit 3: Pure Mathematics B)Proof by contradiction assumes the logical negation of the proposition to be proved and demonstrates that this hypothesis inescapably yields a mathematical…3 objectives
- Algebra and Functions (A2 Unit 3: Pure Mathematics B)6 specification points covering Simplify rational expressions, including by factorising and cancelling and by algebraic division (by linear expressions…18 objectives
- Coordinate geometry in the (x, y) plane (A2 Unit 3: Pure Mathematics B)2 specification points covering Understand and use the parametric equations of curves and conversion between Cartesian and parametric forms., Use parametric…6 objectives
- Sequences and Series (A2 Unit 3: Pure Mathematics B)9 specification points covering Understand and use the binomial expansion of (a + bx)n , for any rational n, including its use for approximation., Be aware…28 objectives · 1 study page
- Trigonometry (A2 Unit 3: Pure Mathematics B)11 specification points covering Work with radian measure, including use for arc length, area of sector and area of segment., Understand and use the…33 objectives
- Differentiation (A2 Unit 3: Pure Mathematics B)8 specification points covering Differentiation from first principles for sin x and cos x., Understand and use the second derivative as the rate of change…24 objectives
- Integration (A2 Unit 3: Pure Mathematics B)10 specification points covering Integrate eᵏˣ , 1/x , sinkx, coskx and related sums, differences and constant multiples., Use a definite integral to find…30 objectives
- Numerical Methods (A2 Unit 3: Pure Mathematics B)7 specification points covering Locate roots of f (x) = 0 by considering changes in sign of f (x) in an interval of x in which f (x) is sufficiently…21 objectives
Unit 4: Applied Mathematics B11 topics
- Probability (A2 Unit 4: Applied Mathematics B)3 specification points covering Understand and use conditional probability, including the use of tree diagrams, Venn diagrams and two-way tables.,…9 objectives
- Statistical distributions (A2 Unit 4: Applied Mathematics B)4 specification points covering Understand and use the continuous uniform distribution and Normal distributions as models., Find probabilities using the…12 objectives
- Statistical hypothesis testing (A2 Unit 4: Applied Mathematics B)3 specification points covering Understand and apply statistical hypothesis testing to correlation coefficients as measures of how close data points lie to…9 objectives
- Trigonometry (A2 Unit 4: Applied Mathematics B)Trigonometric functions sin θ, cos θ, and tan θ are indispensable across mechanics for resolving vectors, analysing inclined planes, and modelling periodic…3 objectives
- Differentiation (A2 Unit 4: Applied Mathematics B)Translating contextual physical descriptions into differential equations involves expressing rates of change as derivatives.3 objectives · 1 study page
- Integration (A2 Unit 4: Applied Mathematics B)2 specification points covering Evaluate the analytical solution of simple first order differential equations with separable variables, including finding…6 objectives
- Quantities and units in mechanics (A2 Unit 4: Applied Mathematics B)The moment of a force measures its turning effect about a chosen point or axis of rotation.3 objectives
- Kinematics (A2 Unit 4: Applied Mathematics B)3 specification points covering Extend, use and derive the formulae for constant acceleration for motion in a straight line to 2 dimensions using vectors.,…9 objectives
- Forces and Newton’s laws (A2 Unit 4: Applied Mathematics B)8 specification points covering Extend Newton’s second law to situations where forces need to be resolved (restricted to two dimensions)., Resolve forces in…24 objectives
- Moments (A2 Unit 4: Applied Mathematics B)For a rigid body (such as a uniform beam, rod, or ladder) to remain in static equilibrium, two conditions must be satisfied simultaneously: 1.3 objectives
- Vectors (A2 Unit 4: Applied Mathematics B)2 specification points covering Understand and use vectors in three dimensions., Use vectors to solve problems in context, including forces and kinematics..7 objectives · 1 study page
Assessment and exam guidance
Assessment Objectives
AO1
50%Use and apply standard techniques. Learners should be able to: select and correctly carry out routine procedures; and accurately recall facts, terminology and definitions.
AO2
25%Reason, interpret and communicate mathematically. Learners should be able to: construct rigorous mathematical arguments (including proofs); make deductions and inference; assess the validity of mathematical arguments; explain their reasoning; and use mathematical language and notation correctly.
AO3
25%Solve problems within mathematics and in other contexts. Learners should be able to: translate problems in mathematical and non-mathematical contexts into mathematical processes; interpret solutions to problems in their original context, and, where appropriate, evaluate their accuracy and limitations; translate situations in context into mathematical models; use mathematical models; and evaluate the outcomes of modelling in context, recognise the limitations of models and, where appropriate, explain how to refine them.
Exam Structure
WJEC A-Level (603/1977/X)
Unit 1: Pure Mathematics A
2h 30m
Duration
120
Marks
25%
Weighting
Unit 2: Applied Mathematics A
1h 45m
Duration
75
Marks
15%
Weighting
Unit 3: Pure Mathematics B
2h 30m
Duration
120
Marks
35%
Weighting
Unit 4: Applied Mathematics B
1h 45m
Duration
80
Marks
25%
Weighting
Tips and common mistakes
Common Exam Mistakes
Pitfalls to avoid in your exams
- •using the equivalence arrow ⇔ between steps that are not reversible, such as after squaring both sides of an equation
- •confusing an equation that holds for discrete roots with an identity that holds for all values of the variable
- •treating an expression as an equation by spontaneously introducing "= 0" without mathematical justification
- •writing long chains of equals signs connecting expressions that are not equal, known as running equality
- •asserting a two-way equivalence when an algebraic operation introduces extraneous roots or loses branches
- •confusing union ∪ ("or") with intersection ∩ ("and") when combining solution regions; correct by translating the words into the connective first, then choosing the symbol
- •using round and square brackets interchangeably, misrepresenting whether endpoints are included; correct by checking each inequality for strict < or ≤ before writing the interval
- •treating ⊆ and ⊂ as identical; correct by reserving ⊂ for proper subsets, where equality is excluded
Top Examiner Tips
Expert advice for exam success
- •State defining assumptions explicitly and label key features on diagrams, including intercepts and asymptotes.
- •Reserve the identity symbol ≡ for relationships that remain true across the entire domain, such as trigonometric expansions.
- •Write distinct steps on separate lines rather than chaining equals signs across the page.
- •Verify whether an implication is reversible before using the bidirectional equivalence symbol ⇔.
- •When asked for solutions in set form, use {x ∈ ℝ : ...} and make the inequality strictness match the original question exactly.
- •Sketch a number line to visualise overlap when intersecting intervals, then read off included and excluded endpoints for the bracket choice.
- •When solving quadratic inequalities, sketch the parabola first to see whether the solution is a single interval or two separate tails.
- •Write disjoint intervals with "or" or the union symbol ∪, never as a combined inequality like 2 > x > 5.
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