Mathematics Methods – Foundation Level 3 course MTM315117, Version 4
The external written examination is 180 working minutes with an additional 15-minute preparation period and totals 180 marks. Section A is 80 marks without a calculator and is collected 80 minutes after the examination starts. Section B is 100 marks and may be started earlier, but a calculator may be used only after Section A has been collected. Each section has five compulsory parts aligned to criteria 4–8. The exam supplies the current MTM315117 information sheet; students may use TASC-approved calculators under the stated timing rule. The exam contributes five of the thirteen ratings used for the final award; TASC does not state this as a percentage weighting.
Past papers on this subject span more than one course document. Papers written under an older one still work as practice, but the modules they test have changed — the index labels every paper with the course document it was set under.
MTM315117 papers — compare with the current Version 4 course · 2019–2025
The modules, one by one
Each area below lists the concepts named in the course document, what the TASC exam asks of them, and the mistake that most often costs marks.
- Area of study 1: Algebra
- Area of study 2: Polynomial functions and graphs
- Area of study 3: Exponential, logarithmic and circular (trigonometric) functions and graphs
- Area of study 4: Calculus
- Area of study 5: Probability and statistics
Area 1 of 5
Area of study 1: Algebra
Build fluent symbolic work with formulae, quadratics, cubics, indices, surds and simultaneous equations, including binomial expansions for powers from 2 to 5.
What the exam asks
Expand, factorise and solve accurately; use the discriminant, factor theorem, index laws and exact algebraic forms; communicate steps that justify each result.
Where marks go missing
Do not infer that every cubic has three real zeros or discard domain restrictions introduced by radicals, logarithms or algebraic fractions.
Area 2 of 5
Area of study 2: Polynomial functions and graphs
Connect equations and graphs for linear, quadratic and cubic functions, including intercepts, turning points, repeated zeros, domain, range and permitted transformations.
What the exam asks
Find equations from features, sketch with labelled evidence and interpret polynomial models on a stated domain. The reciprocal and square-root power graphs are introductory and non-examinable.
Where marks go missing
A correct algebraic equation does not by itself show a complete sketch; label the key features and honour the domain of a model.
Area 3 of 5
Area of study 3: Exponential, logarithmic and circular (trigonometric) functions and graphs
Use exponential and logarithmic laws and models, radian measure, arc length, right-triangle trigonometry, sine and cosine rules, unit-circle exact values and circular-function graphs.
What the exam asks
Solve equations, interpret growth and decay, calculate sides and angles, and sketch the specified dilations, reflections and period changes of sine, cosine and tangent graphs.
Where marks go missing
The course graph scope uses a sin(bx), a cos(bx) and tan(bx) forms without phase or vertical shifts; keep exact values until a decimal is requested.
Area 4 of 5
Area of study 4: Calculus
Interpret average and instantaneous rates, differentiate permitted polynomial, rational and negative-power expressions, and use gradients to study tangents, normals, stationary points and motion.
What the exam asks
Apply the power rule, difference quotients and first principles in the specified cases, then connect the derivative's sign and value to the original function and its context.
Where marks go missing
Integration and the product, quotient and chain rules are outside this Foundation course; a rate answer in context needs the correct units.
Area 5 of 5
Area of study 5: Probability and statistics
Represent events with lists, grids, Venn and tree diagrams, then apply complements, addition, conditional probability, independence, combinations and relative frequency.
What the exam asks
Choose a representation, show the relevant event counts or probabilities, distinguish conditional from independent events and interpret simulations and experimental estimates.
Where marks go missing
nCr counts unordered selections. Mutually exclusive events and independent events are different conditions and use different probability relationships.