AQA Level 2 Certificate Further Mathematics Revision
Explore AQA Level 2 Certificate Further Mathematics revision topics. This qualification is not a GCSE; the existing guide address and saved checklist are retained. Check the official specification for complete requirements.
Course details
Assessment The assessment includes Paper 1 and Paper 2; see the official specification for the full structure.
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Reviewed course guidance
Revision points, with the explanation beside them
Open a point to read what to know, how to use it in an assessment, a plain-language explanation and a self-check. Answers stay hidden until you choose to reveal them.
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Topic group
Reviewed requirements
- Core
Scope: Core · §4 Calculus, 4.3 — differentiate kx^n for integer n and sums of such functions
Open revision guidance
What to know
- For a constant k and integer n, the power rule gives d(kx^n)/dx = knx^(n−1). Differentiate each term of a sum separately; a constant term has derivative zero.
What to do in an assessment
- Simplify the expression if needed, apply the power rule term by term, and collect like terms. Check the result by differentiating each original term independently.
In plain language
Differentiation measures how quickly the function changes. The exponent moves in front as a multiplier, then falls by one. For example, the derivative of 3x^4 − 2x^2 + 7 is 12x^3 − 4x: the constant 7 disappears because it does not change as x changes. The qualification's 4.3 specifically covers integer powers and sums, so this guide does not extend that rule to non-integer powers as though they were required here.
Self-check
Differentiate y = 5x^3 − 4x + 9.
Show the answer
dy/dx = 15x^2 − 4.
- Core
Scope: Core · §3 Number, 1.3 — manipulate surds and rationalise denominators; includes all three specification examples
Open revision guidance
What to know
- Surds are irrational roots kept in exact form. Simplify by extracting square factors, combine only like surds, and rationalise a denominator by multiplying by a suitable surd or conjugate.
What to do in an assessment
- Rewrite each radical using square factors, collect matching terms, and use the conjugate when a denominator is a binomial. Simplify the resulting integer and surd coefficients fully.
In plain language
The specification's first example becomes √200−√72+3√162=10√2−6√2+27√2=31√2. For the second, multiply (3√2+4)/(5√2−7) by (5√2+7)/(5√2+7); the denominator is 50−49=1, giving 58+41√2. For its third example, multiplying (3√3+7)/(3√3−5) by the conjugate gives (62+36√3)/2=31+18√3. Keeping exact values avoids premature rounding and makes each simplification checkable.
Self-check
Rationalise 10/√5 and simplify √20.
Show the answer
10/√5=2√5; √20=2√5.
- Core
Scope: Core · §3 Matrix Transformations, 5.3 — unit-square transformations about the origin; rotations, listed reflections and enlargements
Open revision guidance
What to know
- A 2×2 matrix maps a point vector (x,y) to its transformed coordinates. The specification limits these transformations to rotations by 90°, 180° or 270° about the origin, reflections in x=0, y=0, y=x or y=−x, and enlargements centred at the origin.
What to do in an assessment
- Apply the matrix to each coordinate column, then identify the image of the unit square's vertices. For a combination, apply the rightmost matrix first when matrices act on column vectors.
In plain language
An anticlockwise quarter-turn about the origin is represented by [[0,−1],[1,0]]. It sends (1,0) to (0,1), so the bottom-right vertex of the unit square moves to the top-left. The matrices for reflections in the axes swap or reverse the appropriate coordinate; for example, reflection in y=0 uses [[1,0],[0,−1]]. An enlargement by scale factor k uses [[k,0],[0,k]]. The listed centres and lines matter: this specification does not ask this matrix card to cover arbitrary translated transformations.
Self-check
Apply the 180° rotation matrix [[−1,0],[0,−1]] to the point (1,1).
Show the answer
The image is (−1,−1).
Earlier topic checklist
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Further Mathematics topic list
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These ticks keep your earlier topic checklist. They do not count towards the new reviewed requirements above. Its numbering may be internal; use the linked references above for the exact reviewed source requirements.
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