Spec coverage
Every spec point, and what actually teaches it
The real numbered content list from the official Pearson specification, each point matched to the lesson that covers it. Click through to a lesson from its spec point below, or rate how confident you feel — saved in this browser so it’s there next time you come back. Any point with no matching lesson is flagged, not hidden.
18 spec points · 18 covered
0/18 self-rated
1 — Algebra and functions
- 1.1
Simplification of rational expressions and algebraic division
- Simplification of rational expressions including factorising and cancelling, and algebraic division.
- Guidance: denominators of rational expressions will be linear or quadratic, e.g. 1/(ax+b), (ax+b)/(px²+qx+r), (x³+1)/(x²−1).
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- 1.2
Functions: domain, range, composition, inverse
- Definition of a function. Domain and range of functions. Composition of functions. Inverse functions and their graphs.
- Guidance: the concept of a function as a one-one or many-one mapping from ℝ (or a subset of ℝ) to ℝ. The notation f: x ↦ … and f(x) will be used. Students should know that fg means 'do g first, then f', and that if f⁻¹ exists, f⁻¹f(x) = ff⁻¹(x) = x.
Functions: Domain, Range, Composition and Inverseseˣ, ln x, and Estimating Parameters from Logarithmic GraphsHow confident are you on this?
- 1.3
The modulus function
- The modulus function.
- Guidance: students should be able to sketch the graphs of y = |ax + b| and the graphs of y = |f(x)| and y = f(|x|), given the graph of y = f(x).
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- 1.4
Combinations of graph transformations
- Combinations of the transformations y = f(x) as represented by y = af(x), y = f(x) + a, y = f(x + a), y = f(ax).
- Guidance: the graph of y = f(ax + b) will not be required.
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2 — Trigonometry
- 2.1
Secant, cosecant, cotangent, and inverse trig functions
- Knowledge of secant, cosecant and cotangent and of arcsin, arccos and arctan. Their relationships to sine, cosine and tangent. Understanding of their graphs and appropriate restricted domains.
- Guidance: angles measured in both degrees and radians.
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- 2.2
sec²θ and cosec²θ identities
- Knowledge and use of sec²θ = 1 + tan²θ and cosec²θ = 1 + cot²θ.
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- 2.3
Double angle and compound angle formulae; harmonic form
- Knowledge and use of double angle formulae; use of formulae for sin(A ± B), cos(A ± B) and tan(A ± B) and of expressions for a cos θ + b sin θ in the equivalent forms of r cos(θ ± α) or r sin(θ ± α).
- Guidance: to include application to half angles. Knowledge of the t (tan ½θ) formulae will not be required. Students should be able to solve equations such as a cos θ + b sin θ = c in a given interval, and to prove identities such as cos x cos 2x + sin x sin 2x ≡ cos x.
Compound Angle and Double Angle Formulae: From sin(A±B) to sin2A, cos2A and tan2AHarmonic Form: Writing a cos t + b sin t as R cos(t ± a)Integration by Recognising a Known DerivativeHow confident are you on this?
3 — Exponential and logarithms
- 3.1
The function eˣ and its graph
- The function eˣ and its graph.
- Guidance: to include the graph of y = e^(ax+b) + c.
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- 3.2
The function ln x and its graph
- The function ln x and its graph; ln x as the inverse function of eˣ.
- Guidance: solution of equations of the form e^(ax+b) = p and ln(ax + b) = q is expected.
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- 3.3
Logarithmic graphs to estimate parameters
- Use logarithmic graphs to estimate parameters in relationships of the form y = axⁿ and y = kbˣ.
- Guidance: plot log y against log x and obtain a straight line where the intercept is log a and the gradient is n. Plot log y against x and obtain a straight line where the intercept is log k and the gradient is log b.
eˣ, ln x, and Estimating Parameters from Logarithmic GraphsExponential Growth and Decay, Rates of Change, and the Limits of a ModelHow confident are you on this?
4 — Differentiation
- 4.1
Differentiation of e^(kx), ln kx, sin kx, cos kx, tan kx
- Differentiation of e^(kx), ln kx, sin kx, cos kx, tan kx and their sums and differences.
Differentiating Standard Functions, and the Product, Quotient and Chain RulesExponential Growth and Decay, Rates of Change, and the Limits of a ModelHow confident are you on this?
- 4.2
Product, quotient and chain rules
- Differentiation using the product rule, the quotient rule and the chain rule.
- Guidance: differentiation of cosec x, cot x and sec x are required. Skill will be expected in the differentiation of functions generated from standard functions using products, quotients and composition, such as 2x⁴ sin x, e^(3x)/x, cos x² and tan² 2x.
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- 4.3
dy/dx = 1 / (dx/dy)
- The use of dy/dx = 1 / (dx/dy).
- Guidance: for example, finding dy/dx for x = sin 3y.
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- 4.4
Exponential growth and decay
- Understand and use exponential growth and decay.
- Guidance: students should be familiar with terms such as 'initial', meaning when t = 0. Students may need to explore the behaviour for large values of t or to consider whether the range of values predicted is appropriate. Consideration of a second improved model may be required. Knowledge and use of the result d/dx(aˣ) = aˣ ln a is expected.
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5 — Integration
- 5.1
Integration of e^(kx), 1/x, sin kx, cos kx
- Integration of e^(kx), 1/x, sin kx, cos kx and their sums and differences.
- Guidance: to include integration of standard functions such as sin 3x, e^(5x), 1/(2x).
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- 5.2
Integration by recognition of known derivatives
- Integration by recognition of known derivatives to include integrals of the form ∫ f′(x)/f(x) dx = ln(f(x)) + c and ∫ f′(x)[f(x)]ⁿ dx = [f(x)]ⁿ⁺¹/(n+1) + c.
- Guidance: for example, to include integration of tan x, sec² 2x. Students are expected to be able to use trigonometric identities to integrate, for example, sin² x, tan² x, cos² 3x.
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6 — Numerical methods
- 6.1
Location of roots by sign change
- Location of roots of f(x) = 0 by considering changes of sign of f(x) in an interval of x in which f(x) is continuous.
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- 6.2
Approximate solution of equations using iteration
- Approximate solution of equations using simple iterative methods, including recurrence relations of the form xₙ₊₁ = f(xₙ).
- Guidance: solution of equations by use of iterative procedures, for which leads will be given.
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