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 — Proof
- 1.1
Proof by contradiction
- Proof by contradiction.
- Guidance: Including proof of the irrationality of √2 and the infinity of primes, and application to unfamiliar proofs.
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2 — Algebra and functions
- 2.1
Partial fractions decomposition
- Decompose rational functions into partial fractions (denominators not more complicated than repeated linear terms).
- Guidance: Partial fractions to include denominators such as (ax + b)(cx + d)(ex + f) and (ax + b)(cx + d)². The degree of the numerator may equal or exceed the degree of the denominator. Applications to integration, differentiation and series expansions. Quadratic factors in the denominator such as (x² + a), a > 0, are not required.
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3 — Coordinate geometry in the (x, y) plane
- 3.1
Parametric equations and conversion between forms
- Parametric equations of curves and conversion between cartesian and parametric forms.
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4 — Binomial expansion
- 4.1
Binomial series for any rational n
- Binomial Series for any rational n.
- Guidance: For |x| < b/a, students should be able to obtain the expansion of (ax + b)ⁿ, and the expansion of rational functions by decomposition into partial fractions.
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5 — Differentiation
- 5.1
Implicit and parametric differentiation
- Differentiation of simple functions defined implicitly or parametrically.
- Guidance: The finding of equations of tangents and normals to curves given parametrically or implicitly is required.
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- 5.2
Formation of simple differential equations
- Formation of simple differential equations.
- Guidance: Questions involving connected rates of change may be set.
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6 — Integration
- 6.1
Volume of revolution
- Evaluation of volume of revolution.
- Guidance: π∫y² dx is required, but not π∫x² dy. Students should be able to find a volume of revolution, given parametric equations.
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- 6.2
Integration by substitution and by parts
- Simple cases of integration by substitution and integration by parts. Understand these methods as the reverse processes of the chain and product rules respectively.
- Guidance: Students will be expected to use a substitution to find, e.g. ∫x√(x − 2) dx. The substitution will be given in more complicated integrals. The integral ∫ln x dx is required. More than one application of integration by parts may be required, for example, ∫x²eˣ dx, ∫eˣ sin x dx.
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- 6.3
Integration using partial fractions
- Simple cases of integration using partial fractions.
- Guidance: Integration of rational expressions such as those arising from partial fractions, e.g. 2/(3x+5), 3/(x−1)². Note that the integration of other rational expressions, such as x/(x²+5) and 2/(2x−1)⁴ is also required (see P3 section 5.2).
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- 6.4
Separable differential equations
- Analytical solution of simple first order differential equations with separable variables.
- Guidance: General and particular solutions will be required.
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- 6.5
Area under a parametric curve
- Use integration to find the area under a curve given its parametric equations.
- Guidance: Students should be able to find the area under a curve given its parametric equations. Students will not be expected to sketch a curve from its parametric equations.
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7 — Vectors
- 7.1
Vectors in two and three dimensions
- Vectors in two and three dimensions.
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- 7.2
Magnitude of a vector
- Magnitude of a vector.
- Guidance: Students should be able to find a unit vector in the direction of a, and be familiar with |a|.
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- 7.3
Vector addition and scalar multiplication
- Algebraic operations of vector addition and multiplication by scalars, and their geometrical interpretations.
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- 7.4
Position vectors
- Position vectors.
- Guidance: OB − OA = AB = b − a (with an arrow/overbar on OB, OA and AB in the original, denoting directed line segment vectors; not reproducible in plain text here).
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- 7.5
The distance between two points
- The distance between two points.
- Guidance: The distance d between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) is given by d² = (x₁ − x₂)² + (y₁ − y₂)² + (z₁ − z₂)².
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- 7.6
Vector equations of lines
- Vector equations of lines.
- Guidance: To include the forms r = a + tb and r = c + t(d − c). Conditions for two lines to be parallel, intersecting or skew.
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- 7.7
The scalar product
- The scalar product. Its use for calculating the angle between two lines.
- Guidance: Students should know that for OA = a = a₁i + a₂j + a₃k and OB = b = b₁i + b₂j + b₃k then a.b = a₁b₁ + a₂b₂ + a₃b₃ and cos∠AOB = a.b/|a||b|. Students should know that if a.b = 0, and a and b are non-zero vectors, then a and b are perpendicular.
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