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.
19 spec points · 19 covered
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1 — Proof
- 1.1
Structure of mathematical proof
- Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof stated below:
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- 1.2
Proof by exhaustion
- Proof by exhaustion
- Guidance: Proof by exhaustion. This involves trying all the options. Suppose x and y are odd integers less than 7. Prove that their sum is divisible by 2.
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- 1.3
Disproof by counter example
- Disproof by counter example.
- Guidance: Disproof by counter example – show that the statement “n² − n + 1 is a prime number for all values of n” is untrue.
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2 — Algebra and functions
- 2.1
Simple algebraic division; Factor and Remainder Theorems
- Simple algebraic division; use of the Factor Theorem and the Remainder Theorem.
- Guidance: Only division by (ax + b) or (ax − b) will be required, e.g. students should know that if f(x) = 0 when x = b/a, then (ax − b) is a factor of f(x). Students may be required to factorise cubic expressions such as x³ + 3x² − 4 and 6x³ + 11x² − x − 6. Students should be familiar with the terms ‘quotient’ and ‘remainder’ and be able to determine the remainder when the polynomial f(x) is divided by (ax + b).
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3 — Coordinate geometry in the (x, y) plane
- 3.1
Coordinate geometry of the circle
- Coordinate geometry of the circle using the equation of a circle in the form (x − a)² + (y − b)² = r² and including use of the following circle properties: (i) the angle in a semicircle is a right angle; (ii) the perpendicular from the centre to a chord bisects the chord; (iii) the perpendicularity of radius and tangent.
- Guidance: Students should be able to find the radius and the coordinates of the centre of the circle, given the equation of the circle and vice versa.
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4 — Sequences and series
- 4.1
Sequences: nth term formulae and recurrence relations
- Sequences, including those given by a formula for the nth term and those generated by a simple relation of the form x_(n+1) = f(x_n).
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- 4.2
Arithmetic sequences and series
- Understand and work with arithmetic sequences and series, including the formula for the nth term and the sum of a finite arithmetic series; the sum of the first n natural numbers.
- Guidance: The proof of the sum formula should be known. Understanding of ∑ notation will expected.
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- 4.3
Increasing, decreasing and periodic sequences
- Increasing sequences, decreasing sequences and periodic sequences.
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- 4.4
Geometric sequences and series
- Understand and work with geometric sequences and series, including the formulae for the nth term and the sum of a finite geometric series; the sum to infinity of a convergent geometric series, including the use of |r| < 1.
- Guidance: For example, given the sum of a series students should be able to use logs to find the value of n. The proof of the sum formula for a finite series should be known. The sum to infinity may be expressed as S∞.
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- 4.5
Binomial expansion of (a + bx)^n
- Binomial expansion of (a + bx)^n for positive integer n.
- Guidance: The notations n!, (n choose r) and ⁿC_r may be used.
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5 — Exponentials and logarithms
- 5.1
The graph of y = a^x
- y = a^x and its graph.
- Guidance: a > 0, a ≠ 1
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- 5.2
Laws of logarithms
- Laws of logarithms.
- Guidance: To include log_a(xy) ≡ log_a x + log_a y, log_a(x/y) ≡ log_a x − log_a y, log_a(x^k) ≡ k log_a x, log_a(1/x) ≡ −log_a x, log_a a = 1, where a, x, y > 0, a ≠ 1.
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- 5.3
Solving equations of the form a^x = b
- The solution of equations of the form a^x = b.
- Guidance: Students may use the change of base formula.
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6 — Trigonometry
- 6.1
tan θ = sin θ / cos θ and sin²θ + cos²θ = 1
- Knowledge and use of tan θ = sin θ/cos θ, and sin²θ + cos²θ = 1.
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- 6.2
Solving trigonometric equations in a given interval
- Solution of simple trigonometric equations in a given interval.
- Guidance: Students should be able to solve equations such as sin(x + π/2) = 3/4 for 0 < x < 2π, cos(x + 30°) = 1/2 for −180° < x < 180°, tan 2x = 1 for 90° < x < 270°, 6 cos²x + sin x − 5 = 0 for 0 ≤ x < 360°, sin²(x + π/6) = 1/2 for −π ≤ x < π.
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7 — Differentiation
- 7.1
Stationary points, curve sketching, increasing/decreasing functions
- Applications of differentiation to maxima and minima and stationary points, increasing and decreasing functions.
- Guidance: To include applications to curve sketching. Maxima and minima problems may be set in the context of a practical problem.
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8 — Integration
- 8.1
Evaluation of definite integrals
- Evaluation of definite integrals.
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- 8.2
The definite integral as area under a curve
- Interpretation of the definite integral as the area under a curve.
- Guidance: Students will be expected to be able to evaluate the area of a region bounded by a curve and given straight lines. For example, find the finite area bounded by the curve y = 6x − x² and the line y = 2x. ∫ x dy will not be required. Students will be expected to be able to evaluate the area of a region bounded by two curves.
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- 8.3
Approximating area with the trapezium rule
- Approximation of area under a curve using the trapezium rule.
- Guidance: For example, use the trapezium rule to approximate ∫₀¹ √(2x+1) dx using four strips. Use of increasing number of trapezia to improve accuracy and an estimate of the error may be required.
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