AS and A2‎ > ‎Core 2 (C2)‎ > ‎

C2 Topic List

 

1 Algebra and functions

Simple algebraic division

Use of the Factor Theorem and the Remainder Theorem.

Knowledge that if f(x) = 0 when x = a, then (x a) is a factor of f(x).

 

2 Coordinate geometry in the (x, y) plane

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.

 

3 Sequences and series

The sum of a finite geometric series; the sum to infinity of a convergent geometric series, including the use of |r| < 1.

The general term and the sum to n terms are required.

The proof of the sum formula should be known.

Binomial expansion of (1 + x)n for positive integer n.

Expansion of (a + bx)n may be required.

The notation n! is needed.

 

4 Trigonometry

The sine and cosine rules, and the area of a triangle in the form ½ab sin C.

Radian measure, including use for arc length and area of sector.

Use of the formulae s = rθ and A =  r2θ/2 for a circle.

Sine, cosine and tangent functions. Their graphs, symmetries and periodicity.

Transformations of sin, cos and tan graphs.

Knowledge and use of tan θ = sin θ/tan θ , and sin2θ + cos2 θ ≡ 1.

Solution of simple trigonometric equations in a given interval.

Knowledge of the general solutions for sin, cos and tan

 

5 Exponentials and logarithms

y = ax and its graph.

Laws of logarithms, to include

log a xy = log a x + log a y,

log a xy = log a x log a y,

loga xk = k log a x,

loga (1/x) = − log a x 

logaa = 1

The solution of equations of the form ax = b.

Base change formula.

 

6 Differentiation

Applications of differentiation to maxima and minima and stationary points, increasing and decreasing functions.

Use of the notation f(x) for the second order derivative.

To include applications to curve sketching.

 

Maxima and minima problems may be set in the context of a practical problem.

 

7 Integration

Evaluation of definite integrals.

Interpretation of the definite integral as the area under a curve, including the area of a region bounded by a curve and given straight lines.

Approximation of area under a curve using the trapezium rule.