AS and A2‎ > ‎Core 1 (C1)‎ > ‎

C1 Topic List

1 Algebra and functions

Laws of indices.

Use and manipulation of surds including rationalising denominators.

Quadratic functions and their graphs.

Solution of quadratic equations by factorisation, use of the formula and completing the square.

The discriminant of a quadratic function.

Solution of linear inequalities.

Solution of quadratic inequalities.

Algebraic manipulation of polynomials, including expanding brackets and collecting like terms, factorisation.

Graphs of functions

Sketching curves defined by simple equations. Knowledge of the term asymptote is expected.

Geometrical interpretation of algebraic solution of equations including use of intersection points of graphs of functions to solve equations.

Knowledge of the effect of simple transformations on the graph of y = f(x) as represented by y = af(x), y = f(x) + a, y = f(x + a), y = f(ax).


2 Coordinate geometry in the(x, y) plane

Equation of a straight line, including the forms y  = mx+ c, y y1 = m(x x1),

(y y1)/ (y2 y1) =  (x x1)/ (x2 x1) and ax + by + c = 0.

The equation of a line through two given points

The equation of a line parallel (or perpendicular) to a given line through a given point.

Condition for two straight lines to be parallel to each other.

Condition for two straight lines to be perpendicular to each other.


3 Sequences and series

Sequences, including those given by a formula for the nth term and those generated by a simple relation of the form xn+1 = f(xn).

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

The proof of the sum formula should be known.

Understanding of Σ notation will be expected.


4 Differentiation

The derivative of f(x) as the gradient of the tangent to the graph of y = f (x) at a point; The notation f (x) may be used.

The gradient of the tangent as a limit;

Interpretation as a rate of change;

Second order derivatives. The notation f ′′ (x) may be used.

Applications of differentiation to gradients, tangents and normals.

Use of differentiation to find equations of tangents and normal at specific points on a curve.


5 Integration

Indefinite integration as the reverse of differentiation. Including knowledge  that a constant of integration is required.

Integration of xn.

Given f (x) and a point on the curve, students should be able to find an equation of the curve in the form y = f(x).