MathsQ&A by dot point

Using differentiation to find the optimal value in optimisation problems, the greatest and least values of a function on a closed interval, rates of change, and the motion of a particle through displacement, velocity and acceleration.

Using integration to find the area enclosed between a curve and a line or between two curves, the area below the x-axis, recovering displacement from velocity, and using a definite integral to evaluate an accumulated quantity in context.

Recurrence relations of the form u sub n plus 1 equals a u sub n plus b, generating terms, the condition for a limit to exist, finding the limit, and interpreting a recurrence relation in a real context.

The equation of a circle with centre the origin and with a general centre, the general equation of a circle, finding the centre and radius, the intersection of a line and a circle, and the equation of a tangent to a circle.

The laws of logarithms and their use in simplifying expressions and solving equations, the relationship between exponential and logarithmic form, and the use of logarithms to find the parameters in experimental laws of the form y equals k x to the n and y equals a b to the x.

Functions and their domain and range, composite functions, inverse functions, exponential and logarithmic graphs, and the graphs that result from translating, reflecting and stretching a known function.

The gradient of a line including the connection to the angle it makes with the x-axis, the equation of a line through a point with a given gradient, parallel and perpendicular lines, and the medians, altitudes and perpendicular bisectors of a triangle.

Radian measure and the conversion between degrees and radians, exact values of sine, cosine and tangent for the standard angles, the graphs of the trigonometric functions, and the transformations that change their amplitude, period and phase.

Vectors in three dimensions, the magnitude and unit vector, addition and scalar multiplication, the section formula and collinearity, and the scalar product including its use to find the angle between two vectors and to test for perpendicularity.

Differentiation of polynomial, root and reciprocal functions and of sine and cosine, the gradient of a curve and the equation of a tangent, increasing and decreasing functions, and stationary points and their nature.

Integration as the reverse of differentiation, the indefinite integral of polynomial and trigonometric functions with the constant of integration, the definite integral, and the use of integration to find the area under a curve and the area between two curves.

Completing the square and the properties of the quadratic, the discriminant and the nature of the roots, the condition for a quadratic to be always positive or always negative, the factor and remainder theorems, and solving and sketching polynomials.

The addition (compound angle) formulae for sine and cosine, the double angle formulae, their use in proving identities and solving equations, and the wave function that expresses a sin x plus b cos x in the form k sin of x plus a.

Differentiating composite functions with the chain rule, including expressions of the form a function of a linear expression and sine and cosine of a linear expression, and reversing the process to integrate functions of the form (ax + b) to the n, sin(ax + b) and cos(ax + b).

Solving trigonometric equations in degrees and radians over a given interval, using the CAST diagram and the symmetry of the graphs, the trigonometric identities, and equations that reduce to a quadratic in a single trigonometric ratio.