Library

Find out how to measure the instantaneous change in a function, from the rate of change to the derivative and on to the equation of the tangent line.

Learn how to determine whether a function is increasing or decreasing, and how to summarise its behaviour in a table of variations.

Discover the affine, square, inverse and square root functions: their definitions, variations and graphs, to build a solid foundation in analysis.

Discover the inverse function, its hyperbola and its variations, then learn how to solve equations and inequalities whilst avoiding the usual pitfalls.

Discover the square function, its parabola and its variations, then learn how to solve the equations and inequalities that arise from them.

Discover affine functions, their graphical representations and their real-world applications to master a key tool of analysis at sixth-form level.

Find out how functions model the relationships between quantities, from their definitions and representations right through to the study of their variations.

Study the sine and cosine functions: domain, parity, periodicity, variations, representative graphs and standard transformations.

Learn how to systematically solve common trigonometric equations, and then move on to more complex equations involving changes of variable and multiple angles.

Understands the fundamental relationships and the addition and multiplication formulas to solve equations and calculate angles effectively.

Find out how the unit circle can be used to define the cosine and sine of any real number, including notable values and essential properties.

Discover the unit circle, the key tool for understanding angles in radians, cosine, sine and tangent, along with their notable values and symmetries.

Find out how the cross product can be used to construct a vector perpendicular to two others, to calculate areas and volumes, and to solve problems in solid geometry.

Has a thorough understanding of vectors in three-dimensional space: coordinates, collinearity, coplanarity and the dot product, together with the key methods of three-dimensional geometry.

Use the dot product to calculate angles, prove perpendicularity and solve any type of triangle using efficient methods.

Discover the scalar product and learn how to calculate it in various ways to demonstrate orthogonality and determine lengths or angles.

Learn how to identify two collinear vectors and how to use coordinates to show that points lie on the same line or that two lines are parallel.

Find out how vectors can be used to describe motion and carry out calculations: a key concept that links geometry, algebra and trigonometry.

Move from a sheet of paper to three-dimensional shapes: learn how to describe common solids, calculate their surface areas and volumes, and avoid common mistakes.

Learn how to plot points on a coordinate system, calculate distances and midpoints, and then work with vectors and equations of straight lines.

Discover two transformations of the plane that rotate or enlarge shapes: rotation and similarity, along with their properties and common pitfalls.

Find out how a reflection, a half-turn and a slide can transform a geometric shape, then learn how to construct the image of points and shapes step by step.

Learn how to work out the volume of a cube, a rectangular prism, a cylinder, a pyramid and a sphere using simple formulas and practical examples.

Learn how to work out the perimeter and area of common shapes — rectangles, squares, triangles, circles and discs — using simple formulas.