Library

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

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

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.

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

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.

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

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

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.

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.

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

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

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

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

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

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

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

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

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

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

Learn how to recognise the multiples and divisors of a number, how to use the criteria for divisibility, and how to factorise a number into prime factors, with simple examples and pitfalls to avoid.

Find out what a fraction really is, how to read it, where to place it on a number line and how to compare it with others, using examples from everyday life.

Performing calculations with letters, simplifying an expression, solving a linear equation. A natural progression from the basics of arithmetic.

What we measure, what we use to measure it, and how to record the result. The foundation of all physics. No prior knowledge required.