This is where maths becomes a language: equations that describe lines and curves, triangles that measure heights you cannot reach, and patterns that continue for ever. Each topic starts from its key idea and works through the standard method step by step, with graded practice, so you can explain a method as well as use it.
Rational and irrational numbers, surds and rational powers.
Rational numbers can be written as p/q. Irrational numbers like √2 and π cannot: their decimals never end and never repeat.
Degree, values, zeroes and the remainder and factor theorems.
A polynomial is a sum of terms with whole-number powers of x. Putting x = a into it gives p(a). If p(a) = 0, then (x − a) is a factor.
The four quadrants, points with negative coordinates, and the axes.
Every point is (x, y): x is how far right (+) or left (−), and y is how far up (+) or down (−).
Solutions of ax + by = c, and seeing them as a straight line.
An equation like 2x + y = 6 has infinitely many solutions. Plotted on a graph, they all lie on one straight line.
Parallel lines, triangle angles, congruence and parallelograms.
Parallel lines create equal angles. Triangles add up to 180°. Congruent triangles match exactly, side for side and angle for angle.
Chords, the angle at the centre, semicircles and cyclic quadrilaterals.
Circle theorems link angles and chords. Most of them come from one fact: the angle at the centre is twice the angle at the edge.
The area of any triangle from its three sides.
If you know all three sides of a triangle, Heron’s formula gives the area without needing the height.
Cones, spheres, hemispheres and cylinders.
Surface area is the outside skin, in square units. Volume is the space inside, in cubic units.
Frequency tables, class marks, mean and median.
A frequency table counts how often each value appears. The mean is Σfx ÷ Σf.
