National 5 Mathematics

Simplifying surds, rationalising denominators, and the laws of indices.

Significant figures, reverse percentages, and appreciation/depreciation.

The four operations on fractions and mixed numbers.

Expanding brackets (including trinomials and combined expressions) and factorising by common factor, difference of squares, and trinomials.

Simplifying algebraic fractions and applying the four operations to them.

Gradient, the equation of a line, and reading gradient/intercept from any form of the equation.

Solving linear equations and inequations with rational coefficients and solutions.

Constructing simultaneous equations from text, and solving graphically and algebraically.

Rearranging a linear formula, and a formula involving a square or square root.

Recognising, sketching from either factorised or turning-point form, and identifying features of a quadratic function's graph.

Writing a quadratic in turning-point form without needing to graph it.

Solving by factorising, the quadratic formula, graphical treatment, and using the discriminant.

Volume of spheres, cones and pyramids, and arc length/sector area of a circle.

Pythagoras' theorem in complex and 3D situations, and angle properties of shapes.

The scale relationship between length, area, and volume in similar shapes.

2D and 3D vectors, components, magnitude, and reading 3D coordinates from a diagram.

Graphs of sine, cosine and tan (including multiple angle graphs), and solving trig equations between 0° and 360°.

Area of a triangle, the sine and cosine rules for a side or an angle, and bearings.

Comparing data sets with interquartile range and standard deviation, and linear models.