National 5 Mathematics

Converting between forms and using percentage change accurately.

Choosing suitable accuracy and rounding answers sensibly.

Using index laws with positive, negative and fractional powers.

Writing very large and very small numbers in standard form.

Simplifying exact square-root expressions and rationalising simple denominators.

Multiplying out single and double brackets correctly.

Taking out common factors and recognising useful factorisations.

Simplifying, multiplying and adding fractions with algebraic terms.

Rearranging formulae using inverse operations.

Solving equations and representing inequality solutions.

Solving two linear equations by elimination or substitution.

Using y = mx + c and plotting straight lines

Finding and interpreting gradient and y-intercept.

Sketching lines from equations and key points.

Using f(x), substitution and inverse processes at National 5 level.

Recognising parabolas, roots, intercepts and turning points.

Sketching simple translations and stretches from a known graph.

Using intersections and roots to estimate solutions.

Multiplying two brackets and collecting like terms.

Writing quadratic trinomials as two brackets.

Finding roots from factorised form.

Rewriting quadratics to reveal the turning point.

Solving quadratics when factorising is not efficient.

Using b² − 4ac to identify the number of real roots

Sketching quadratic graphs using roots, intercepts and turning points.

Finding missing sides in right-angled triangles.

Using right-angled triangles inside 3D shapes.

Using standard formulae with correct units.

Comparing similar shapes and corresponding sides.

Using length, area and volume scale factors.

Using radius, diameter, circumference and area relationships.

Finding arc length and sector area from a fraction of a circle.

Measuring and using three-figure bearings.

Using sine, cosine and tangent in right-angled triangles.

Solving non-right-angled triangles with matching angle-side pairs.

Solving non-right-angled triangles when the included angle or all sides are known.

Using Area = 12 ab sin C for non-right-angled triangles

Recognising sine, cosine and tangent graph features.

Using exact trig values for 0, 30, 45, 60 and 90 degrees.

Solving simple trig equations over a given interval.

Writing and interpreting vectors using components and directed line segments.

Combining vectors using paths and components.

Multiplying vectors by constants and interpreting direction.

Using origin-based vectors to describe points.

Proving points lie on the same straight line.

Finding points that divide a line in a given ratio.

Finding and interpreting mean, median, mode, range and interquartile range.

Comparing consistency using standard deviation.

Describing correlation and using a line of best fit.

Calculating probabilities and using complements.

Using branches to calculate combined probabilities.