National 5 Mathematics practice

Converting between forms and using percentage change accurately.

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Choosing suitable accuracy and rounding answers sensibly.

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Using index laws with positive, negative and fractional powers.

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Writing very large and very small numbers in standard form.

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Simplifying exact square-root expressions and rationalising simple denominators.

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Multiplying out single and double brackets correctly.

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Taking out common factors and recognising useful factorisations.

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Simplifying, multiplying and adding fractions with algebraic terms.

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Rearranging formulae using inverse operations.

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Solving equations and representing inequality solutions.

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Solving two linear equations by elimination or substitution.

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Using y = mx + c and plotting straight lines

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Finding and interpreting gradient and y-intercept.

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Sketching lines from equations and key points.

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

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Recognising parabolas, roots, intercepts and turning points.

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Sketching simple translations and stretches from a known graph.

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Using intersections and roots to estimate solutions.

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Multiplying two brackets and collecting like terms.

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Writing quadratic trinomials as two brackets.

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Finding roots from factorised form.

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Rewriting quadratics to reveal the turning point.

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Solving quadratics when factorising is not efficient.

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

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Sketching quadratic graphs using roots, intercepts and turning points.

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Finding missing sides in right-angled triangles.

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Using right-angled triangles inside 3D shapes.

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Using standard formulae with correct units.

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Comparing similar shapes and corresponding sides.

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Using length, area and volume scale factors.

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Using radius, diameter, circumference and area relationships.

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

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Measuring and using three-figure bearings.

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

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

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

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

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Recognising sine, cosine and tangent graph features.

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

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Solving simple trig equations over a given interval.

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Writing and interpreting vectors using components and directed line segments.

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Combining vectors using paths and components.

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Multiplying vectors by constants and interpreting direction.

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Using origin-based vectors to describe points.

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Proving points lie on the same straight line.

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Finding points that divide a line in a given ratio.

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

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Comparing consistency using standard deviation.

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Describing correlation and using a line of best fit.

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Calculating probabilities and using complements.

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Using branches to calculate combined probabilities.

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