National 5 Mathematics practice

Simplify surds, combine suitable surds and rationalise denominators in exact form.

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Use positive, negative and fractional indices in single and combined calculations.

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Write, compare and calculate with numbers in scientific notation.

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Round values to a stated number of significant figures and judge suitable accuracy.

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Find an original quantity before a percentage increase or decrease.

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Model repeated percentage change, including compound interest, appreciation and depreciation.

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Add, subtract, multiply and divide fractions, including mixed numbers and combined operations.

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Expand single, double and linear-by-quadratic brackets with positive and negative coefficients.

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Factorise common factors, difference of squares and unitary or non-unitary trinomials.

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Rewrite a unitary quadratic in completed-square form and identify its turning point.

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Simplify and use all four operations with algebraic fractions while respecting excluded values.

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Find gradients and equations of straight lines from points, gradients and equation forms.

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Solve multi-step linear equations and inequations with rational coefficients and solutions.

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Construct and solve simultaneous linear equations algebraically, graphically and from contexts.

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Rearrange linear formulae and formulae involving a simple square or square root.

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Recognise, sketch and interpret quadratic functions in factorised and completed-square forms.

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Solve quadratic equations by factorising or by reading roots from a graph.

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Use the quadratic formula accurately, including careful sign handling and rounding.

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Use the discriminant to calculate and describe the number and nature of real roots.

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Use the relationship between a circle's centre, a chord and its perpendicular bisector.

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Calculate arc lengths, sector areas and reverse circle measures.

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Calculate and reverse the volume of spheres, cones and pyramids.

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Apply Pythagoras in complex, converse and three-dimensional situations.

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Use at least two linked angle facts in polygons, triangles, quadrilaterals and circles.

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Use linked length, area and volume scale factors in forward and reverse problems.

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Use directed line segments and two− or three-dimensional vector components, including magnitude.

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Determine the coordinates of points from diagrams of three-dimensional objects.

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Use sine, cosine and tangent to find sides and angles in right-angled triangles.

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Recognise and interpret basic and transformed sine, cosine and tangent graphs.

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Solve sine, cosine and tangent equations in degrees over stated intervals.

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Use the two National 5 identities to find values and simplify expressions.

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Use the sine area formula in direct and reverse non-right-angled triangle problems.

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Use the sine rule to find a missing side or angle from matching side-angle pairs.

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Use the cosine rule to find a missing side or angle in a non-right-angled triangle.

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Use three-figure bearings with trigonometry to find distances and directions.

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Determine quartiles and use the interquartile range to compare the spread of data.

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Calculate or determine standard deviation and interpret it as a measure of spread.

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Compare centre and spread using interquartile range and standard deviation in context.

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Form and use a best-fitting straight-line model from scattergraph data.

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