National 5 Mathematics

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

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

Write, compare and calculate with numbers in scientific notation.

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

Find an original quantity before a percentage increase or decrease.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Calculate arc lengths, sector areas and reverse circle measures.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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