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12 dot points across 12 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you rearrange a formula to change its subject, including formulae with squares and roots?

Changing the subject of a formula, including formulae involving brackets, fractions, squares and square roots.
A focused answer to the SQA National 5 Mathematics changing-the-subject content, covering how to rearrange a formula to make a different variable the subject, including formulae with brackets, fractions, squares and square roots.
8 min answer →

How do you solve linear equations and inequations, including those with brackets and fractions?

Solving linear equations and inequations in one variable, including equations with brackets, fractions and the unknown on both sides, and representing inequation solutions.
A focused answer to the SQA National 5 Mathematics equations and inequations content, covering solving linear equations with brackets, fractions and the unknown on both sides, and solving linear inequations including the rule for reversing the sign when dividing by a negative.
9 min answer →

How do you read and use function notation, evaluate a function and solve for an input?

Working with functional notation: evaluating a function f of x for a given input, finding the input that gives a required output, and identifying a function from its formula.
A focused answer to the SQA National 5 Mathematics functional notation content, covering how to read f of x notation, evaluate a function for a given value including negatives, find the input that produces a given output, and substitute expressions into a function.
8 min answer →

How do you use angle properties of triangles, polygons, parallel lines and circles to find missing angles?

Using the angle properties of triangles, quadrilaterals and polygons, angles in parallel lines, and the symmetry and angle properties of the circle to calculate missing angles.
A focused answer to the SQA National 5 Mathematics shape and angle content, covering angle sums of triangles and polygons, angles in parallel lines, the angle in a semicircle, the tangent-radius right angle, and using the symmetry of the circle to find missing angles.
9 min answer →

How do you use Pythagoras theorem to find a missing side in a right-angled triangle, including in three dimensions?

Using Pythagoras theorem to find a missing side of a right-angled triangle, including the converse to test for a right angle and applications in three dimensions.
A focused answer to the SQA National 5 Mathematics Pythagoras content, covering finding the hypotenuse and a shorter side of a right-angled triangle, using the converse to check for a right angle, and applying Pythagoras in three dimensions.
9 min answer →

How do you sketch a quadratic function and solve a quadratic equation by factorising, by formula or graphically?

Sketching and interpreting quadratic functions and their graphs, and solving quadratic equations by factorising, by the quadratic formula and graphically.
A focused answer to the SQA National 5 Mathematics quadratics content, covering the shape and key features of a parabola, the roots and turning point, and solving quadratic equations by factorising, by the quadratic formula, and from a graph.
10 min answer →

How do you use similar shapes to find missing lengths, areas and volumes?

Using similarity to find missing lengths in similar shapes, and applying the linear, area and volume scale factors between similar figures.
A focused answer to the SQA National 5 Mathematics similarity content, covering similar shapes and the linear scale factor, finding missing lengths in similar triangles, and the area and volume scale factors as the square and cube of the linear scale factor.
9 min answer →

How do you solve a pair of simultaneous linear equations by elimination, substitution or graphically?

Solving simultaneous linear equations in two variables algebraically by elimination and substitution, and graphically as the point of intersection.
A focused answer to the SQA National 5 Mathematics simultaneous equations content, covering solving two linear equations in two unknowns by elimination and by substitution, the link to the point of intersection of two lines, and setting up simultaneous equations from a context.
9 min answer →

How do you find and use the equation of a straight line, and how do gradient and intercept describe it?

Determining and using the equation of a straight line in the forms y equals mx plus c and y minus b equals m times x minus a, including the gradient, the y-intercept, and parallel lines.
A focused answer to the SQA National 5 Mathematics straight line content, covering the equation y equals mx plus c, reading the gradient and y-intercept, the point-gradient form, finding the equation from a gradient and a point, and parallel lines.
9 min answer →

How does the discriminant tell you the number and nature of the roots of a quadratic equation?

Using the discriminant b squared minus 4ac to determine the number and nature of the roots of a quadratic equation.
A focused answer to the SQA National 5 Mathematics discriminant content, covering how the value of b squared minus 4ac determines whether a quadratic has two real roots, one repeated root or no real roots, and what this means for the graph.
8 min answer →

How do you use the sine rule, the cosine rule and the area formula to solve any triangle?

Using the sine rule and the cosine rule to find sides and angles in non-right-angled triangles, and using the formula one half ab sin C to find the area of a triangle.
A focused answer to the SQA National 5 Mathematics sine and cosine rule content, covering when to use each rule to find a missing side or angle in a non-right-angled triangle, and using the area formula one half ab sin C.
10 min answer →

How do you work with the sine, cosine and tangent graphs, and solve simple trigonometric equations?

Working with the graphs of sine, cosine and tangent including amplitude and period, and solving simple trigonometric equations using the graphs and exact values.
A focused answer to the SQA National 5 Mathematics trigonometry graphs content, covering the shape, amplitude and period of the sine, cosine and tangent graphs, the effect of multipliers, and solving simple trigonometric equations in degrees.
10 min answer →