Scotland Β· SQASyllabus
Maths syllabus, dot point by dot point
Every dot point in the Scotland Mathssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Applications
Module overview β- How do you apply trigonometry to bearings, angles of elevation and depression, and problems in three dimensions?Applying trigonometry, the sine and cosine rules and the area formula to practical problems involving bearings, angles of elevation and depression, and three-dimensional shapes.10 min answer β
- How do you summarise and compare data sets using the five-figure summary, quartiles, the interquartile range and a boxplot?Calculating the five-figure summary (minimum, lower quartile, median, upper quartile, maximum), the range and interquartile range, drawing boxplots, and comparing two data sets.9 min answer β
- How do you add, subtract, multiply and divide fractions, including mixed numbers, without a calculator?Calculating with fractions: adding, subtracting, multiplying and dividing fractions and mixed numbers, and finding a fraction of a quantity.9 min answer β
- How do you work with percentage increase and decrease, reverse percentages, and repeated percentage change such as compound interest and appreciation?Calculating percentage increase and decrease, finding the original amount in reverse percentage problems, and using a multiplier for repeated percentage change including appreciation, depreciation and compound interest.10 min answer β
- How do you use a scattergraph and a line of best fit to describe correlation and make predictions?Drawing and interpreting scattergraphs, describing correlation, drawing a line of best fit, finding its equation and using it to estimate values.9 min answer β
- How do you calculate the standard deviation of a data set and use it to compare the spread of two data sets?Calculating the standard deviation of a data set using the standard formula, and using the mean and standard deviation to compare two data sets.10 min answer β
- How do you add, subtract and scale vectors, and find the magnitude of a vector in two and three dimensions?Working with vectors in two and three dimensions: vector components, adding and subtracting vectors, multiplying by a scalar, and calculating the magnitude of a vector.9 min answer β
Expressions and Formulae
Module overview β- How do you expand brackets and factorise algebraic expressions, including common factors, the difference of two squares and trinomials?Expanding brackets (including the product of two brackets) and factorising algebraic expressions using a common factor, the difference of two squares, and trinomials with unitary and non-unitary leading coefficients.10 min answer β
- How do you simplify, add, subtract, multiply and divide algebraic fractions?Working with algebraic fractions: simplifying by factorising and cancelling, and adding, subtracting, multiplying and dividing algebraic fractions.9 min answer β
- How do you find the length of an arc, the area of a sector, and the volume of standard solids?Calculating the length of an arc and the area of a sector of a circle, and calculating the volume of standard solids including the prism, cylinder, pyramid, cone and sphere.10 min answer β
- How do you write a quadratic expression in the completed-square form, and what does that form tell you about the graph?Writing a quadratic expression of the form x squared plus bx plus c in the completed-square form (x plus p) squared plus q, and using it to identify the turning point of the parabola.9 min answer β
- How do you calculate the gradient of a straight line from two points, and what does the sign and size of a gradient tell you?Calculating the gradient of a straight line from two points using the gradient formula, and interpreting positive, negative, zero and undefined gradients.8 min answer β
- How do you write very large and very small numbers in scientific notation, and how do you calculate with numbers in that form?Writing numbers in scientific notation (standard form), converting between ordinary and scientific notation, and multiplying and dividing numbers written in scientific notation.8 min answer β
- How do you simplify and combine surds, rationalise a denominator, and apply the laws of indices including negative and fractional powers?Simplifying and working with surds (simplifying, adding and subtracting, expanding brackets, rationalising the denominator) and applying the laws of indices including negative and fractional indices.9 min answer β
Relationships
Module overview β- 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.8 min answer β
- 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.9 min answer β
- 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.8 min answer β
- 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.9 min answer β
- 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.9 min answer β
- 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.10 min answer β
- 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.9 min answer β
- 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.9 min answer β
- 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.9 min answer β
- 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.8 min answer β
- 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.10 min answer β
- 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.10 min answer β