Scotland · SQAQ&A
MathsQ&A by dot point
A short Q&A bank for every Scotland Maths syllabus dot point. Each question and answer is drawn directly from our worked dot-point page, so you can scan key concepts before opening the long-form answer.
Applications
- 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.3Q&A pairs
- Calculating the five-figure summary (minimum, lower quartile, median, upper quartile, maximum), the range and interquartile range, drawing boxplots, and comparing two data sets.3Q&A pairs
- Calculating with fractions: adding, subtracting, multiplying and dividing fractions and mixed numbers, and finding a fraction of a quantity.4Q&A pairs
- 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.3Q&A pairs
- Drawing and interpreting scattergraphs, describing correlation, drawing a line of best fit, finding its equation and using it to estimate values.3Q&A pairs
- Calculating the standard deviation of a data set using the standard formula, and using the mean and standard deviation to compare two data sets.3Q&A pairs
- 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.3Q&A pairs
Expressions and Formulae
- 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.4Q&A pairs
- Working with algebraic fractions: simplifying by factorising and cancelling, and adding, subtracting, multiplying and dividing algebraic fractions.3Q&A pairs
- 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.3Q&A pairs
- 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.3Q&A pairs
- Calculating the gradient of a straight line from two points using the gradient formula, and interpreting positive, negative, zero and undefined gradients.3Q&A pairs
- Writing numbers in scientific notation (standard form), converting between ordinary and scientific notation, and multiplying and dividing numbers written in scientific notation.3Q&A pairs
- 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.3Q&A pairs
Relationships
- Changing the subject of a formula, including formulae involving brackets, fractions, squares and square roots.3Q&A pairs
- Solving linear equations and inequations in one variable, including equations with brackets, fractions and the unknown on both sides, and representing inequation solutions.5Q&A pairs
- 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.3Q&A pairs
- 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.3Q&A pairs
- 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.3Q&A pairs
- Sketching and interpreting quadratic functions and their graphs, and solving quadratic equations by factorising, by the quadratic formula and graphically.4Q&A pairs
- Using similarity to find missing lengths in similar shapes, and applying the linear, area and volume scale factors between similar figures.3Q&A pairs
- Solving simultaneous linear equations in two variables algebraically by elimination and substitution, and graphically as the point of intersection.4Q&A pairs
- 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.3Q&A pairs
- Using the discriminant b squared minus 4ac to determine the number and nature of the roots of a quadratic equation.3Q&A pairs
- 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.3Q&A pairs
- Working with the graphs of sine, cosine and tangent including amplitude and period, and solving simple trigonometric equations using the graphs and exact values.3Q&A pairs