β Scotland Applications of Mathematics
Scotland Β· SQASyllabus
Applications of Mathematics syllabus, dot point by dot point
Every dot point in the Scotland Applications of Mathematicssyllabus, 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.
Finance
Module overview β- How do you determine the best deal from several options and convert between currencies in both directions?Determining the best deal given several pieces of information by comparing unit costs or total costs, and converting between currencies using an exchange rate in both directions.11 min answer β
- How do you analyse a financial position using budget information, working out a balance, a surplus or a deficit, and applying profit, loss and VAT?Analysing a financial position using budget information, calculating total income and total expenditure to find a surplus or deficit, and working with profit, loss and VAT in financial contexts.11 min answer β
- How do you analyse and interpret the factors affecting income, working out gross and net pay from overtime, income tax, National Insurance and other deductions?Analysing and interpreting factors affecting income, including calculating gross pay from a wage and overtime, and working out net pay after deductions such as income tax, National Insurance and pension contributions.11 min answer β
- How do interest rates affect savings and borrowing, and how do you compare simple interest, compound interest, hire purchase and loans?Investigating the impact of interest rates on savings and borrowing, calculating simple and compound interest, finding appreciation and depreciation, and comparing the total cost of borrowing through loans and hire purchase.12 min answer β
Geometry and Measurement
Module overview β- How do you find the area of a composite shape including part of a circle, and the volume of a composite solid built from prisms, cylinders, cones, spheres or pyramids?Solving a problem involving the area of a composite shape including part of a circle, and the volume of a composite solid made from standard solids such as cuboids, cylinders, cones, spheres and pyramids.12 min answer β
- How do you carry out efficient container packing, and use precedence tables to plan tasks and solve a time-management problem?Carrying out efficient container packing to fit items into a space, and using precedence tables to plan tasks in order, find the minimum completion time and solve a time-management problem.11 min answer β
- How do you investigate a situation involving gradient, calculating the steepness of a slope or ramp as a ratio and relating it to vertical and horizontal distance?Investigating a situation involving gradient, calculating gradient as vertical height divided by horizontal distance, and using it to find an unknown height or distance, including ramps and slopes.11 min answer β
- How do you apply Pythagoras' theorem in a two-stage calculation, and use the properties of shapes to find an angle over at least two steps?Using Pythagoras' theorem within a two-stage calculation to find a length, and applying the properties of shapes and angles to determine an angle in a calculation involving at least two steps.12 min answer β
- How do you construct a scale drawing and choose a sensible scale, and plan a navigation course using bearings and distances?Constructing a scale drawing including choosing a suitable scale, converting between scaled and real distances, and planning a navigation course using three-figure bearings and distances.11 min answer β
- How do you consider the effects of tolerance, finding the maximum and minimum acceptable values and deciding whether a measurement is within tolerance?Considering the effects of tolerance, calculating the maximum and minimum acceptable values from a stated tolerance, and deciding whether a given measurement lies within the acceptable range.10 min answer β
Numeracy
Module overview β- How do you carry out everyday calculations, work in scientific notation, and round answers correctly to a sensible degree of accuracy?Selecting and carrying out calculations including multiplication and division, writing very large or very small numbers in scientific notation, and rounding answers to a given number of decimal places or significant figures.11 min answer β
- How do you find fractions and percentages of quantities, work with ratio, and solve direct proportion and rate problems in everyday contexts?Finding fractions and percentages of shapes and quantities, sharing in a given ratio, solving direct proportion problems, and calculating a rate such as miles per hour or cost per unit.11 min answer β
- How do you read scales on instruments, convert between units of measure, and interpret measurements of time, length, weight, volume and temperature to make decisions?Recording measurements using a scale on an instrument, converting between metric units of length, mass and capacity, working with time and the 12 and 24 hour clock, and interpreting measurements and results to justify a decision.11 min answer β
Statistics
Module overview β- How do you use averages and measures of spread, including the five-figure summary, the semi-interquartile range and standard deviation, to compare two data sets?Using a combination of statistics to compare data sets, calculating the mean, median, mode and range, the five-figure summary and semi-interquartile range, and the standard deviation, then comparing an average with a measure of spread.12 min answer β
- How do you calculate the probability of an event, interpret it on the likelihood scale, and use probability and risk to make and justify a decision?Calculating the probability of an event as a fraction, decimal or percentage, interpreting probability on the scale from 0 to 1, using expected frequency, and using probability and risk to make and justify decisions.11 min answer β
- How do you describe correlation on a scattergraph, draw a line of best fit, find its equation and use it to estimate values?Drawing a line of best fit from given data on a scattergraph, describing the type of correlation, finding the equation of the line of best fit, and using it to estimate values.11 min answer β
- How do you extract and interpret data from tables and statistical diagrams such as bar charts, pie charts, line graphs and stem-and-leaf diagrams?Extracting and interpreting data from different graphical forms including tables, bar charts, pie charts, line graphs and stem-and-leaf diagrams, and constructing these diagrams from raw data.11 min answer β