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.
Course Assessment
Module overview βFinance
Module overview β- How do tax, inflation and insurance affect personal financial planning and the real value of money?Applying personal financial planning skills, including income tax and national insurance, the effect of inflation on purchasing power, and analysing insurance premiums, excess and risk.10 min answer β
- How do loans, credit cards and APR work, and how do you compare the true cost of borrowing?Analysing loans, credit cards and other borrowing, calculating repayments and outstanding balances, understanding APR as a measure of the true cost of credit, and comparing borrowing options.10 min answer β
- How do you find what a sum of money is worth in the future, or what a future sum is worth today?Calculating the future value of a sum or of regular savings under compound interest, and the present value of a future payment, including comparing savings products and the effect of compounding frequency.10 min answer β
Mathematical Modelling
Module overview β- How do you turn a real situation into a formula or graph, and use that model to predict and explain?Modelling real-life situations with variables, formulae and graphs, including linear, piecewise linear and exponential growth and decay models, and using the model to make predictions.9 min answer β
- How do you build a model in a spreadsheet using formulae, cell references and functions to calculate and explore?Using a spreadsheet to support modelling: entering formulae with relative and absolute cell references, filling down a recurrence, using built-in functions, and using goal seek to find an input for a target output.9 min answer β
- How do you keep units consistent and report a result with the right accuracy and tolerance?Working with units and dimensional consistency, converting between units, rounding appropriately, and using tolerance, absolute error and percentage error to judge whether a result is acceptable.9 min answer β
Planning and Decision Making
Module overview β- How do you use expected values to choose between options when outcomes are uncertain?Calculating expected values to compare decisions under risk, using decision tables and decision trees, and justifying a choice while recognising the limits of an expected-value approach.9 min answer β
- How do you represent a project schedule over time and use it to plan resources and deadlines?Representing project activities over time with Gantt charts and PERT, scheduling activities and resources, and using the schedule to track progress and manage deadlines.9 min answer β
- How do you model a project as a network and find the shortest time to complete it?Modelling a project with an activity network, finding the critical path and minimum completion time, and calculating the float (slack) of non-critical activities.10 min answer β
Statistics and Probability
Module overview β- How do you measure how strongly two variables are related, and use a line of best fit to predict?Measuring linear association with Pearson's correlation coefficient, fitting a simple linear regression line, interpreting its slope and intercept, and using it to predict while distinguishing interpolation from extrapolation.9 min answer β
- How do you test a claim about data and estimate a population value with a confidence interval?Carrying out and interpreting hypothesis tests (t-tests and z-tests), using the p-value and significance level to reach a conclusion, constructing and interpreting confidence intervals, and recognising errors in statistical testing.10 min answer β
- How do you calculate probabilities of combined events and the expected value of an uncertain outcome?Calculating probabilities of single and combined events using the addition and multiplication rules and tree diagrams, working with conditional probability, and finding the expected value of a situation with uncertain outcomes.9 min answer β
- How do you choose, draw and read statistical diagrams, and sample data without bias?Selecting and interpreting statistical diagrams, comparing data sets using measures of centre and spread, identifying outliers and misleading graphs, and choosing an appropriate sampling method.9 min answer β