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Applications of MathematicsQ&A by dot point
A short Q&A bank for every Scotland Applications of Mathematics 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.
Finance
- 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.3Q&A pairs
- 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.3Q&A pairs
- 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.3Q&A pairs
- 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.4Q&A pairs
Geometry and Measurement
- 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.3Q&A pairs
- 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.3Q&A pairs
- 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.3Q&A pairs
- 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.4Q&A pairs
- 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.4Q&A pairs
- 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.3Q&A pairs
Numeracy
- 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.4Q&A pairs
- 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.4Q&A pairs
- 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.3Q&A pairs
Statistics
- 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.3Q&A pairs
- 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.3Q&A pairs
- 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.3Q&A pairs
- 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.3Q&A pairs