3 Quantitative skills
- Syllabus
- 2026
- Section
- 3
- Level
- —
Exam analysis
Calculations
- Syllabus
- 2026
- Topic
- —
- Level
- —
Calculate percentages, changes and savings interest
| Task | Calculation |
|---|---|
| part as a percentage of total | part ÷ total × 100 |
| percentage change | (new − original) ÷ original × 100 |
| simple annual interest | savings × annual rate ÷ 100 × years |
\text{percentage change}=\frac{\text{new value}-\text{original value}}{\text{original value}}\times100
A positive result is an increase; a negative result is a decrease. Always divide a change by the original value, not the new value.
Examples: profit rises from 80,750 to 87,100, so 6,350 ÷ 80,750 × 100 = 7.86%. Interest on ¥8,000 at 2.25% for one year is 8,000 × 0.0225 = ¥180.
A percentage-point change is subtraction between two percentage rates; a percentage change divides that difference by the original rate. They are not interchangeable.
Calculate and interpret economic averages
\text{mean}=\frac{\text{sum of values}}{\text{number of values}}
\text{average cost}=\frac{\text{total cost}}{\text{quantity produced}}
| Average | Numerator | Denominator | Interpretation |
|---|---|---|---|
| mean FDI per year | total FDI across years | number of years | typical annual value over the period |
| GDP per capita | total GDP | population | output per person, not each person's income |
| average cost | total cost | units produced | cost per unit |
Keep units consistent before dividing. If GDP and population are both in millions, the million units cancel; attach the correct currency and per-person or per-unit label to the result.
An average can hide variation across years, people or units. GDP per capita is not the same as median income, and average cost is not total cost.
Build revenue, cost and profit totals
\text{total revenue}=\text{price per unit}\times\text{quantity sold}
\text{total cost}=\text{total fixed cost}+\text{total variable cost}
\text{profit}=\text{total revenue}-\text{total cost}
| Given | Find | Operation |
|---|---|---|
| price and quantity | total revenue | multiply |
| fixed and variable costs | total cost | add |
| revenue and total cost | profit or loss | subtract cost from revenue |
At a price of £12, 500 units give revenue of £6,000. If fixed cost is £1,500 and variable cost is £3,500, total cost is £5,000 and profit is £1,000. A negative profit result is a loss.
Revenue is not profit. Revenue ignores costs; profit is the residual after all relevant costs have been subtracted.
Calculate gross pay and net pay
Gross pay is earnings before deductions. Net pay is the amount received after deductions such as income tax, pension contributions or social-insurance payments.
\text{gross pay}=\text{hourly wage}\times\text{hours worked}+\text{other gross earnings}
\text{net pay}=\text{gross pay}-\text{total deductions}
At €6.04 per hour for 35 hours, weekly gross pay is €6.04 × 35 = €211.40. If deductions total €31.40, net pay is €180.00.
Match the time period first: hourly × weekly hours gives weekly gross pay; annual salary must be divided appropriately before comparison. Add overtime or bonuses before subtracting deductions unless the context says otherwise.
The only exact-tagged Question Bank row, 216041, incorrectly keys €6.04 × 35 as option A. The mathematically correct result is €211.40 (option C), so the row is excluded as representative evidence.
Gross income is not disposable/net income. A deduction reduces take-home pay even though it may finance a benefit such as a pension.
Graph construction
- Syllabus
- 2026
- Topic
- —
- Level
- —
Construct accurate economic graphs from data
A graph converts numerical relationships into a visual form. A correct economic graph must preserve the data, variables, units and scale before any interpretation is added.
| Step | Construction decision | Check |
|---|---|---|
| 1 identify variables | decide what each axis measures; independent/category variable usually on x, measured outcome on y | names and units match the data |
| 2 choose graph type | line for change over continuous time; bar for categories; scatter for paired observations; supply/demand for price–quantity schedules | type fits the relationship |
| 3 choose scale | cover the full range with equal numerical intervals | no distorted or unexplained break |
| 4 plot | mark every coordinate accurately | x and y values read from the same row |
| 5 connect/represent | join ordered time or curve points appropriately; keep categories separate in bars | no invented intermediate values |
| 6 label | title, axes, units, curves and relevant equilibrium | another reader can identify every element |
For supply and demand data, put price on the vertical axis and quantity on the horizontal axis. Plot demand and supply schedules, label D and S, and mark their intersection as equilibrium price and quantity. Do not assume straight lines if the plotted data do not support them.
Read two or more plotted points back from the graph and compare them with the source table. Check that a larger plotted movement represents a genuinely larger numerical movement under the chosen scale.
Constructing a graph is not the same as explaining it. First reproduce the data accurately; then use direction, gradient, turning points or equilibrium for interpretation only when asked.
Quantitative interpretation and decision-making
- Syllabus
- 2026
- Topic
- —
- Level
- —
Interpret graphs and charts as decision evidence
| Pass | Question to answer | Evidence produced |
|---|---|---|
| identity | what is measured, where, when and by which source? | correct variable and context |
| axes and encoding | what do axes, units, scale, colours, bars, lines or categories mean? | accurate reading rather than visual guess |
| pattern | what is the direction, size, peak, trough, turning point or ranking? | a quantified observation |
| comparison | compared with which year, group or benchmark? | difference, ratio or percentage change |
| decision link | which option/objective does the pattern support and through what mechanism? | evidence-based recommendation |
| limitation | what is missing or potentially misleading? | qualified judgement |
Use the structure claim → exact graph evidence → economic mechanism → decision. Example: 'Unemployment rose from 5% to 8% (3 percentage points), indicating spare labour; a training policy may be justified if the rise reflects structural mismatch.'
Check truncated axes, unequal time intervals, cumulative versus period values, nominal versus real data, and whether the graph shows levels, rates or percentage changes. These can change the conclusion.
A graph can show association, sequence and magnitude but does not by itself prove causation. A decision needs economic reasoning and, where possible, corroborating evidence.
Use economic data to justify a decision
| Data | Meaning/calculation | Decision signal and caution |
|---|---|---|
| unemployment rate | unemployed people ÷ labour force × 100 | high/rising rate may justify demand or training policy; distinguish cyclical, structural and seasonal causes |
| exports | value of domestically produced goods/services sold abroad | growth may support export industries, but compare volume and price/ currency effects |
| imports | value of foreign goods/services bought domestically | may indicate strong demand or input access, not automatically economic weakness |
| visible trade balance | exports of goods − imports of goods | positive is a goods surplus; negative is a goods deficit; it excludes services and income flows |
\text{visible trade balance}=\text{exports of goods}-\text{imports of goods}
Use a four-step chain: define the measure → calculate or compare on a consistent basis → identify the economic implication → select and qualify the decision. State exact units, dates and whether the change is absolute, percentage or percentage points.
Do not decide from one number alone. Compare over time, with a target or another economy, and combine related indicators—for example unemployment with vacancies/output, or trade balance with exchange rates and export competitiveness.
A visible trade deficit is not the same as a current-account deficit, and a lower unemployment rate is not automatically better if participation has fallen or job quality is weak.