HSC Minimum Standard Numeracy cheat sheet

Percentage of a quantity: multiply by the percentage divided by 100, e.g. 15% of 80 = 0.15 × 80 = 12.

Percentage change = (new − old) ÷ old × 100; a negative result is a decrease. A 20% rise then 20% fall returns below the original value.

Fractions, decimals and percentages are interchangeable: 1/4 = 0.25 = 25%; divide numerator by denominator to convert a fraction to a decimal.

To find a unit rate, divide the total by the quantity: 12 items for $36 gives $3 per item; scale up by multiplying the unit rate.

Simple interest: I = P × r × t, where r is the decimal rate per year and t is time in years.

Area formulas: rectangle = length × width; triangle = ½ × base × height; circle = π × r² (π ≈ 3.14).

Perimeter of a rectangle = 2 × (length + width); volume of a rectangular prism = length × width × height.

Mean = sum of values ÷ number of values; median = middle value of an ordered list; mode = most frequent value.

Time and timetable arithmetic: convert to 24-hour time, then subtract start from finish; 1 hour = 60 minutes, so 2 h 45 min = 165 minutes.

Identify the question stem first: 'how much', 'how many', 'which is cheaper' signal the operation required before reading the data.

Distinguish relevant from distractor numbers: figures not referenced by the question or needed for the calculation are usually distractors.

Watch for qualifiers that change meaning: 'approximately', 'at least', 'per person', 'excluding', 'before tax'.

Units must match before comparing: convert metres to centimetres (×100) or minutes to hours (÷60) before choosing an answer.

Tables: read row and column headings first, then locate the intersection cell; totals may appear in the last row or column.

Graphs: check axis labels and scale increments; a bar graph starting above zero exaggerates differences.

Inference questions ask what the text suggests, not what it states directly; choose the option supported by evidence in the passage.

Sequential instructions should be followed in order; conditional steps ('if… then') apply only when the condition is met.

A complete numerical explanation states the operation, the working, and the answer with its unit, e.g. '3 × $4.50 = $13.50'.

Show the calculation line before the final answer; markers award method marks even when the final figure is wrong.

Justify a comparison with a stated value: 'Shop A is cheaper because $2.40 < $2.55', not 'Shop A is cheaper'.

Use one sentence per step in a written procedure; sequence markers (first, then, finally) make order explicit.

Word answers must answer the question asked: 'how many boxes' needs a whole number, so round up if part-boxes remain.

Keep units and labels attached to every number written in a response; an unlabelled figure is ambiguous.

Avoid vague quantifiers ('a lot', 'some'); replace them with the calculated figure or a stated range.

When asked to explain an error, name the faulty step and give the corrected value in the same response.