Revision notes
Keep key ideas close at hand. Each section includes a concise reminder, a worked example, and a check to help you spot common slips.
Use these notes actively
Cover the answer, try the example yourself, then compare your steps. These are revision prompts—not a replacement for the methods or notation required by your course.
Numbers and percentages
Keep the original amount clear when comparing or finding a percentage change.
- Percentage of an amount
- percentage as a decimal × amount
- Percentage
- part ÷ whole × 100
- Percentage change
- change ÷ original amount × 100
- Mean
- sum of values ÷ number of values
- Ratio
- compare quantities in the same order, then simplify by a common factor
Worked example
Find 15% of 80.
- 1Convert 15% to 0.15.
- 2Multiply 0.15 × 80.
12
Check: For percentage change, divide by the original amount—not the new amount. Convert the percentage to a decimal before multiplying.
Algebra and geometry
Write down the relationship first, then keep each step clear and balanced.
- Rectangle area
- length × width
- Triangle area
- ½ × base × perpendicular height
- Rectangle perimeter
- 2 × (length + width)
- Solve an equation
- do the same operation to both sides
- Check a solution
- substitute your value into the original equation
Worked example
Solve 3x + 5 = 20.
- 1Subtract 5 from both sides: 3x = 15.
- 2Divide both sides by 3: x = 5.
Check: 3 × 5 + 5 = 20.
Check: Area is measured in square units. Perimeter is a length, so use ordinary units.
Science and measurement
Choose the formula that matches the quantities, then check that the units agree.
- Speed
- distance ÷ time
- Density
- mass ÷ volume
- Force
- mass × acceleration
- Electrical current
- voltage ÷ resistance
- Unit check
- convert quantities to compatible units before calculating
Worked example
A runner travels 150 metres in 30 seconds. What is the average speed?
- 1Use speed = distance ÷ time.
- 2Calculate 150 m ÷ 30 s.
5 m/s
Check: Include units in the final answer. In force = mass × acceleration, kilograms and metres per second squared give newtons.
English and reading
Clear writing connects a precise idea with evidence the reader can follow.
- Subject and verb
- check that they agree in number
- Apostrophe
- marks possession or a contraction; it does not make a word plural
- Text evidence
- support an interpretation with a relevant detail from the text
- Context clues
- use nearby words and sentences to work out an unfamiliar meaning
- Editing
- reread the full sentence after changing punctuation or wording
Worked example
How can you support a claim about a character?
- 1State the interpretation clearly.
- 2Choose a relevant action, quotation, or detail from the text.
- 3Explain how that evidence supports your interpretation.
A focused claim, relevant evidence, and a clear explanation make the reasoning easier to follow.
Check: Use the writing structure your teacher or course expects. A quotation should support your point, not replace your explanation.
Data and probability
Organise the information before calculating, and check what the question is asking for.
- Median
- middle value after ordering the data
- Range
- largest value − smallest value
- Probability
- favourable outcomes ÷ total equally likely outcomes
- Probability scale
- a value from 0 (impossible) to 1 (certain)
- Frequency
- the number of times a result occurs
Worked example
A fair six-sided die is rolled. What is the probability of an even number?
- 1The even outcomes are 2, 4, and 6: three favourable outcomes.
- 2There are six equally likely outcomes in total.
- 3Calculate 3 ÷ 6 and simplify.
½ (or 0.5)
Check: Order data before finding the median. For probability fractions, make sure the outcomes are equally likely before using this rule.
Turn a reminder into practice
Pick a related quiz section, work through a short round, and review the explanations for any answers you want to strengthen. You can return to these notes whenever you need a refresher.
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