1. Which is prime?
- 15
- 13
- 21
Check the answer and reasoning
13
13 has only two positive integer factors, 1 and 13.
MATH / IGCSE
Number, sets and financial arithmetic
Prime factors, indices, standard form and bounds organise calculations with very large, small or approximate numbers. Set notation distinguishes membership from inclusion.
Learning objectives
- Explain number, sets and financial arithmetic using a concrete example.
- Apply the worked method and justify each step.
- Recognise the limitation described in the final check.
The big idea
Prime factors, indices, standard form and bounds organise calculations with very large, small or approximate numbers. Set notation distinguishes membership from inclusion.
Compound interest multiplies a balance each period. Upper and lower bounds come from the stated rounding interval; carrying extra displayed digits does not remove measurement uncertainty.
Equations and relationships
Compound growth with a fixed rate r per period.
Worked example
£200 earns 10% annually for two years. Find the balance.
Follow the solution
200 × 1.1² = 242; the second year earns interest on £220.
Investigate and explain
Predict the worked result before calculating. Change one input, record the new result, and explain which assumptions still hold.
Related interactive model. Compare its assumptions with the explanation; it is not a complete syllabus lesson.
Check your understanding
2. £200 earns 10% annually for two years. Find the balance.
- £240
- £220
- £242
Check the answer and reasoning
£242
200 × 1.1² = 242; the second year earns interest on £220.
3. A length rounds to 5 cm to the nearest cm. Which interval applies?
- 4.5 ≤ length < 5.5
- 5 ≤ length < 6
- 4 < length < 5
Check the answer and reasoning
4.5 ≤ length < 5.5
The nearest-centimetre rounding interval extends half a centimetre either side, with the upper boundary excluded.