Why do speed and wavelength use different powers?

Deep-water speed grows linearly with period while wavelength grows with its square, so wavelength is always the larger figure.

Why not divide the years by the return period?

A return period is the reciprocal of the annual chance, so a run of years needs 1 minus the chance of never meeting it.

S5 Geography | Coastal Landforms and Sea-Level Rise Paper 4 (Error Review)

2026-11-04

Tutor Prep Guide · Secondary Geography

Paper 4 retrains the ten most frequent slips: unit conversion, the two wave formulas, tidal range, Bruun retreat, multiplying energy factors, nourishment volume, sediment budgets and return-period chance.

Write the unit before the number　Allow about twenty-five minutes; state the unit each answer needs before substituting numbers, which removes most conversion and inversion errors.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10 items
Suggested time	About 25 minutes
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S5 Geography \| Coastal Landforms and Sea-Level Rise
Level	S5 (Secondary 5) Geography

02　Questions (10 items)

FoundationSea level rises 3.2 mm a year. How much is that in 100 years, in mm and in metres?
FoundationA deep-water wave has a period of 10 s. Using c = 1.56T and L = 1.56T², find its speed and wavelength.
FoundationLongshore drift moves 30,000 m³ of sediment a year past a point. How much passes in 15 years?
FoundationOn one day high water is 2.8 m and low water 0.9 m. What is the tidal range?
IntermediateA beach face slopes at 1/100 and sea level rises 0.24 m. By the Bruun rule how far does the shoreline retreat?
IntermediateWave height rises from 1.5 m to 3.0 m while the period rises from 8 s to 12 s. By what factor does wave energy change?
IntermediateA beach 900 m long and 25 m wide is to be raised by 1.5 m. How much sand is needed?
ChallengeA coast gains 42,000 m³ of sediment a year and loses 55,000 m³, with 156,000 m³ in store. What is the net budget and how long does the store last?
ChallengeA scheme is designed for the 20-year return period. What is the chance of at least one such event in the next 30 years?
Error redoSea level rises 0.32 m on a beach sloping at 1/80. A student answers “retreat of 0.32 m”. What is correct, and where is the error?

03　Answers and one-line notes

#	Answer	One-line note
1	320 mm, that is 0.32 m.	Millimetres become metres by dividing by 1,000: 320 mm is only 0.32 m, not 3.2 m.
2	Speed about 15.6 m/s and wavelength about 156 m.	Speed uses T to the first power and wavelength T squared; the two formulas are not interchangeable.
3	450,000 m³.	Longshore drift is a steady one-way flow, so the annual volume times the years gives the total.
4	1.9 m.	Tidal range is the difference between high and low water, never the sum; adding them gives the common wrong 3.7 m.
5	It retreats 24 m.	Retreat is the rise divided by the slope; multiplying instead gives the classic wrong 0.0024 m.
6	About 6 times (4 × 1.5).	Energy varies with the square of height and directly with period, so the two factors multiply rather than add.
7	33,750 m³.	Nourishment volume is length × width × depth; quoting only the 22,500 m² area omits the depth.
8	A net 13,000 m³ a year deficit, lasting 12 years.	Subtract the loss first, then divide the store by the deficit; a negative figure means erosion, not deposition.
9	About 78.5%.	Use 1 − (1 − 1/20)³⁰, not 30 ÷ 20; a return period is a long-run average, not a schedule.
10	Retreat is 25.6 m (0.32 / 0.0125).	The error is treating vertical rise as horizontal retreat; the flatter the beach, the further the shoreline moves.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.