Treat, pump, store, test and bill: the work of a water authority uses every one of your subjects.
0 of 18 tasks attempted
Tick “I have attempted this” on each task. Your progress is saved in this browser only.
Southfield Water Authority (a fictional utility) supplies about 12 000 people. After a week of heavy rain, four problems land on the manager’s desk:
The manager asks a small technical team for a short briefing with numbers and recommendations.
The same ideas keep appearing. Each row shows one shared topic and where you meet it in your lessons.
Water pressure in the pipes depends on height; tank size depends on volume of a cylinder; flow rates tell you how long filling takes.
The chemist measures acidity by titration, then the same concentration idea sizes the lime dose for a whole river’s worth of waste.
Bacteria in warm stagnant water double at a steady rate. Add Maths exponentials model it, and Biology explains why it matters.
Calculus finds when the reservoir is fullest and how fast it is filling or emptying.
A pump does work against gravity; its efficiency decides how much electrical power the Authority must buy.
The storage tank is a cylinder. You will find its capacity, the time to fill it, and check a customer’s bill.
(a) V = πr²h = 3.14 × 3.0² × 4.0 = 3.14 × 9 × 4 = 113.04 m³ (≈ 113 m³). [2]
(b) 1 m³ = 1000 dm³, so 113.04 × 1000 = 113 040 dm³. [1]
Time = 113.04 ÷ 0.5 = 226.08 minutes. [2]
226 min = 3 × 60 + 46, so about 3 hours 46 minutes. [1]
(a) 18 × $4.50 = $81.00 [1]. Tax = 15% of 81.00 = $12.15 [1]. Bill = 81.00 + 12.15 = $93.15. [1]
(b) 93.15 × 1.08 = 100.602 ≈ $100.60. [2]
Task total: 11 marks
The volume of water in the hillside reservoir changes after rain. Warm stagnant water also grows bacteria quickly.
(a) dV/dt = 12 − 2t. [1]
(b) Set dV/dt = 0: 12 − 2t = 0, so t = 6 hours. [2] (The second derivative is −2, which is negative, so this is a maximum.)
(c) V = 200 + 12(6) − 36 = 200 + 72 − 36 = 236 m³. [2]
(d) dV/dt = 12 − 16 = −4. At t = 8 the volume is decreasing at 4 m³ per hour. [2]
Set 50 × 2^(t/3) = 3200, so 2^(t/3) = 64. [1]
64 = 2⁶, so t/3 = 6. [1]
t = 18 hours. After 18 hours there are exactly 3200 bacteria, so N first exceeds 3200 just after 18 hours. [1]
Task total: 10 marks
The Authority stores water high on a hill so that gravity provides pressure. A pump lifts water up to the tower.
(a) P = hρg = 25 × 1000 × 10 = 250 000 Pa (250 kPa). [2]
(b) Pressure in a liquid increases with depth (the height of water above the point), so the lower house has a taller column of water above it. [1]
(a) E = mgh = 2000 × 10 × 30 = 600 000 J. [2]
(b) Power = energy ÷ time = 600 000 ÷ 60 = 10 000 W. [1]
(c) Input power = 10 000 ÷ 0.80 = 12 500 W (12.5 kW). [2]
Density = mass ÷ volume = 262.5 ÷ 250 = 1.05 g/cm³. [2]
The suspended mud (soil particles) is denser than water, so it increases the mass per unit volume. [1]
Task total: 11 marks
A factory upstream releases acidic waste. The chemist finds its concentration by titration, then calculates the lime needed to neutralise a day’s discharge.
Moles NaOH = 0.100 × 20.0 ÷ 1000 = 0.00200 mol. [1]
HCl + NaOH → NaCl + H₂O, a 1 : 1 ratio, so moles HCl = 0.00200 mol. [1]
Concentration = 0.00200 ÷ 0.0250 dm³ = 0.0800 mol/dm³. [2]
Moles HCl = 0.0800 × 10 000 = 800 mol. [1]
Mole ratio Ca(OH)₂ : HCl = 1 : 2, so moles Ca(OH)₂ = 400 mol. [1]
M(Ca(OH)₂) = 40 + 2(16 + 1) = 74 g/mol, mass = 400 × 74 = 29 600 g = 29.6 kg. [2]
(a) Calcium ions (Ca²⁺) and magnesium ions (Mg²⁺). [1]
(b) Disadvantage: it wastes soap by forming scum / it forms scale that blocks pipes and kettles. [1] Softening: boiling (for temporary hardness) or ion exchange / adding washing soda. [1]
Task total: 11 marks
A stretch of river below the sewage outlet has lost its fish, and stagnant pools around the town are breeding mosquitoes.
| Position | 2 km upstream | 0.5 km below outlet | 3 km below | 8 km below |
|---|---|---|---|---|
| Oxygen (mg/dm³) | 8.2 | 3.0 | 4.5 | 7.0 |
(a) Oxygen is high upstream (8.2), falls sharply just below the outlet (3.0), then rises steadily to 7.0 by 8 km. [2]
(b) Sewage contains organic matter and nutrients. Bacteria (decomposers) multiply and use up dissolved oxygen in aerobic respiration as they break it down. [1] Nutrients may cause an algal bloom; when the algae die, more bacteria decompose them and use more oxygen (eutrophication). [1] Fish and other animals cannot get enough oxygen and die. [1]
(c) The organic matter is used up or diluted; oxygen dissolves from the air and is added by photosynthesis of water plants. [1]
(a) Egg → larva → pupa → adult. [2]
(b) The eggs, larvae and pupae develop in water; removing standing water takes away the breeding sites, so the life cycle is broken and fewer adult mosquitoes can bite people and pass on the disease. [2]
(c) Dengue fever (also malaria, Zika, chikungunya). [1]
Any two: treat sewage before it is released; stop dumping waste and chemicals in the river; plant vegetation along the banks to filter runoff; reduce fertiliser use near the river; educate the public. [1 each]
Task total: 13 marks
The data officer must record water-quality tests, flag unsafe samples, and design a small database for the laboratory.
| A | B | C | |
|---|---|---|---|
| 1 | Sample | pH | Status |
| 2 | A | 7.2 | |
| 3 | B | 6.8 | |
| 4 | C | 8.9 | |
| 5 | D | 7.5 | |
| 6 | E | 6.1 |
Safe drinking-water pH range: 6.5 to 8.5.
=AVERAGE(B2:B6) [1] = (7.2 + 6.8 + 8.9 + 7.5 + 6.1) ÷ 5 = 36.5 ÷ 5 = 7.3. [1]
=IF(AND(B2>=6.5,B2<=8.5),"OK","FAIL") [3: IF structure, both conditions joined with AND, correct text results]. (An equivalent nested IF is also accepted.)
Samples C (8.9) and E (6.1) fail. [1]
A column (bar) chart of pH for each sample. [1] It needs a title and axis labels (sample on the x-axis, pH on the y-axis); a legend or data labels is also acceptable. [1]
(a) Site (SiteID, SiteName, Parish); Sample (SampleID, SiteID, Date, pH, Turbidity). Primary keys: SiteID and SampleID. Foreign key: SiteID in Sample, which links each sample to its site (one-to-many). [3]
(b) pH must be between 0 and 14: a range check. [2]
Task total: 13 marks
Combine your results into a one- to two-page briefing note (or a short presentation of 5 slides). Use the numbers you found: the tank capacity and filling time, the lime dose, the reservoir’s peak volume, the pump’s power, the oxygen trend and the failed samples. End with three prioritised recommendations.
| Criterion | What a top answer shows | Marks |
|---|---|---|
| Accuracy of calculations | Correct values with units from all six tasks, with working shown | 6 |
| Use of subject knowledge | Explains why each result matters using ideas from Chemistry, Biology and Physics | 5 |
| Data presentation | Clear labelled chart or table; consistent units | 3 |
| Recommendations | Practical, prioritised and linked to the evidence | 4 |
| Communication | Clear, well organised and suited to a manager | 2 |
Each of these people uses the subjects in this project every day.
Runs and designs the plants that make water safe: dosing chemicals, monitoring tanks, pumps and pressure.
Uses: Chemistry (pH, concentration), Physics (pressure, power), Maths (volume, flow)
Pathway: Technical diploma or associate degree in water treatment, or a degree in chemical or civil engineering.
Tests water and wastewater for acidity, hardness, bacteria and pollutants and reports results.
Uses: Chemistry (titration, analysis), Biology (microbes), IT (data recording)
Pathway: Degree in chemistry, biochemistry or environmental science.
Inspects pollution sources and mosquito breeding sites and enforces regulations.
Uses: Biology (disease, ecology), Chemistry, Maths (statistics)
Pathway: Degree or diploma in environmental health.
Predicts rainfall, river flow and reservoir levels and designs dams, pipes and drains.
Uses: Add Maths (rates, optimisation), Physics, Maths
Pathway: Degree in civil engineering or hydrology.
Builds the spreadsheets, databases and dashboards that turn readings into decisions.
Uses: IT (spreadsheets, databases), Maths (statistics)
Pathway: Degree or certificates in IT, statistics or data science.