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The brief
The Joseph family farm wants to modernise
The Joseph family (fictional) farms 1 260 m² of coastal land. Drought, rising fertiliser prices and pests are cutting profits. They ask your team to plan a smarter farm:
how much seed and land they need and what profit they make;
how to fence the largest possible plot with limited fencing;
which fertiliser gives the most nitrogen for the money and how to correct acid soil;
how to dry the harvest with solar heat and breed disease-resistant plants;
an irrigation controller and a website for the farm stall.
Your role: agricultural advisor in a team of six: each of you looks after one part of the plan.
How this project works. Each subject has a short task set from the point of view of the team. The lessons that give you the skills are linked at the top of each task. Work in any order, then bring your results together in the final briefing. Use g = 10 N/kg and π = 3.14 unless told otherwise. Worked solutions are hidden: attempt each task on paper first.
The big idea
How the six subjects connect in this project
The same ideas keep appearing. Each row shows one shared topic and where you meet it in your lessons.
Area, scale and money
Planning a plot uses area and scale drawings; costs, profit and percentage profit decide whether the farm survives.
The plot is a rectangle 45 m long and 28 m wide. (a) Find its area. (b) Seed is sown at 0.02 kg per m². How many kg are needed? (c) Seed costs $8.50 per kg. Find the cost.[3 marks]
Show worked solution
(a) 45 × 28 = 1260 m². [1]
(b) 1260 × 0.02 = 25.2 kg. [1]
(c) 25.2 × 8.50 = $214.20. [1]
On a farm plan the scale is 1 : 500. A boundary of 45 m is drawn as 9 cm. How long should the 28 m boundary be drawn?[2 marks]
Show worked solution
28 m = 2800 cm; 2800 ÷ 500 = 5.6 cm. [2] (Check: 45 m = 4500 cm ÷ 500 = 9 cm ✓.)
The farmer sells 1500 kg of produce at $2.20 per kg. The total cost of growing it was $2400. Calculate the profit and the percentage profit.[3 marks]
A rectangular plot is fenced on three sides with 120 m of fencing, the fourth side being the river. Let the two sides at right angles to the river each be x metres. (a) Show that the area is A = x(120 − 2x). (b) Find the value of x that makes A a maximum. (c) Find the maximum area. (d) Show that this is a maximum.[5 marks]
Show worked solution
(a) The side parallel to the river = 120 − 2x, so A = x(120 − 2x) = 120x − 2x². [1]
(b) dA/dx = 120 − 4x = 0, so x = 30 m. [2]
(c) A = 30 × (120 − 60) = 30 × 60 = 1800 m². [1]
(d) d²A/dx² = −4, which is negative, so it is a maximum. [1] (Completing the square also works: A = −2(x − 30)² + 1800.)
A sprinkler at the origin waters a circle of radius 8 m. (a) Write the equation of the circle. (b) A tree is at the point (5, 6). Is it watered?[3 marks]
Show worked solution
(a) x² + y² = 64. [1]
(b) At (5, 6): 5² + 6² = 25 + 36 = 61, which is less than 64, so the tree is inside the circle: it is watered. [2]
Task total: 8 marks
Task · Physics
Drying the harvest with the sun
A solar dryer removes 50 kg of water from the harvest so that it can be stored without spoiling.
Data: specific latent heat of vaporisation of water = 2.26 × 10⁶ J/kg. The collector has area 4 m² and receives 600 W/m². It is 40% efficient.
(a) Calculate the energy needed to evaporate 50 kg of water. (b) Calculate the useful power from the collector. (c) How long does the drying take? Give your answer in hours.[6 marks]
(b) Power in = 4 × 600 = 2400 W; useful power = 40% × 2400 = 960 W. [2]
(c) Time = energy ÷ power = 1.13 × 10⁸ ÷ 960 = 117 700 s ÷ 3600 = about 32.7 hours (roughly four 8-hour sunny days). [2]
The inside of the dryer is painted matt black and covered with glass. Explain how each helps it to get hot.[3 marks]
Show worked solution
Matt black surfaces are good absorbers of thermal radiation, so they absorb more of the sun’s energy. [1] Glass lets the short-wavelength radiation from the sun in [1] but traps the longer-wavelength heat radiation from the hot inside (the greenhouse effect); it also stops warm air escaping by convection. [1]
Task total: 9 marks
Task · Chemistry
Which fertiliser is the better buy? Correcting acid soil
Plants need nitrogen. The farmer compares two fertilisers and treats acidic soil.
Calculate the cost of 1 kg of nitrogen from each fertiliser, and say which is the better buy.[3 marks]
Show worked solution
Ammonium nitrate: $1.20 ÷ 0.35 = $3.43 per kg N. [1] Urea: $1.30 ÷ 0.467 = $2.79 per kg N. [1]
Urea gives nitrogen for less money, so it is the better buy. [1]
The soil is too acidic. The farmer adds calcium carbonate (limestone). Write a balanced equation for its reaction with hydrochloric acid and explain why this helps the crop.[3 marks]
Show worked solution
CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂. [2]
The carbonate neutralises acid in the soil, raising the pH to a level where nutrients are available to plants. [1]
Task total: 10 marks
Task · Biology
Disease-resistant plants and thirsty leaves
The farmer breeds tomatoes for resistance to a disease, and wants to understand why plants wilt on hot days.
Resistance to a tomato disease is controlled by a dominant allele R; susceptibility is caused by the recessive allele r. Two heterozygous plants (Rr) are crossed. (a) Show the cross using a Punnett square. (b) State the genotype and phenotype ratio. (c) Out of 400 seedlings, how many are expected to be susceptible?[5 marks]
Show worked solution
(a) Gametes R, r from each parent. Offspring: RR, Rr, Rr, rr. [2]
(a) Describe how water moves from the soil to the leaves of a plant. (b) State two conditions that increase the rate of transpiration. (c) Suggest the best time of day to irrigate and why.[6 marks]
Show worked solution
(a) Root hairs absorb water by osmosis; water moves across the root into the xylem, travels up the xylem and out through the stomata of the leaves as water vapour (transpiration pull draws it up). [3]
(b) Any two: high temperature; low humidity; wind; bright light. [2]
(c) Early morning or evening, when it is cooler and less water evaporates. [1]
Explain how growing legumes in rotation with other crops can reduce the amount of nitrogen fertiliser needed.[2 marks]
Show worked solution
Legumes have nitrogen-fixing bacteria in their root nodules that change nitrogen from the air into nitrates. [1] These enrich the soil for the next crop, so less fertiliser is needed. [1]
Task total: 13 marks
Task · Information Technology
The irrigation controller, farm stall site and records
A soil moisture sensor tells a controller when to switch on the pump. The family also needs a website and a sales chart.
The controller reads the soil moisture (%) four times. If the reading is below 30 the pump is switched ON; otherwise it is OFF. (a) Write pseudocode. (b) Complete a trace table for the readings 45, 28, 33 and 25.[7 marks]
Show worked solution
(a) FOR i ← 1 TO 4 INPUT moisture IF moisture < 30 THEN OUTPUT "ON" ELSE OUTPUT "OFF" ENDIF NEXT i [4: loop of 4, input, correct condition, both outputs]
(b) 45 → OFF; 28 → ON; 33 → OFF; 25 → ON. A correct table has a column for moisture, a column for the condition (moisture < 30: False, True, False, True) and one for the output. [3]
The family builds a one-page website for the farm stall. List the four design features it should have and two different types of hyperlink.[3 marks]
Show worked solution
Features: logo, navigation area, content area (text and pictures), contact details. [Any 3 features = 2 marks.] Hyperlinks: an email link (mailto) and a link to another page, a file or a place in the same page. [1]
A spreadsheet lists the income from five crops. Name a chart that shows each crop’s share of total income and state one thing the chart must have.[2 marks]
Show worked solution
A pie chart. [1] It must have a title and a legend or labels for each slice. [1]
Task total: 12 marks
Put it together
The farm improvement plan
Produce a one- to two-page plan (or a poster) for the Joseph family. Include a scale drawing of the best plot, the seed cost and expected profit, the fertiliser comparison, the drying time, the controller algorithm and a short paragraph on how the farm could cope with drought.
Checklist
How it will be judged (20 marks)
Criterion
What a top answer shows
Marks
Accuracy
Correct calculations with units from all six tasks
6
Use of evidence
Plan follows from the numbers: plot, fertiliser, drying and irrigation
5
Scale drawing and chart
Accurate, neat and labelled
3
Sustainability
Considers soil, water and energy use
4
Communication
Clear and practical for a farming family
2
Careers
Who does this work in real life?
Each of these people uses the subjects in this project every day.
Agronomist / crop scientist
Advises farmers on seeds, soil, fertilisers and pests to raise yields.