INTEGRATED PROJECT 3 · HOSPITALS AND PUBLIC HEALTH · 6 SUBJECTS

The Fever Ward

A rising number of fever cases: lab results, medicine doses, imaging and patient records all depend on the same six subjects.

MathematicsAdditional MathematicsPhysicsChemistryBiologyInformation Technology
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The brief

Bayview Regional Hospital needs a response plan

Bayview Regional Hospital (a fictional hospital) is seeing a steady rise in patients with high fever in the rainy season. The hospital director has asked for a fast, evidence-based plan covering:

Your role: member of the hospital’s response team: a pharmacist, a radiographer, a laboratory scientist, a public health officer and a records clerk, all sharing one set of data.
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.

Disease, prevention and immunity

Biology explains pathogens, mosquitoes and vaccines; Maths turns case counts into growth rates and risk.

Exponential decay and half-life

Medicine leaves the body and a radioactive tracer decays by the same half-life pattern.

Waves and imaging

Ultrasound and X-rays are waves; their speed and absorption let us see inside the body.

Acids, bases and concentration

Antacids neutralise stomach acid; the mole calculation from titration decides the dose.

Statistics and probability

Mean, median, standard deviation and tree diagrams are used to interpret test results and fevers.

Records, privacy and security

Patient data must be organised in a database and protected from misuse.

Task · Mathematics

Doses, averages and the chance of a positive test

The pharmacist works out a child’s dose, the public health officer summarises weekly cases, and the lab estimates how often a screening test is positive.

Skills from your lessons: Maths A4 Maths A2 Maths B2 Maths B3 Maths C3
Fever cases per week
Week123456
Cases1220356095110
  1. A child’s dose is 5 mg per kg of body mass. A child has mass 24 kg. The syrup contains 40 mg of medicine in every 5 ml. How many ml should the child receive?[3 marks]
    Show worked solution

    Dose = 5 × 24 = 120 mg. [1]

    Volume = 120 ÷ 40 × 5 = 3 × 5 = 15 ml. [2]

  2. Using the table: (a) calculate the mean number of cases per week; (b) find the median; (c) calculate the percentage increase in cases from week 3 to week 4.[6 marks]
    Show worked solution

    (a) Total = 12 + 20 + 35 + 60 + 95 + 110 = 332; mean = 332 ÷ 6 = 55.3 (to 1 d.p.). [2]

    (b) Middle two values are 35 and 60, so median = (35 + 60) ÷ 2 = 47.5. [2]

    (c) Increase = 25; 25 ÷ 35 × 100 = 71.4%. [2]

  3. In the community, 2% of people have the disease. A screening test is positive for 95% of people who have the disease and for 5% of people who do not. Draw a tree diagram and calculate the probability that a randomly chosen person tests positive.[4 marks]
    Show worked solution

    First branches: disease 0.02, no disease 0.98. [1] Second branches: positive 0.95 (if diseased) and 0.05 (if not). [1]

    P(positive) = 0.02 × 0.95 + 0.98 × 0.05 = 0.019 + 0.049 = 0.068. [2]

Task total: 13 marks

Task · Additional Mathematics

How long does the medicine stay in the blood?

A drug’s concentration in the blood halves every 4 hours. The doctor needs to know when it is safe to give the next dose. A nurse also measures temperature spread.

  1. The concentration of a drug is C = 100 × (0.5)^(t/4) mg per litre, where t is the time in hours after the dose. Find C (a) when t = 8, (b) when t = 10, and (c) the time when C = 10 mg per litre.[6 marks]
    Show worked solution

    (a) t/4 = 2, C = 100 × 0.25 = 25 mg/l. [1]

    (b) C = 100 × 0.5^2.5 = 100 × 0.1768 = 17.7 mg/l. [2]

    (c) 0.5^(t/4) = 0.1, so (t/4) log 0.5 = log 0.1 [1], t = 4 × (−1) ÷ (−0.3010) = 13.3 hours. [2]

  2. Five patients have temperatures (°C) of 38.0, 38.6, 39.1, 37.8 and 38.9. Calculate the mean and the standard deviation.[4 marks]
    Show worked solution

    Mean = 192.4 ÷ 5 = 38.48 °C. [1]

    Deviations squared: 0.2304, 0.0144, 0.3844, 0.4624, 0.1764; sum = 1.268. [1]

    Variance = 1.268 ÷ 5 = 0.2536. [1] Standard deviation = √0.2536 = 0.50 °C. [1]

Task total: 10 marks

Task · Physics

Seeing inside the body: ultrasound, X-rays and a radioactive tracer

The radiographer uses ultrasound and X-rays, and the nuclear medicine unit uses a radioactive tracer with a short half-life.

Skills from your lessons: Physics C2 Physics C3 Physics E3 Physics E4
  1. An ultrasound pulse travels at 1500 m/s in body tissue. An echo from an organ returns 0.00004 s after the pulse is sent. Calculate the depth of the organ.[3 marks]
    Show worked solution

    Total distance travelled = speed × time = 1500 × 0.00004 = 0.06 m. [1]

    The pulse goes there and back, so depth = 0.06 ÷ 2 = 0.03 m = 3.0 cm. [2]

  2. A tracer has an activity of 80 MBq and a half-life of 6 hours. (a) What is its activity after 18 hours? (b) State why a short half-life is useful for a tracer given to a patient.[4 marks]
    Show worked solution

    (a) 18 h = 3 half-lives: 80 → 40 → 20 → 10 MBq. [3]

    (b) The tracer decays quickly, so the patient is exposed to radiation for a shorter time. [1]

  3. (a) Why do X-rays make an image of bones? (b) State one safety precaution for a radiographer.[2 marks]
    Show worked solution

    (a) Bones absorb more X-rays than soft tissue, so fewer reach the film or detector behind them. [1]

    (b) Any one: stand behind a lead screen; wear a lead apron; limit exposure time; wear a radiation badge. [1]

Task total: 9 marks

Task · Chemistry

The antacid tablet

Night-shift staff are given antacid tablets containing magnesium hydroxide. The pharmacist checks that one tablet can neutralise the acid in the stomach.

Data: Stomach acid: 100 cm³ of hydrochloric acid of concentration 0.10 mol/dm³. One tablet contains 0.50 g of Mg(OH)₂. Mg(OH)₂ + 2HCl → MgCl₂ + 2H₂O. (Ar: Mg = 24, O = 16, H = 1)
  1. (a) Calculate the moles of HCl in the stomach acid. (b) Calculate the moles of Mg(OH)₂ needed to neutralise it. (c) Calculate the mass of Mg(OH)₂ needed. (d) Is one tablet enough? Explain.[5 marks]
    Show worked solution

    (a) n = 0.10 × 100 ÷ 1000 = 0.010 mol. [1]

    (b) Ratio Mg(OH)₂ : HCl = 1 : 2, so n = 0.0050 mol. [1]

    (c) M(Mg(OH)₂) = 24 + 2(16 + 1) = 58 g/mol; mass = 0.0050 × 58 = 0.29 g. [2]

    (d) Yes: the tablet contains 0.50 g, which is more than the 0.29 g needed. [1]

  2. Explain why sodium hydroxide solution is not used as an antacid, even though it neutralises acid.[2 marks]
    Show worked solution

    Sodium hydroxide is a strong, corrosive alkali [1] which would burn and damage the throat and stomach lining; antacids use weak, insoluble bases such as magnesium hydroxide that are safe. [1]

  3. A patient chews the tablet rather than swallowing it whole. Explain, using collision theory, why it neutralises the acid faster.[2 marks]
    Show worked solution

    Chewing breaks it into smaller pieces, which increases the surface area exposed to the acid. [1] More acid particles can collide with the base each second, so the reaction rate is higher. [1]

Task total: 9 marks

Task · Biology

The outbreak, the vaccine and the heart

The public health officer studies the outbreak, and the doctor explains how vaccines work and checks a patient’s heart output.

Skills from your lessons: Biology B19 Biology B9 Biology B8 Biology A7
  1. Using the weekly case data in the Maths task: (a) describe the trend in cases; (b) outline three measures that would reduce the spread of a mosquito-borne disease.[5 marks]
    Show worked solution

    (a) Cases rise every week, slowly at first and then very quickly (35 → 60 → 95), and the increase slows at week 6 (110). [2]

    (b) Any three: remove standing water and cover containers; use larvicide or biological control (fish); use insect repellent, nets and screens; fogging in outbreaks; public education; early treatment and isolation. [3]

  2. Explain how vaccination gives protection against a disease.[3 marks]
    Show worked solution

    A vaccine contains weakened or dead pathogens, or their antigens. [1] This stimulates the white blood cells (lymphocytes) to make antibodies and memory cells. [1] If the real pathogen later invades, the memory cells respond quickly with a large antibody response, so the person does not become ill. [1]

  3. A patient’s heart beats 72 times per minute and pumps 70 cm³ of blood each beat. Calculate the cardiac output in cm³ per minute and in dm³ per minute.[2 marks]
    Show worked solution

    72 × 70 = 5040 cm³/min = 5.04 dm³/min. [2]

Task total: 10 marks

Task · Information Technology

Patient records, privacy and appointment letters

The records clerk builds a patient database, protects it, and sends reminder letters.

Skills from your lessons: IT B7 IT B8 IT B3 IT A8 IT A12 IT A13
Table Patient
PatientIDNameAgeTemp (°C)
P1Ana838.6
P2Ben3537.0
P3Cy1039.1
P4Dee637.8
P5Eli4138.9
  1. (a) Describe the criteria for a query that lists children (under 12) with a temperature above 38 °C. (b) Which patients does it show? (c) Why is PatientID a suitable primary key? (d) Suggest a validation rule for Temp.[5 marks]
    Show worked solution

    (a) In the query design grid, Age: <12 and Temp: >38 on the same criteria row (AND). [2]

    (b) Ana and Cy (Dee’s 37.8 is not above 38). [1]

    (c) It is unique for every patient and never empty. [1]

    (d) A range check, for example between 30 and 45 °C. [1]

  2. Patient records are confidential. State two measures to protect them and one risk of storing them in the cloud.[3 marks]
    Show worked solution

    Any two measures: passwords and access levels; encryption; firewall and antivirus; regular backups; locked server room. [2]

    Risk: data may be hacked or accessed by unauthorised people, or lost if the provider fails; needs an internet connection. [1]

  3. The hospital sends appointment reminders to 200 patients. Name the feature to be used in the word processor and identify the primary document, the data source and two merge fields.[3 marks]
    Show worked solution

    Mail merge. [1] The primary document is the letter with the fixed text; the data source is the patient table (name, address, appointment date). [1] Merge fields such as «Name» and «Date». [1]

Task total: 11 marks

Put it together

Response plan for the hospital director

Write a one- to two-page response plan or record a 3-minute briefing. Include a graph of the weekly cases, the dose calculation, the antacid check, the imaging and tracer results, and the privacy measures. Finish with a timeline of actions for the next four weeks.

Checklist

How it will be judged (20 marks)

CriterionWhat a top answer showsMarks
AccuracyCorrect calculations and units from all six tasks6
Health reasoningLinks the numbers to disease, medicine and safety5
Graph and dataClear graph of cases; correct averages3
Safety and ethicsConsiders patient privacy and radiation safety4
CommunicationClear and calm; suitable for a director2

Careers

Who does this work in real life?

Each of these people uses the subjects in this project every day.

Medical laboratory technologist

Analyses blood and other samples to diagnose disease and track outbreaks.

Uses: Biology, Chemistry, IT (data), Maths (statistics)

Pathway: Degree in medical laboratory science.

Radiographer / sonographer

Takes X-ray, ultrasound and other images and keeps patients and staff safe.

Uses: Physics (waves, radiation), Biology (anatomy)

Pathway: Degree or diploma in radiography or sonography.

Pharmacist

Prepares and checks medicines, doses and interactions.

Uses: Chemistry (concentration, acids), Maths (dosage), Biology

Pathway: Degree in pharmacy.

Public health officer / epidemiologist

Tracks diseases in the population and designs prevention.

Uses: Biology, Maths (statistics, probability), IT (data)

Pathway: Degree in public health, biology or medicine.

Health informatics officer

Designs and secures hospital databases and systems.

Uses: IT (databases, security), Maths

Pathway: Degree in IT or health informatics.

Reflect

Think about it

  1. Which two subjects together gave you the most useful information about the outbreak?
  2. Is it fair that a short half-life makes a tracer safer but harder to use? How do hospitals plan for this?
  3. What are the ethical issues in keeping patient data? Who should be allowed to see it?