📱 Part 1: Phone Plan Problem

Scenario: You're choosing between two mobile phone plans in New Zealand:

Plan A: $25 monthly fee + $0.50 per GB of data

Plan B: $40 monthly fee + $0.20 per GB of data

1. Write an algebraic expression for the monthly cost of Plan A if you use x GB of data:

2. Write an algebraic expression for the monthly cost of Plan B if you use x GB of data:

3. At what amount of data usage (in GB) would both plans cost the same? Show your working:

4. If you typically use 35 GB per month, which plan would be cheaper?

Plan A

Plan B

Both cost the same

🚗 Part 2: Statistical Enquiry - Car Fuel Efficiency

Data: Fuel consumption (litres per 100km) for different car models:

Toyota Corolla: 6.2L, Honda Civic: 6.8L, Mazda 3: 6.5L, Hyundai i30: 7.1L, Nissan Sentra: 6.9L

5. Using the PPDAC cycle, what Problem question could you investigate with this data?

6. How would you Plan to collect more data to answer your question?

7. Calculate the mean fuel consumption for these five cars:

8. If petrol costs $2.40 per litre, which car would be most economical for a 500km trip?

Toyota Corolla

Honda Civic

Mazda 3

Hyundai i30

Nissan Sentra

🎫 Part 3: Event Planning Problem

Scenario: Your school is organising a fundraising concert. The venue costs $800 to hire, and each ticket costs $2 to print. You plan to sell tickets for $15 each.

9. Write an equation for the total profit P if you sell n tickets:

10. How many tickets do you need to sell to break even (profit = $0)? Show your working:

11. If the venue capacity is 150 people, what is the maximum profit you could make?

12. Is your answer reasonable? Explain your thinking:

🚌 Part 4: Travel Time Analysis

Data: Travel times (in minutes) from Auckland to Hamilton on different days:

Monday: 125, Tuesday: 118, Wednesday: 132, Thursday: 128, Friday: 145, Saturday: 115, Sunday: 120

13. Complete the PPDAC cycle for this data:

Problem: What question could you investigate? ________________________

Plan: What additional data might be useful? ________________________

14. Calculate the following statistics:

Mean travel time: _______ minutes

Range: _______ minutes

Median travel time: _______ minutes

15. Which day(s) had unusually long travel times? What might explain this?

Monday (work traffic)

Friday (weekend traffic)

Wednesday (road works)

Saturday (clear roads)

16. Based on this data, what would you predict for next Friday's travel time? Justify your answer:

🎯 Part 5: Reflection and Communication

17. Choose one problem from this worksheet. Explain how mathematics helped you understand and solve a real-world situation:

18. What assumptions did you make in your mathematical models? How might these affect your conclusions?

19. Graph the break-even analysis for the concert problem (Question 9-11) below:

Real-World Math Modeling

Real-World Math Modeling

📱 Part 1: Phone Plan Problem

🚗 Part 2: Statistical Enquiry - Car Fuel Efficiency

🎫 Part 3: Event Planning Problem

🚌 Part 4: Travel Time Analysis

🎯 Part 5: Reflection and Communication

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