📊 Part 1: Multiple Choice Questions

1. The ratio of red to blue balls is 3:7. How many blue balls are there if there are 30 red balls?

10

20

70

90

2. A jacket costs $120. If GST is 15%, what is the total price including GST?

$135

$138

$140

$142

3. Which number is greater?

7.35 × 10⁻³

0.008

They are equal

Cannot be determined

4. A recipe for 4 people uses 200g of flour. How much flour is needed for 10 people?

400g

500g

600g

800g

5. If 1 NZ dollar = 0.62 US dollars, how many US dollars would you get for $50 NZ?

$31.00 US

$32.50 US

$30.50 US

$31.50 US

💰 Part 2: Short Answer Problem Solving

6. Currency Conversion Problem: You are planning a trip to Australia. The exchange rate is 1 NZ dollar = 0.93 Australian dollars. You have $250 NZ to exchange. Calculate how many Australian dollars you will receive and explain your working.

7. Discount Calculation: A laptop normally costs $800. It is on sale with a 25% discount. Calculate the sale price and show your working step by step.

8. Scientific Notation Comparison: Compare these two measurements and explain which is larger: 4.2 × 10⁻⁴ metres or 0.0005 metres. Show your reasoning.

📈 Part 3: Visual Data Interpretation

9. The graph below shows the population of a small New Zealand town over 5 years. Use proportional reasoning to answer the following questions:

Year 1: 2,000 people

Year 2: 2,200 people

Year 3: 2,420 people

Year 4: 2,662 people

Year 5: 2,928 people

a) What is the percentage increase from Year 1 to Year 2?

b) If the pattern continues, predict the population for Year 6. Show your working.

c) What is the ratio of Year 5 population to Year 1 population? Express as a simplified ratio.

🤔 Part 4: Real-World Applications

10. Speed and Distance: A car travels 180 kilometres in 2 hours. Using proportional reasoning:

a) How far will it travel in 5 hours at the same speed?

b) How long will it take to travel 270 kilometres?

11. Scale Drawing: A map has a scale of 1:50,000. If two cities are 8 centimetres apart on the map, what is the actual distance between them in kilometres?

12. Mixing Solutions: A cleaning solution is made by mixing water and detergent in the ratio 5:1. How much water and detergent would you need to make 600ml of cleaning solution?

✍️ Part 5: Reflection

13. Explain how you used proportional reasoning in one of the problems above. Why is this mathematical method useful in everyday life? Give at least two real-world examples where proportional reasoning is important.

14. Which type of proportional reasoning problem did you find most challenging today? Explain what made it difficult and what strategy helped you solve it.