Mastering Operations Challenge

Name:

Date:

Mathematical operations and problem solving illustration

💰 Part 1: Financial Planning Challenge

1. Sarah borrows $15,000 to buy a car with an annual interest rate of 6%. Calculate the total interest after 4 years using simple interest.

Formula: Interest = Principal × Rate × Time

2. Using your answer from question 1, what would Sarah's estimated monthly repayments be if she pays back the total amount (principal + interest) equally over 4 years?

3. Check your answer using estimation. Round the numbers to make a quick mental calculation:

4. If Sarah could only afford to pay $400 per month, how many months would it take her to repay the loan?

🔢 Part 2: Pattern Exploration with Exponents

5. Given the sequence defined as a_n = 2ⁿ + 3ⁿ, calculate the first four terms:

a₁ = _________ a₂ = _________ a₃ = _________ a₄ = _________

6. If a_n = 35, solve for n. Show your working:

7. What pattern do you notice in the differences between consecutive terms? Explain using properties of exponents:

📏 Part 3: Measurement & Scaling

8. A recipe requires ¾ cup of sugar for 6 servings. How much sugar is needed for 15 servings?

9. Sugar is sold in 1.5kg bags. If 1 cup of sugar = 200g, how many bags would you need for a large event requiring 240 servings? Show all unit conversions:

10. A scale drawing of a rectangular garden has dimensions 12cm × 8cm. If the scale is 1:50, what are the actual dimensions of the garden in metres?

11. Reflection: Describe two different problem-solving strategies you used in this worksheet. Which strategy was most helpful and why?