📝 Part 1: Simplifying Expressions

Instructions: Simplify each expression by collecting like terms. Show all working.

1. Simplify: 3x + 5x - 2x + 7

2. Simplify: 4a + 3b - 2a + 5b - 1

3. Simplify: 2x² + 5x - 3x² + 4x - 6

4. Simplify: 7y - 3z + 2y + 8z - 4y

🔢 Part 2: Expanding Expressions

Instructions: Expand each expression using the distributive property. Show all working.

5. Expand: 3(x + 4)

6. Expand: -2(3y - 5)

7. Expand: (x + 3)(x + 5)

8. Expand: (2a - 1)(a + 4)

9. Expand: (x - 2)(x - 6)

🧩 Part 3: Factorising Expressions

Instructions: Factorise each expression completely. Show all working.

10. Factorise: 6x + 12

11. Factorise: 4a² - 8a

12. Factorise: x² + 7x + 12

13. Factorise: x² - 5x + 6

14. Factorise: x² - 9

🔄 Part 4: Substitution

Instructions: Substitute the given values into each expression and calculate the result. Show all working.

15. If x = 3, find the value of: 2x + 5

16. If a = -2 and b = 4, find the value of: 3a + 2b

17. If x = 5, find the value of: x² - 3x + 2

18. If p = 2 and q = -1, find the value of: p² + 3pq - q²

🌍 Part 5: Real-World Applications

Instructions: Solve these problems involving algebraic expressions in real contexts.

19. The cost of hiring a car in New Zealand is $45 per day plus $0.30 per kilometre driven. Write an expression for the total cost if the car is hired for d days and driven k kilometres.

20. Using your expression from question 19, calculate the total cost if the car is hired for 3 days and driven 250 kilometres.

21. A rectangular garden has length (2x + 3) metres and width (x - 1) metres. Write an expression for the area of the garden in expanded form.

22. If x = 4 metres in the garden from question 21, what is the actual area of the garden in square metres?

🎯 Part 6: Challenge Questions

Instructions: These questions combine multiple algebraic skills. Show all working clearly.

23. Simplify and then factorise: 2x² + 6x + 4x² - 2x

24. If y = 2x + 1 and x = 3, find the value of y² - 3y + 5

25. Expand (x + 2)² and then substitute x = -1 to find the numerical value.

💭 Reflection

26. Which algebraic skill did you find easiest in this assessment and why?

27. Which concept challenged you the most? How did you work through the difficulty?

28. Give one example of how algebra might be useful in everyday life in New Zealand.

Algebra Mastery Assessment

Algebra Mastery Assessment

📝 Part 1: Simplifying Expressions

🔢 Part 2: Expanding Expressions

🧩 Part 3: Factorising Expressions

🔄 Part 4: Substitution

🌍 Part 5: Real-World Applications

🎯 Part 6: Challenge Questions

💭 Reflection

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