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Year 10 Algebra Quiz

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Year 10 Algebra Quiz worksheet preview

Year 10 Algebra Quiz

Algebra symbols and equations

🎯 WALT: Manipulate algebraic expressions and solve equations

Instructions: Answer all questions. Show your working where appropriate. Use the spaces provided for your answers.

1. Simplify: 3x + 5x - 2x
2. Expand: 4(2x - 3)
3. If x = 3, find the value of 2x² - 5x + 1
4. Solve: 3x + 7 = 22
5. Factorise: x² + 7x + 12
6. Simplify: x⁵ × x³

📝 Problem Solving & Applications

7. A rectangle has length (2x + 3) cm and width (x - 1) cm. Write an expression for its perimeter.
8. Solve: 2x - 5 = x + 8
9. Expand and simplify: (x + 4)(x + 2)
10. If y = 2x - 3 and x = 5, find the value of y.
11. Simplify: (3x²)³
12. The sum of two consecutive integers is 47. If the smaller integer is n, write an equation and solve to find both numbers.

🌟 Extension Questions

13. Extension: Solve the simultaneous equations: x + y = 8 and 2x - y = 1
14. Factorise: 2x² + 7x + 3
15. Challenge: If 3ˣ = 27, find the value of x. Then use this to find the value of 3^(x+2).

📋 Answer Key

1. 6x

2. 8x - 12

3. 4 (Working: 2(9) - 5(3) + 1 = 18 - 15 + 1 = 4)

4. x = 5

5. (x + 3)(x + 4)

6. x⁸

7. 6x + 4 cm

8. x = 13

9. x² + 6x + 8

10. y = 7

11. 27x⁶

12. n + (n + 1) = 47, so n = 23. The numbers are 23 and 24.

13. x = 3, y = 5

14. (2x + 1)(x + 3)

15. x = 3, then 3^(x+2) = 3⁵ = 243

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