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Year 8 Algebra Quiz
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Year 8 Algebra Quiz
Show your working for short-answer questions. Simplify expressions fully and include units where needed.
Part A: Algebra moves
Use your algebra skills to help plan a chess tournament.
1.Ivy scores 7x points in the first round and 4x points in the second round, then loses 3x points for a penalty. Simplify her total score expression: 7x + 4x − 3x.
- 8x
- 14x
- 8x − 3
- 11x
2.A chess club packs 5 boards into each crate, with b spare pieces added to every crate. Expand the expression for the contents of 3 crates: 3(5 + b).
- 15 + b
- 15 + 3b
- 8b
- 15b
3.Oliver-Mae earns 12t points for a win and 8 points for a draw. Factorise 12t + 8 by taking out the greatest common factor.
- 4(3t + 2)
- 2(6t + 8)
- 4(12t + 8)
- t(12 + 8)
4.What is the value of 3x + 4 when x = 5?
Part B: Show your strategy
Write each step clearly. Check that your final expression is simplified.
5.A team orders 2x + 3 snack packs for each of 4 rounds, then gets 5 extra packs. Expand and simplify 4(2x + 3) + 5.
6.Collect like terms in the tournament budget expression: 6a + 2c − 4a + 5c − 7.
7.A chess set costs $x, and a clock costs $9. Write and simplify the total cost of 3 chess sets and 3 clocks by factorising the expression 3x + 27.
8.Solve for n: 4n + 7 = 31. Show the inverse operations you use.
9.A rectangular chess analysis board has length (x + 5) cm and width 3 cm. Write a simplified expression for its perimeter.
10.A square tournament display has side length (x + 4) cm. Expand an expression for its area, (x + 4)².
11.Two players’ scores are represented by (x + 3)(x + 2). Expand and simplify the product.
12.A team’s total score is 5p + 12. If p = 4, calculate the score. Then state whether the expression is equivalent to 5(p + 12), explaining briefly.
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