Algebra - solving
Algebra
- Crossover
- Non-calculator
- 8 questions
- 29 marks
Questions marked Higher are aimed at the Higher tier.
These are original practice questions, not a past paper. This site is independent and not affiliated with AQA or Pearson.
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Solve $3x + 5 = 20$.
2 marks
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Solve $2(x - 4) = 10$.
2 marks
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Solve $5x - 3 = 2x + 9$.
3 marks
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Solve $\dfrac{x + 2}{3} = 4$.
3 marks
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Solve $3(2x - 1) = 4(x + 3)$.
4 marks
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Solve $\dfrac{2x}{3} - 1 = 5$.
4 marks
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Solve $\dfrac{2x + 1}{3} - \dfrac{x - 2}{2} = 1$. Higher
5 marks
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A rectangle has length $(3x + 2)$ cm and width $(x - 1)$ cm. The perimeter is $46$ cm. Find $x$ and the area. Higher
6 marks
Mark scheme
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Answer. $x = 5$
- $3x = 15$
- $x = 5$
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Answer. $x = 9$
- $x - 4 = 5$
- $x = 9$
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Answer. $x = 4$
- $3x = 12$
- $x = 4$
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Answer. $x = 10$
- $x + 2 = 12$
- $x = 10$
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Answer. $x = 7.5$
- $6x - 3 = 4x + 12$
- $2x = 15$
- $x = 7.5$
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Answer. $x = 9$
- $\dfrac{2x}{3} = 6$
- $2x = 18$, so $x = 9$.
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Answer. $x = -2$
- Multiply by $6$: $2(2x + 1) - 3(x - 2) = 6$.
- $4x + 2 - 3x + 6 = 6$
- $x + 8 = 6$, so $x = -2$.
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Answer. $x = 5.5$, area $83.25$ cm$^{2}$
- $2(4x + 1) = 46$, so $4x + 1 = 23$.
- $x = 5.5$.
- Length $18.5$ cm and width $4.5$ cm.
- Area $= 18.5 \times 4.5 = 83.25$ cm$^{2}$.