Algebra - rearranging
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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Make $x$ the subject of $y = x + 7$.
2 marks
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Make $x$ the subject of $y = 4x$.
2 marks
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Make $t$ the subject of $v = u + at$.
3 marks
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Make $r$ the subject of $A = \pi r^{2}$.
3 marks
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Make $x$ the subject of $y = \dfrac{x + 3}{5}$.
4 marks
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Make $x$ the subject of $ax + b = cx + d$. Higher
4 marks
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Make $x$ the subject of $y = \dfrac{2x - 1}{x + 3}$. Higher
5 marks
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The area of a trapezium is $A = \dfrac{(a + b)h}{2}$. Make $h$ the subject, then make $a$ the subject. Find $a$ when $h = 6$, $A = 45$ and $b = 4$. Higher
6 marks
Mark scheme
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Answer. $x = y - 7$
- Subtract $7$ from both sides.
- $x = y - 7$
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Answer. $x = \dfrac{y}{4}$
- Divide both sides by $4$.
- $x = \dfrac{y}{4}$
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Answer. $t = \dfrac{v - u}{a}$
- $v - u = at$
- $t = \dfrac{v - u}{a}$
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Answer. $r = \sqrt{\dfrac{A}{\pi}}$
- $\dfrac{A}{\pi} = r^{2}$
- $r = \sqrt{\dfrac{A}{\pi}}$
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Answer. $x = 5y - 3$
- $5y = x + 3$
- $x = 5y - 3$
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Answer. $x = \dfrac{d - b}{a - c}$
- $ax - cx = d - b$
- $x(a - c) = d - b$
- $x = \dfrac{d - b}{a - c}$
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Answer. $x = \dfrac{3y + 1}{2 - y}$
- $y(x + 3) = 2x - 1$
- $yx - 2x = -1 - 3y$
- $x(y - 2) = -(3y + 1)$
- $x = \dfrac{3y + 1}{2 - y}$
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Answer. $h = \dfrac{2A}{a + b}$, $a = \dfrac{2A}{h} - b$, and $a = 11$
- $2A = (a + b)h$, so $h = \dfrac{2A}{a + b}$.
- $a = \dfrac{2A}{h} - b$.
- $a = \dfrac{90}{6} - 4 = 11$.
- Check: $\dfrac{(11 + 4) \times 6}{2} = 45$.