Rearrange to make variable subject (quadratic)

A question is this type if and only if it asks to rearrange an equation or formula to make a specified variable the subject where the rearrangement involves solving a quadratic equation in that variable (e.g., making h the subject of an equation where h appears squared).

10 questions · Moderate -0.7

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Edexcel C1 Q8
5 marks Standard +0.3
\includegraphics{figure_4} A manufacturer produces cartons for fruit juice. Each carton is in the shape of a closed cuboid with base dimensions 2\(x\) cm by \(x\) cm and height \(h\) cm, as shown in Fig. 4. Given that the capacity of a carton has to be 1030 cm\(^3\),
  1. express \(h\) in terms of \(x\), [2]
  2. show that the surface area, \(A\) cm\(^2\), of a carton is given by $$A = 4x^2 + \frac{3090}{x}.$$ [3]
OCR MEI C1 Q9
4 marks Moderate -0.8
Rearrange the equation \(5c + 9t = a(2c + t)\) to make \(c\) the subject. [4]
OCR MEI C1 Q11
3 marks Easy -1.8
Rearrange the following equation to make \(h\) the subject. $$4h + 5 = 9a - ha^2$$ [3]
OCR MEI C1 Q3
4 marks Moderate -0.5
Make \(x\) the subject of the formula \(y = \frac{1 - 2x}{x + 3}\). [4]
OCR MEI C1 Q6
3 marks Moderate -0.8
Rearrange the formula \(c = \sqrt{\frac{a + b}{2}}\) to make \(a\) the subject. [3]
OCR MEI C1 Q7
3 marks Easy -1.2
Make \(a\) the subject of the formula \(s = ut + \frac{1}{2}at^2\). [3]
OCR MEI C1 Q13
4 marks Moderate -0.5
Rearrange \(y + 5 = x(y + 2)\) to make \(y\) the subject of the formula. [4]
OCR MEI C1 Q2
4 marks Moderate -0.5
Make \(x\) the subject of the equation \(y = \frac{x + 3}{x - 2}\). [4]
OCR MEI C1 Q6
3 marks Moderate -0.8
Make \(a\) the subject of the equation $$2a + 5c = af + 7c.$$ [3]
OCR MEI C1 Q10
4 marks Moderate -0.5
Make \(C\) the subject of the formula \(P = \frac{C}{C + 4}\). [4]