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Exam-Style Questions on Quadratic EquationsProblems on Quadratic Equations adapted from questions set in previous Mathematics exams. |
1. | IGCSE Extended |
(a) Show that the equation \(\frac{3}{x+1}+\frac{3x-9}{2}=1\) can be simplified to \(3x^2-8x-5=0\).
(b) Solve the equation \(3x^2-8x-5=0\) showing all of your working and giving answers to three significant figures.
(c) The total surface area of a cone with radius \(x\) and slant height \(8x\) is equal to the area of a circle with radius r. Show that \(r = 3x\).
[The curved surface area, \(A\), of a cone with radius \(r\) and slant height \(l\) is \(A=\pi rl\).]
2. | IB Studies |
A red rug has a width of \(x-3\) cm and a length of \(4x\) cm.
(a) Write down an ex
The area of the rug is 3240 cm2.
(b) Calculate the value of \(x\).
(c) Hence, write down the value of the length and of the width of the rug in centimetres.
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