Exam-Style Questions.

1.	GCSE Higher

The diagram below is a sketch of \(y = f(x)\) where \(f(x)\) is a quadratic function.

The graph intersects the x-axis where \(x=-2\) and \(x = 0.5\).

Which of the following is the solution of \(f(x) \le 0\) ?

• (a) \( x \ge -2 \) or \(x \ge 0.5\)
  
  
• (b) \( -2 \ge x \ge 0.5\)
  
  
• (c) \( x \ge -2 \) and \( x \le 0.5\)
  
  
• (d) \( x \le -2 \) and \( x \ge 0.5\)
  
  

Worked Solution

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2.	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 \(A=\pi rl\).]

Worked Solution

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3.	IB Studies

A red rug has a width of \(x-3\) cm and a length of \(4x\) cm.

(a) Write down an expression for the area, A, in cm², of the rug.

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.

Worked Solution

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4.	GCSE Higher

In the diagram below, which is not drawn to scale, all dimensions are in centimetres and all angles are multiples of 90^o. If the shaded area is 698cm², work out the value of \(x\).

Worked Solution

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5.	GCSE Higher

Given that:

$$ x^2 : (5x + 3) = 1 : 3 $$

find the possible values of \(x\).

Worked Solution

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6.	GCSE Higher

The area of triangle ABC (not drawn to scale) is

$$ \frac{35 \sqrt{3}}{4} m^2$$

If AB = \(x+2\) metres and AC = \(2x+1 \) metres, find the value of \(x\).

Worked Solution

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