## Exam-Style Questions.## Problems adapted from questions set for previous Mathematics exams. |

## 1. | GCSE Higher |

The diagram shows part of the graph \(y=x^2-3x+6\).

(a) By drawing a suitable straight line, use your graph to find estimates for the solutions of \(x^2 - 4x + 2 = 0\) to one decimal place.

(b) A is the point (2,4). Calculate an estimate for the gradient of the graph at the point A.

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

## 3. | 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 698cm^{2}, work out the value of \(x\).

## 4. | GCSE Higher |

Given that:

$$ x^2 : (5x + 3) = 1 : 3 $$find the possible values of \(x\).

## 5. | GCSE Higher |

Given that \(x^2 – 8x + 3 = (x – a)^2 – b\) for all values of x,

(a) find the value of a and the value of b.

(b) Hence write down the coordinates of the turning point on the graph of \(y = x^2 – 8x + 3\)

## 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 \(x\).

## 7. | GCSE Higher |

If \(y = 5x^4 + 3x^2\) and \(x=\sqrt{w+2}\), find \(w\) when \(y = 12\) showing each step of your working.

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