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

## 1. | GCSE Higher |

Sketch the graph of \(y=0.5^x +1\) for \(0 \le x \le 5\) labeling the y intercept.

## 2. | GCSE Higher |

(a) Use the red graphs to solve the simultaneous equations:

$$4x-7y=-47$$ $$3y=-5x$$(b) Use the blue graph to find estimates for the solutions of the quadratic equation:

$$x^2-5x+3=0$$## 3. | GCSE Higher |

The images below show a graphic display calculator screen with different functions displayed as graphs.

a) Which function is trigonometric?

b) Which function is inversely proportional to \(x\)?

c) Which function is exponential?

d) Which function is proportional to \(x^3\)?

## 4. | GCSE Higher |

Match the equation with the letter of its graph

Equation | Graph |
---|---|

$$y=3-\frac{10}{x}$$ | |

$$y=2^x$$ | |

$$y=\sin x$$ | |

$$y=x^2+7x$$ | |

$$y=x^2-8$$ | |

$$y=2-x$$ |

## 5. | IGCSE Extended |

The table shows some values (rounded to one decimal place) for the function \(y=\frac{2}{x^2}-x, x\neq 0\).

\(x\) | -3 | -2 | -1 | -0.5 | 0.5 | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|---|---|---|---|

\(y\) | 3.2 | 2.5 | 8.5 | 7.5 | 1.0 | -2.8 |

(a) Complete the table of values.

(b) Draw the graph of \(y=\frac{2}{x^2}-x\) for \(-3\le x \le -0.5\) and \(0.5\le x\le 4\).

(c) Use your graph to solve the equation \(\frac{2}{x^2}-x-3=0\)

(d) Use your graph to solve the equation \(\frac{2}{x^2}-x=1-2x\)

(e) By drawing a suitable tangent, find an estimate of the gradient of the curve at the point where x = 1.

(f) Using algebra, show that you can use the graph at \(y=0\) to find \(\sqrt[3]2\)

## 6. | GCSE Higher |

(a) Find the coordinates of the point at which the curve \(y = k^x\) intersects the y-axis.

The equation of circle \(A\) is \(x^2+y^2=25\). This circle is translated by the vector \( \begin{pmatrix} 0 \\ 4 \\ \end{pmatrix} \) to give circle \(B\).

(b) Draw a sketch of circle \(B\) clearly labelling the points of intersection with the y-axis.

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