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

## 1. | GCSE Higher |

The equation of the line L_{1} is \(y = 2 - 5x\).

The equation of the line L_{2} is \(3y + 15x + 17 = 0\).

Show that these two lines are parallel.

## 2. | GCSE Higher |

Which of the following lines is parallel to the x-axis?

\(y=-7\)

\(x-y=1\)

\(x=10\)

\(x+y=0\)

\(x=y\)

## 3. | GCSE Higher |

Show that line \(5y = 7x - 7\) is perpendicular to line \(7y = -5x + 55\).

## 4. | GCSE Higher |

The straight line \(L\) has the equation \(4y = 3x + 5\).

The point A has coordinates \((6,7)\).

Find an equation of the straight line that is perpendicular to L and passes through A.

## 5. | GCSE Higher |

(a) Complete the table of values for \(y=\frac{(x^3-5x)}{10}\)

\(x\) | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |

\(y\) | 0.2 | 1.2 |

(b) On the grid below, draw the graph of \(y=\frac{(x^3-5x)}{10}\) for values of \(x\) from -3 to 4.

## 6. | GCSE Higher |

Suppose a rhombus ABCD is drawn on a coordinate plane with the point A situated at (4,7). The diagonal BD lies on the line \(y = 2x - 5 \)

Find the equation the line that passes through A and C.

## 7. | GCSE Higher |

On the grid below, draw the graph of \(y = 1 - 2x\) for values of \(x\) from -2 to 2.

## 8. | IB Studies |

The vertices of quadrilateral ABCD are A (2, 4), B (-1, 5), C (–3, 4) and D (–2, 2).

(a) Calculate the gradient of line CD.

(b) Show that line AD is perpendicular to line CD.

(c) Find the equation of line CD. Give your answer in the form \(ax+by=c\) where \(a,b,c\in \mathbf Z\)

Lines AB and CD intersect at point E.

(d) Find the coordinates of E.

(e) Find the distance between A and D.

The distance between D and E is \(\sqrt{20}\).

(f) Find the area of triangle ADE.

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