## 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 |

A straight line goes through the points \((a, b)\) and \((c, d)\), where

$$a + 3 = c$$ $$b + 6 = d$$Find the gradient of the line.

## 5. | 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.

## 6. | GCSE Higher |

A is the point (-5, -9) and B is the point (10, 1).

(a) Find the length of AB.

(b) Find the equation of the perpendicular bisector of AB.

(c) C is a point on AB.

C divides AB in the ratio 3 : 2.

Find the coordinates of C.

## 7. | 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.

## 8. | IB Analysis and Approaches |

Consider the points A(-5, 15). B(4, 6) and C(-8, 12). The line \(L\) passes through the point A and is perpendicular to [BC].

(a) Find the equation of \(L\).

The line \(L\) passes through the point (\(k\), 5).

(b) Find the value of \(k\).

## 9. | IB Studies |

Consider a straight line graph L1, which intersects the x-axis at A(8, 0) and the y-axis at B (0, 4).

(a) Write down the coordinates of C, the midpoint of line segment AB.

(b) Calculate the gradient of the line L1.

The line L2 is parallel to L1 and passes through the point (5 , 9).

(c) Find the equation of L2. Give your answer in the form \(ay + bx + c = 0\) where \(a, b \text{ and } c \in \mathbb{Z}\).

## 10. | 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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