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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | GCSE Higher |
Show that line \(5y = 7x - 7\) is perpendicular to line \(7y = -5x + 55\).
2. | 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.
3. | 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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