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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | GCSE Higher |
The equation of the line L1 is \(y = 2 - 5x\).
The equation of the line L2 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 |
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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