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Pure Mathematics Year 1 (AS) Unit Test 2: Coordinate geometry in the (x, y) plane
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Pure Mathematics Year 1 (AS) Unit Test 2: Coordinate geometry in the (x, y) plane. Question paper
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Pure Mathematics Year 1 (AS) Unit Test 2: Coordinate geometry in the(x, y) plane
1 The points A and B have coordinates (3k − 4, −2) and (1, k + 1) respectively, where k is a constant.
3
Given that the gradient of AB is :
2
a show that k = 3 (2 marks)
b find an equation of the line through A and B (3 marks)
c find an equation of the perpendicular bisector of A and B, leaving your answer
in the form ax by c 0 where a, b and c are integers. (4 marks)
2 a Find an equation of the straight line passing through the points with coordinates
(4, −7) and (−6, 11), giving your answer in the form ax by c 0 ,where a, b
and c are integers. (3 marks)
The line crosses the x-axis at point A and the y-axis at point B and O is the origin.
b Find the area of triangle AOB. (3 marks)
3 The line with equation mx y 2 0 touches the circle with equation
x 2 6 x y 2 8 y 4 . Find the two possible values of m, giving your answers
in exact form. (7 marks)
4 The equations of two circles are x 2 10 x y 2 12 y 3 and x 2 6 x y 2 2qy 9.
a Find the centre and radius of each circle, giving your answers in terms of q
where necessary. (6 marks)
b Given that the distance between the centres of the circles is 80, find the two
possible values of q. (3 marks)
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