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8 17 11 y l NOT TO SCALE 3 0 4 x The diagram shows the straight line, l, which passes through the points (0, 3) and (4, 11). (a) Find the equation of line l in the form y = mx + c. Answer(a) y =... [3] (b) Line p is perpendicular to line l. Write down the gradient of line p. Answer(b)... [1] UCLES 2015 0580/22/M/J/15

8 17 (a) V = IR In an experiment I and R are both measured correct to 1 decimal place. When I = 4.0 and R = 2.7, find the lower bound for V.... [2] (b) S D = T In an experiment D and T are both measured correct to 2 significant figures. When D = 7.6 and T = 0.23, find the upper bound for S.... [2] 18 y 7 6 5 L 4 3 2 1 3 2 1 0 1 2 3 4 5 6 1 x 2 3 (a) Work out the gradient of the line L.... [2] (b) Write down the equation of the line parallel to the line L that passes through the point (0, 6).... [2] UCLES 2016 0580/23/M/J/16

3 4 C 8 cm NOT TO SCALE B 28 A Calculate the length of AB. Answer AB =... cm [2] 5 y P l NOT TO SCALE 0 x The equation of the line l in the diagram is y = 5 x. (a) The line cuts the y-axis at P. Write down the co-ordinates of P. Answer(a) (...,...) [1] (b) Write down the gradient of the line l. Answer(b)... [1] UCLES 2014 0580/22/M/J/14 [Turn over

11 20 y 7 6 A 5 4 3 2 1 0 1 2 3 4 5 6 7 8 B x Point A has co-ordinates (3, 6). (a) Write down the co-ordinates of point B. (...,... ) [1] (b) Find the gradient of the line AB.... [2] (c) Find the equation of the line that and is perpendicular to the line AB passes through the point (0, 2).... [3] UCLES 2016 0580/22/O/N/16

14 7 (a) The co-ordinates of P are ( 4, 4) and the co-ordinates of Q are (8, 14). (i) Find the gradient of the line PQ. For Examiner s Use Answer(a)(i)... [2] (ii) Find the equation of the line PQ. Answer(a)(ii)... [2] (iii) Write as a column vector. Answer(a)(iii) = f p [1] (iv) Find the magnitude of. Answer(a)(iv)... [2] UCLES 2013 0580/43/O/N/13

9 18 A (5, 23) and B ( 2, 2) are two points. (a) Find the co-ordinates of the midpoint of the line AB. For Examiner s Use Answer(a) (...,...) [2] (b) Find the equation of the line AB. Answer(b)... [3] (c) Show that the point (3, 17) lies on the line AB. Answer(c) [1] UCLES 2013 0580/22/O/N/13 [Turn over

10 17 (a) Find the co-ordinates of the midpoint of the line joining A( 8, 3) and B( 2, 3). For Examiner's Use Answer(a) (, ) [2] (b) The line y = 4x + c passes through (2, 6). Find the value of c. Answer(b) c = [1] (c) The lines 5x = 4y + 10 and 2y = kx 4 are parallel. Find the value of k. Answer(c) k = [2] UCLES 2012 0580/22/M/J/12

16 9 A line joins the points A ( 2, 5) and B (4, 13). (a) Calculate the length AB. AB =... [3] (b) Find the equation of the line through A and B. Give your answer in the form y = mx + c. y =... [3] (c) Another line is parallel to AB and passes through the point (0, 5). Write down the equation of this line.... [2] (d) Find the equation of the perpendicular bisector of AB.... [5] Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. UCLES 2016 0580/42/M/J/16

14 8 A line AB joins the points A (3, 4) and B (5, 8). (a) Write down the co-ordinates of the midpoint of the line AB. Answer(a) (...,... ) [2] (b) Calculate the distance AB. Answer(b) AB =... [3] (c) Find the equation of the line AB. Answer(c)... [3] (d) A line perpendicular to AB passes through the origin and through the point (6, r). Find the value of r. Answer(d) r =... [3] UCLES 2015 0580/42/O/N/15

12 20 (a) The two lines y = 2x + 8 and y = 2x 12 intersect the x-axis at P and Q. Work out the distance PQ. For Examiner's Use Answer(a) PQ = [2] (b) Write down the equation of the line with gradient O4 passing through (0, 5). Answer(b) [2] (c) Find the equation of the line parallel to the line in part (b) passing through (5, 4). Answer(c) [3] Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. UCLES 2012 0580/22/O/N/12

8 14 A(5, 10) NOT TO SCALE B(13, 2) A(5, 10) and B(13, 2) are two points on the line AB. The perpendicular bisector of the line AB has gradient 3 2. Find the equation of the perpendicular bisector of AB. Answer... [4] UCLES 2014 0580/21/M/J/14