Mathematics · May / June 2025 · Paper 22 · Question 24
0580
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The question as text
0580/22/M/J/25 © UCLES 2025 24 The line y x 7 3 È intersects the curve y x x 5 12 2 È Á at the points A and Í. Find the coordinates of A and Í. A ( , ) Í ( , ) [5]
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(5, 38) and (–3, –18) [5]
B4 for one correct coordinate or for x = 5 and x = –3 OR
M2 for x2 – 2x – 15 [= 0] or y2 – 20y – 684 [= 0]
or M1 for 7x + 3 = x2 + 5x – 12 oe − 2 − y 3 y 3 = + − or y 5 12 7 7
M1 for correct method to solve their three- term quadratic (x – 5)(x + 3) ( ) ( ) −− ± − 2 −××− 2 2 4 1 15 oe × 2 1 If B0 scored and at least 2 method marks scored,
SC1 for correct substitution of both of their x values or their y values into y = 7x + 3 or y = x2 + 5x – 12
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