University:
University of Cambridge
Course:
0580 IGCSE | Mathematics
Academic year:

2022
Views:

257

Pages:

2
Author:

Shahbaz A.

Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level May-June 2015 MATHEMATICS (US) Paper 1 Pure Mathematics 1 (P1) Solution by shahbaz ahmed June 2024 Q2 The diagram shows the curve y = 2x2 and the points X(−2, 0) and P (p, 0). The point Q lies on the curve and and PQ is parallel to the y-axis. (i) Express the area, A, of triangle XPQ in terms of p. 1 The point P moves along the x-axis at a constant rate of 0.02 units per second and Q moves along the curve so that PQ remains parallel to the y-axis. (ii) Find the rate at which A is increasing when p = 2 Solution XP=p + 2 QP=2p2 (1)Let A be the area of the triangle XPQ A= 12 (XP )(P Q) A= 12 (p + 2)(2p2 ) = p3 + 2p2 dp dt = 0.02 units per second (ii) Now dA dp = d(p3 +2p2 ) dA dA dp = d(p3 ) dA + d(2p2 ) dA dA dp = d(p3 ) dA ) + 2 d(p dA dA dp = 3p2 + 2(2p) = 3p2 + 4p 2 Putting p = 2 dA dp = (3)(22 ) + (4)(2) = 20 dA dt = dA dp dp dt Putting dA dt = dA dp dA dp dp dt = 20, dp dt = 0.02 units per second . = 20 × 0.02 = 0.4 square units 2

Cambridge International Advanced Subsidiary May-June 2015

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