Hits: 428

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#7

Hits: 428     Question The diagram shows the part of the curve y=ex cos x for . The curve meets the y-axis at the  point A. The point M is a maximum point. i. Write down the coordinates of A. ii. Find the x-coordinate of M. iii. Use the trapezium rule with three intervals […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#4

Hits: 223     Question The equation of a curve is y = 2x − tan x, where x is in radians. Find the coordinates of the stationary points of the curve for which Solution We are required to find the coordinates of stationary points of the curve with equation; A stationary point on the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#3

Hits: 343   Question The parametric equations of a curve are for t > 1.      i.       Express in terms of t.     ii.       Find the coordinates of the only point on the curve at which the gradient of the curve is equal to 1. Solution      i.   We are required […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | June | Q#4

Hits: 179   Question A model helicopter takes off from a point O at time t=0 and moves vertically so that its height, y cm,  above O after time t seconds is given by  , a.   Find:                            i.                                  ii.        b.   Verify that y has a stationary value when  and determine whether this stationary value is a  maximum value […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January | Q#6

Hits: 115   Question The curve with equation  is sketched below. The curve cuts the x-axis at the point A (-1, 0) and cuts the y-axis at the point B. a.                                i.       State the coordinates of the point B and hence find the area of the triangle AOB, where  O is the origin.          […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2007 | January | Q#5

Hits: 249   Question The diagram shows an open-topped water tank with a horizontal rectangular base and four vertical  faces. The base has width  metres and length  metres, and the height of the tank is  metres. The combined internal surface area of the base and four vertical faces is 54m2. a.                        i.       Show that .                   ii.       Hence express  in terms of . […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#11

Hits: 769   Question The diagram shows the graph of , where  for .      i.       Find an expression, in terms of , for  and explain how your answer shows that  is a decreasing function.    ii.       Find an expression, in terms of , for  and find the domain of .   iii.       Copy the diagram and, on your copy, sketch the graph of , making clear the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | Oct-Nov | (P1-9709/01) | Q#9

Hits: 503 Question A curve is such that  and the point P(2, 9) lies on the curve. The normal to the curve at P meets the curve again at Q. Find i.       the equation of the curve,    ii.       the equation of the normal to the curve at P   iii.       the coordinates of Q. Solution      i.   We are given the equation; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | Oct-Nov | (P1-9709/01) | Q#8

Hits: 281 Question The equation of a curve is .     i.       Express  and  in terms of .    ii.       Find the  coordinates of the two stationary points and determine the nature of each stationary point. Solution      i.   We are given the equation; For the given case; Rule for differentiation of  is: Rule for differentiation of  is: Rule for differentiation […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#10

Hits: 540 Question The equation of a curve is  . i.       Obtain expressions for  and .    ii.       Find the coordinates of the stationary point on the curve and determine the nature of the stationary point.   iii.       Show that the normal to the curve at the point (−2, −2) intersects the x-axis at the point (−10, 0).   iv.       Find the area of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#1

Hits: 478 Question Find the value of the constant  for which the line  is a tangent to the curve . Solution Since line is tangent to the curve i.e. both intersect each other at a single point. To find that point; If two lines (or a line and a curve) intersect each other at a point then that point […]