Hits: 444

# 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: 444     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: 229     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: 352   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 | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | June | Q#10

Hits: 252 Question The curve C has equation , . The points P and Q lie on C and have x-coordinates 1 and 2 respectively. a.   Show that the length of PQ is . b.   Show that the tangents to C at P and Q are parallel. c.   Find an equation for the normal to […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | June | Q#3

Hits: 24   Question Given that , x > 0 , find a.   . b.   . c.   Solution a.   We are required to find . Therefore, we are required to differentiate; We are required to find . Rule for differentiation of  is: Rule for differentiation of  is: b.   We are required to find . Second derivative is […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#8

Hits: 300   Question The curve C has equation , x > 0. a.   Find an expression for . b.   Show that the point P (4, 8) lies on C. c.   Show that an equation of the normal to C at the point P is 3y=x + 20. The normal to C at P cuts the […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | January | Q#1

Hits: 12   Question Given that    , Find . Solution We are required to differentiate; We are required to find . Rule for differentiation of  is: Rule for differentiation of  is: Rule for differentiation is of  is:

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

Hits: 191   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: 117   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: 260   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: 786   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: 516 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: 289 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: 553 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: 494 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 […]