Hits: 333

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | May-Jun | (P2-9709/02) | Q#6

Hits: 333     Question The diagram shows the part of the curve  for . The curve cuts the x-axis at A and  its maximum point is M.      i.       Write down the coordinates of A.    ii.       Show that the x-coordinate of M is e, and write down the y-coordinate of M […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | Oct-Nov | (P2-9709/02) | Q#7

Hits: 173     Question      i.       Given that y = tan 2x, find .    ii.       Hence, or otherwise, show that and, by using an appropriate trigonometrical identity, find the exact value of   iii.       Use the identity cos 4x ≡ 2cos2 2x − 1 to find the exact value of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | Oct-Nov | (P2-9709/02) | Q#6

Hits: 206     Question The diagram shows the part of the curve  for , and its minimum point M.      i.       Find the coordinates of M.    ii.       Use the trapezium rule with 2 intervals to estimate the value of Giving your answer correct to 1 decimal place.   iii.       State, with a reason, […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | May-Jun | (P2-9709/02) | Q#7

Hits: 325 Question      i.       Differentiate ln(2x + 3).    ii.       Hence, or otherwise, show that   iii.       Find the quotient and remainder when 4×2 + 8x is divided by 2x + 3.   iv.       Hence show that Solution      i.   We are required to find; If we define , […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | May-Jun | (P2-9709/02) | Q#5

Hits: 355   Question The equation of a curve is 3×2 + 2xy + y2 = 6. It is given that there are two points on the curve where the tangent is parallel to the x-axis. i.       Show by differentiation that, at these points, y = −3x. ii.       Hence find the coordinates of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | May-Jun | (P2-9709/02) | Q#3

Hits: 746    Question The equation of a curve is y = x + 2cos x. Find the x-coordinates of the stationary points of the  curve for 0 ≤ x ≤ 2π, and determine the nature of each of these stationary points. Solution We are required to find the x-coordinates of stationary points of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2006 | Oct-Nov | (P1-9709/01) | Q#9

Hits: 1324 Question The diagram shows an open container constructed out of 200 cm2 of cardboard. The two vertical end pieces are isosceles triangles with sides  cm,  cm and  cm, and the two side pieces are rectangles of length  cm and width  cm, as shown. The open top is a horizontal rectangle.      i.       Show that      ii.       Show that the volume, […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2006 | May-Jun | (P1-9709/01) | Q#10

Hits: 752 Question The diagram shows the curve , where  is a constant. The curve has a minimum point on the x-axis.      i.       Find the value of .    ii.       Find the coordinates of the maximum point of the curve.   iii.       State the set of values of  for which  is a decreasing function of .   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 2006 | Oct-Nov | (P1-9709/01) | Q#8

Hits: 878 Question The equation of a curve is  . i.       Calculate the gradient of the curve at the point where x = 1.    ii.       A point with coordinates (x, y) moves along the curve in such a way that the rate of increase of y has a constant value of 0.02 units per second. Find the rate of increase of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2006 | Oct-Nov | (P1-9709/01) | Q#7

Hits: 1705   Question The diagram shows the curve y = x(x − 1)(x − 2), which crosses the x-axis at the points O(0, 0), A(1, 0) and B(2, 0).     i.       The tangents to the curve at the points A and B meet at the point C. Find the x-coordinate of C.    ii.       Show by integration that the area of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2006 | May-Jun | (P1-9709/01) | Q#9

Hits: 571 Question A curve is such that  and P (1, 8) is a point on the curve. i.       The normal to the curve at the point P meets the coordinate axes at Q and at R. Find the coordinates of the mid-point of QR.    ii.   Find the equation of the curve. Solution      i.   To find […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2006 | May-Jun | (P1-9709/01) | Q#1

Hits: 327 Question A curve has equation . . Given that the gradient of the curve is −3 when x = 2, find the value of the constant k. Solution Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve  with respect to  is: In this case; Therefore; We can rewrite the expression; […]