Hits: 84

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#10

Hits: 84 Question The diagram shows part of the curve  and the lines  and . The curve and the line  intersect at point A. i.       Find, showing all necessary working, the volume obtained when the shaded region is rotated  through 3600 about the x-axis.    ii.       Find the equation of the normal to the curve […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#8

Hits: 64 Question A curve passes through (0, 11) and has an equation for which , where a and b are  constants.      i.      Find the equation of the curve in terms of a and b.    ii.       It is now given that the curve has a stationary point at (2, 3). Find […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#11

Hits: 302 Question The diagram shows part of the curve . The curve crosses the y-axis at A and the stationary point on the curve is M. i.       Obtain expressions for and ii.       Find the coordinates of M. iii.    Find, showing all necessary working, the area of the shaded region. Solution i.   We […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/11) | Q#7

Hits: 203 Question The diagram shows part of the curve with equation y = k(x3 − 7×2 + 12x) for some constant k. The  curve intersects the line y = x at the origin O and at the point A(2, 2).     i.       Find the value of k.    ii.       Verify that the curve meets […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/11) | Q#6

Hits: 164 Question A curve has a stationary point at  and has an equation for which , where  is a non-zero constant. i.Find the value of . ii.Find the equation of the curve. iii.Determine, showing all necessary working, the nature of the stationary point Solution i. We are given that; A stationary point on the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#11

Hits: 376 Question The diagram shows part of the curve intersecting the x-axis at the origin O  and at . The line AB intersects the y-axis at B and has equation .     i.       Show that AB is the tangent to the curve at A.    ii.       Show that the area of the shaded region […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#1

Hits: 334 Question A curve passes through the point (4, −6) and has an equation for which . Find the equation of the curve. Solution We are required to find the equation of the curve from the given derivative. We can find equation of the curve from its derivative through integration; We are given; Therefore; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#11

Hits: 779 Question The diagram shows part of the curve  and the line x = 1.  The point A is the minimum point on the curve.     i.       Show that the x-coordinate of A satisfies the equation and find the  exact value of  at A.    ii.       Find, showing all necessary working, the volume obtained […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#4

Hits: 132 Question A curve with equation y = f(x) passes through the point A(3, 1) and crosses the y- axis at B. It is given that  . Find the y-coordinate of B. Solution We are given that curve crosses y-axis at point B. The point at which curve (or line) intercepts y-axis, the value […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#9

Hits: 786 Question A curve is such that  and (2,5) is a point on the curve.     i.       Find the equation of the curve.    ii.       A point P moves along the curve in such a way that the y-coordinate is  increasing at a constant rate of 0.06 units per second. Find the rate of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#10

Hits: 764 Question The curve with equation  passes through the origin.     i.       Show that the curve has no stationary points.    ii.       Denoting the gradient of the curve by m, find the stationary value of m and  determine its nature. Solution i.   We are required to show that curve has no stationary points. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#3

Hits: 335 Question A curve is such that . The point (1,1) lies on the curve. Find the  coordinates of the point at which the curve intersects the x-axis. Solution We are required to find the coordinates of the point at which the curve intersects the  x-axis. The point at which a line or curve intersects […]