Hits: 182

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: 182 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: 155 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 | (P1-9709/13) | Q#2

Hits: 157 Question The function f is defined by  for . Determine, showing all necessary working, whether f is an increasing function, a decreasing  function or neither. Solution We are given function;   We are required to find whether is an increasing function, decreasing function or neither. To test whether a function is increasing or […]

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: 424 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#10

Hits: 334 Question A curve has equation  . The point A on the curve has coordinates .     i.                      a.   Find and simplify the equation of the normal through A.              b.   Find the x-coordinate of the point where this normal meets the […]

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: 242 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: 487 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#9

Hits: 343 Question A curve has equation  and a line has equation , where  is a constant. i.Find the set of values of  for which the curve and the line meet. ii.The line is a tangent to the curve for two particular values of . For each of these values find  the x-coordinate of the […]

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: 1014 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 | (P1-9709/12) | Q#9

Hits: 1135 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: 1108 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#2

Hits: 724 Question A point is moving along the curve   in such a way that the x-coordinate is  increasing at a constant rate of 0.02 units per second. Find the rate of change of the  y-coordinate when x = 1. Solution i.   We are given that; We are required to find; We know […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/22) | Q#6

Hits: 59 Question a.   Show that b.   Find the exact value of showing all necessary working. Solution a.     We are required to show; Rule for integration of  is: Division Rule; Power Rule;   b.     We are required to find; We know that Therefore, we can rearrange; Hence; Similarly, we know that; Therefore, we […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/22) | Q#5

Hits: 77 Question The curve with equation crosses the x-axis at only one point. This point has coordinates .   i.               Show that satisfies the equation ii.               Show by calculation that 0.75 < p < 0.85.  iii.               Use an iterative formula based on the equation in part (i) to find the value of p  correct […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/22) | Q#4

Hits: 62   Question Find the gradient of the curve at the point (0, 2). Solution We are required to find gradient of the curve ta the point (0 , 2). Gradient (slope) of the curve at the particular point is the derivative of equation of the  curve at that particular point. Gradient (slope) of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/22) | Q#3

Hits: 95   Question The diagram shows the curve with equation for values of x such that . Find the x-coordinate of the stationary point M, giving your answer correct to 3  significant figures. Solution We are required to find the x-coordinate of stationary point M. A stationary point on the curve is the point […]