Hits: 60

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#11

Hits: 60 Question The diagram shows part of the curve and the minimum point M. i.Find the expressions for and ii.Find the coordinates of M. The shaded region is bounded by the curve, the y-axis and the line through M parallel to the x-axis. iii.Find, showing all necessary working, 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 2019 | May-Jun | (P1-9709/12) | Q#3

Hits: 130 Question A curve is such that . The point P (2,9) lies on the curve. i.  A point moves on the curve in such a way that the x-coordinate is decreasing at a constant rate of 0.05 units per second. Find the rate of change of the y-coordinate when the point is at […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/11) | Q#11

Hits: 88 Question The diagram shows part of the curve  and a point P(2, 1) lying on the curve. The normal  to the curve at P intersects the x-axis at Q.     i.       Show that the x-coordinate of Q is .    ii.       Find, showing all necessary working, the area of the shaded region. Solution […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/11) | Q#10

Hits: 42 Question A curve for which has a stationary point at (3, 6).      i.       Find the equation of the curve.    ii.       Find the x-coordinate of the other stationary point on the curve.  iii.       Determine the nature of each of the stationary points. Solution i.   We can find equation of the curve […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Feb-Mar | (P1-9709/12) | Q#9

Hits: 56 Question The diagram shows part of the curve with equation . The shaded region is bounded by  the curve, the x-axis and the line x = 3.      i.       Find, showing all necessary working, the volume obtained when the shaded region is rotated  through 360O about the x-axis.    ii.       P is the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Feb-Mar | (P1-9709/12) | Q#8

Hits: 76 Question     i.      Express in the form of . The function f is defined by  for , where is constant.   ii.     State the largest value of for which is a decreasing function. The value of is now given to be 1.  iii.     Find an expression for and state the domain of . […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Feb-Mar | (P1-9709/12) | Q#4

Hits: 50 Question A curve has equation .     i.       Find  and  .     ii.       Find the x-coordinates of the stationary points and, showing all necessary working, determine  the nature of each stationary point. Solution i.   We are required to find and  . Therefore, we find the derivative of equation of 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#10

Hits: 85 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: 65 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: 31 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: 307 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: 198 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: 165 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: 377 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: 247 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: 783 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 […]