Hits: 57

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/22) | Q#5

Hits: 57   Question Find the exact coordinates of the stationary point of the curve with equation Solution We are required to find the exact coordinates of the stationary point of the curve. A stationary point on the curve is the point where gradient of the curve is  equal to zero; Therefore, we find the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | May-Jun | (P2-9709/21) | Q#3

Hits: 32 Question Find the equation of the normal to the curve at the point (3, 1). Solution  We are given equation of the curve as; We are required to find the equation of normal to the curve at the point (3, 1). To find the equation of the line either we need coordinates of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/23) | Q#3

Hits: 38 Question A curve has equation Find the exact gradient of the curve at the point for which y = 4. Solution We are required to find the gradient of the curve at a point where y=4. Gradient (slope) of the curve at the particular point is the derivative of equation of the  curve […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/21) | Q#3

Hits: 14 Question A curve has equation Find the exact gradient of the curve at the point for which y = 4. Solution We are required to find the gradient of the curve at a point where y=4. Gradient (slope) of the curve at the particular point is the derivative of equation of the  curve […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | May-Jun | (P2-9709/23) | Q#6

Hits: 23   Question The diagram shows the curve with parametric equations  ,    for 0 ≤ t ≤ 2. At the point P on the curve, the y-coordinate is 1.     i.       Show that the value of t at the point P satisfies the equation .    ii.       Use the iterative formula  with t1 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | May-Jun | (P2-9709/23) | Q#3

Hits: 15   Question Find the exact coordinates of the stationary point of the curve with equation Solution We are required to find the exact coordinates of the stationary point of the curve. A stationary point on the curve is the point where gradient of the curve is  equal to zero; Therefore, we find the expression […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | May-Jun | (P2-9709/22) | Q#6

Hits: 37   Question The diagram shows the curve with parametric equations  ,    for 0 ≤ t ≤ 2. At the point P on the curve, the y-coordinate is 1.     i.       Show that the value of t at the point P satisfies the equation .    ii.       Use the iterative formula  with t1 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | May-Jun | (P2-9709/22) | Q#3

Hits: 36   Question Find the exact coordinates of the stationary point of the curve with equation Solution We are required to find the exact coordinates of the stationary point of the curve. A stationary point on the curve is the point where gradient of the curve is  equal to zero; Therefore, we find the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Feb-Mar | (P2-9709/22) | Q#5

Hits: 70 Question The curve with equation and the point P on the curve has y-coordinate 10. i.               Show that the x-coordinate of P satisfies the equation ii.               Use the iterative formula to find the x-coordinate of P correct to 4 significant figures. Give the  result  of each iteration to 6 significant figures. iii.               Find […]

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: 20 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: 33 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: 27   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 | (P2-9709/23) | Q#5

Hits: 58 Question A curve has parametric equations      i.       Find the equation of the tangent to the curve at the origin.    ii.       Find the coordinates of the stationary point, giving each coordinate correct to 2  decimal places. Solution i.   We are required to find the equation of tangent to the curve at […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/21) | Q#5

Hits: 35 Question A curve has parametric equations      i.       Find the equation of the tangent to the curve at the origin.    ii.       Find the coordinates of the stationary point, giving each coordinate correct to 2  decimal places. Solution i.   We are required to find the equation of tangent to the curve at […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | May-Jun | (P2-9709/23) | Q#2

Hits: 30 Question A curve has equation      i.       Find the x-coordinate of the stationary point.    ii.       Determine whether the stationary point is a maximum or minimum point. Solution i.   First we are required to find the x-coordinate of the stationary point of the curve. A stationary point on the curve is the […]

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

Hits: 18 Question A curve has equation      i.       Find the x-coordinate of the stationary point.    ii.       Determine whether the stationary point is a maximum or minimum point. Solution i.   First we are required to find the x-coordinate of the stationary point of the curve. A stationary point on the curve is the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | May-Jun | (P2-9709/21) | Q#4

Hits: 61 Question The diagram shows the curve . The curve crosses the x-axis at the point P and has a maximum point M.      i.       Find the gradient of the curve at the point P.    ii.       Show that the x-coordinate of the point M satisfies the equation   iii.       Use an iterative formula […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Feb-Mar | (P2-9709/22) | Q#6

Hits: 16   Question The diagram shows the part of the curve  for , and the stationary point M.        i.       Find the equation of the tangent to the curve at the origin.    ii.       Find the coordinates of M, giving each coordinate correct to 3 decimal places. Solution      i.   We are […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Oct-Nov | (P2-9709/23) | Q#6

Hits: 36 Question The parametric equations of a curve are  ,        i.       Find  in terms of t and hence find the coordinates of the stationary point, giving each  coordinate correct to 2 decimal places.    ii.       Find the gradient of the normal to the curve at the point where the curve crosses the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Oct-Nov | (P2-9709/22) | Q#5

Hits: 25 Question The diagram shows the curve y=4e−2x and a straight line. The curve crosses the y-axis at the point  P. The straight line crosses the y-axis at the point (0, 9) and its gradient is equal to the gradient of  the curve at P. The straight line meets the curve at two points, […]