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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#5

Hits: 27 Question A curve has equation Find the equation of the tangent to the curve at the point where it crosses the y-axis. Solution We are given that curve with equation  and we are required to find the equation of  the tangent to the curve at point where it crosses the y-axis i.e.  . […]

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#5

Hits: 23   Question A curve has equation Find the equation of the tangent to the curve at the point where it crosses the y-axis. Solution We are given that curve with equation  and we are required to find the equation of  the tangent to the curve at point where it crosses the y-axis i.e.  […]

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#5

Hits: 14 Question The parametric equations of a curve are for .     i.       Find the gradient of the curve at the point for which  radian.    ii.       Find the value of at the point on the curve where the tangent is parallel to the y-axis. Solution      i.   We are required to find […]

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

Hits: 18   Question A curve has equation . Find the equation of the tangent to the curve at the point for which . Solution      i.   We are given that curve with equation  and we are required to find the equation of the  tangent to the curve at origin . To find the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Feb-Mar | (P2-9709/22) | Q#4

Hits: 16   Question Find the gradient of the curve at the point . Solution We are required to find the gradient of the curve at point . Gradient (slope) of the curve at the particular point is the derivative of equation of the curve at that  particular point. Gradient (slope) of the curve at […]

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: 8   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 | (P2-9709/22) | Q#3

Hits: 6 Question The equation of a curve is . The curve has a stationary point M in the interval . Find the coordinates of M, giving each coordinate correct to 3 significant figures.  Solution We are required to find the x-coordinates of stationary point of the curve. A stationary point on the curve is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Oct-Nov | (P2-9709/21) | Q#7

Hits: 8 Question The diagram shows the curve The curve crosses the y-axis at the point P and the gradient of the curve at P is m. The point Q on  the curve has x-coordinate q and the gradient of the curve at Q is −m.     i.       Find the value of m and hence […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/23) | Q#8

Hits: 30 Question The diagram shows the curve with parametric equations for . The end-points of the curve are (1, 4) and (3, 3). i.       Show that .    ii.       Find the coordinates of the minimum point, giving each coordinate correct to 3 significant  figures.   iii.       Find the exact gradient of the normal to […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/22) | Q#8

Hits: 17 Question The diagram shows the curve with parametric equations for . The end-points of the curve are (1, 4) and (3, 3). i.       Show that .    ii.       Find the coordinates of the minimum point, giving each coordinate correct to 3 significant  figures.   iii.       Find the exact gradient of the normal to […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/22) | Q#7

Hits: 28 Question The diagram shows the curve with parametric equations for .     i.       Show that can be expressed in the form    ii.       Find the equation of the normal to the curve at the point where the curve crosses the positive y-axis. Give your answer in the form y = mx +c, where […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/21) | Q#3

Hits: 18 Question A curve has equation y = 2 sin 2x − 5 cos 2x +6 and is defined for 0 ≤ x ≤ π. Find the x-coordinates of the stationary points of the curve, giving your answers correct to 3 significant figures. Solution We are required to find the x-coordinates of stationary points […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | May-Jun | (P2-9709/23) | Q#7

Hits: 41 Question The diagram shows the curve with parametric equations for . The minimum point is M and the curve crosses the x-axis at points P and Q.     i.       Show that .    ii.       Find the coordinates of M.   iii.       Find the gradient of the curve at P and at Q. Solution […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | May-Jun | (P2-9709/22) | Q#7

Hits: 27 Question The diagram shows the curve with parametric equations for . The minimum point is M and the curve crosses the x-axis at points P and Q.     i.       Show that .    ii.       Find the coordinates of M.   iii.       Find the gradient of the curve at P and at Q. Solution […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | May-Jun | (P2-9709/21) | Q#5

Hits: 25 Question A curve is defined by the parametric equations for .       i.       Show that .    ii.       Find the coordinates of the stationary point.   iii.       Find the gradientof the curve at point . Solution      i.   We are required to show that  for the parametric equations given below; If […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/23) | Q#7

Hits: 79 Question The equation of a curve is      i.       Show that;    ii.       Find the x-coordinate of each stationary point of the curve in the interval . Give each answer correct to 3 significant figures. Solution      i.   We are required to show that; We are given; We utilize Quotient Rule to […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/22) | Q#6

Hits: 27 Question The diagram shows the curve with parametric equations for .     i.       Show that .    ii.       Find the equation of the tangent to the curve at the point where the curve crosses the positive y-axis. Give the answer in the form y = mx +c. Solution      i.   We are […]