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Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/23) | Q#5

Hits: 75     Question The parametric equations of a curve are  ,  ,     i.       Show that .  ii.       Find the equation of the normal to the curve at the point where t = 0. Solution      i.   We are given that; We are required to show that . If a curve is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/21) | Q#5

Hits: 16     Question The parametric equations of a curve are  ,  , i.       Show that .    ii.       Find the equation of the normal to the curve at the point where t = 0. Solution      i.   We are given that; We are required to show that . If a curve is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/22) | Q#7

Hits: 42     Question The equation of a curve is        i.       Show that    ii.       Find the coordinates of each of the points on the curve where the tangent is parallel to the x- axis. Solution      i.   We are given; We are required to find . To find from an […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/23) | Q#4

Hits: 48   Question The parametric equations of a curve are for t < 0.      i.       Show that in terms of t.    ii.       Find the exact coordinates of the only point on the curve at which the gradient is 3. Solution      i.   We are required to find  for the parametric equations […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/21) | Q#4

Hits: 24   Question The parametric equations of a curve are for t < 0.      i.       Show that in terms of t.    ii.       Find the exact coordinates of the only point on the curve at which the gradient is 3. Solution      i.   We are required to find  for the parametric equations […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | May-Jun | (P2-9709/22) | Q#5

Hits: 27   Question The parametric equations of a curve are      i.       Find an expression for in terms of t.      i.       Find the equation of the normal to the curve at the point for which t = 0. Give your answer in  the form ax + by + c = 0, where a, […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/22) | Q#3

Hits: 30     Question The diagram shows the curve y= x − 2 ln x and its minimum point M.      i. Find the x-coordinates of M.    ii. Use the trapezium rule with three intervals to estimate the value of giving your answer correct to 2 decimal places.   iii. State, with a […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/21) | Q#7

Hits: 33     Question The parametric equations of a curve are  ,  , i.       Show that . ii.       Show that the tangent to the curve at the point (1, 3) is parallel to the x-axis. iii.       Find the exact coordinates of the other point on the curve at which the tangent is parallel to […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#5

Hits: 23     Question A curve has equation x2+2y2+5x+6y =10. Find the equation of the tangent to the curve at the point (2,-1). Give your answer in the form ax+by+c=0, wher a,b and c are integers. Solution We are required to find equation of tangent to the curve at the point (2,-1). To find […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/22) | Q#5

Hits: 25     Question A curve has equation x2+2y2+5x+6y =10. Find the equation of the tangent to the curve at the point (2,-1). Give your answer in the form ax+by+c=0, wher a,b and c are integers. Solution We are required to find equation of tangent to the curve at the point (2,-1). To find […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/23) | Q#7

Hits: 235     Question The diagram shows the curve and its maximum point M.      i.       Find the exact coordinates of M.    ii.       Use the trapezium rule with three intervals to estimate the value of giving your answer correct to 2 decimal places. Solution      i.   We are required to […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/22) | Q#8

Hits: 135   Question The diagram shows the curve , for . The point  lies on the curve. i.       Show that the normal to the curve at Q passes through the point .    ii.       Find .   iii.       Hence evaluate Solution      i.   If a point P(x,y) lies on a […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/22) | Q#6

Hits: 50     Question The curve with equation intersects the line y = x + 1 at the point P.      i.       Verify by calculation that the x-coordinate of P lies between 1.4 and 1.6.    ii.       Show that the x-coordinate of P satisfies the equation   iii.       Use the iterative […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/22) | Q#4

Hits: 40   Question The parametric equations of a curve are for t > 2.      i.       Show that in terms of t.      ii.       Find the coordinates of the only point on the curve at which the gradient of the curve is equal  to 0. Solution      i.   We are required […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/21) | Q#8

Hits: 44   Question The diagram shows the curve , for . The point  lies on the curve.     i.       Show that the normal to the curve at Q passes through the point .    ii.       Find .   iii.       Hence evaluate Solution      i.   If a point P(x,y) lies on […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/21) | Q#6

Hits: 32     Question The curve with equation intersects the line y = x + 1 at the point P.      i.       Verify by calculation that the x-coordinate of P lies between 1.4 and 1.6.    ii.       Show that the x-coordinate of P satisfies the equation   iii.       Use the iterative […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/21) | Q#4

Hits: 30   Question The parametric equations of a curve are for t > 2.      i.       Show that in terms of t.      ii.       Find the coordinates of the only point on the curve at which the gradient of the curve is equal  to 0. Solution      i.   We are required […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/23) | Q#5

Hits: 52   Question The equation of a curve y=x3e-x.      i.       Show that the curve has a stationary point where x = 3.    ii.       Find the equation of the tangent to the curve at the point where x = 1. Solution      i.   We are required to show that the […]