Hits: 182

Please follow and like us:
0

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: 71     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: 14   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#4

Hits: 7   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: 5   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#4

Hits: 2   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: 7   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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/22) | Q#5

Hits: 7     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 […]

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

Hits: 9 Question      i.       By differentiating , show that if y = cot x then    ii.       By expressing in terms of and using the result of part (i), show that   iii.       Express cos 2x in terms of sin2 x and hence show that can be expressed as .  Hence […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | Oct-Nov | (P2-9709/22) | Q#7

Hits: 21   Question The diagram shows the curve y = x2 cos x, for , and its maximum point M.     i.       Show by differentiation that the x-coordinate of M satisfies the equation    ii.       Verify by calculation that this equation has a root (in radians) between 1 and 1.2.   iii. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | Oct-Nov | (P2-9709/22) | Q#4

Hits: 17     Question The parametric equations of a curve are  ,  ,     i.       Show that .    ii.       Hence find the exact value of t at the point on the curve at which the gradient is 2. Solution      i.   We are given that; We are required to show […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | Oct-Nov | (P2-9709/21) | Q#8

Hits: 16     Question The equation of a curve is y2 + 2xy − x2 = 2.      i.       Find the coordinates of the two points on the curve where x = 1.    ii.       Show by differentiation that at one of these points the tangent to the curve is parallel to […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | Oct-Nov | (P2-9709/21) | Q#6

Hits: 7     Question The curve with equation y = x ln x has one stationary point. i.       Find the exact coordinates of this point, giving your answers in terms of e. ii.       Determine whether this point is a maximum or a minimum point. Solution      i.   We are required […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | May-Jun | (P2-9709/02) | Q#8

Hits: 18     Question a)   Find the equation of the tangent to the curve at the point where . b)                  i.       Find the value of the constant A such that           ii.       Hence show that Solution a.     We are given that curve with […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | May-Jun | (P2-9709/02) | Q#7

Hits: 13     Question The diagram shows the curve and its minimum point M.      i.       Find the exact coordinates of M.    ii.       Show that the curve intersects the line y = 20 at the point whose x-coordinate is the root of  the equation   iii.       Use the iterative formula […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | May-Jun | (P2-9709/02) | Q#6

Hits: 79   Question The equation of a curve is        i.       Show, by differentiation, that the gradient of the curve is always negative.    ii.       Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 2 significant figures.     iii.   The diagram […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | May-Jun | (P2-9709/02) | Q#5

Hits: 37     Question The diagram shows the part of the curve y = xe-x for , and its maximum point M.      i.       Find the x-coordinate of M.    ii.       Use the trapezium rule with two intervals to estimate the value of giving your answer correct to 2 decimal places.   […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | May-Jun | (P2-9709/02) | Q#6

Hits: 20     Question The diagram shows the part of the curve  for . The curve cuts the x-axis at A and  its maximum point is M.      i.       Write down the coordinates of A.    ii.       Show that the x-coordinate of M is e, and write down the y-coordinate of M […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#7

Hits: 25     Question The diagram shows the part of the curve y=ex cos x for . The curve meets the y-axis at the  point A. The point M is a maximum point. i. Write down the coordinates of A. ii. Find the x-coordinate of M. iii. Use the trapezium rule with three intervals […]