Hits: 32

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# 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#4

Hits: 32     Question The diagram shows the part of the curve  for .      i.       Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 2 decimal places.    ii.       The line y=x intersects the curve at point P. Use the iterative formula to determine the […]

# 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#6

Hits: 37     Question      i.       Use the trapezium rule with 2 intervals to estimate the value of Giving your answer correct to 2 decimal places.    ii.       Find Solution      i.   We are required to apply Trapezium Rule to evaluate; The trapezium rule with  intervals states that; We are given that there […]

# 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#6

Hits: 24     Question      i.       Use the trapezium rule with 2 intervals to estimate the value of Giving your answer correct to 2 decimal places.    ii.       Find Solution      i.   We are required to apply Trapezium Rule to evaluate; The trapezium rule with  intervals states that; We are given that there […]

# 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 | May-Jun | (P2-9709/23) | Q#2

Hits: 18   Question The diagram shows the curve . Region A is bounded by the curve and the lines x = 0,  x = 2 and y = 0. Region B is bounded by the curve and the lines x = 0 and y = 3.      i. Use the trapezium rule with two […]

# 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#2

Hits: 26   Question The diagram shows the curve . Region A is bounded by the curve and the lines x = 0,  x = 2 and y = 0. Region B is bounded by the curve and the lines x = 0 and y = 3.      i.       Use the trapezium rule with two […]

# 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 | May-Jun | (P2-9709/23) | Q#2

Hits: 32     Question The diagram shows the part of the curve y = xe-x. The shaded region R is bounded by the curve and by the lines x = 2, x = 3 and y = 0.       i.       Use the trapezium rule with two intervals to estimate the area of R, […]

# 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#2

Hits: 48   Question The diagram shows the part of the curve y = xe-x. The shaded region R is bounded by the curve and by the lines x = 2, x = 3 and y = 0.      i.       Use the trapezium rule with two intervals to estimate the area of R, giving […]

# 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#3

Hits: 43     Question      i.       Use the trapezium rule with two intervals to estimate the value of Giving your answer correct to 2 decimal places.      ii.       Using a sketch of the graph of y = sec x for , explain whether the trapezium rule  gives an under-estimate or an over-estimate […]

# 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#3

Hits: 45     Question The diagram shows the curve for values of x from 0 to 2.      i.       Use the trapezium rule with two intervals to estimate the value of giving your answer correct to 2 decimal places.    ii.       State, with a reason, whether the trapezium rule gives an under-estimate […]

# 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: 131   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: 87     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: 77     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: 80     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 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#8

Hits: 84   Question The diagram shows the curve and its maximum point M.      i.       Find the x-coordinate of M.    ii.       Show that the tangent to the curve at the point where x = 1 passes through the origin.   iii.       Use the trapezium rule with two intervals to estimate […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | Oct-Nov | (P2-9709/02) | Q#6

Hits: 46     Question The diagram shows the part of the curve  for , and its minimum point M.      i.       Find the coordinates of M.    ii.       Use the trapezium rule with 2 intervals to estimate the value of Giving your answer correct to 1 decimal place.   iii.       State, […]