Hits: 27

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# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | Oct-Nov | (P2-9709/02) | Q#8

Hits: 27   Question      i.                     a.   Prove the identity                  b.   Hence prove that    ii.       By differentiating , show that if  then .     iii.       Using the results of parts (i) and (ii), […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | Oct-Nov | (P2-9709/02) | Q#5

Hits: 3     Question Show that Solution We are required to show that; Rule for integration of  is: For ; Rule for integration of  is: This integral is valid only when . Division Rule; Power Rule; Division Rule; 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 2008 | May-Jun | (P2-9709/02) | Q#8

Hits: 6   Question The constant , where , is such that     i.       Find an equation satisfied by , and show that it can be written in the form ii.       Verify, by calculation, that the equation  ) has a root between 3 and 3.5.    iii.       Use the iterative […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | May-Jun | (P2-9709/02) | Q#3

Hits: 4     Question Find the exact value of Solution We are required to find exact value of; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: 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 2007 | Oct-Nov | (P2-9709/02) | Q#8

Hits: 14   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 2007 | Oct-Nov | (P2-9709/02) | Q#7

Hits: 10     Question      i.       Prove the identity    ii.       Using the identity, or otherwise, find the exact value of Solution      i.   We are given that; We have algebraic formula; Since we know that ; We have the trigonometric identity; From this we can write ; Since we know […]

# 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#1

Hits: 9     Question Show that Solution We are required to show that; Rule for integration of  is: This integral is valid only when . Division Rule; 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 2007 | May-Jun | (P2-9709/02) | Q#6

Hits: 4 Question      i.       Express cos2 x in terms of cos 2x.    ii.       Hence show that   iii.       By using an appropriate trigonometrical identity, deduce the exact value of Solution      i.   We are required to show   in terms of . From this we can write; Therefore;    […]

# 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#7

Hits: 2     Question      i.       Given that y = tan 2x, find .    ii.       Hence, or otherwise, show that and, by using an appropriate trigonometrical identity, find the exact value of   iii.       Use the identity cos 4x ≡ 2cos2 2x − 1 to find the exact value of […]

# 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: 5     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, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | May-Jun | (P2-9709/02) | Q#7

Hits: 10 Question      i.       Differentiate ln(2x + 3).    ii.       Hence, or otherwise, show that   iii.       Find the quotient and remainder when 4×2 + 8x is divided by 2x + 3.   iv.       Hence show that Solution      i.   We are required to find; If we define , […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | Oct-Nov | (P2-9709/02) | Q#7

Hits: 168     Question The diagram shows the part of the curve y = sin2 x for  .      i.       Show that    ii.       Hence find the x-coordinates of the points on the curve at which the gradient of the curve is  0.5.   iii.       By expressing sin2 x in terms […]

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

Hits: 63     Question A curve is such that . The point (0, 1) lies on the curve.      i. Find the equation of the curve.    ii. The curve has one stationary point. Find the x-coordinate of this point and determine whether it  is a maximum or a minimum point. Solution      i. […]

# 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#7

Hits: 19   Question      i. By expanding , and using double-angle formulae, show that    ii. Hence, or otherwise, show that Solution      i.   We have; We apply following addition formula. Therefore; We apply following two formulae. We have the trigonometric identity; Therefore, we can replace; Hence;    ii.   We are required […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | Oct-Nov | (P2-9709/02) | Q#8

Hits: 52   Question i.       Express  in the form , where  and , giving the exact values of R and .    ii.       Hence show that   iii.       By differentiating , show that if  then .   iv.       Using the results of parts (ii) and (iii), show that Solution      i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | Oct-Nov | (P2-9709/02) | Q#7

Hits: 33     Question The diagram shows the curve y = 2ex + 3e-2x. The curve cuts the y-axis at A.      i.       Write down the coordinates of A.    ii.       Find the equation of the tangent to the curve at A, and state the coordinates of the point where  this tangent […]

# 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#7

Hits: 17   Question      i.By expanding , show that    ii.Hence, or otherwise, show that Solution      i.   We have; We apply following addition formula. Therefore; We apply following two formulae. We have the trigonometric identity; Therefore, we can replace; Hence;    ii.   We are required to show that; As we have […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | Oct-Nov | (P2-9709/02) | Q#7

Hits: 88 Question      i.       By differentiating  , show that if y = cot x then    ii.       Hence, show that   By using appropriate trigonometrical identities, find the exact value of     iii.     iv.   Solution      i.   We are given; Gradient (slope) of the curve is the derivative of equation of the curve. Hence […]

# 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#3

Hits: 28   Question The diagram shows the curve . The shaded region R is bounded by the curve and by the  lines x = 0, y = 0 and x = p.             i.       Find, in terms of p, the area of R.           ii.       Hence calculate the value of p for which the area of R is equal to 5. Give […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2002 | Oct-Nov | (P2-9709/02) | Q#6

Hits: 32   Question a)   Find the value of b)    The diagram shows part of the curve  . The shaded region R is bounded by the curve and by  the lines x =1, y = 0 and x = p. i.       Find, in terms of p, the area of R. ii.   iii.       Hence find, correct to 1 decimal place, […]