Hits: 72

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/23) | Q#6

Hits: 72     Question A.  Find i.        ii.          B.  Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 2 decimal places. Solution A.    i.   We are required to find; Rule for integration of  is: Rule for integration of  is: Rule for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/23) | Q#3

Hits: 54 Question The equation of a curve is . Find the exact x-coordinate of each of the stationary points of the curve and determine the nature of each stationary point. Solution First we are required to find the exact x-coordinate of each of the stationary points of the curve. A stationary point on the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/22) | Q#5

Hits: 83   Question The parametric equations of a curve are      i.       Find the exact value of the gradient of the curve at the point P where y = 6.    ii.       Show that the tangent to the curve at P passes through the point . Solution      i.   We are need  for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/22) | Q#2

Hits: 22   Question The curve  has one stationary point. Find the coordinates of this stationary point. Solution We are required to find the coordinates of point M which is minimum point of the curve; A stationary point on the curve is the point where gradient of the curve is equal to zero; Since point […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/21) | Q#6

Hits: 63     Question A.  Find i.        ii.        B.  Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 2 decimal places. Solution A.    i.   We are required to find; Rule for integration of  is: Rule for integration of  is: Rule for integration […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/21) | Q#3

Hits: 60   Question The equation of a curve is . Find the exact x-coordinate of each of the stationary points of the curve and determine the nature of each stationary point. Solution First we are required to find the exact x-coordinate of each of the stationary points of the curve. A stationary point on […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#6

Hits: 101     Question      i.       By sketching a suitable pair of graphs, show that the equation   has only one root.    ii.       Verify by calculation that this root lies between x = 0.7 and x = 0.8.   iii.       Show that this root also satisfies the equation   iv.       Use the iterative […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#1

Hits: 48 Question A curve is such that . The point (3, 2) lies on the curve. Find the equation of the curve.  Solution We can find equation of the curve from its derivative through integration; For the given case; Therefore; Rule for integration of  is: This integral is valid only when . If a […]

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#1

Hits: 257   Question Solve the equation , giving answers correct to 2 decimal places where appropriate. Solution i.   Let, . We can write it as; We have to consider two separate cases; When When We have the equation; We have to consider two separate cases; When ; When ; Taking logarithm of both […]

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#1

Hits: 86   Question Solve the equation , giving answers correct to 2 decimal places where appropriate. Solution i.   Let, . We can write it as; We have to consider two separate cases; When When We have the equation; We have to consider two separate cases; When ; When ; Taking logarithm of both […]

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#2

Hits: 180   Question Solve the equation ln(3 − 2x) − 2 ln x = ln 5. Solution We are given; Power Rule; Division Rule; Taking anti-logarithm of both sides;  for any Now we have two options. Since logarithm of a negative number is not possible, therefore is not possible because we  have the term […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#4

Hits: 224   Question The variables x and y satisfy the relation .      i.       By taking logarithms, show that the graph of y against x is a straight line.    ii.       Find the exact value of the gradient of this line and state the coordinates of the point at which  the line […]

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#2

Hits: 96   Question Solve the equation ln(3 − 2x) − 2 ln x = ln 5. Solution We are given; Power Rule; Division Rule; Taking anti-logarithm of both sides;  for any Now we have two options. Since logarithm of a negative number is not possible, therefore is not possible because we  have the term […]