Hits: 78

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Feb-Mar | (P2-9709/22) | Q#8

Hits: 78 Question      i.       Show that .    ii.       Using the identity in part (i),                a.   find the least possible value of as x varies.                             b.  find the exact value of Solution      […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Feb-Mar | (P2-9709/22) | Q#5

Hits: 39 Question Given that find the value of the constant a correct to 3 decimal places. Solution      i.   We are given that; Rule for integration of , or ; Taking logarithm of both sides;  for any

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/23) | Q#5

Hits: 74 Question The diagram shows the curve for 0 ≤ x ≤ 6. The region bounded by the curve and the lines x = 0, x = 6 and y = 0 is denoted by R.        i.       Use the trapezium rule with 2 strips to find an estimate of the area of R, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/23) | Q#3

Hits: 61 Question      i.       Find    ii.       Without using a calculator, find the exact value of Solution      i.   We are required to find; We know that ; Therefore; Hence; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is:    ii.   We are required to find […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/22) | Q#6

Hits: 65 Question      i.       Show that    ii.       Solve the equation for .   iii.       Find the exact value of Solution      i.   We are required to show that; Since ; Therefore; provided that ii.   We are required to solve the equation for . We are given that; As demonstrated in (i); […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/22) | Q#3

Hits: 56 Question The definite integral  is defined by    i.   Show that  .    ii.   Sketch the curve  for .   iii.   State whether an estimate of obtained by using the trapezium rule will be more than or less than 8e −2. Justify your answer. Solution      i.   We are given that; Rule […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/21) | Q#5

Hits: 56   Question      i.       Show that    ii.       Hence find the exact value of; Solution      i.   We are required to show that; Since ; Therefore; ii.   We are required to find the exact value of; As demonstrated in (i); Therefore; Rule for integration of  is: Rule for integration of  is: […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/21) | Q#4

Hits: 58 Question     i.       It is given that the positive constant a is such that    ii.       Show that   iii.       Use an iterative formula , to find a correct to 3 decimal places. Give the result of each iteration to 5 decimal places. Solution      i.   We are given that; Rule for […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | May-Jun | (P2-9709/23) | Q#6

Hits: 71   Question a)   Find b)  Without using a calculator, find the exact value of giving your answer in the form . c)     The diagram shows the curve for 0 ≤ x ≤ 6. The region bounded by the curve and  the lines x = 0, x = 6 and y = 0 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | May-Jun | (P2-9709/22) | Q#6

Hits: 104 Question a)   Find b)  Without using a calculator, find the exact value of giving your answer in the form . c)     The diagram shows the curve for 0 ≤ x ≤ 6. The region bounded by the curve and  the lines x = 0, x = 6 and y = 0 is […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | May-Jun | (P2-9709/21) | Q#7

Hits: 124 Question      i.       Find      ii.       Without using a calculator, find the exact value of giving your answer in the form , where a and b are integers.   Solution      i.   We are required to find;   provided that   Rule for integration of  is: We integrate both parts  and […]