Hits: 81

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/22) | Q#7

Hits: 81 Question i.       Express  in the form , where  and , giving the  value of  correct to 2 decimal places.    ii.       Hence solve the equation for .   iii.       Find the greatest possible value of as  varies, and determine the smallest positive value of  for which this greatest value occurs. Solution      i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/23) | Q#7

Hits: 76 Question The angle lies between  and and is such that       i.       Show that and hence find the exact value of .    ii.       It is given that the angleis such that . Without using a calculator, find the exact  value of . Solution      i.   We are given; We know that; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/21) | Q#7

Hits: 79   Question The angle lies between  and and is such that      i.       Show that and hence find the exact value of .    ii.       It is given that the angleis such that . Without using a calculator, find the exact  value of . Solution      i.   We are given; We know […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/23) | Q#8

Hits: 93 Question The diagram shows the curve , for and its maximum point M.     i.       Show that    ii.       Hence find the x-coordinate of M, giving your answer correct to 2 decimal places.. Solution      i.   We are given that; Therefore; We apply product rule to find the derivative. If  and  are […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/23) | Q#3

Hits: 99 Question A.         Find B.   i.       Use the trapezium rule with three intervals to find an approximation to giving your answer correct to 3 significant figures. Solution A.   We are required to find; Rule for integration of  is: B.   i.   We are required to apply Trapezium Rule to evaluate; The […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/23) | Q#2

Hits: 78 Question Solve the equation , giving all solutions in the interval . Solution We are required to solve the equation; We know that; Therefore; Hence; Now we have two options. Using calculator we can find that; We utilize the symmetry property of   to find another solution (root) of : Properties of Domain […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/22) | Q#8

Hits: 137 Question The diagram shows the curve , for and its maximum point M. i.       Show that      ii.       Hence find the x-coordinate of M, giving your answer correct to 2 decimal places.. Solution      i.   We are given that; Therefore; We apply product rule to find the derivative. If  and  are […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/22) | Q#3

Hits: 95   Question A.         Find B.   i.       Use the trapezium rule with three intervals to find an approximation to giving your answer correct to 3 significant figures. Solution A.   We are required to find; Rule for integration of  is:   B.   i.   We are required to apply Trapezium Rule to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/22) | Q#2

Hits: 85 Question Solve the equation , giving all solutions in the interval . Solution We are required to solve the equation; We know that; Therefore; Hence; Now we have two options. Using calculator we can find that; We utilize the symmetry property of   to find another solution (root) of : Properties of Domain […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/21) | Q#5

Hits: 149   Question i.       Prove that  .    ii.       Hence a.  Find the exact value of b.  Evaluate Solution      i.   We are given that; except where  or undefined   provided that We have the trigonometric identity; Therefore; Hence;      ii.   a.   We are required to find the exact value […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/21) | Q#2

Hits: 174 Question Find the gradient of each of the following curves at the point for which x = 0.     i.           ii.         Solution      i.   We are required to find the gradient of the curve at the point for which x = 0. Therefore first we need to find the […]