Hits: 77

# 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: 77 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#7

Hits: 62   Question It is given that i.       Show that    ii.       Show by calculation that the value of a lies between 1.0 and 1.5.   iii.       Use an iterative formula, based on the equation in part (i), to find the value of a correct to 3  decimal places. Give the result of each […]

# 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: 61 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: 62 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 | (P2-9709/23) | Q#1

Hits: 59 Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases;  OR We have the equation; We have to consider both moduli separately and it leads to following cases; It cannot be solved for x.   Hence, the only solution […]

# 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: 92 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#7

Hits: 51 Question It is given that     i.       Show that    ii.       Show by calculation that the value of a lies between 1.0 and 1.5.   iii.       Use an iterative formula, based on the equation in part (i), to find the value of a correct to 3  decimal places. Give the result of each […]

# 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#4

Hits: 68   Question The parametric equations of a curve are Find the equation of the tangent to the curve at the point for which t = 0. Give your answer in the  form ax + by + c = 0, where a, b and c are integers. Solution We are required to find the […]

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

Hits: 55   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: 59 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#1

Hits: 60     Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases;  OR We have the equation; We have to consider both moduli separately and it leads to following cases; It cannot be solved for x. Hence, the only […]

# 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#7

Hits: 124     Question The equation of a curve is 3×2+3xy+y2=3      i.       Find the equation of the tangent to the curve at the point (2, −1), giving your answer in the form  ax +by +c = 0, where a, b and c are integers.    ii.       Show that the curve has no stationary […]

# 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#6

Hits: 56   Question i.       Show that ii.       Use the trapezium rule with four intervals to find an approximation to giving your answer correct to 3 significant figures. Solution i.   We are required to show that; Rule for integration of  is: This integral is valid only when . Division Rule; Power Rule; ii.   […]

# 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: 84   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#4

Hits: 130   Question      i.       By sketching a suitable pair of graphs, show that the equation has exactly one real root.    ii.       Show by calculation that the root lies between 2.0 and 2.5.   iii.       Use the iterative formula to find the root correct to 3 decimal places. Give  the result of each […]

# 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: 120 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 […]

# 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#3

Hits: 112    Question     i.       Find the quotient when  is divided by ,  and confirm that the  remainder is 7. ii.       Hence solve the equation . Solution      i.   Hence quotient is and remainder is .    ii.  We are required to solve; When a polynomial, , is divided by a […]

# 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#1

Hits: 164     Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate […]