# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#8

Question i.       Prove that    ii.       Hence a.   Solve for  the equation b.   find the exact value of . Solution      i.   We are given that; We utilize following relations;   provided that   provided that Therefore; We utilize following relation; Therefore;    ii.   We are required to solve; As demonstrated in […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#6

Question The curve y = 4×2 ln x has one stationary point.      i.       Find the coordinates of this stationary point, giving your answers correct to 3 decimal places.    ii.       Determine whether this point is a maximum or a minimum point. Solution      i.   We are required to find the coordinates […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#5

Question A curve has equation x2+2y2+5x+6y =10. Find the equation of the tangent to the curve at the point (2,-1). Give your answer in the form ax+by+c=0, wher a,b and c are integers. Solution We are required to find equation of tangent to the curve at the point (2,-1). To find the equation […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#4

Question a.   Find the value of b.   Find Solution a.     We are required to find the value of; Rule for integration of  is: b.     We are required to find; Rule for integration of  is: Rule for integration of , or ; Rule for integration of  is:

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#3

Question The sequence defined by , Converges to the value .      i.       Find the value of correct to 3 decimal places. Show your working, giving each calculated  value of the sequence to 5 decimal places.    ii.       Find, in the form , an equation of which is a root. Solution      i.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#2

Question The diagram shows the curve . Region A is bounded by the curve and the lines x = 0,  x = 2 and y = 0. Region B is bounded by the curve and the lines x = 0 and y = 3.      i. Use the trapezium rule with two intervals to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#7

Question The cubic polynomial  is defined by where  and  are constants. It is given that  is a factor of  and that, when is divided by , the remainder is 24.      i.       Find the values of  and .    ii.       When  and  have these values, factorise p(x) completely. Solution      i.  We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#1

Question Use logarithms to solve the equation 3x = 2x+2, giving your answer correct to 3 significant figures. Solution We are given; Taking natural logarithm of both sides; Power Rule;