Hits: 47

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: 47   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 | Oct-Nov | (P2-9709/21) | Q#6

Hits: 40   Question The diagram shows part of the curve  and its maximum point M. The x-coordinate of M is denoted by m.      i.       Find  and hence show that m satisfies the equation .    ii.       Show by calculation that m lies between 0.7 and 0.8.   iii.       Use an iterative formula based […]

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#5

Hits: 33   Question i.       Given that  and  are factors of    ii.       When a and b have these values, factorise completely, and hence solve the equation giving any answers correct to 3 significant figures. Solution      i.   We are given that;    We are also given that and are factors of . We […]

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#4

Hits: 49 Question For each of the following curves, find the exact gradient at the point indicated: i.        at  ii.        at Solution      i.   We are required to find the gradient of the curve at the point .  Therefore first we need to find the expression for gradient of the given curve. Gradient (slope) […]

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#3

Hits: 27   Question A.         Find B.         Find the exact value of Solution A.   We are required to find; We know that; It can be written for  as; It can be rearranged as; Hence, integral can be written as; Rule for integration of  is: 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 2014 | Oct-Nov | (P2-9709/21) | Q#1

Hits: 22 Question Use the trapezium rule with four intervals to find an approximation to Solution We are required to apply Trapezium Rule to evaluate; The trapezium rule with  intervals states that; We are given that there are three intervals, . We are also given that and . Hence; 1 2 3 4 5 Therefore;

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#2

Hits: 83   Question The variables x and y satisfy the equation y = a(bx), where a and b are constants. The graph of      ln y against x is a straight line passing through the points (0.75,1.70) and (1.53,2.18), as shown in  the diagram. Find the values of a and b, correct to […]