Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Feb-Mar | (P2-9709/22) | Q#5

Question It is given that a is a positive constant such that i.       Show that    ii.       Use an iterative formula based on the equation in part (i) to find the value of a correct to 4  significant figures. Give the result of each iteration to 6 significant figures. Solution      i.   We are […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Feb-Mar | (P2-9709/22) | Q#1

Question Solve the equation 2 ln(2x) − ln(x + 3)= ln(3x + 5). Solution We are given that; Power Rule; Multiplication Rule;  and are inverse functions. The composite function is an identity function, with  domain the positive real numbers. Therefore; Taking anti-logarithm of both sides; Now we have two options. If  then will be undefined […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Oct-Nov | (P2-9709/23) | Q#6

Question The parametric equations of a curve are  ,        i.       Find  in terms of t and hence find the coordinates of the stationary point, giving each  coordinate correct to 2 decimal places.    ii.       Find the gradient of the normal to the curve at the point where the curve crosses the x-axis. Solution […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Oct-Nov | (P2-9709/23) | Q#4

Question      i.       Find    ii.       Given that find the value of the positive constant a. Solution      i.   We are required to find; We have the trigonometric identity; It can be rearranged as; Therefore;   provided that It can be rearranged as; 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 2017 | Oct-Nov | (P2-9709/22) | Q#6

Question      i.       Find the exact value of    ii.       Given that Find the value of positive constant a. Solution      i.   We are required to find; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: Rule for integration of  is:      ii.   We are given […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Oct-Nov | (P2-9709/22) | Q#5

Question The diagram shows the curve y=4e−2x and a straight line. The curve crosses the y-axis at the point  P. The straight line crosses the y-axis at the point (0, 9) and its gradient is equal to the gradient of  the curve at P. The straight line meets the curve at two points, one of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Oct-Nov | (P2-9709/21) | Q#6

Question The parametric equations of a curve are  ,        i.       Find  in terms of t and hence find the coordinates of the stationary point, giving each  coordinate correct to 2 decimal places.    ii.       Find the gradient of the normal to the curve at the point where the curve crosses the x-axis.  Solution […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Oct-Nov | (P2-9709/21) | Q#4

Question      i.       Find    ii.       Given that find the value of the positive constant a. Solution      i.   We are required to find; We have the trigonometric identity; It can be rearranged as; Therefore;   provided that It can be rearranged as; 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 2017 | May-Jun | (P2-9709/23) | Q#5

Question The variables x and y satisfy the equation , where K and a are constants. The graph of ln y  against x is a straight line passing through the points (0.6, 1.81) and (1.4, 1.39), as shown in the  diagram. Find the values of K and a, correct to 2 significant figures.   Solution […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/22) | Q#5

Question The variables x and y satisfy the equation , where K and a are constants. The graph of ln y against x is a straight line passing through the points (0.6, 1.81) and (1.4, 1.39), as shown in the diagram. Find the values of K and a, correct to 2 significant figures. Solution We are given; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/21) | Q#8

Question The diagram shows the curve with equation The curve crosses the x-axis at the point P and has a minimum point M.      i. Find the gradient of the curve at the point P.    ii. Find the exact coordinates of the point M. Solution      i.   We are required to find the […]