Hits: 84

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Feb-Mar | (P2-9709/22) | Q#8

Hits: 84 Question      i.       Show that .    ii.       Using the identity in part (i),                a.   find the least possible value of as x varies.                             b.  find the exact value of Solution      […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/23) | Q#3

Hits: 62 Question      i.       Find    ii.       Without using a calculator, find the exact value of Solution      i.   We are required to find; We know that ; Therefore; Hence; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is:    ii.   We are required to find […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/22) | Q#6

Hits: 68 Question      i.       Show that    ii.       Solve the equation for .   iii.       Find the exact value of Solution      i.   We are required to show that; Since ; Therefore; provided that ii.   We are required to solve the equation for . We are given that; As demonstrated in (i); […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/22) | Q#3

Hits: 60 Question The definite integral  is defined by    i.   Show that  .    ii.   Sketch the curve  for .   iii.   State whether an estimate of obtained by using the trapezium rule will be more than or less than 8e −2. Justify your answer. Solution      i.   We are given that; Rule […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/21) | Q#5

Hits: 57   Question      i.       Show that    ii.       Hence find the exact value of; Solution      i.   We are required to show that; Since ; Therefore; ii.   We are required to find the exact value of; As demonstrated in (i); 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 2016 | Oct-Nov | (P2-9709/21) | Q#4

Hits: 62 Question     i.       It is given that the positive constant a is such that    ii.       Show that   iii.       Use an iterative formula , to find a correct to 3 decimal places. Give the result of each iteration to 5 decimal places. Solution      i.   We are given that; Rule for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | May-Jun | (P2-9709/21) | Q#7

Hits: 129 Question      i.       Find      ii.       Without using a calculator, find the exact value of giving your answer in the form , where a and b are integers.   Solution      i.   We are required to find;   provided that   Rule for integration of  is: We integrate both parts  and […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2016 | June | Q#7

Hits: 116   Question The diagram shows the sketch of a curve and the tangent to the curve at P. The curve has equation  and the point P(-2,24) lies on the curve. The tangent at P  crosses the x-axis at Q. a.                       i.               Find the equation of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/13) | Q#11

Hits: 2782   Question A curve has equation , where k is a non-zero constant.      i.       Find the x-coordinates of the stationary points in terms of k, and determine the nature of each  stationary point, justifying your answers.    ii.   The diagram shows part of the curve for the case when k = 1. Showing all necessary working, […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/13) | Q#10

Hits: 938   Question A curve is such that  , where a is a positive constant. The point A(a2, 3) lies on the  curve. Find, in terms of a,      i.       the equation of the tangent to the curve at A, simplifying your answer,    ii.       the equation of the curve.  It is now given that B(16,8) also lies on the curve. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/12) | Q#1

Hits: 717 Question A curve is such that . The point (2,5) lies on the curve. Find the equation of the curve. Solution We are given that; We can find equation of the curve from its derivative through integration; Therefore; Rule for integration of  is: If a point   lies on the curve , we can find out value of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#10

Hits: 867 Question A curve has equation  and it is given that . The point A is the only point  on the curve at which the gradient is −1.      i.       Find the x-coordinate of A.    ii.       Given that the curve also passes through the point (4,10), find the y-coordinate of A, giving  your answer as a fraction. Solution      […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#7

Hits: 987 Question The diagram shows parts of the curves  and , intersecting at points A and  B.      i.       State the coordinates of A.    ii.       Find, showing all necessary working, the area of the shaded region. Solution      i.   It is evident that point A is the intersection point of the two curves given by equations; It […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#3

Hits: 823 Question A curve is such that  and passes through the point P(1,9). The gradient of the curve at P is 2. i.       Find the value of the constant k. ii.       Find the equation of the curve. Solution i.   We are given that; Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#2

Hits: 680 Question The diagram shows part of the curve  and the point P(2,3) lying on the curve. Find,  showing all necessary working, the volume obtained when the shaded region is rotated through  360o about the x-axis. Solution Expression for the volume of the solid formed when the shaded region under the curve  is rotated completely about the x-axis is; […]