Hits: 28

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/23) | Q#5

Hits: 28 Question It is given that     i.       Show that    ii.       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 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 2015 | Oct-Nov | (P2-9709/23) | Q#1

Hits: 9 Question Find the exact value of giving the answer in the form ln k. Solution We are required to find the exact value of Rule for integration of  is: This integral is valid only when . Division Rule; Power Rule; Please follow and like us:

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/22) | Q#7

Hits: 21   Question      i.       Show that the exact value of    ii.   The diagram shows the curve  for . The shaded region is bounded by the  curve and the lines ,  and . Find the exact volume of the solid obtained when  the shaded region is rotated completely about the x-axis. Solution      i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/21) | Q#5

Hits: 5   Question      i.       Find    ii.       Find the exact value of Solution      i.   We are required find; We know that;  Therefore; Hence; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: Rule for integration of  is:        ii.   We are required […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/23) | Q#6

Hits: 35 Question The diagram shows part of the curve and its point of intersection P with the x-axis.      i.       Find the exact x-coordinate of P.    ii.       Show that the equation of the curve can be written and use integration to find the exact area of the shaded region enclosed by the curve […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/23) | Q#4

Hits: 34 Question The diagram shows the curve  and its minimum point M.      i.       Show that the x-coordinate of M is .    ii.       The region shaded in the diagram is enclosed by the curve and the lines ,   and  . Use integration to show that the area of the shaded region is . […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/22) | Q#6

Hits: 21 Question The diagram shows part of the curve and its point of intersection P with the x-axis.      i.       Find the exact x-coordinate of P.    ii.       Show that the equation of the curve can be written and use integration to find the exact area of the shaded region enclosed by the curve […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/22) | Q#4

Hits: 29     Question The diagram shows the curve  and its minimum point M.      i.       Show that the x-coordinate of M is .    ii.       The region shaded in the diagram is enclosed by the curve and the lines ,   and  . Use integration to show that the area of the shaded region […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/21) | Q#6

Hits: 16 Question     i.       Prove that  .    ii.       Hence A.  Solve the equation  for . B.  Find the exact value of Solution      i.  We are given that;   provided that   provided that    ii.  a.  We are required to solve the equation; As demonstrated in (i); Hence;   provided that Now […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/21) | Q#5

Hits: 13 Question i.       Given that show that the positive constant a satisfies the equation    ii.       Use an iterative formula, , with  to find the value of correct to 3 decimal places. Give the result of each iteration to 5 decimal places. Solution      i.  We are given that; Rule for integration of  is: […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#10

Hits: 51   Question A curve with equation y=f(x) passes through the point (4,9). Given that  , x > 0 a.   find f(x), giving each term in its simplest form. Point P lies on the curve. The normal to the curve at P is parallel to the line 2y + x = 0 b.   Find x […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2015 | June | Q#3

Hits: 14   Question Given that , ,  , find in their simplest form, a.   b.   . Solution a.   We are given; We are required to find . Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve  with respect to  is: Therefore; Rule for differentiation is of  is: Rule for […]

# Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2015 | June | Q#3

Hits: 36   Question The diagram shows a sketch of a curve and a line. The curve has equation  . The points A(-1,6) and B(2,30) lie on the curve. a.   Find an equation of the tangent to the curve at the point A. b.                 i.       Find           ii.       Calculate the area of the shaded region bounded by the curve and the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/13) | Q#10

Hits: 347 Question The function  is defined by  for .      i.       Find  and  and hence verify that the function  has a minimum value at . The points  and  lie on the curve , as shown in the diagram.      i.       Find the distance AB.    ii.       Find, showing all necessary working, the area of the shaded region. Solution i.   We are given; Rule […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/13) | Q#9

Hits: 562 Question A curve passes through the point A(4,6) and is such that  . A point P is moving along  the curve in such a way that the x-coordinate of P is increasing at a constant rate of 3 units per  minute.      i.       Find the rate at which the y-coordinate of P is increasing when P is at […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/12) | Q#9

Hits: 382 Question The curve y=f(x) has a stationary point at (2,10) and it is given that      i.       Find f(x).    ii.       Find the coordinates of the other stationary point.   iii.       Find the nature of each of the stationary points. Solution      i.   We are given; We are required to find . We can find equation of the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/11) | Q#11

Hits: 694 Question The diagram shows part of the curve  and a point P(6,5) lying on the curve. The line  PQ intersects the x-axis at Q(8,0).      i.       Show that PQ is a normal to the curve.   ii.       Find, showing all necessary working, the exact volume of revolution obtained when the shaded  region is rotated through 360o about the x-axis. [In part […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/11) | Q#2

Hits: 292 Question The function f is such that  and . Find . Solution i. We are given that; We are also given that . We are required to find the equation of the curve. We can find equation of the curve from its derivative through integration; For the given case; Rule for integration of  is: Rule for integration of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/13) | Q#10

Hits: 614 Question Points A(2,9) and B(3,0) lie on the curve y=9+6x−3×2, as shown in the diagram. The tangent at A  intersects the x-axis at C. Showing all necessary working,     i.       find the equation of the tangent AC and hence find the x-coordinate of C,    ii.       find the area of the shaded region ABC. Solution      i.   To find the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/13) | Q#2

Hits: 278   Question A curve is such that  and the point (4, 7) lies on the curve. Find the equation of the curve. Solution We are required to find the equation of the curve whose derivative is given as below. We can find equation of the curve from its derivative through integration; Rule for integration of […]