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Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/12) | Q#3

Hits: 534   Question The length,  metres, of a Green Anaconda snake which is t years old is given  approximately by the formula where 1 t 10. Using this formula, find      i.           ii.       the rate of growth of a Green Anaconda snake which is 5 years old. Solution      i.   We are given; We are required to […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#10

Hits: 552 Question A curve has equation y=f(x) and it is given that , where a and b are positive  constants. i.       Find, in terms of a and b, the non-zero value of x for which the curve has a stationary point and  determine, showing all necessary working, the nature of the stationary point.    ii.       It is now given that […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#8

Hits: 496 Question The diagram shows parts of the graphs of  and  intersecting at points A and  B.      i.       Find by calculation the x-coordinates of A and B.    ii.       Find, showing all necessary working, the area of the shaded region. Solution i.   We are required to find the x-coordinates of points A and B which are intersection points of a […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#10

Hits: 602   Question The diagram shows part of the curve  and the normal to the curve at the point P(2, 3).  This normal meets the x-axis at Q.      i.       Find the equation of the normal at P.    ii.       Find, showing all necessary working, the area of the shaded region. Solution i.   We are required to find the equation of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#8

Hits: 425   Question A curve is such that .                    i.       Find the x-coordinate of each of the stationary point on the curve.                  ii.       Obtain an expression for  and hence or otherwise find the nature of each of the  stationary points.   […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#10

Hits: 438   Question The diagram shows part of the curve , defined for .      i.       Find, showing all necessary working, the area of the shaded region.    ii.       Find, showing all necessary working, the volume obtained when the shaded region is rotated  through 360O about the x-axis.   iii.       Find, showing all necessary working, the volume obtained when the shaded region […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/13) | Q#11

Hits: 396   Question The function  is defined for . It is given that  has a minimum value when  and that . (i)          Find . It is now given that ,  and  are the first three terms respectively of an arithmetic progression. (ii)        Find the value of . (iii)       Find , and hence find the minimum value of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/13) | Q#10

Hits: 483   Question a.     Fig. 1 shows part of the curve  and the line y = h, where h is a constant.        (i)          The shaded region is rotated through 360o about the y-axis. Show that the volume of                         revolution, V, is given by […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/12) | Q#6

Hits: 308   Question The diagram shows the straight line  intersecting the curve  at the points A(1,4) and  B(4,1). 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; It is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#10

Hits: 316   Question The diagram shows the curve  defined for x>0. The curve has a minimum point at A and  crosses the x-axis at B and C. It is given that  and that the curve passes through the  point . i.       Find the x-coordinate of A. ii.       Find . iii.       Find the x-coordinates of B and C. iv.       Find, showing all […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#10

Hits: 494 Question The diagram shows part of the curve .      i.       Find the equation of the normal to the curve at the point where x=1 in the form ,  where m and c are constants. The shaded region is bounded by the curve, the coordinate axes and the line x=1.    ii.       Find, showing all necessary working, the volume obtained […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#7

Hits: 357   Question A curve for which  passes through the point (3,-10).      i.       Find the equation of the curve.    ii.       Express   in the form , where a and b are constants.   iii.       Find the set of values of x for which the gradient of the curve is positive. Solution      i.   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 2016 | Oct-Nov | (P1-9709/13) | Q#11

Hits: 387   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: 331   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: 320 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: 356 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: 430 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: 311 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: 272 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; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/12) | Q#10

Hits: 439 Question The diagram shows the part of the curve  for , and the minimum point M.      i.         Find expressions for ,  and .    ii.       Find the coordinates of M and determine the coordinates and nature of the stationary point on          the part of the curve for which .   […]