Hits: 1687

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: 1687 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: 1025 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: 5758   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: 1002   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: 2940   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: 1375   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: 2362   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: 1262   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: 1342   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: 1656 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: 1102   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 […]