Hits: 487

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/13) | Q#11

Hits: 487   Question The diagram shows the curve with equation . The minimum point on the curve has coordinates  and the x-coordinate of the maximum point is , here  and  are constants.      i.       State the value of .    ii.       Find the value of .   iii.       Find the area of the shaded region.   iv.       The gradient, , of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/13) | Q#8

Hits: 330   Question A curve is such that    i.       Find  ii.    Verify that the curve has a stationary point when  and determine its nature. iii.   It is now given that the stationary point on the curve has coordinates (−1, 5). Find the equation of the curve. Solution i.   Second derivative is the derivative of the derivative. If […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/12) | Q#10

Hits: 469   Question A curve is defined for x > 0 and is such that  . The point P(4, 8) lies on the curve.     i.       Find the equation of the curve.    ii.     Show that the gradient of the curve has a minimum value when x = 2 and state this minimum value. Solution i.   We are given that; Therefore, for the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/12) | Q#9

Hits: 546   Question The diagram shows part of the curve  , crossing the y-axis at the point B(0, 3). The point A on the curve has coordinates (3, 1) and the tangent to the curve at A crosses the y-axis at C.     i.       Find the equation of the tangent to the curve at A.    ii.    Determine, showing all necessary working, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/11) | Q#8

Hits: 591   Question The diagram shows the curve  and the straight line . The curve and straight line intersect at  and , where  is a constant. i.      Show that . ii.   Find, showing all necessary working, the area of the shaded region. Solution i.   It is evident from the diagram that line and the curve intersect […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/11) | Q#2

Hits: 298   Question A curve is such that  and the point (2, 4) lies on the curve. Find the equation of the curve. Solution i.   We can find equation of the curve from its derivative through integration; We are given that; Rule for integration of  is: Rule for integration of  is: If a point   lies on […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/13) | Q#9

Hits: 642   Question A curve is such that . The curve has a maximum point at (2, 12). i. Find the equation of the curve. A point P moves along the curve in such a way that the x-coordinate is increasing at 0.05 units per second. ii. Find the rate at which the y-coordinate is changing when x = 3, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/13) | Q#5

Hits: 846 Question The diagram shows part of the curve  , crossing the y-axis at the point A. The point B(6, 1) lies on the curve. The shaded region is bounded by the curve, the y-axis and the line y = 1. Find the exact volume obtained when this shaded region is rotated through about the y-axis. Solution i.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/12) | Q#9

Hits: 729   Question The diagram shows part of the curve  which passes through the points A and B. The curve has a maximum point at A and the gradient of the line BA is 2.     i.      Find the coordinates of A and B.    ii.    Find a  and hence evaluate the area of the shaded region. Solution […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/12) | Q#1

Hits: 475 Question The diagram shows the region enclosed by the curve  , the x-axis and the lines  and . Find, in terms of , the volume obtained when this region is rotated through  about the x-axis. Solution i.   Expression for the volume of the solid formed when the shaded region under the curve  is rotated completely […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/11) | Q#11

Hits: 556 Question The diagram shows the line  and part of the curve  .     i.       Show that the equation  can be written in the form .    ii.       . Hence find the area of the shaded region.   iii.       The shaded region is rotated through  about the y-axis. Find the exact value of the volume of revolution obtained. Solution i.   […]