Hits: 115

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#8

Hits: 55 Question A function  is defined for  and is such that .     i.      Find the set of values of  for which f is decreasing.   ii.      It is now given that . Find . Solution      i.   We are given derivative of the function as; We are also given that it is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#5

Hits: 52 Question The dimensions of a cuboid are x cm, 2x cm and 4x cm, as shown in the diagram. i.Show that the surface area S cm2 and the volume V cm3 are connected by the relation  ii.When the volume of the cuboid is 1000 cm3 the surface area is increasing at 2 cm2 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#3

Hits: 41 Question The equation of a curve is . The curve has no stationary points in the interval  . Find the least possible value of and the greatest possible value of . Solution We are given; We are given that curve has no stationary point. A stationary point on the curve is the point […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#10

Hits: 110 Question The diagram shows part of the curve . The curve intersects the x-axis at A. The normal to the curve at A intersects the y-axis at B. i.       Obtain expressions for  and ii.    Find the coordinates of B. iii. Find, showing all necessary working, 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 2019 | Oct-Nov | (P1-9709/11) | Q#9

Hits: 75 Question A curve for which passes through the point (2,3).      i.       Find the equation of the curve.     ii.      Find .  iii.      Find the coordinates of the stationary point on the curve and, showing all necessary working,  determine the nature of this stationary point. Solution i.   We […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#6

Hits: 52 Question A straight line has gradient  and passes through the point (0, −2). Find the two values of for  which the line is a tangent to the curve y = x2 − 2x + 7 and, for each value of , find the coordinates  of the point where the line touches the curve. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#2

Hits: 43 Question An increasing function, , is defined for x > n, where n is an integer. It is given that . Find the least possible value of n.  Solution We are given derivative of the function as; We are also given that it is an increasing function. To test whether a function is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/13) | Q#10

Hits: 47 Question The diagram shows part of the curve with equation  and the tangent to the curve at the  point A. The x-coordinate of A is 4.      i.      Find the equation of the tangent to the curve at A.    ii.       Find, showing all necessary working, the area of the shaded […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/13) | Q#8

Hits: 46 Question A curve is such that . The curve has stationary points at (−1, 2) and (3, k). Find  the values of the constants a, b and k. Solution We are given that derivative of the equation of the of the curve is; We are also given that curve has stationary points at […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#11

Hits: 537 Question The diagram shows part of the curve and the minimum point M. i.Find the expressions for and ii.Find the coordinates of M. The shaded region is bounded by the curve, the y-axis and the line through M parallel to the x-axis. iii.Find, showing all necessary working, the area of the shaded region. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#3

Hits: 394 Question A curve is such that . The point P (2,9) lies on the curve. i.  A point moves on the curve in such a way that the x-coordinate is decreasing at a constant rate of 0.05 units per second. Find the rate of change of the y-coordinate when the point is at […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/11) | Q#11

Hits: 286 Question The diagram shows part of the curve  and a point P(2, 1) lying on the curve. The normal  to the curve at P intersects the x-axis at Q.     i.       Show that the x-coordinate of Q is .    ii.       Find, showing all necessary working, 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 2019 | May-Jun | (P1-9709/11) | Q#10

Hits: 183 Question A curve for which has a stationary point at (3, 6).      i.       Find the equation of the curve.    ii.       Find the x-coordinate of the other stationary point on the curve.  iii.       Determine the nature of each of the stationary points. Solution i.   We can find equation of the curve […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Feb-Mar | (P1-9709/12) | Q#9

Hits: 224 Question The diagram shows part of the curve with equation . The shaded region is bounded by  the curve, the x-axis and the line x = 3.      i.       Find, showing all necessary working, the volume obtained when the shaded region is rotated  through 360O about the x-axis.    ii.       P is the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Feb-Mar | (P1-9709/12) | Q#8

Hits: 284 Question     i.      Express in the form of . The function f is defined by  for , where is constant.   ii.     State the largest value of for which is a decreasing function. The value of is now given to be 1.  iii.     Find an expression for and state the domain of . […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Feb-Mar | (P1-9709/12) | Q#4

Hits: 188 Question A curve has equation .     i.       Find  and  .     ii.       Find the x-coordinates of the stationary points and, showing all necessary working, determine  the nature of each stationary point. Solution i.   We are required to find and  . Therefore, we find the derivative of equation of the curve. […]