# 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

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 region.  iii. […]

# 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#9

Question The functions is defined for , where and are positive constants. The diagram shows the graph of y = f(x).     i.      In terms of and state the range of .    ii.       State the number of solutions of the following equations.                  a)        […]

# 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

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 (−1, 2) […]

# 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#7

Question The coordinates of two points A and B are (1, 3) and (9, −1) respectively and D is the mid-point of  AB. A point C has coordinates (x, y), where x and y are variables. i.State the coordinates of D. ii.It is given that CD2 = 20. Write down an equation relating x and […]

# 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#6

Question The diagram shows a solid figure ABCDEF in which the horizontal base ABC is a triangle right- angled at A. The lengths of AB and AC are 8 units and 4 units respectively and M is the mid-point of  AB. The point D is 7 units vertically above A. Triangle DEF lies in a […]

# 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#5

Question Two heavyweight boxers decide that they would be more successful if they competed in a lower  weight class. For each boxer this would require a total weight loss of 13 kg. At the end of week 1  they have each recorded a weight loss of 1 kg and they both find that in each […]

# 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#4

Question The function f is defined by  for . The function g is defined by for   where  and are constants.     i.       Find the greatest value of and the least value of which will permit the formation of the composite function gf. It is now given that the conditions for the formation of gf are satisfied. […]

# 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#3

Question The diagram shows triangle ABC which is right-angled at A. Angle radians and AC = 8  cm. The points D and E lie on BC and BA respectively. The sector ADE is part of a circle with centre  A and is such that BDC is the tangent to the arc DE at D. i. […]

# 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#2

Question i. In the binomial expansion of , the first three terms are . Find the  remaining three terms of the expansion. ii. Hence find the coefficient of  in the expansion of . Solution i. Expression for the Binomial expansion of is: First rewrite the given expression in standard form. In the given case: Hence; […]

# 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#1

Question The function f is defined by for . i. Express in the form of . ii. Hence find the set of values of for which , giving your answer in exact form.   Solution i. We have the expression; We use method of “completing square” to obtain the desired form. We complete the square […]