# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#11

Question The diagram shows part of the curve . The curve crosses the y-axis at A and the stationary point on the curve is M. i.       Obtain expressions for and ii.       Find the coordinates of M. iii.    Find, showing all necessary working, the area of the shaded region. Solution i.   We are given; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#10

Question The equation of a curve is  and the equation of a line is , where k is a constant. i.       Find the set of values of k for which the line does not meet the curve. In the case where k = 15, the curve intersects the line at points A and B. ii. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#9

Question The function f is defined by  for .     i.      Express in the form of where a and b are constants.   ii.     State the range of .  The function g is defined by  for .  iii.       State the largest value of k for which g has an inverse.   iv.     Given that g has […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#8

Question The diagram shows an isosceles triangle ACB in which AB = BC = 8 cm and AC = 12 cm. The arc  XC is part of a circle with centre A and radius 12 cm, and the arc YC is part of a circle with centre B  and radius 8 cm. The points A, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#7

Question The diagram shows a solid cylinder standing on a horizontal circular base with centre O and radius  4 units. Points A, B and C lie on the circumference of the base such that AB is a diameter and angle  BOC = 90o. Points P, Q and R lie on the upper surface of the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#6

Question The diagram shows a triangle ABC in which BC = 20 cm and angle ABC = 90o. The perpendicular  from B to AC meets AC at D and AD = 9 cm. Angle BCA = .     i.      By expressing the length of BD in terms of in each of the triangles ABD and […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#5

Question The first three terms of an arithmetic progression are 4, x and y respectively. The first three terms of  a geometric progression are x, y and 18 respectively. It is given that both x and y are positive. a)   Find the value of x and the value of y. b)   Find the fourth term […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#4

Question The functions f and g are defined by  for  ,  for      i.      Solve the equation .   ii.     Sketch the graph of . Solution i.   We are given;  for  for We are required to solve equation ; To solve this equation for , we can substitute . Hence, Since given interval is […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#3

Question The diagram shows part of the curve  and the line , intersecting at the origin O and the point R. Point P lies on the line  between O and R and the x-coordinate of P is .  Point Q lies on the curve and PQ is parallel to the y-axis.      i.       Express the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#2

Question Showing all necessary working, find . Solution Rule for integration of  is: Rule for integration of  is:

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#1

Question Find the coefficient of in the expansion of . Solution We are required to expand; Expression for the general term in the Binomial expansion of is: In the given case: Hence; Since we are looking for the coefficient of the term : we can equate; Finally substituting  in: Therefore, the coefficient of is 840. […]