# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#10

Question The diagram shows part of the curve , which touches the x-axis at the point P. The  point Q(3,4) lies on the curve and the tangent to the curve at Q crosses the x-axis at R.      i.       State the x-coordinate of P.  Showing all necessary working, find by calculation ii.       the x-coordinate of R, iii.    the area of the shaded […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#9

Question a.     Figure 1 In Fig. 1, OAB is a sector of a circle with centre O and radius r. AX is the tangent at A to the arc AB and angle .      i.       Show that angle .    ii.       Find the area of the shaded segment in terms of r and .   b.     Figure 2 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#8

Question The function  is such that  for , where a and b are constants.      i.       For the case where  and , find the possible values of  a and b.    ii.       For the case where  and , find an expression for  and give the domain of  . Solution i.   We are given that function  is represented as; We are given that; First we substitute […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#7

Question The diagram shows a pyramid OABC with a horizontal triangular base OAB and vertical height OC.  Angles AOB, BOC and AOC are each right angles. Unit vectors ,  and are parallel to OA, OB and OC respectively, with OA = 4 units, OB = 2.4 units  and OC = 3 units. The point P […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#6

Question A vacuum flask (for keeping drinks hot) is modelled as a closed cylinder in which the internal radius  is r cm and the internal height is h cm. The volume of the flask is 1000 cm3. A flask is most efficient when the total internal surface area, A cm2, is a minimum.      i.       Show that      […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#5

Question Two points have coordinates A(5,7) and B(9,-1).      i.       Find the equation of the perpendicular bisector of AB. The line through C(1,2) parallel to AB meets the perpendicular bisector of AB at the point X.    ii.       Find, by calculation, the distance BX. Solution a.   We are required to write equation of perpendicular bisector of AB with points A(5,7) and B(9,-1). […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#4

Question a.   Solve the equation , giving the solution in an exact form. b.   Solve, by factorising, the equation  for . Solution a.   We are given; b.   We are required to solve, by factorising, the following equation for . Now we have two options. We utilize the periodic property of   to find other solutions (roots) of : […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#3

Question The 12th term of an arithmetic progression is 17 and the sum of the first 31 terms is 1023. Find the  31st term. Solution From the given information, we can compile following data about Arithmetic Progression (A.P); Expression for the general term  in the Arithmetic Progression (A.P) is: Therefore, for 12th term; Expression for the sum of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#2

Question A curve for which  passes through . Find the equation of the curve. Solution i.   We can find equation of the curve from its derivative through integration; We are given that; Therefore; Rule for integration of  is: Rule for integration of  is: If a point   lies on the curve , we can find out value of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#1

Question      i.       Find the coefficients of  and  in the expansion of .    ii.       It is given that, when  is expanded, there is no term in . Find the value of the constant . Solution i.   Expression for the general term in the Binomial expansion of  is: First we rewrite the expression in the standard form; In the […]