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Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#10

Hits: 86 Question The diagram shows part of the curve .      i.       Find the equation of the normal to the curve at the point where x=1 in the form ,  where m and c are constants. The shaded region is bounded by the curve, the coordinate axes and the line x=1.    ii.       Find, showing all necessary working, the volume obtained […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#9

Hits: 110   Question The function f is defined by  for , .      i.        Find an expression for . The function g is defined by  for , where a is a constant.    ii.       Find the value of a for which .   iii.       Find the possible values of a given that the equation  has two equal roots. Solution      i. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#8

Hits: 204   Question In the diagram, OAXB is a sector of a circle with centre O and radius 10 cm. The length of the chord  AB is 12 cm. The line OX passes through M, the mid-point of AB, and OX is perpendicular to  AB. The shaded region is bounded by the chord AB and by the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#7

Hits: 69   Question A curve for which  passes through the point (3,-10).      i.       Find the equation of the curve.    ii.       Express   in the form , where a and b are constants.   iii.       Find the set of values of x for which the gradient of the curve is positive. Solution      i.   We can find equation of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#6

Hits: 130   Question The horizontal base of a solid prism is an equilateral triangle of side x cm. The sides of the prism  are vertical. The height of the prism is h cm and the volume of the prism is 2000 cm3.      i.       Express h in terms of x and show that the total surface area of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#5

Hits: 146   Question The equation of a curve is .      i.       Sketch the graph of  for , stating the coordinates of the point of  intersection with the y-axis. Points P and Q lie on the curve and have x-coordinates of  and  respectively.    ii.       Find the length of PQ correct to 1 decimal place. The line through […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#4

Hits: 102   Question a.   An arithmetic progression has a first term of 32, a 5th term of 22 and a last term of −28. Find the  sum of all the terms in the progression. b.   Each year a school allocates a sum of money for the library. The amount allocated each year  increases by 2.5%of the amount […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#3

Hits: 138   Question i.       Prove the identity      ii.       Hence solve the equation  for .   Solution      i.   We have the trigonometric identity; We can write from this identity; Therefore;    ii.   We have the equation; From (i) we know that left hand side of given equation can be written as; Therefore; Using calculator […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#2

Hits: 98   Question Relative to an origin O, the position vectors of points A and B are given by and and angle AOB=90o. i.       Find the value of . The point C is such that .    ii.       Find the unit vector in the direction of . Solution      i.   It is evident that angle AOB is between  and . […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#1

Hits: 107   Question The coefficients of  and  in the expansion of  are  and  respectively. Find the value  of . . Solution We can find the coefficients of  and  in the expansion of given expression.  Let us first find the coefficient of  in the expansion of . We are given expression as;  Expression for the general term in the Binomial expansion of  is: […]