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Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#11

Hits: 161   Question The diagram shows parts of the curves  and  intersecting at points  and . The angle between the tangents to the two curves at  is .      i.       Find , giving your answer in degrees correct to 3 significant figures.    ii.       Find by integration the area of the shaded region. Solution i.   Angle between two curves is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#10

Hits: 103   Question      i.       Express  in the form .  The function  is defined for , where  and  are positive constants, by The range of  is given by , where  and  are constants.    ii.       State the smallest possible value of . For the case where  and ,   iii.       find  and ,   iv.       find an expression for . Solution i.   We have the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#9

Hits: 82   Question The function  is defined for  and is such that . The curve  passes through the point .      i.       Find the equation of the normal to the curve at P.    ii.       Find the equation of the curve.    iii.     Find the x-coordinate of the stationary point and state with a reason whether this point is a maximum […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#8

Hits: 351   Question In the diagram, AB is an arc of a circle with centre O and radius 4 cm. Angle AOB is  radians. The  point D on OB is such that AD is perpendicular to OB. The arc DC, with centre O, meets OA at C.      i.       Find an expression in terms of  for the perimeter of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#6

Hits: 130   Question Relative to an origin O, the position vector of A is  and the position vector of B is  .      i.       Show that angle OAB is a right angle.    ii.       Find the area of triangle OAB. Solution i.   It is evident that angle OAB is the angle between vectors  and . We are given  but we need […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#5

Hits: 98 Question Find the set of values of  for which the line  meets the curve                     at two distinct points. Solution If two lines (or a line and a curve) intersect each other at a point then that point lies on both lines i.e.  coordinates of that point have same values on both lines (or on the line and the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#4

Hits: 78 Question The line  passes through the points  and , where  and  are constants.      i.       Find the values of  and .    ii.       Find the coordinates of the mid-point of . Solution i.   Since the line  through the points  and , coordinates of both points must satisfy equation of the line. For point For point Substituting  in equation ; ii.   We are given […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#3

Hits: 81 Question Solve the equation  for . Solution We are given the equation; We have the trigonometric identity; We can rewrite it as; Substituting this in above equation; Now we have two options. Using calculator we can find that; Since we are required to solve the equation  for , we consider angles only in this range. Therefore; We utilize  the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#1

Hits: 83 Question In the expansion of , the coefficient of  is equal to the coefficient of . Find the value of the non-zero constant . Solution Expression for the general term in the Binomial expansion of  is: In the given case: Hence; Since we are looking for the terms with  :  we can  equate Now we can find the term […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#7

Hits: 199 Question i.       A geometric progression has first term , common ratio  and sum to infinity . A  second geometric progression has first term , common ratio  and sum to infinity . Find the  value of .    ii.       An arithmetic progression has first term 7. The nth term is 84 and the (3n)th term is 245. Find  the […]