Hits: 923

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#2

Hits: 923 Question Find the set of values of a for which the curve  and the straight line  meet at two  distinct points. Solution We need to find the equation that satisfies the x-coordinates of the points of intersection of given  curve and line. If two lines (or a line and a curve) intersect each other at a point then […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#7

Hits: 1464   Question Points A and B lie on the curve . Point A has coordinates (4,7) and B is the  stationary point of the curve. The equation of a line L is , where m is a constant.                             i.       In the case where L passes through the mid-point of AB, find the value of m.                           ii.       Find the set of […]

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

Hits: 1037   Question Functions f and g are defined for x > 3 by;      i.       Find and simplify an expression for gg(x).    ii.       Find an expression for  and state the domain of .   iii.       Solve the equation .  Solution      i.   We are given that; It can be written as; Therefore for ;    ii. […]

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

Hits: 1328   Question a.   Relative to an origin O, the position vectors of two points P and Q are p and q respectively. The  point R is such that PQR is a straight line with Q the mid-point of PR. Find the position vector of R in  terms of p and q, simplifying your answer. b.   The vector […]

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

Hits: 1120   Question A function f is defined by  for . It is given that f is an increasing  function. Find the largest possible value of the constant a. Solution We are given that function f is increasing function. To test whether a function  is increasing or decreasing at a particular point , we  take derivative of a function […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/12) | Q#9

Hits: 1281   Question The equation of a curve is  .       i.       Find the coordinates of the stationary point of the curve.    ii.       Find an expression for  and hence, or otherwise, determine the nature of the                                 stationary point.   iii.       Find the values of x […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/12) | Q#7

Hits: 3122   Question a.   The first two terms of an arithmetic progression are 16 and 24. Find the least number of terms of  the progression which must be taken for their sum to exceed 20 000. b.   A geometric progression has a first term of 6 and a sum to infinity of 18. A new geometric  progression […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#1

Hits: 1393   Question Find the set of values of k for which the equation  has distinct real roots. Solution We are given the equation; Standard form of quadratic equation is; Expression for discriminant of a quadratic equation is; If   ; Quadratic equation has two distinct real roots. If   ; Quadratic equation has no real roots. If   ; Quadratic equation […]

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: 1067   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#7

Hits: 1075   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 | Feb-Mar | (P1-9709/12) | Q#5

Hits: 1446 Question The diagram shows the graphs of  and  for . The graphs intersect at  points A and B. i.       Find by calculation the x-coordinate of A. ii.       Find by calculation the coordinates of B. Solution      i.   We are required to find the x-coordinate of point A which is point of intersection of the two given  curves. If two […]