Hits: 1109

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#10

Hits: 1109 Question The curve with equation  passes through the origin.     i.       Show that the curve has no stationary points.    ii.       Denoting the gradient of the curve by m, find the stationary value of m and  determine its nature. Solution i.   We are required to show that curve has no stationary points. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#8

Hits: 1418 Question a)   A geometric progression has a second term of 12 and a sum to infinity of 54. Find  the possible values of the first term of the progression. b)  The nth term of a progression is p + qn, where p and q are constants, and Sn is  the sum of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#7

Hits: 474 Question Relative to an origin O, the position vectors of points A, B and C are given by and                     i.       Find .                ii.       The point M is the mid-point of AC. Find the unit vector in the direction of  .                  iii.       Evaluate and hence […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#6

Hits: 1509 Question The diagram shows a circle with centre O and radius r cm. The points A and B lie on  the circle and AT is a tangent to the circle. Angle radians and OBT is a  straight line.      i.       Express the area of the shaded region in terms of r and . […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#5

Hits: 1412 Question The diagram shows a kite OABC in which AC is the line of symmetry. The  coordinates of A and C are (0, 4) and (8, 0) respectively and O is the origin.      i.       Find the equations of AC and OB.    ii.       Find, by calculation, the coordinates of B. Solution      […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#4

Hits: 623 Question i.Prove the identity    ii.Hence solve the equation  for . Solution i.       We have the trigonometric identity;         ii. We have the equation;   From (i) we know that left hand side of given equation can be written as;      Therefore;         […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#3

Hits: 447 Question A curve is such that . The point (1,1) lies on the curve. Find the  coordinates of the point at which the curve intersects the x-axis. Solution We are required to find the coordinates of the point at which the curve intersects the  x-axis. The point at which a line or curve intersects […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#2

Hits: 725 Question A point is moving along the curve   in such a way that the x-coordinate is  increasing at a constant rate of 0.02 units per second. Find the rate of change of the  y-coordinate when x = 1. Solution i.   We are given that; We are required to find; We know […]

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

Hits: 761 Question                     i.       Find the first three terms in the expansion, in ascending powers of , of .                   ii.       Given that the coefficient of  in the expansion of is 12, find the value of the constant a. Solution i.   Expression for the Binomial expansion of  is: First rewrite the given expression […]