Hits: 709

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#10

Hits: 316 Question     i.       Solve the equation  for .    ii.       Sketch, on the same diagram, the graphs of  and for  .   iii.       Use your answers to parts (i) and (ii) to find the set of values of x for   for which . Solution      i.   We have the equation; We know that […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#9

Hits: 298 Question A curve is such that  and (2,5) is a point on the curve.     i.       Find the equation of the curve.    ii.       A point P moves along the curve in such a way that the y-coordinate is  increasing at a constant rate of 0.06 units per second. Find the rate of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#8

Hits: 282 Question Points A and B have coordinates (h, h) and (4h + 6, 5h) respectively. The equation of  the perpendicular bisector of AB is 3x + 2y = k. Find the values of the constants h  and k. Solution We are given that line AB has coordinates of the two points  and . […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#7

Hits: 383 Question The function is defined by  for .      i.       Express   in the form , where a and b are constants.    ii.       State the coordinates of the stationary point on the curve y = f(x). The function is defined by  for .   iii.       State the smallest value of k for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#6

Hits: 455 Question The diagram shows points A and B on a circle with centre O and radius r. The  tangents to the circle at A and B meet at T. The shaded region is bounded by the  minor arc AB and the lines AT and BT. Angle AOB is  radians.      i.       In the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#5

Hits: 140 Question The diagram shows a three-dimensional shape. The base OAB is a horizontal  triangle in which angle AOB is 90o. The side OBCD is a rectangle and the side OAD  lies in a vertical plane. Unit vectors  and are parallel to OA and OB respectively  and the unit vector  is vertical. The position […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#4

Hits: 191 Question The function f, is such that   for . It is given that  and .                             i.       Find the values of the constants a and b.                           ii.       Find the set of values of k for which the equation f(x) = k has no  solution. Solution i.   We are given the function […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#3

Hits: 199 Question A company producing salt from sea water changed to a new process. The amount of  salt obtained each week increased by 2% of the amount obtained in the preceding  week. It is given  that in the first week after the change the company obtained 8000  kg of salt. i. Find the amount […]

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

Hits: 140 Question The equation of a curve is  , where  is a constant.     i.       Find the set of values of  for which the whole of the curve lies above the x-axis.    ii.       Find the value of  for which the line y + 2x = 7 is a tangent to the curve. Solution […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#1

Hits: 138 Question The coefficient of  in the expansion of is 330. Find the value of  the constant a. Solution We can find the coefficient of in the expansion of given expression by finding  coefficients of in the expansion of individual terms of expression and then adding  them. Let us first find the coefficient of […]

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: 361 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#7

Hits: 195 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: 481 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: 287 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: 159 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: 130 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: 134 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 […]