Hits: 22

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#11

Hits: 22 Question The diagram shows part of the curve  and the line x = 1.  The point A is the minimum point on the curve.     i.       Show that the x-coordinate of A satisfies the equation and find the  exact value of  at A.    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 2018 | May-Jun | (P1-9709/13) | Q#10

Hits: 19 Question The one-one function f is defined by  for , where c is a  constant.   i.       State the smallest possible value of c. In parts (ii) and (iii) the value of c is 4.    ii.       Find an expression for  and state the domain of .   iii.       Solve the equation , […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#9

Hits: 68 Question The diagram shows a pyramid OABCD with a horizontal rectangular base OABC.  The sides OA and AB have lengths of 8 units and 6 units respectively. The point E on  OB is such that OE = 2 units. The point D of the pyramid is 7 units vertically  above E. Unit vectors […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#7

Hits: 35 Question a.                         i.       Express  in the form , where  and are constants to be  found.       ii.       Hence, or otherwise, and showing all necessary working, solve the equation  For .   b.     The diagram shows the graphs of  and  for . The  graphs intersect at the points A […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#6

Hits: 19 Question The coordinates of points A and B are (−3k – 1, k + 3) and (k + 3, 3k + 5)  respectively, where k is a constant (k ≠ −1). i.       Find and simplify the gradient of AB, showing that it is independent of k.  ii.       Find and simplify the equation of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#4

Hits: 1 Question A curve with equation y = f(x) passes through the point A(3, 1) and crosses the y- axis at B. It is given that  . Find the y-coordinate of B. Solution We are given that curve crosses y-axis at point B. The point at which curve (or line) intercepts y-axis, the value […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#3

Hits: 12 Question The common ratio of a geometric progression is 0.99. Express the sum of the first  100 terms as a percentage of the sum to infinity, giving your answer correct to 2  significant figures. Solution We are given that common ration of a Geometric Progression is; Expression for Common Ratio () in a […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#2

Hits: 23 Question Find the coefficient of   in the expansion of . Solution We are required to find the coefficient of in the expansion of . We are given expression as; Expression for the general term in the Binomial expansion of  is: First rewrite the given expression in standard form. In the given case: […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#1

Hits: 2 Question Express 3×2 − 12x + 7 in the form a(x + b)2 + c, where a, b and c are constants.  Solution We have the expression; We use method of “completing square” to obtain the desired form. Next we complete the square for the terms which involve . We have the algebraic […]

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: 346 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: 326 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: 334 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: 423 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: 544 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: 154 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: 205 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: 237 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 […]