Hits: 27

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: 27 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: 10 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: 7 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: 7 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: 10 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: 339 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: 321 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: 321 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: 412 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: 507 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: 149 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: 200 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: 215 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: 153 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: 172 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 […]