Hits: 1027

# 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: 1027 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: 735 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: 349 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: 469 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: 551 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#5

Hits: 1072 Question The diagram shows a triangle OAB in which angle OAB = 90o and OA = 5 cm. The  arc AC is part of a circle with centre O. The arc has length 6 cm and it meets OB at  C. Find the area of the shaded region. Solution It is evident from […]

# 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: 296 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: 542 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: 447 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: 207 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 […]