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Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#11

Hits: 256   Question The function  is defined for .      i.       Find the exact value of  for which .    ii.       State the range of .   iii.       Sketch the graph of .   iv.       Find an expression for . Solution i.   We are given that; We can write it as; We are given that , therefore; Using calculator; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#10

Hits: 76   Question A curve is such that . The curve has a stationary point at  where .      i.            State, with a reason, the nature of this stationary point.    ii.              Find an expression for .   iii.       Given that the curve passes through the point , find the coordinates […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#9

Hits: 183   Question The diagram shows a trapezium ABCD in which AB is parallel to DC and angle BAD is . The coordinates of A, B and C are ,  and  respectively.      i.       Find the equation of AD.    ii.       Find, by calculation, the coordinates of D. The point E is such that ABCE is a parallelogram.   iii.       Find […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#7

Hits: 452   Question The diagram shows a pyramid OABCX. The horizontal square base OABC has side 8 units and the  centre of the base is D. The top of the pyramid, X, is vertically above D and XD = 10 units. The mid- point of OX is M. The unit vectors  and  are parallel to  and  respectively and the unit […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#6

Hits: 111   Question The equation of a curve is , where  and  are constants.      i.       In the case where the curve has no stationary point, show that .    ii.       In the case where  and , find the set of values of  for which  is a decreasing               function of . Solution i.   We are […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#5

Hits: 79 Question      i.       Show that the equation  can be expressed as    ii.       Hence solve the equation  for . Solution i.   We are given; We know that; We can write the given equation as; We have the trigonometric identity; We can rearrange this identity as; Substituting in above equation; ii.   From (i) we know that we can write the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#4

Hits: 107   Question A curve has equation .      i.       Find .   A point moves along this curve. As the point passes through A, the x-coordinate is increasing           at a rate of 0.15 units per second and the y-coordinate is increasing at a rate of 0.4 units per            second. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#1

Hits: 94 Question The diagram shows part of the curve . Find the volume obtained when the shaded region  is rotated through  about the y-axis. Solution Expression for the volume of the solid formed when the shaded region under the curve  is rotated completely about the y-axis is; We are given; We can rearrange it to change the subject; We can see […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#3

Hits: 98 Question      i.       Find the first 3 terms, in ascending powers of , in the expansion of . The coefficient of  in the expansion of  is 95.    ii.       Use the answer to part (i) to find the value of the positive constant . Solution i.   Expression for the Binomial expansion of  is: In the given case: Hence; ii. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#8

Hits: 221 Question a)   The sum, , of the first  terms of an arithmetic progression is given by . Find the  first term and the common difference. b)   A geometric progression in which all the terms are positive has sum to infinity 20. The sum of the  first two terms is 12.8. Find the first term of the […]