Hits: 30

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/13) | Q#2

Hits: 30 Question i. In the binomial expansion of , the first three terms are . Find the  remaining three terms of the expansion. ii. Hence find the coefficient of  in the expansion of . Solution i. Expression for the Binomial expansion of is: First rewrite the given expression in standard form. In the given […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#10

Hits: 53 Question a.In an arithmetic progression, the sum of the first ten terms is equal to the sum of the next five  terms. The first term is . i.Show that the common difference of the progression is . ii.Given that the tenth term is 36 more than the fourth term, find the value of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#1

Hits: 107 Question Find the coefficient of x in the expansion of .   Solution We are required to find the coefficient of in the expansion of given expression. 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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/11) | Q#8

Hits: 37 Question a)  The third and fourth terms of a geometric progression are  and  respectively. Find the sum to infinity of the progression. b)  Two schemes are proposed for increasing the amount of household waste that is recycled each  week. Scheme A is to increase the amount of waste recycled each month by 0.16 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Feb-Mar | (P1-9709/12) | Q#6

Hits: 62 Question      i.       The first and second terms of a geometric progression are p and 2p respectively, where p is a  positive constant. The sum of the first n terms is greater than 1000p. Show that 2n > 1001.    ii.       In another case, p and 2p are the first and second terms […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#5

Hits: 47 Question In an arithmetic progression the first term is and the common difference is 3. The nth term is 94  and the sum of the first  terms is 1420. Find  and . Solution We can compile following data from the given information for Arithmetic Progression (A.P) ; First we consider the nth term […]

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

Hits: 139 Question The first three terms of an arithmetic progression are 4, x and y respectively. The first three terms of  a geometric progression are x, y and 18 respectively. It is given that both x and y are positive. a)   Find the value of x and the value of y. b)   Find the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/11) | Q#4

Hits: 155 Question The first term of a series is 6 and the second term is 2.     i.               For the case where the series is an arithmetic progression, find the sum of the first 80 terms.    ii.               For the case where the series is a geometric progression, find the sum to infinity. Solution […]

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Hits: 993 Question On a certain day, the height of a young bamboo plant was found to be 40 cm. After  exactly one day its height was found to be 41.2 cm. Two different models are used to  predict its height exactly 60 days after it was first measured. ·       Model A assumes that the […]

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

Hits: 296 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 | (P1-9709/12) | Q#3

Hits: 721 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 | May-Jun | (P1-9709/11) | Q#8

Hits: 1001 Question a)   A geometric progression has a second term of 12 and a sum to infinity of 54. Find  the possible values of the first term of the progression. b)  The nth term of a progression is p + qn, where p and q are constants, and Sn is  the sum of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#1

Hits: 1509 Question An arithmetic progression has first term −12 and common difference 6. The sum of the first n terms  exceeds 3000. Calculate the least possible value of n. Solution We can compile following data from the given information for Arithmetic Progression (A.P) ; Expression for the sum of  number of terms in the Arithmetic Progression (A.P) is: […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#3

Hits: 1938   Question a)   Each year, the value of a certain rare stamp increases by 5% of its value at the beginning of the  year. A collector bought the stamp for $10 000 at the beginning of 2005. Find its value at the  beginning of 2015 correct to the nearest $100.  b)   The sum of the first n […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#3

Hits: 3964   Question a.   A geometric progression has first term 3a and common ratio r. A second geometric progression  has first term a and common ratio −2r. The two progressions have the same sum to infinity. Find the  value of r. b.   The first two terms of an arithmetic progression are 15 and 19 respectively. The first […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/13) | Q#11

Hits: 1198   Question The function  is defined for . It is given that  has a minimum value when  and that . (i)          Find . It is now given that ,  and  are the first three terms respectively of an arithmetic progression. (ii)        Find the value of . (iii)       Find , and hence find the minimum value of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/13) | Q#2

Hits: 1609   Question The common ratio of a geometric progression is r. The first term of the progression is  and the sum to infinity is S.      i.       Show that S = 2 − r.    ii.       Find the set of possible values that S can take. Solution      i.   From the given information, we can compile following data about […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/12) | Q#7

Hits: 2651   Question a.   The first two terms of an arithmetic progression are 16 and 24. Find the least number of terms of  the progression which must be taken for their sum to exceed 20 000. b.   A geometric progression has a first term of 6 and a sum to infinity of 18. A new geometric  progression […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#7

Hits: 749   Question The function f is defined for  by .                     i.       Find  and . The first, second and third terms of a geometric progression are respectively ,   and .                   ii.       Find the value of the constant k. Solution      i.   We are given the function; Therefore; Rule for differentiation of  is: Therefore; Second derivative is the derivative […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#4

Hits: 1799   Question a.   An arithmetic progression has a first term of 32, a 5th term of 22 and a last term of −28. Find the  sum of all the terms in the progression. b.   Each year a school allocates a sum of money for the library. The amount allocated each year  increases by 2.5%of the amount […]