Progressions/Sequences/Series (CIE-P1-2017) Archives — O/A Level Solutions

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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: 1143 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: 1222   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: 2046   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: 949   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: 1011   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: 1338   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: 547   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: 1061   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 […]