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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: 1144 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: 2047   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: 953   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: 1018   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: 1341   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: 548   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: 1064   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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/13) | Q#9

Hits: 860   Question a.   Two convergent geometric progressions, P and Q, have the same sum to infinity. The first and  second terms of P are 6 and 6r respectively. The first and second terms of Q are 12 and −12r  respectively. Find the value of the common sum to infinity. b.   The first term of an […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/12) | Q#8

Hits: 957 Question a)   A cyclist completes a long-distance charity event across Africa. The total distance is 3050 km.  He starts the event on May 1st and cycles 200 km on that day. On each subsequent day he reduces  the distance cycled by 5 km. (i)          How far will he travel on May 15th? (ii)        On what date will he finish the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#5

Hits: 783 Question The sum of the 1st and 2nd terms of a geometric progression is 50 and the sum of the 2nd and 3rd terms is 30. Find the sum to infinity. Solution From the given information, we can compile following data about Geometric Progression (G.P); Expression for the sum to infinity of the Geometric Progression (G.P) […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#4

Hits: 1366 Question The 1st, 3rd and 13th terms of an arithmetic progression are also the 1st, 2nd and 3rd terms  respectively of a geometric progression. The first term of each progression is 3. Find the common  difference of the arithmetic progression and the common ratio of the geometric progression. Solution From the given information, we can compile following data […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/12) | Q#9

Hits: 1457 Question A water tank holds 2000 litres when full. A small hole in the base is gradually getting bigger so that  each day a greater amount of water is lost.      i.       On the first day after filling, 10 litres of water are lost and this increases by 2 litres each day.          a.   […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/11) | Q#9

Hits: 793 Question a.   The first term of a geometric progression in which all the terms are positive is 50. The third  term is 32. Find the sum to infinity of the progression. b.   The first three terms of an arithmetic progression are ,  and  respectively, where x is an acute angle. i.       Show that  . ii.       Find the sum […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#3

Hits: 689 Question The 12th term of an arithmetic progression is 17 and the sum of the first 31 terms is 1023. Find the  31st term. Solution From the given information, we can compile following data about Arithmetic Progression (A.P); Expression for the general term  in the Arithmetic Progression (A.P) is: Therefore, for 12th term; Expression for the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/13) | Q#6

Hits: 1709 Question A ball is such that when it is dropped from a height of 1 metre it bounces vertically from the ground  to a height of 0.96 metres. It continues to bounce on the ground and each time the height the ball  reaches is reduced. Two different models, A and B, describe  this. Model A : The […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/11) | Q#8

Hits: 573 Question The first term of a progression is  and the second term is . i.       For the case where the progression is arithmetic with a common difference of 12, find the  possible values of  and the corresponding values of the third term.    ii.       For the case where the progression is geometric with a sum to infinity of 8, find the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/13) | Q#4

Hits: 962 Question Three geometric progressions, P, Q and R, are such that their sums to infinity are the first three  terms respectively of an arithmetic progression. Progression P is; Progression Q is; i.       Find the sum to infinity of progression R.    ii.       Given that the first term of R is 4, find the sum of the first three terms […]

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: 768 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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#7

Hits: 1389 Question i.       A geometric progression has first term , common ratio  and sum to infinity . A  second geometric progression has first term , common ratio  and sum to infinity . Find the  value of .    ii.       An arithmetic progression has first term 7. The nth term is 84 and the (3n)th term is 245. Find  the […]