# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#9

Question On John’s 10th birthday he received the first of an annual birthday gift of money from his uncle. This  first gift was £60 and on each subsequent birthday the gift was £15 more than the year before.  The amounts of these gifts form an arithmetic sequence. a.   Show that, immediately after his 12th birthday, the total of […]

# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2016 | June | Q#6

Question A sequence  is defined by  , Where  is a constant. a)   Write down expressions for  and  in terms of k. Find, b)   in terms of k, giving your answer in its simplest form. c)   . Solution a)     We are given that sequence  is defined by We are required to find  and . We can utilize the given expression […]

# 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

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 arithmetic progression […]

# 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

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 event? b)  […]

# 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

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) when  or […]

# 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

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 about Arithmetic […]

# 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

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.   How many […]

# 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

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 of the […]

# 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

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 sum of […]