# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2020 | Feb-Mar | (P1-9709/12) | Q#8

Question A woman’s basic salary for her first year with a particular company is $30000 and at the end of the year she also gets a bonus of$600. a)For her first year, express her bonus as a percentage of her basic salary. At the end of each complete year, the woman’s basic salary will […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#9

Question The first, second and third terms of a geometric progression are ,  and  respectively. (i)       Show that  satisfies the equation 7k2 − 48k + 36 = 0. (i)       Find, showing all necessary working, the exact values of the common ratio corresponding to  each of the possible values of k. (ii)        One of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#8

Question a)   Over a 21-day period an athlete prepares for a marathon by increasing the distance she runs each  day by 1.2 km. On the first day she runs 13 km. (i)          Find the distance she runs on the last day of the 21-day period. (ii)        Find the total distance […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#4

Question A runner who is training for a long-distance race plans to run increasing distances each day for 21  days. She will run km on day 1, and on each subsequent day she will increase the distance by  10% of the previous day’s distance. On day 21 she will run 20 km.       i.       Find […]

# 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#5

Question Two heavyweight boxers decide that they would be more successful if they competed in a lower  weight class. For each boxer this would require a total weight loss of 13 kg. At the end of week 1  they have each recorded a weight loss of 1 kg and they both find that in each […]

# 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

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 case: Hence; […]

# 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

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 . b.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

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 tonnes. Scheme […]

# 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

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 respectively of […]

# 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

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 which is […]

# 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

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 fourth term […]

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

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 i.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#3

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 daily amount […]

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

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 Geometric Progression […]

# 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

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 of salt […]

# 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

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 first n […]

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

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: Therefore for the […]

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

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 terms of […]

# 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

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 two terms […]

# 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

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 . Solution […]