CIE IGCSE ADDITIONAL MATHEMATICS (0606) TOPICAL PRACTICE QUESTIONS TOPIC 12: SERIES Compiled from: Paper 1 Variants 1, 2 and 3 2016- 2020 "Discipline is doing what needs to be done, even if you don't feel like doing it." Source: 0606/11/M/J/18 - Question No. 9 1 8 J 1 NO K (i) Find the first 3 terms in the expansion of K2x O in descending powers of x. 16xP L 8 J N2 1 NO JK 1 OO . 1 + (ii) Hence find the coefficient of x4 in the expansion of KK2x O K 2 x 16 x L P L P © UCLES 2018 Page 1 [3] [3] Compilation: www.mystudycompass.com Page 2 Source: 0606/11/M/J/19 - Question No. 4 2 (i) The first 3 terms, in ascending powers of x, in the expansion of `2 + bxj a + 256x + cx2. Find the value of each of the constants a, b and c. (ii) Using the values found in part (i), find the term independent of x in the expansion of 8 `2 + bxj b2x - 3l . x 8 © UCLES 2019 2 can be written as [4] [3] Compilation: www.mystudycompass.com Source: 0606/11/M/J/20 - Question No. 9 3 Page 3 (a) An arithmetic progression has a second term of - 14 and a sum to 21 terms of 84. Find the first term and the 21st term of this progression. [5] © UCLES 2020 Compilation: www.mystudycompass.com Source: 0606/11/M/J/20 - Question No. 9 Page 4 (b) A geometric progression has a second term of 27p 2 and a fifth term of p 5 . The common ratio, r, is such that 0 1 r 1 1. (i) Find r in terms of p. [2] (ii) Hence find, in terms of p, the sum to infinity of the progression. [3] (iii) Given that the sum to infinity is 81, find the value of p. [2] © UCLES 2020 Compilation: www.mystudycompass.com Source: 0606/11/O/N/16 - Question No. 4 4 5 J 1N 2 K O (i) Find the first 3 terms in the expansion of 2x , in descending powers of x. 3xP L 5 J 1N 1 NJ (ii) Hence find the coefficient of x7 in the expansion of K3 + 3OK2x 2 - O . 3xP x PL L © UCLES 2016 Page 5 [3] [2] Compilation: www.mystudycompass.com Source: 0606/11/O/N/18 - Question No. 3 5 Page 6 The coefficient of x2 in the expansion of (2 - x) (3 + kx) 6 is equal to 972. Find the possible values of the constant k. [6] © UCLES 2018 Compilation: www.mystudycompass.com Source: 0606/11/O/N/20 - Question No. 10 6 Page 7 (a) An arithmetic progression has a second term of 8 and a fourth term of 18. Find the least number of terms for which the sum of this progression is greater than 1560. [6] © UCLES 2020 Compilation: www.mystudycompass.com Source: 0606/11/O/N/20 - Question No. 10 Page 8 (b) A geometric progression has a sum to infinity of 72. The sum of the first 3 terms of this progression 333 is . 8 (i) Find the value of the common ratio. [5] (ii) Hence find the value of the first term. [1] © UCLES 2020 Compilation: www.mystudycompass.com Source: 0606/12/M/J/16 - Question No. 2 7 1 5 (i) The first 3 terms in the expansion of c2 - m are 4x integers a, b and c. a+ b c + . Find the value of each of the x x2 [3] (ii) Hence find the term independent of x in the expansion of c2 - © UCLES 2016 Page 9 1 m5 ^ 3 + 4xh. 4x [2] Compilation: www.mystudycompass.com Source: 0606/12/M/J/17 - Question No. 4 83 Page 10 n J x NO x-axis and y-axis2respectively. Vectors j areinunit vectors parallel - the The firsti 3and terms the expansion of KK3 to O are 81 + ax + bx . Find the value of each of the constants 6P n, a and b. [5] L (a) The vector v has a magnitude of 3 5 units and has the same direction as i - 2 j. Find v giving your answer in the form a i + b j, where a and b are integers. [2] (b) The velocity vector w makes an angle of 30° with the positive x-axis and is such that w = 2 . Find w giving your answer in the form c i + d j, where c and d are integers. [2] © UCLES 2017 Compilation: www.mystudycompass.com Source: 0606/12/M/J/18 - Question No. 5 9 Page 11 5 J 1 ON b c K (i) The first three terms in the expansion of K3 - O can be written as a + + 2 . Find the value x x 9xP of each of the constants a, b and c. [3] L (ii) Use your values of a, b and c to find the term independent of x in the expansion of N5 J KK3 - 1 OO (2 + 9x) 2 . 9x P L © UCLES 2018 [3] Compilation: www.mystudycompass.com Source: 0606/12/M/J/20 - Question No. 3 Page 12 x 6 10 (a) Find the first 3 terms in the expansion of b4 - l in ascending powers of x. Give each term in 16 its simplest form. [3] (b) Hence find the term independent of x in the expansion of b4 - © UCLES 2020 2 x 6b l x - 1l . x 16 [3] Compilation: www.mystudycompass.com Source: 0606/12/O/N/16 - Question No. 4 11 5 J 1N 2 K O (i) Find the first 3 terms in the expansion of 2x , in descending powers of x. 3xP L 5 J 1N 1 NJ (ii) Hence find the coefficient of x7 in the expansion of K3 + 3OK2x 2 - O . 3xP x PL L © UCLES 2016 Page 13 [3] [2] Compilation: www.mystudycompass.com Source: 0606/12/O/N/17 - Question No. 3 12 5 J x 2NO K (i) Find, in ascending powers of x, the first 3 terms in the expansion of K2 - O . 4P L 5 2 J x 2NO JK1 3 NO K (ii) Hence find the term independent of x in the expansion of K2 - O K - 2O . 4 P Lx x P L © UCLES 2017 Page 14 [3] [3] Compilation: www.mystudycompass.com Source: 0606/12/O/N/18 - Question No. 5 13 Page 15 The 7th term in the expansion of (a + bx) 12 in ascending powers of x is 924x 6 . It is given that a and b are positive constants. (i) 1 Show that b = . a [2] The 6th term in the expansion of (a + bx) 12 in ascending powers of x is 198x 5 . (ii) Find the value of a and of b. © UCLES 2018 [4] Compilation: www.mystudycompass.com Source: 0606/12/O/N/19 - Question No. 3 Page 16 x 14 14 The first three terms in the expansion of b1 - l (1 - 2x) 4 can be written as 1 + ax + bx 2 . Find the value 7 of each of the constants a and b. [6] © UCLES 2019 Compilation: www.mystudycompass.com Source: 0606/12/O/N/20 - Question No. 4 Page 17 15 The 7th and 10th terms of an arithmetic progression are 158 and 149 respectively. (a) Find the common difference and the first term of the progression. [3] (b) Find the least number of terms of the progression for their sum to be negative. [3] © UCLES 2020 Compilation: www.mystudycompass.com Source: 0606/12/O/N/20 - Question No. 5 3 2 16 Find the coefficient of x 2 in the expansion of bx - lbx + l . x x 5 © UCLES 2020 Page 18 [5] Compilation: www.mystudycompass.com Source: 0606/13/M/J/18 - Question No. 9 17 8 J 1 NO K (i) Find the first 3 terms in the expansion of K2x O in descending powers of x. 16xP L 8 J N2 1 NO JK 1 OO . 1 + (ii) Hence find the coefficient of x4 in the expansion of KK2x O K 2 x 16 x L P L P © UCLES 2018 Page 19 [3] [3] Compilation: www.mystudycompass.com Source: 0606/13/M/J/20 - Question No. 8 Page 20 18 (a) An arithmetic progression has a first term of 7 and a common difference of 0.4. Find the least number of terms so that the sum of the progression is greater than 300. [4] (b) The sum of the first two terms of a geometric progression is 9 and its sum to infinity is 36. Given that the terms of the progression are positive, find the common ratio. [4] © UCLES 2020 Compilation: www.mystudycompass.com Source: 0606/13/O/N/16 - Question No. 4 19 6 J xN K O (i) Find, in ascending powers of x, the first 3 terms in the expansion of 2 . 4P L 6 J xN 2 3 NJ (ii) Hence find the term independent of x in the expansion of K4 + + 2OK2 - O . x x PL 4P L © UCLES 2016 Page 21 [3] [3] Compilation: www.mystudycompass.com Page 22 Source: 0606/13/O/N/17 - Question No. 7 20 2 6 x (i) Find, in ascending powers of x, the first 3 terms in the expansion of c2 - m . Give each term in 4 its simplest form. [3] (ii) 2 6 x2 1 Hence find the coefficient of x in the expansion of c2 - m c + xm . x 4 © UCLES 2017 2 [4] Compilation: www.mystudycompass.com Source: 0606/13/O/N/18 - Question No. 1 21 (a) In the expansion of (2 + px) 5 the coefficient of x 3 is equal to - (b) Find the term independent of x in the expansion of e2x 2 + © UCLES 2018 8 1 o . 4x 2 Page 23 8 . Find the value of the constant p. 25 [3] [3] Source: 0606/13/O/N/20 - Question No. 5 Page 24 25 xn r the expansion of point is , find the value of the (1 + at x) btime 1 - tls is given 22 Given thatdisplacement, the coefficient ofofx 2a in (b) The x m, particle from a fixed 4 by x = 6 cos b3t + 3 l. 2 positive integer n. [5] 2r Find the acceleration of the particle when t = . [3] 3 © UCLES 2020