CIE IGCSE ADDITIONAL MATHEMATICS (0606) TOPICAL PRACTICE QUESTIONS TOPIC 13: VECTORS IN TWO DIMENSIONS Compiled from: Paper 1 Variants 1, 2 and 3 2016- 2020 "DON'T STRESS. Do your best and forget the rest." Page 1 Source: 0606/11/M/J/17 - Question No. 5 1 (a) B A a M O c b C The diagram shows a figure OABC, where OA = a , OB = b and OC = c . The lines AC and OB intersect at the point M where M is the midpoint of the line AC. (i) Find, in terms of a and c, the vector OM . [2] (ii) Given that OM : MB = 2 : 3, find b in terms of a and c. [2] © UCLES 2017 Compilation: www.mystudycompass.com Source: 0606/11/M/J/17 - Question No. 5 Page 2 (b) Vectors i and j are unit vectors parallel to the x-axis and y-axis respectively. The vector p has a magnitude of 39 units and has the same direction as -10i + 24j. (i) Find p in terms of i and j. [2] (ii) Find the vector q such that 2p + q is parallel to the positive y-axis and has a magnitude of 12 units. [3] (iii) Hence show that q = k 5 , where k is an integer to be found. © UCLES 2017 [2] Compilation: www.mystudycompass.com Source: 0606/11/M/J/18 - Question No. 8 2 (a) Given that p = 2i - 5j and q = i - 3j, find the unit vector in the direction of 3p - 4q. © UCLES 2018 Page 3 [4] Compilation: www.mystudycompass.com Source: 0606/12/M/J/16 - Question No. 3 3 Page 4 J2N J1N J- 5N K O K O Vectors a, b and c are such that a = , b= and c = K O . y 3 L P L P L 5P (i) Given that a = b - c , find the possible values of y. [3] (ii) Given that n ^b + ch + 4 ^b - ch = m ^2b - ch, find the value of n and of m. [3] © UCLES 2016 Compilation: www.mystudycompass.com Source: 0606/12/M/J/17 - Question No. 3 4 Page 5 Vectors i and j are unit vectors parallel to the x-axis and y-axis respectively. (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 Page 6 Source: 0606/12/M/J/20 - Question No. 8 5 A P Q O B R The diagram shows a triangle OAB such that OA = a and OB = b . The point P lies on OA such that 3 OP = OA . The point Q is the mid-point of AB. The lines OB and PQ are extended to meet at the 4 point R. Find, in terms of a and b, (a) AB, [1] (b) PQ. Give your answer in its simplest form. [3] © UCLES 2020 Compilation: www.mystudycompass.com Source: 0606/12/M/J/20 - Question No. 8 Page 7 It is given that nPQ = QR and BR = kb, where n and k are positive constants. (c) Find QR in terms of n, a and b. [1] (d) Find QR in terms of k, a and b. [2] (e) Hence find the value of n and of k. [3] © UCLES 2020 Compilation: www.mystudycompass.com Source: 0606/12/O/N/18 - Question No. 7 6 - 12 o . Write v in the (a) The vector v has a magnitude of 39 units and is in the same direction as e 5 a form e o , where a and b are constants. b Page 8 [2] r+s 5r + 1 o and q = e o , where r and s are constants. Given that (b) Vectors p and q are such that p = e r+6 2s - 1 0 2p + 3q = e o , find the value of r and of s. [4] 0 © UCLES 2018 Compilation: www.mystudycompass.com Source: 0606/13/M/J/20 - Question No. 6 7 Page 9 5 o. (a) Find the unit vector in the direction of e - 12 [1] 4 -2 - 10 o, find the value of each of the constants k and r. (b) Given that e o + k e o = r e 1 3 5 [3] © UCLES 2020 Compilation: www.mystudycompass.com Source: 0606/13/M/J/20 - Question No. 6 Page 10 (c) Relative to an origin O, the points A, B and C have position vectors p, 3q - p and 9q - 5p respectively. (i) Find AB in terms of p and q. [1] (ii) Find AC in terms of p and q. [1] (iii) Explain why A, B and C all lie in a straight line. [1] (iv) Find the ratio AB : BC. [1] © UCLES 2020 Compilation: www.mystudycompass.com Page 11 Source: 0606/13/O/N/18 - Question No. 7 8 A B D O C The diagram shows a quadrilateral OABC. The point D lies on OB such that OD = 2DB and AD = mAC , where m is a scalar quantity. OA = a OB = b OC = c (i) Find AD in terms of m, a and c. [1] (ii) Find AD in terms of a and b. [2] (iii) Given that 15a = 16b - 9c , find the value of m. [3] © UCLES 2018 Compilation: www.mystudycompass.com Page 12 Source: 0606/13/O/N/20 - Question No. 9 9 A a Y X O b C B The diagram shows the triangle OAC. The point B is the midpoint of OC. The point Y lies on AC such that OY intersects AB at the point X where AX : XB = 3:1. It is given that OA = a and OB = b . (a) Find OX in terms of a and b, giving your answer in its simplest form. [3] (b) Find AC in terms of a and b. [1] © UCLES 2020 Compilation: www.mystudycompass.com Source: 0606/13/O/N/20 - Question No. 9 Page 13 (c) Given that OY = h OX , find AY in terms of a, b and h. [1] (d) Given that AY = mAC , find the value of h and of m. [4] © UCLES 2020 Compilation: www.mystudycompass.com