(a) Write down the first three terms of the sequence = 3n, for 1. 1. un n (1) (b) Find (i) (ii) . (5) (Total 6 marks) 2. Arturo goes swimming week. He swims 200 metres in the first week. Each week he swims 30 metres more than the previous week. He continues for one year (52 weeks). (a) How far does Arturo swim in the final week? (b) How far does he swim altogether? (Total 6 marks) 3. Find the term in in the expansion of x3 (Total 5 marks) 4. Find the cosine of the between the two vectors and . 6 marks) 5. Consider the points A (1, 5, 4), B (3, 1, 2) and D (3, 2), with (AD) perpendicular to (AB). k, (a) Find (i) (ii) , giving your answer in terms of k. (3) (b) Show that = 7. k (3) The point C is such that = (c) Find the position vector of C. (4) (d) Find cos . (3) (Total 13 marks) 6. Consider the vectors = 3i + 4j and = 5i 12j. c d – Calculate the scalar product cd. 2 marks) 7. Find the size of the angle between the two vectors and . Give your answer to the nearest degree. (Total 4 marks)
1. (a) Write down the first three terms of the sequence un = 3n, for n 1. (1) (b) Find (i) (ii) . (5) (Total 6 marks) 2. Arturo goes swimming week. He swims 200 metres in the first week. Each week he swims 30 metres more than the previous week. He continues for one year (52 weeks). (a) How far does Arturo swim in the final week? (b) How far does he swim altogether? (Total 6 marks) 3. Find the term in x3 in the expansion of (Total 5 marks) 4. Find the cosine of the between the two vectors and . 6 marks) 5. Consider the points A (1, 5, 4), B (3, 1, 2) and D (3, k, 2), with (AD) perpendicular to (AB). (a) Find (i) (ii) , giving your answer in terms of k. (3) (b) Show that k = 7. (3) The point C is such that = (c) Find the position vector of C. (4) (d) Find cos . (3) (Total 13 marks) 6. Consider the vectors c = 3i + 4j and d = 5i – 12j. Calculate the scalar product cd. 2 marks) 7. Find the size of the angle between the two vectors and . Give your answer to the nearest degree. (Total 4 marks)
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