Finance > EXAM > AS1051 CITY UNIVERSITY London BSc Honours Degree in Actuarial Science Part 1 Mathematics for Actuari (All)

AS1051 CITY UNIVERSITY London BSc Honours Degree in Actuarial Science Part 1 Mathematics for Actuarial Science: Paper 1 2016

Document Content and Description Below

Time allowed: 2 hours Full marks may be obtained for correct answers to ALL of the SIX questions in Section A and TWO of the THREE questions in Section B. If more than TWO questions from Section B... are answered, the best TWO marks will be credited. All necessary working must be shown. 1 Turn over : : : Section A 1. Find the set of values of x for which: (a) [4 marks] j2x - 6j > 2: (b) [4 marks] 1+ 1-x x > 1: 2. [8 marks] Solve 3 tan3(x) - 3 tan2(x) - tan(x) + 1 = 0 in full generality for x, giving your general solution in radians as multiples of π. 3. Compute the integrals (a) [4 marks] R0π=2 cos2 θdθ; (b) [4 marks] R xp1 + xdx: 4. Evaluate the limits (a) [3 marks] lim x!1 -6x3 + x + 15 x2 - 3x + 12x3 ; (b) [5 marks] lim x!0 e-5x - 3 tan(x) - 1 2e4x - 2 cosh(x) : 5. Differentiate the following equations with respect to x (a) [3 marks] y = e5x coth x; (b) [5 marks] ye-2x = x ln(y) - 5xy: 6. [8 marks] Prove by induction that Time allowed: 2 hours Full marks may be obtained for correct answers to ALL of the SIX questions in Section A and TWO of the THREE questions in Section B. If more than TWO questions from Section B are answered, the best TWO marks will be credited. All necessary working must be shown. 1 Turn over : : : Section A 1. Find the set of values of x for which: (a) [4 marks] j2x - 6j > 2: (b) [4 marks] 1+ 1-x x > 1: 2. [8 marks] Solve 3 tan3(x) - 3 tan2(x) - tan(x) + 1 = 0 in full generality for x, giving your general solution in radians as multiples of π. 3. Compute the integrals (a) [4 marks] R0π=2 cos2 θdθ; (b) [4 marks] R xp1 + xdx: 4. Evaluate the limits (a) [3 marks] lim x!1 -6x3 + x + 15 x2 - 3x + 12x3 ; (b) [5 marks] lim x!0 e-5x - 3 tan(x) - 1 2e4x - 2 cosh(x) : 5. Differentiate the following equations with respect to x (a) [3 marks] y = e5x coth x; (b) [5 marks] ye-2x = x ln(y) - 5xy: 6. [8 marks] Prove by induction that [Show More]

Last updated: 2 years ago

Preview 1 out of 4 pages

Buy Now

Instant download

We Accept: