A LEVEL QUESTION BANK.pdf

Ans:   2 2 ln 4 2 2 ln 2 x x x x c x                   7. Find: i)   2 ln 4 x dx   2 1 1 iii) Find the area enclosed by the curve and the y – value of u  to evaluate Hence solve the equation  6x  tan1   12x2  | | cosx2x | tangent. (Ans: (0, t) b) A point P(x, y) is equidistant from X and T. Show that (Ans: 0.334) 6. Differentiate with respect to x: the ratios, show that    to 4 decimal places x x   ii)   1 tan 1 x y    b) Find all the solutions of the equation (Ans:     2 2 cos lncos tan x x x x x   Ans: 3 ii) Sketch the curve for (x2 + x − 2) Q(x) + Ax + B; where Q(x) is a polynomial in x and A and B are constants. Determine the values of A and B and the expression Q(x). (Ans: A = -3, B = 3), Q(x) = 2x + 3 3. i) Show that ln2r, r = 1, 2, 3 is an arithmetic progression. ii) Find the sum of the first 10 terms of the progression. (Ans: 38.1231) iii) Determine the least value of m for which the sum of the first 2m terms exceeds 883.7. (Ans: m = 25) b) Given that the equations y2 + py + q = 0 and y2 + my + k = 0 have a common root. Show that (q − k)2 = (m − p)(pk − mq). 4. Solve the simultaneous equations z1 + z2 = 8 4z1 − 3iz2 = 26 + 8i Using the values of z1 and z2, find the modulus and argument of z1 + z2 − z1z2 (Ans: z1 = 8 + 2i; z2 = -2i) 5. Use the Maclaurin’s theorem to show that the 2 4 6 12 1 32 4 x x x    1 2 2 tan 5 tan 5 3 3 4 3 0 3 x x    (Ans: -18.2, -59.1) 10. Given that tan-1(α) = x and tan-1(β) = y by expr