a) Simplify (x5 + 5)(\\( 5). b) Express V12 + V2? in the form m5, where n is an integer. c} Rationalise the expression 1 1+v2 3) Express x2 + 4x 7 in the form {x + p)2 - q, where p and q are integers. 13) Hence, or otherwise, find the coordinates of the minimum point of the curve y = x2 + 4x 7. c) Solve the equation for x and sketch a graph to show the root/s ofthe equation. _x__+_;_=% X+4 x 3. The quadratic equation x2 + (3k + 1)x + {4 - 9k), where k is constant, has repeated roots. 3) Show that 53k2 + 42k - 15 = D. b) Hence find the possible values of k. a) Find the binomial expansion of (2 + 3x)5, simplifying the terms. b} Hence find the binomial expansion of (2 + 3x)5 - (2 - 3x)5 \f\f6. The first term of an infinite geometric series is 96. The common ratio of the series is 0.4. 3) Find the third term of the series. b) Find the Sum to infinity of the series. c) The nth term of the series is un. Find the value of 00 "n 11:4 7. An arithmetic series has first term a and common difference d. The sum of the first ten terms of the series is 460. a) Show that 2a + 9d = 92. b) Given also that the 25th term of the sequence is 241, find the value of d. \fa) Given that loga b = c, express b in terms of a and c. b) By forming a quadratic equation, show that there is only one value of x satisfying the equation 2|0g3(x 1) - Iog3(x + 5) = 1