Algebra questions | form five Pure Advanced Mathematics

Find Algebra examination questions, form five Pure Advanced Mathematics in acaproso.com

#	Question
1	Show that the term of $sum_{r=1}^{n}ln2^{r}$ are in arithmetic progression. Find the sum of the first n terms . The third term of a convergent geometric progression is the arithmetic mean of the first and second terms. Find the common ratio and the sum to infinity if the first term is 1. Mathematical Calculation
2	The sum of the first n terms of a series is $(2^{n}-1)$ . Find the general term of the series. Prove using Mathematical induction that $6^{n}+8^{n}$ is divisible by 7 for all positive odd numbers n. Mathematical Calculation
3	The sum to infinity of a geometric series whose second term is 4 is 16. Find The first term The common ratio i) Write the statement of the Maclaurin`s series for a function f(x) and use it to expand $f(x)=(x+1)^{-1}$ up to the term $x^{4}$ ii) Give the appropriate value of $frac{5}{6}$ using the first 5 terms of the series in b(i) above correct to 4 decimal places. Mathematical Calculation
4	Show that the Newton Raphson Formula of finding the roots of the equation $12x^{3}+4x^{2}-15x-4=0$ is $x_{n+1}=frac{(24x_{n}+4)x_{n}^{2}+4}{(36x_{n}+8)x_{n}-15}$ and use this formula to find the roots of $12x^{3}+4x^{2}-15x-4=0$ correct to three decimal places. Approximate the area under the curve $y=frac{1}{x-2}$ between x=2 and x=3 with six ordinates by : Trapesoidal rule Simpson rule Which among the rules in (b) above gives a better approximation to the area?. Mathematical Calculation
5	Solve the equation $small log _3 x-3+log_x 9=0$ The equations $small x^{2}+9x+2=0$ and $small x^{2}+kx+5=0$ have common roots. Find the quadratic equation giving two actual possible values of k. Find the sum of the series $small frac{5}{1 imes 2 imes 3}+frac{8}{2 imes 3 imes 4}+frac{11}{3 imes 4 imes 5}+....frac{3n+2}{n(n+1)(n+2)}$ hence find $small sum_{r=1}^{alpha }frac{3r+2}{r(r+1)(r+2)}$ . If $small A=egin{bmatrix} 2 & 1&0 \ 1& 5&2 \ 1& -1 &1 end{bmatrix}$ and $small B=egin{bmatrix} -1 & 2&0 \ 1& 3&2 \ 2& 0 &1 end{bmatrix}$ Find the value of $small A^{-1}B$ . Mathematical Calculation
6	If p,q and r are the roots of the equation $2x^{3}+3x^{2}-x-4=0$ , form the equation whose roots are $p^{2}, q^{2} and , r^{2}$ Find the set of real values of x for which $\|3-2x\|<\|4+x\|$ Mathematical Calculation