Pre RMO Algebra problems for practice

Posted by Nalin Pithwa

Question 1:

Find the square root of $49x^{4}+\frac{1051x^{2}}{25} - \frac{14x^{3}}{5} - \frac{6x}{5} + 9$

Question 2:

The surface area of a circular cone is given by $A= {\pi}r^{2}+{\pi}rs$ , where s cm is the slant height, r cm is the radius of the base and $\pi$ is $\frac{22}{7}$ . Find the radius of the base if a cone of surface area 93.5 square cm has a slant height of 5 cm.

Question 3:

Solve:

$\frac{a+x}{a^{2}+ax+x^{2}} +\frac{a-x}{a^{2}-ax+ x^{2}} = \frac{3a}{x(a^{4}+a^{2}x^{2}+x^{4})}$

Question 4:

Subtract $\frac{x+3}{x^{2}+x-12} + \frac{x+4}{x^{2}-x-12}$ and divide the difference by $1 + \frac{2(x^{2}-12)}{x^{2}+7x+12}$

Question 5:

Solve the following for the unknown x:

$\frac{x}{2(x+3)} - \frac{53}{24} = \frac{x^{2}}{x^{2}-9} - \frac{8x-1}{4(x-3)}$

Question 6:

Find the square root of the following:

$a^{6}+ \frac{1}{a^{6}} -6(a^{4}+\frac{1}{a^{4}}) +12(a^{2}+\frac{1}{a^{2}})-20$ ; also, cube the result.

More later,
Nalin Pithwa.

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