Question

QUESTION 1 1.1 Simplify without using the calculator: 1.1.1 $ \frac{7^{2 x+1}-7^{2 x-1}}{7^{2 x-1}} $ 1.1.2 $ 2^{-3}+\frac{1}{4} \div \frac{2}{7} $ 1.1.3 $ \log _{5} 16+\log _{5} 4-\log _{5} 32-\log _{5} 2 $ 1.2 Prove that $ p-q $ is not a factor of: \[ f(p)=p^{3}+(q+3) p^{2}-p(3 q+3)+3 q \] 1.3 Fully factorise in prime factors: 1.3.1 $ m^{36}-16 n^{4} $ 1.3.2 $ 25 x^{2}-(10 x+2)^{2} $ 1.3.3 $ 24 b x-8 d x-6 b y+2 d y $ 1.4 Simplify the following fractions: 1.4.1 \[ \frac{\frac{1}{\sqrt{x}}+\frac{2}{\sqrt{x}}}{\frac{7}{\sqrt{x}}-\frac{3}{\sqrt{x}}} \] 1.4.2 \[ \frac{2 x}{x^{2}-16}+\frac{1}{4-x} \]

          QUESTION 1
1.1 Simplify without using the calculator:
1.1.1 \( \frac{7^{2 x+1}-7^{2 x-1}}{7^{2 x-1}} \)
1.1.2 \( 2^{-3}+\frac{1}{4} \div \frac{2}{7} \)
1.1.3 \( \log _{5} 16+\log _{5} 4-\log _{5} 32-\log _{5} 2 \)
1.2 Prove that \( p-q \) is not a factor of:
\[
f(p)=p^{3}+(q+3) p^{2}-p(3 q+3)+3 q
\]
1.3 Fully factorise in prime factors:
1.3.1 \( m^{36}-16 n^{4} \)
1.3.2 \( 25 x^{2}-(10 x+2)^{2} \)
1.3.3 \( 24 b x-8 d x-6 b y+2 d y \)
1.4 Simplify the following fractions:
1.4.1
\[
\frac{\frac{1}{\sqrt{x}}+\frac{2}{\sqrt{x}}}{\frac{7}{\sqrt{x}}-\frac{3}{\sqrt{x}}}
\]
1.4.2
\[
\frac{2 x}{x^{2}-16}+\frac{1}{4-x}
\]

$QUESTION 1 1.1 Simplify without using the calculator: 1.1.1 (7^2 x+1-7^2 x-1)/(7^2 x-1) 1.1.2 2^-3+(1)/(4)÷(2)/(7) 1.1.3 log5 16+log5 4-log5 32-log5 2 1.2 Prove that p-q is not a factor of: f(p)=p^3+(q+3) p^2-p(3 q+3)+3 q 1.3 Fully factorise in prime factors: 1.3.1 m^36-16 n^4 1.3.2 25 x^2-(10 x+2)^2 1.3.3 24 b x-8 d x-6 b y+2 d y 1.4 Simplify the following fractions: 1.4.1 ((1)/(√(x))+(2)/(√(x)))/((7)/(√(x))-(3)/(√(x))) 1.4.2 (2 x)/(x^2-16)+(1)/(4-x)$

Added by Barbara B.

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