Quiz: Algebraic Expressions and Equations Practice Questions (set 1)

This quiz contains questions designed to test your understanding of the fundamentals of algebraic expressions and equations. These questions focus on basic mathematical operations involving logarithms, square roots, and the simplification of expressions. Please refrain from using external resources to assist in solving the questions. If your answers are incorrect, you can retake the quiz and aim to get them all correct. If you notice any errors in the questions or answers, please leave a comment. Enjoy the quiz!

1. 
Simplify: $(\sqrt{6} + \sqrt{2})^2 + (\sqrt{6} - \sqrt{2})^2$

2. 
Solve for $x$: $\sqrt{x+5} - \sqrt{x-3} = 2$

3. 
Evaluate: $log_2(8) + log_2(16) - log_2(4)$

4. 
Simplify: $(\sqrt{a} + \sqrt{b})^2 - (\sqrt{a} - \sqrt{b})^2$

5. 
Simplify: $\frac{\sqrt{18} + \sqrt{50}}{\sqrt{2}}$

6. 
Evaluate: $log_5(25) - 2log_5(5) + log_5(1)$

7. 
Solve for $x$: $log_4(x+3) + log_4(x-1) = 2$

8. 
Find $a^2 + b^2$ if $a = \sqrt{7} + \sqrt{3}$ and $b = \sqrt{7} - \sqrt{3}$

9. 
Solve for $x$: $log_2(x^2 - 4) = 3$

10. 
Simplify: $\frac{5 + \sqrt{3}}{5 - \sqrt{3}} + \frac{5 - \sqrt{3}}{5 + \sqrt{3}}$

11. 
Solve for $x$: $\sqrt{(x - 3)^2} = 5$

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