Number System Grade IX

 This is a self assessment based on new syllabus

Self Assessment Test 3 (Based on Chapter 1) Time: 1 hour M.M. 25 Note: Q. 1 - 2 carry 1 mark each, Q. 3 - 5 carry 2 marks each, Q. 6-8 carry 3 marks each and Q.9 - 10 carry 4 marks each.

1. Find the product: $(4-\sqrt{7})(4+\sqrt{7})$.

2. Express $0.4\overline{56}$ (recurring decimal) in the form $\frac{p}{q}$, where p and q are integers and $q \neq 0$.

3. Find a point corresponding to $\frac{7}{3} + \sqrt{2}$ on the number line.

4. Rationalise the denominator of $\frac{1}{\sqrt{7}+\sqrt{3}}$ and subtract it from $\sqrt{7}-\sqrt{3}$.

5. Evaluate: (i) $(59049)^{\frac{1}{5}}$ (ii) $\left(\frac{-1}{64}\right)^{-\frac{1}{3}}$

6. Simplify: $10\sqrt{50} + 3\sqrt{98} - 7\sqrt{200} + 2\sqrt{32} + 4\sqrt{12}$.

7. Find two irrational numbers in decimal form between $\sqrt{7}$ and $3$.

8. If $\sqrt{8}=2.828$ and $\sqrt{18}=4.243$, find the value of $\frac{64}{\sqrt{144}-\sqrt{72}}$.

9. If $\frac{(\sqrt{3}-4)}{(\sqrt{3}+4)} - \frac{(\sqrt{3}+4)}{(\sqrt{3}-4)} = e + f\sqrt{3}$, find e and f where e and f are rational numbers.

10. If $z = 8 + 3\sqrt{5}$, find: (i) $\sqrt{z} + \frac{1}{\sqrt{z}}$ (ii) $\sqrt{z} - \frac{1}{\sqrt{z}}$