Number Systems

Topics in this chapter

• Real Number Properties
• Rational and Irrational Numbers
• Decimal Expansions
• Laws of Exponents
• Surds and Rationalisation
• Algebraic Identities and Conjugates
• Comparing and Ordering Numbers

Cheat sheet

Practice questions

1. Question 1Q-663859

   Which of the following is an irrational number?

   1. A.sqrt(4)
   2. B.3.1416
   3. C.1.232323...
   4. D.sqrt(5)
   See the answer and solution
2. Question 2Q-2684D8

   Express $0.36$ (with 36 repeating) in the form $p/q$, where $p$ and $q$ are integers and $q \neq 0$.

   1. A.36/99
   2. B.36/100
   3. C.4/11
   4. D.Both A and C
   See the answer and solution
3. Question 3Q-D0F559

   What is the value of $(3 + \sqrt{3})(3 - \sqrt{3})$?

   1. A.6
   2. B.9
   3. C.12
   4. D.3 - \sqrt{3}
   See the answer and solution
4. Question 4Q-A3292C

   Simplify the expression: $2^{2/3} \cdot 2^{1/5}$.

   1. A.2^{3/8}
   2. B.2^{13/15}
   3. C.4^{2/15}
   4. D.2^{2/15}
   See the answer and solution
5. Question 5Q-BBDAC7

   Rationalize the denominator of $\frac{1}{\sqrt{7} - 2}$.

   1. A.\frac{\sqrt{7} + 2}{3}
   2. B.\frac{\sqrt{7} - 2}{3}
   3. C.\sqrt{7} + 2
   4. D.\frac{\sqrt{7} + 2}{5}
   See the answer and solution