Topic
Q:
136 Danš chaque cas, représenter sur un axe l'ensemble
réels. \( x \) donné, puis l'écrire sous la forme d'un intervalle.
1. L'ensemble des réels \( x \) supérieurs ou égaux à 3 .
2. L'ensemble des réels \( x \) strictement compris entre -2 et
3. L'ensemble des réels \( x \) strictement inférieurs à 1 .
4. L'ensemble des réels positifs ou nuls et inférieurs à 5 .
Q:
14 Simplify the following operations with surds.
\( \begin{array}{lll}\text { a } 8 \sqrt{7}-\sqrt{7} & \text { b } 2 \sqrt{3}+5 \sqrt{2}-\sqrt{3}+4 \sqrt{2} & \text { c } \sqrt{8} \times \sqrt{8} \\ \text { d } \sqrt{5} \times \sqrt{3} & \text { e } 2 \sqrt{7} \times \sqrt{2} & \text { f } 3 \sqrt{2} \times 5 \sqrt{11} \\ \text { g } \sqrt{42} \div \sqrt{7} & \text { h } 2 \sqrt{75} \div \sqrt{3} & \text { I } \sqrt{50} \div(2 \sqrt{10})\end{array} \)
Q:
9. How many partitions can we make in a set of three?
Q:
Review of Principle of Mathematical Induction and Pigeonhole Principle
11. Prove that for all natural numbers \( n \), the following holds: \( 1+2+3+\ldots+\mathrm{n}=\left[\frac{n(n+1)}{2}\right] \)
12. Prove that for all \( n \geq 1,2^{n}>n \)
13. In a group of 13 people, show that at least two people must share the same birthday
month.
Q:
\( 4 \frac { ( \quad ) } { 7 } = \frac { 25 } { 35 } \)
Q:
(2) \( -11-(-16 \div 4)+3 \)
Q:
Without using mathematical tables, evaluate:
\[ \frac{-7(-5+3)-27 \div 3+7}{3 \times-7+-19 \times-1} \]
Q:
Find the domain of the function in interval notation: \( f(x)=|-5 x| \)
Q:
\( \begin{array}{ll}\text { 16. } w-7 \frac{7}{12}=5 \frac{5}{12} & \text { 17. } 12-m=5 \frac{2}{3} \\ \text { (42) } \\ \begin{array}{ll}\text { 18. } n+2 \frac{3}{4}=5 \frac{1}{4} & \text { 19. }\left(\frac{9}{10}\right)\left(\frac{3}{2}\right)\end{array}\end{array} \)
Q:
Without using mathematical tables, evaluate:
\[ \frac{-7(-5+3)-27 \div 3+7}{3 \times-7+-19 \times-1} \]
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