Inequation (Myanmar Exam Board)

$\newcommand{\inside}[2]{\begin{array}{rcl}\leftarrow-- & \circ\!\frac{\qquad\qquad\qquad\qquad}{}\!\circ & --\rightarrow\\ & #1\qquad\qquad\qquad\qquad #2 & \end{array}}$ $\newcommand{\insideeq}[2]{\begin{array}{rcl}\leftarrow--&\bullet\!\frac{\qquad\qquad\qquad\qquad}{}\!\bullet & --\rightarrow\\& #1\qquad\qquad\qquad\qquad #2&\end{array}}$ $\newcommand{\outside}[2]{\begin{array}{rcl}\leftarrow\!\!\!\frac{\qquad\qquad}{}\!\circ & ---- &\circ\!\frac{\qquad\qquad}{}\!\!\!\rightarrow\\#1& & #2\end{array}}$ $\newcommand{\outsideeq}[2]{\begin{array}{rcl}\leftarrow\!\!\!\frac{\qquad\qquad}{}\!\bullet & ---- &\bullet\!\frac{\qquad\qquad}{}\!\!\!\rightarrow\\#1& & #2\end{array}}$

Group (2015-2019)

1. (2015/Myanmar /q9a)
Use a graphical method to find the solution set of $x^{2} \leq \frac{4}{5}(x+3)$, and illustrate it on the number line. $(5 \mathrm{~m} \mathrm{i} \mathrm{ks})$

2. (2015/FC /q9a)
Find the solution set of the inequation $3 x^{2}<x^{2}-x+3$, by graphical method . and illustrate it on the number line.. $(5$ marks)

3. (2016/Myanmar /q9a)
Find the solution set in $R$ of the inequation $(x-6)^{2}>x$ by graphical method and illustrate it on the number line. (5 marks)

4. (2016/FC /q9a)
Use a sketch graph to obtain the solution set of $\frac{15-4 x}{4} \leq x^{2}$ and illustrate it on the number line. (5 marks)

5. (2017/Myanmar /q9a)
Find the solution set in $R$ of $-7+(2 x+1)^{2} \geq 6 x$ by algebraic method and illustrate it on the number line. (5 marks)

6. (2017/FC /q9a)
Find the solution set of the inequation $12-25 x+12 x^{2} \leq 0$ by graphical method and illustrate it on the number line. $\quad$ (5 marks)

7. (2018/Myanmar /q9a)
Use a graphical method to find the solution set of the inequation $2 x(x-1)<3-x$ and illustrate it on the number line. (5 marks)

8. (2018/FC /q9a)
Find the solution set of the inequation $5 x^{2}<18 x+8$, by graphical method and illustrate it on the number line. (5 marks)

9. (2019/Myanmar /q8a) 
Find the solution set in $\mathrm{R}$ of the inequation $\mathrm{x}^{2}-3 \mathrm{x}+2 \leq 0$ by algebraic method and illastrate it on the number line. $\quad$ (5 marks)

10. (2019/FC /q8a )
Find the solution set in $\mathrm{R}$ of the inequation $\mathrm{x}^{2}-2 \mathrm{x} \leq 0$ by algebraic method and illustrate it on the number line. (5 marks)


Answer (2015-2019)
1.  $\{x|-\frac 65\le x\le 2\}$ 
2.  $\{x|-\frac 32<x<1\}$
3.   $\{x \mid x<4$ or $x>9\}$ 
4.   $\left\{x \mid x \leqslant-\frac{5}{2}\right.$ (or) $\left.x \geqslant \frac{3}{2}\right\}$ 
5.   $\left\{x \mid x \leqslant-1\right.$ or $\left.x \geqslant \frac{3}{2}\right\}$
6.  $\{x|\dfrac{3}{4}\le x\le \dfrac{4}{3}\}$ 
7.   $\left\{x \mid-1<x<\frac{3}{2}\right\}$ 
8.  $\left\{x \mid-\frac{2}{5}<x<4\right\}$
9.  $\{x|1\le x\le 2\}$
10.  {$x|0\le x\le 2$} 

Group (2014)

1. Find the solution set in $R$ of the inequation $3 x^{2}<x^{2}-x+3$ and illustrate it on the number line. (5 marks)

2. Find the solution set of the inequation $x^{2}+6 x \geq 0$ and illustrate it on the number line. (5 marks)

3. Find the solution set in $R$ for the inequation $(x+1)(x+3)<11 x-7$ and illustrate it on the number line. (5 marks)

4. Find the solution set of the inequation $x^{2} \leq \frac{9 x+5}{2}$ by algebraic method and illustrate it on the number line.  (5 marks)

5. Finu the solution set in $R$ for the inequation $(2 x+1)^{2}<4(2 x+1)$ by algebraic method and illustrate it on the number line.  (5 marks)

6. Use a graphical method, to find the solution set of the inequation $x^{2}+5 x-6<0$ and illustrate it on the number line. (5 marks)

7. Use a graphical method to find the solution set of the inequation $2 x^{2}-7 x+3 \geq 0$ and illustrate it on the number line. (5 marks)

8. Find the solution set in $R$ of the inequation $x^{2}>\frac{9 x+5}{2}$ by graphical method and illustrate it on the number line. (5 marks)

9. Use a graphical method to find the solution set of $x^{2} \leq \frac{4}{5}(x+3)$. (5 marks)

10. Find the solution set in $R$ of the inequation $(2 x-3)^{2} \leq 25$ by graphical method and illustrate it on the number line. (5 marks)

11. Find the solution set in $R$ of the inequation $2-x-x^{2}>0$ by graphical method and illustrate it on the number line. (5 marks)

Answer (2014)

1. $\left\{x \mid-\frac{3}{2}<x<1\right\}$
2. $\{x \mid x \leq-6$ or $x \geq 0\}$
3. $\{x \mid 2<x<5\}$,
4. $\left\{x \mid-\frac{1}{2} \leq x \leq 5\right\}$
5. $\left\{x \mid-\frac{1}{2}<x<\frac{3}{2}\right\}$
6. $\{x \mid-6<x<1\}$,
7. $\left\{x \mid x \leq \frac{1}{2}\right.$ or $\left.x \geq 3\right\}$
8. $\left\{x \mid x<-\frac{1}{2}\right.$ or $\left.x>5\right\}$
9. $\left\{x \mid-\frac{6}{5} \leq x \leq 2\right\}$
10. $\{x \mid-1 \leq x \leq 4\}$
11. $\{x |-2<x<1\}$

Group (2013)

1. Find the solution set in $R$ of the inequation $8 x+2 \leq 3 x^{2}-1$. (5 marks)

2. Find the solution set of the inequation 12 $5 x-2 x^{2} \geq 0$ and illustrate it on the number line. (5 marks)

3. Find the solution set of the inequation $x(2 x-3) \leq\left(x^{2}-2\right)$ and illustrate it on the number line. (5 marks)

4. Find the solution set in $R$ of the inequation $(2-x)^{2}-16 \geq 0$ and illustrate it on the number line. (5 marks)

5. Find the solution set of the inequation $(3 x-5)^{2}-2 \frac{1}{4} \geq 0$ and illustrate it on the number line. (5 marks)

6. Find the solution set in $R$ of the inequation $(2 x-1)(x+4)>18$ by graphical method and illustrate it on the number line. (5 marks)

7. Find the solution set in $R$ of the inequation $4(2 x-3)^{2} \geq x^{2}$ and illustrate it on the number line. (5 marks)

8. Find the solution set in $R$ of the inequation $(1+x)(2-x) \geq-10$ and illustrate it on the number line. (5 marks)

9. Find the solution set in $R$ of the inequation $(x+2)^{2} \leq 3(x+8)$ and illustrate it on the number line. (5 marks)

10. Find the solution set of the ineqliation $(x+2)^{2}>2 x+7$ by graphical method. (5 marks)

11. The solution set in $R$ of the inequation $(3 x+1)^{2} \leq 49$ by algebraic method and illustrate it on the number line.  (5 marks)

Answer (2013)

1. $\left\{x \mid x \leq-\frac{1}{3}\right.$ (or) $\left.x \geq 3\right\}$
2. $\left\{x \mid-4 \leq x \leq \frac{3}{2}\right\}$,
3. $\{x \mid 1 \leq x \leq 2\}$,
4. $\{x \mid x \leq-2$ or $x \geq 6\}$,
5. $\left\{x \mid x \leq \frac{7}{6}\right.$ or $\left.x \geq \frac{13}{6}\right\}$,
6. $\left\{x \mid x<-\frac{11}{2}\right.$ or $\left.x>2\right\}$,
7. $\left\{x \mid x \leq \frac{6}{5}\right.$ or $\left.x \geq 2\right\}$
8. $\{x \mid-3 \leq x \leq 4\}$,
9. $\{x \mid-5 \leq x \leq 4\}$,
10. $\{x \mid x<-3$ or $x>1\}$,
11. $\left\{x \mid-\frac{8}{3} \leq x \leq 2\right\}$,


Group (2012)



$\quad\;\,$ $\,$
1.Find the solution set of $(2 x-1)^{2} \geq 9$ and illustrate it on the number line. (5 marks)
2.Find the solution set in $R$ of the inequation $2-3 x \geq 5 x^{2}$ and illustrate it on the number line. (5 marks)
3.Find the solution set of the inequation $12+5 x-2 x^{2}>0$, by graphical method and illustrate it on the number line. (5 marks)
4.Use a graphical method, te find the solution set of the inequation $4 x^{2}-12 x-16>0$ and illustrate it on the rumber line. (5 marks)
5.Find the solution set of the inequation $(2 x+1)(3 x-1) \geq 14$ and illustrate it on the number line. (5 marks)
6.Find the solution set in $R$ of the inequation $(x-2)(5 x-4)+1 \leq 0$ and illustrate it on the number line. (5 marks)
7.Find the solution set in $R$ of the inequation $3 x^{2}-5 x+4>3-x^{2}$ by graphical method and illustrate it on the number line. (5 marks)
8.Find the solution set of the inequation $2+3 x>5 x^{2}$ by graphical method and illustrate it on the number line. (5 marks)
9.Find the solution set of the inequation $8 x-3 \geq 3 x^{2}+2$ by algebraic method and illustrate it on number line. (5 marks)
10.Find the solution set of the inequation $18 x^{2}>45 x-18$ and illustrate it on the number line. (5 marks)
11.Find the solution set of the inequation $\frac{1}{4}(x+1)^{2}>x+4$ and illustrate it on the number line. (5 marks)


Answer (2012)



$\quad$ $\,$
1.$\left\{x \mid x\leq -1 \mbox{ (or) } x\geq 2 \right\}$
$\outsideeq{-1}{2}$
2.$\left\{x \mid-1 \leq x \leq \frac{2}{5}\right\}$
$\insideeq{-1}{\frac 25}$
3.$\left\{x \mid-\frac{3}{2}< x < 4\right\}$
$\inside{-\frac 32}{4}$
4.$\{x \mid x< -1$ (or) $x>4\}$
$\outside{-1}{4}$
5.$\left\{x \mid x \leq-\frac{5}{3}\right.$ or $\left.x \geq \frac{3}{2}\right\} $
$\outsideeq{-\frac 53}{\frac 32}$
6.$\left\{x \mid 1 \leq x \leq \frac{9}{5}\right\}$
$\insideeq{1}{\frac 95}$
7.$\left\{x \mid x< \frac{1}{4}\right.$ (or) $\left.x>1\right\}$
$\outside{\frac 14}{1}$
8.$\left\{x \mid-\frac{2}{5}< x< 1\right\}$
$\inside{-\frac 25}{1}$
9.$\left\{x \mid 1 \leq x \leq \frac{5}{3}\right\}$
$\insideeq{1}{\frac 53}$
10.$\left\{x \mid x< \frac{1}{2}\right.$ (or) $\left.x>2\right\}$
$\outside{\frac 12}{2}$
11.$\{x \mid x< -3$ (or) $x>5\}$
$\outside{-3}{5}$


Group (2011)


$\quad\;\,$$\,$
1.Find the solution set of $2 x^{2}-x-21>0$ and illustrate it on the number line. $\mbox{ (5 marks)}$

2.Find the solution set in $R$ of the inequation $2 x^{2}<7 x+4$ and illustrate it on the number line. $\mbox{ (5 marks)}$

3.Find the solution set in $R$ of the inequation $(4-7 x)(7-4 x) \leq 0$ and illustrate it on the number line. $\mbox{ (5 marks)}$

4.Find the solution set of the inequation $x^{2}>9$. $\mbox{ (5 marks)}$

5.Find the solution set in $R$ for the inequation $(x+1)^{2}>1$. $\mbox{ (5 marks)}$

6.Find the solution set of the inequation $(2 x+3)(x+2)>0$. $\mbox{ (5 marks)}$

7.Find the solution set of the inequation $(3-4 x)(4-3 x) \geq 0$ by algebraic method and illustrate it on the number line. $\mbox{ (5 marks)}$

8.Find the solution set in $R$ of the inequation $(3-8 x)(5-4 x) \leq 0$ by algebraic method and illustrate it on the number line. $\mbox{ (5 marks)}$

9.Find the solution set of the inequation $3 x^{2}< x^{2}-x+3$, by graphical method. $\mbox{ (5 marks)}$

10.Find the solution set of the inequation $12+x-x^{2} \geq 0$, by graphical method. $\mbox{ (5 marks)}$

11.Use graphical method to find the solution set of $(x+2)^{2}>2 x+7$. $\mbox{ (5 marks)}$



Answer (2011)


$\quad\;\,$$\,$
1. $\left\{x \mid x< -3\right.$ (or) $\left.x>\frac{7}{2}\right\}$
$\outside{-3}{\frac 72}$
2.$\left\{x \mid-\frac{1}{2}< x< 4\right\}$
$\inside{-\frac 12}{4}$
3.$\left\{x \mid \frac{4}{7} \leq x \leq \frac{7}{4}\right\}$
$\insideeq{\frac 47}{\frac 74}$
4.$\{x \mid x< -3$ (or) $x>3\}$
$\outside{-3}{3}$
5.$\{x \mid x< -2$ (or) $x>0\}$
$\outside{-2}{0}$
6.$\left\{x \mid x< -2\right.$ (or) $\left.x>-\frac{3}{2}\right\}$
$\outside{-2}{\frac 32}$
7.$\left\{x \mid x \leq \frac{3}{4}\right.$ (or) $\left.x \geq \frac{4}{3}\right\}$
$\outsideeq{\frac 34}{\frac 43}$
8.$\left\{x \mid \frac{3}{8} \leq x \leq \frac{5}{4}\right\}$
$\insideeq{\frac 38}{\frac 54}$
9.$\left\{x \mid-\frac{3}{2}< x< 1\right\}$
$\inside{-\frac 32}{1}$
10.$\{x \mid-3 \leq x \leq 4\}$
$\inside{-3}{4}$
11.$\{x \mid x< -3$ (or) $x> 1 \}$
$\outside{-3}{1}$


Group (2010)


$\quad\;\,$$\,$
1.Find the solution set in $R$ for the inequation $x^{2}+5 x>6$. $\text{ (5 marks)}$

2.Find the solution set in $R$ for which $x^{2} \geq \frac{4}{3}(x+5)$. $\text{ (5 marks)}$

3.Find the solution set of an inequation $2 x(2-x) \leq 3(x-2)$, and illustrate it on the number line. $\text{ (5 marks)}$

4.Find the solution set in $R$ for which $(x+2)^{2}>2 x+7$. $\text{ (5 marks)}$

5.Find the solution set of the inequation $(2+x)(3-2 x) \leq 2 x+1$. $\text{ (5 marks)}$

6.Find the solution set in $R$ for the inequation $x^{2}+2 x>24$ and illustrate it on number line. $\text{ (5 marks)}$

7.Find the solution set in $R$ for the inequation $12 x^{2} \geq 10-7 x$. Illustrate it on the number line. $\text{ (5 marks)}$

8.Find the solution set in $R$ of the inequation $(x+2)^{2} \leq 3(x+8)$ and illustrate it on the number line. $\text{ (5 marks)}$

9.Use the graphical method to find the solution set of the inequation $x^{2}-5 x+6>0$. $\text{ (5 marks)}$

10.Use the graphical method to find the solution set of the inequation $x^{2}-7 x+10< 0$. $\text{ (5 marks)}$

11.Find the solution set of the inequation $8 x+3< 3 x^{2}$ by algebraic method and illustrate it on the number line. $\text{ (5 marks)}$



Answer (2010)


$\quad\;\,$
1.$\{x \mid x< -6$ (or) $x>1\}$
$\outside{-6}{1}$
2.$\left\{x \mid x \leq-2\right.$ (or) $\left.x \geq \frac{10}{3}\right\}$
$\outsideeq{-2}{\frac{10}{3}}$
3.$\left\{x\mid x\leq-\frac{3}{2}\right.$ (or) $\left.x \geq 2\right\}$
$\outsideeq{-\frac 32}{2}$
4.$\{x \mid x< -3$ (or) $x>1\}$
$\outside{-3}{1}$
5.$\left\{x \mid x \leq-\frac{5}{2}\right.$ (or) $\left.x \geq 1\right\}$
$\outsideeq{-\frac 52}{1}$
6.$\{x \mid x< -6$ (or) $x>4\}$
$\outside{-6}{4}$
7.$\left\{x \mid x \leq-\frac{5}{4}\right.$ (or) $\left.x \geq \frac{2}{3}\right\}$
$\outsideeq{-\frac 54}{\frac 23}$
8.$\{x \mid-5 \leq x \leq 4\}$
$\insideeq{-5}{4}$
9.$\{x \mid x< 2$ (or) $x>3\}$
$\outside{2}{3}$
10.$\{x \mid 2< x< 5\} $
$\inside{2}{5}$
11.$\left\{x \mid x< -\frac{1}{3}\right.$ (or) $\left.x>3\right\}$
$\outside{-\frac 13}{3}$

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