Algebra2 [CIE E math 2017-18 Topic questions]

1	$( 2017/$s$/22/$q$15) $ Make q the subject of $p=2q^2$ [2]
2	$( 2017/$w$/22/$img$/$q$19) $ Make x the subject of the formula. $y=\sqrt{x^2+2}$ [3]
3	$( 2018/$s$/22/$img$/$q$4) $ Complete these statements, (a) When $w=$...., $10w = 10$ [1] (b)When $5x = 15$, $12x =$ .... [1]
4	$( 2018/$w$/22/$img$/$q$20) $ Make m the subject of the formula. $x=\frac{3m}{2-m}$ [4]
5	$( 2017/$s$/23/$img$/$q$4) $ Make a the subject of the formula. $x=y+\sqrt{a}$ [2]
6	$( 2017/$w$/23/$img$/$q$16) $ Make x the subject of the formula. $3m+xy=\frac{xp}{4}$ [4]
7	$( 2018/$s$/23/$img$/$q$11) $ $A=(2\pi+y)x^2$ Rearrange the formula to make x the subject. [2]
8	$( 2018/$w$/23/$img$/$q$11) $ $A=\pi r l+\pi r^2$ Rearrange the formula to make $l$ the subject. [2]
9	$( 2017/$s$/21/$img$/$q$10) $ By shading the unwanted regions of the grid, find and label the region R that satisfies the following four inequalities. $y\leq 2 \;\;\;\;\;\; y \geq 1\;\;\;\;\;\; y \leq 2x - 1 \;\;\;\;\;\; y \leq 5 - x$ [3]
10	$( 2017/$w$/21/$img$/$q$23) $ In one week, Neha spends x hours cooking and y hours cleaning. The time she spends cleaning is at least equal to the time she spends cooking. This can be written as $y \geq x$. She spends no more than 16 hours in total cooking and cleaning. She spends at least 4 hours cooking. (a) Write down two more inequalities in x and/or y to show this information. [2] (b) Complete the diagram to show the three inequalities. Shade the unwanted regions.[3] (c) Neha receives $10 for each hour she spends cooking and $8 for each hour she spends cleaning. Work out the largest amount she could receive.[2]
11	$( 2018/$s$/21/$img$/$q$21) $ There are four inequalities that define the region R. One of these is $y\leqslant x+1.$ Find the other three inequalities. [4]
12	$( 2018/$s$/22/$img$/$q$19) $ Find the two inequalities that define the region on the grid that is not shaded. [3]
13	$( 2018/$w$/22/$img$/$q$14) $ By shading the unwanted regions of the grid, find and label the region $R$ that satisfies the following four inequalities. $$ x\leqslant3\quad x\geqslant2\quad y\leqslant2x+1\quad y\geqslant4-x $$ [3]
14	$( 2017/$s$/23/$img$/$q$11) $ By shading the unwanted regions of the grid above, find and label the region $R$ that satisfies the following four inequalities. $$ x\geqslant0\quad x+y\geqslant7\quad y\geqslant x\quad x+2y\leqslant20 $$ [3]
15	$( 2017/\mathrm{m/42/img/q9a) }$ Bernie buys $x$ packets of seeds and $\gamma$ plants for his garden. He wants to buy more packets of seeds than plants. The inequality $x>y$ shows this information. He also wants to buy   $\begin{array}{l}\\\bullet&\text{less than 10 packets of seeds}\\\bullet&\text{at least 2 plants.}\\\end{array}$  (a) Write down two more inequalities in $x$ or $\gamma$ to show this information. $\cdot[2]$  (b) Each packet of seeds costs Șl and each plant costs $\$3$. The maximum amount Bernie can spend is $\$21$. Write down another inequality in $x$ and $y$ to show this information.[1]  (c) The line $x=y$ is drawn on the grid. Draw three more lines to show your inequalities and shade the unwanted regions. [5] (d) Bernie buys 8 packets of seeds. (i) Find the maximum number of plants he can buy.[1] (ii) Find the total cost of these packets of seeds and plants[1]
16	$( 2018/$m/42/img/q6a$) $ Klaus buys $x$ silver balloons and $y$ gold balloons for a party. He buys $\begin{array}{lll}\bullet&\text{more gold balloons than silver balloons}\\\bullet&\text{at least 15 silver balloons}\\\bullet&\text{less than 50 gold balloons}\\\bullet&\text{a total of no more than 70 balloons}\end{array}$ (a) Write down four inequalities, in terms of $x$ and/or $y$, to show this information.[4] (b) On the grid, show the information from part(a) by drawing four straight lines and shading the unwanted regions. (c) Silver balloons cost $\$2$ and gold balloons cost $\$3$. Calculate the most that Klaus could spend.[2]
17	$( 2018/$s/43/img/q9$) $ (a) Find the equation of the straight line that is perpendicular to the line $y=\frac{1}{2}x+1$ and passes through the point (1,3).[3]  (b) (i) Find the three inequalities that define the region $R.$ [4] (ii) Find the point (x,y), with integer co-ordinates, inside the region $R$ such that $3x+5y=35.$ [2]