2$( 2017/s/21/img/q22) $

Write as a single fraction in its simplest form.
(a) $\frac{x^2-3x}{x^2-9}$....[3]

(b) $\frac {3}{x-4}+\frac {2}{2x+5}$.....[3]
2$( 2018/s/21/img/q4$)

Find the value of $7x+3y$ when $x=12 \quad and \quad y=-6$.....[2]


3$( 2017/$m/22/img/q5$) $

Write the recurring decimal $0.1 \dot{7}$ as a fraction.
Show all your working......[2]

4$( 2017/s/22/img/q7) $

Find the value of $5a-3b$ when $a=7 \quad and \quad b=-2$......[2]


5$( 2017/$s/21/img/q6$) $

(a) $2^r=\frac {1}{16}$
Find the value of $r$......[1]
(b)$3^t=\sqrt[5]3$
Find the value of $t$......[1]
6$( 2018/$s/21/img/q9$) $

$3^{-q} \times \frac {1}{27}=81$
Find the value of $q$......[2]

7$( 2018/$w/21/img/q18$) $

Solve the simultaneous equations.
You must show all your working..........[4]

$2x+3y=-12$
$5x+2y=14$
8$( 2017/$s/22/img/q10$) $

solve....[2]
$2-x=x+1$

9$( 2017/$w/22/img/q18$) $

Solve the simultaneous equations.
You must show all your working......[3]

$y=\frac x2$

$2x-y=1$

10$( 2017/$w/22/img/q24$) $

Solve the equation.

(a)$7-3n=11n+2$.....[2]

(b)$\frac{p-3}{5}=3.....[2]$

11$( 2018/$m/22/img/q9$) $
$\begin{array}{c}{2^{p}=\frac{1}{8^{4}}}\end{array}$
 Find the value of $p.$
 $p=..................[2]$

12$(2018/\mathfrak{m}/22/\mathfrak{img}/\mathfrak{q}13)$
Solve the simultaneous equations. You must show all your working. $$2x+\frac{1}{2}y=13$$ $$3x+2y=17$$ $x=\dots\dots\dots\dots\dots$ $y=\dots\dots\dots$ .......[3]

13$( 2017/$w$/23/$img$/$q$6) $
$${\sqrt[3]{10}})^{2}=10^{p}$$
 Find the value of $p.$
 $p=...........................[1]$

14$( 2017/$w/23/img/q14$) $
Solve by factorising. $$ 3x^{2}-7x-20=0 $$ $x=..........$ or $x= ...........[3]$

15$( 2018/$s/23/img/q9$) $
Solve. $$ \frac{1-p}{3}=4 $$ $p=........................[2]$

16$( 2018/$w/23/img/q10$) $
Solve. $$3w-7=32$$  $w=............[2]$

17$( 2017/$w/41/img/q3$) $
(a) Solve. $$11x+15=3x-7$$ $x=...................[2]$

 $\mathbf{( b) }( i) \quad $Factorise.$$\quad x^2+ 9x- 22$$  ..... [2]
 $( \mathbf{ii}) \quad $Solve. $$x^{2}+9x-22=0$$  $x=...............$ or $x=...............[1]$

 (c) Rearrange $y=\frac{2(x-a)}{x}$ to make x the subject.
 $x=........................[4]$

 $( \mathbf{d} ) \quad $Simplify.$$\quad \frac {x^2- 6x}{x^2- 36}$$ $x=........................[3]$

18$( 2018/\mathrm{w/42/img/q2a) }$
$(\mathbf{a})$ Solve $$30+2x=3(3-4x).$$
 $x=..................[3]$

 (b) Factorise $$12ab^3+18a^3b^2.$$ 

(c) Simplify.
 $(\mathbf{i})\quad5a^3c^2\times2a^2c^7$ .........[2]
(ii)$\quad \left ( \frac {16a^8}{c^{12}}\right ) ^{\frac 34}$..........[2]

 (d) $y$ is inversely proportional to the square of $(x+2)$
 When $x=3,y=2.$ Find $y$ when $x=8.$
 $y=...............[3]$

 (e) Write as a single fraction in its simplest form.$\ldots\ldots[3]$ $$ \frac5{x-2}-\frac{x-5}2 $$ 

19$( 2017/$s/43/img/q7$) $
(a) Solve the simultaneous equations. You must show all your working.
 $\begin{array}{l}2x+3y=11\\3x-5y=-50\end{array}$
 $x=.................$ $y=...............[4]$

 $(\mathbf{b})\quad x^2-12x+a=(x+b)^2$ Find the value of $\alpha$ and the value of $b.$

 $a=\ldots$ $b=\ldots$ [3]

 (c) Write as a single fraction in its simplest form......[4]  $$ \frac x{2x-5}\:+\:\frac{3x+2}{x-1} $$ 

20$( 2017/$s$/21/$img$/$q$5) $
Factorise completely. $$12n^2-4mn$$    $\cdot\cdot\cdot\cdot\cdot\cdot$[2]


Answer Key

1.(a) \( \frac{x}{x+3} \)     (b) \( \frac{8 x+7}{(x-4)(2 x+5)} \)
2. \( 7.36 \times 10^{7} \)
3. 150
4. 41
5. (a) -4 (b) \( \frac{1}{5} \)
6. 896
7. \( [x-] 6,[y-]-8 \)
8. \( \frac{1}{6} \)
9. \( x-\frac{2}{3}, y-\frac{1}{3} \)
10. (a) \( \frac{5}{14} \) (b) 18

11. -12
12. \( x-7, y--2 \)
13. \( 2 / 3 \)
14. \( 4,-\frac{5}{3} \)
15. 11
16. 13
17. (a) \( -2 \cdot 75 \) (b)(i) \( (x+11)(x-2)(b)(i i)-11 \) and 2 (c) \( x-\frac{2 a}{2-y} \)
18. (a) -1.5 (b) \( 6 a b^{2}\left(2 b+3 a^{2}\right) \) (c)(i) \( 10 a^{5} c^{9} \) 
(ii)\( \frac{8 a^{6}}{c^{9}} \) (d) 0.5 (e) \( \frac{7 x-x^{2}}{2(x-2)} \)
19. (c) \( \frac{7 x^{2}-12 x-10}{(2 x-5)(x-1)} \)
20. \( 4 n(3 n-m) \)
21. \( 3 x(4 x+5 y-3) \)
22. (a) \( 5 c(3 c-1) \) (b) \( (2 p-m)(k+3) \)
23. \( 7(2 x-3 y) \)