CIE Extended Mathematics(0580) (2017-2018) Algebra 1

 Algebra 1 (2017-2018)

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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]