CAIE FP2 (Further Pure Mathematics 2) 2014 June

1 Tmall mt ad a ual ad ad a ma ad ctly Ty a mg a tagt \(l\) tam dc \(\quad t\) a mt tal tabl \(T d\) ad td - clld dctly \(t\) T cct ttut
bt t -

1. tat t d at t cll $$\begin{array} { c c } \pi & \theta
   \hline \pi & \theta \end{array}$$
2. G tat \(t\) magtud \(t\) mul xcd by dug \(t\) cll - \(d t\) alu

2 Aatcl ma kgmaacaccltct adadu mt At tm tatcl at tt At tm cd agl tat tadal cmt \(t\) acclat at tm cd a magtud \(\quad \pi \quad \theta m\) Fd

1. talu ta cmt t acclat t ual t
2. \(t\) magtud \(t\) ultat \(c\) actg

3 A atcl attacd \(t d\) a lgt xtbl tg lgt \(\quad T t d\) t tg attacd t a xd t t atcl agg ulbum t \(t\) tg tcal \(t\) ga tal mul magtud t tg mak a agl t t dad tcal at \(\quad\) t \(t\)

1. tat - \(\pi \quad c \quad \theta\)
2. It g tat \(\quad { } _ { \pi } ^ { \alpha } \quad \theta \quad\) a t ctat Jut \(\quad\) yg yu a dcb tmt ac tllg ca
   (a)
   (b)

4
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5
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6 Emly at a atcula cmay a \(b\) ty \(t\) duc abc \(t\) cmay dcd \(t t\)
\(t u\) ac day at ay tm bt am ad m F a adm aml mly
\(t u m b u a b c t y a b\)
a \(g\) t llg tabl
\(k g u a c\) daym am \(t m T\)
duc xtm ad all mly \(t k\)
ad \(t\) ya at \(t\) tduct xtm a ad aml tt t tt at t gcac ll t t ulat ma umb
\(u\) abc a dcad ll g t tduct xtm

7 Jam t a dcu atdly
a attmt \(t\) ac a uccul \(t A t\) cutd a
uccul \(t\) dtac acd mt \(F\) ac \(t\) t bablty tat Jam
uccul - ddtly all \(t\) t Fd t bablty tat Jam tak

1. xactly \(t\) tact \(t\) uccul \(t\)
2. \(m\) ta \(t\) tac \(t\) tuccul \(t\) I \(d t\) ualy a cmtt a dcut mut \(t\) mt \(t\) at mt \(x\)
   attmt a uccul \(t\) acd ut \(t\) a tak Fd t bablty tat
   Jam ual t cmtt Cl at dcut Fact \(\quad t\) bablty tat ll ac a \(t\)
   mt - ddtly all t t Fd t bablty tat xactly Jam ad
   Cl ual t cmtt

8 A adm aml tak \(m\) t adult ul d ty ca Tult a
at a tad clad by aggu ad
\(g\) t llg tabl Tt at t gcac ll \(t\)
d ty ca d
dt aggu

9 T ctuu adm aabl
a dtbut uct \(F g\) by
Z
\(F \pi \theta\) Fd talu
c \(P\)
\(\pi\)
\(\theta\) T adm aabl dd by \(l \quad\) Fd t dtbut uct
Fd t bablty dty uct
ad ktc t ga Aumg tat lgt a mally dtbutd

1. tt at \(t\) gcac ll \(t\) t ulat ma lgt \(t c\) gat ta cm
2. calculat a cdc tal \(t\) ulat ma lgt \(t c\) EITHE

   A atcl			gt latc tg atual lgt	\multirow{4}{*}{}
   T atcl		\(t\) ad ac \(t\) gatt \(g t\)	\multirow{4}{*}{}
   t lgt t tg
   (i) tat \(t\) mdulu latcty \(t\) tg	-
   (ii) tat \(m m l\) amc mt abut \(t\) ulbum \(t\) ad tat \(t\) d t mt
   (iii)		\(t\) ual t al t maxmum alu
   O
   \(F\) a adm aml \(b\) ad t uat \(t g l\)	at a alu	θt uat \(t g l\)
   ad
   ctly aml	a ctat \(T\) duct mmt \(c\)		lat cct \(t\)
   (i) Tt at \(t\) gcac ll \(t\) t dc \(t\) clat bt \(t\) aabl
   (ii)	d talu
   (iii)	alu taml data d t alu			ad ktc \(t\)
   \(F\) ac \(t\) a alu	\(\pi\)		cdd
   (iv)	t uat \(\operatorname { tg } l\)	utyg yu a	ad d talu \(t\)

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