The perimeter oftriangle xyz express terms the cosine rule

	IB DIPLOMA PROGRAMME	M06/5/MATME/SP2/ENG/TZ2/XX

Thursday 4 May 2006 (morning)

1 hour 30 minutes

2206-7304 7 pages

– 2 – M06/5/MATME/SP2/ENG/TZ2/XX

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																							5 and g x ( ) = x
(a)	Find the inverse function, f −1.																						[3 marks]
(b)	Given that g			−1	( )		=		x	+	2	, find (				g	−1 o		f	)( )	.		[2 marks]
(c)						f		−1	o	g	)( )		=	x	+		3	, solve (				f	−1		o	g	)( )	=	(	g	−1	o		f		)( )		[2 marks]
(c)						f		−1	o	g	)( )				3		3	, solve (				f	−1			g	)( )		(		−1	o		f		)( )		[2 marks]
		=	g x ( ) ,	x	≠ 2.
(d)	(i)	Sketch the graph of h for − ≤																				x		≤	7	and − ≤							y		≤		8

(f)	(i)				[5 marks]
	(ii)	5∫	h x ( )dx	.	[5 marks]
	On your sketch, shade the region whose area is represented by				[1 mark]
2206-7304					Turn over

(ii) this maximum value of y. [4 marks]

The triangle XYZ has XZ = 6, YZ = ,x XY = z as shown below. The perimeter of

(c)								[2 marks]
(d)	Hence, show that A 2	= −16 2	+	160	x	−	256	[4 marks]
(e)	(i)							[3 marks]
(e)	(ii)							[3 marks]

(a)
(b)	Given that 10 % of the girls are shorter than x cm , find x.
(c)
(c)		<r	, find the value of q and of r.

In the group of fourteen-year-old students, 60 % are girls and 40 % are boys. The probability that a girl is taller than 170 cm was found in part (a).
The probability that a boy is taller than 170 cm is 0.202 .

5.		– 6 –

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(b)						−		−	2	[5 marks]
						6		−	4
						3		−	4
						3		4
	(i)
	(ii)	Calculate AB AD⋅					.


(c)	Calculate the volume of the solid ABCDEFGH.									[2 marks]
(d)
(e)
	→Given that AG		=		2
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