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1. Solve
(a) 042232 =+ xx
x=............. or ..............(4)
(b)x2 10x=0
x=............. or ..............(4)
(c) 0352 2 = xx
x=............. or ..............(5)
2. Solve the equation 5x 2 2x 4 = 0
Give your answers correct to 3 significant figures.
x=....................... or ................ (6)
3.(a)Solve the inequalityx2! " # 11
a
acbb
x 2
42
=
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...............................(2)
(a)Solve the inequality 2x25x 3 # 0
...............................(2)
4. $he %iagra& shows a sha'e.ABis an arc of a circle( centre O.
)ngleAOB= *0+.
Given that the area of the sha'e is ,0 c&2calculate its ra%ius.
Give your answers correct to 3 significant figures.
r= ............................. c&(Total 4 marks)
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5. /alculate the area an% the 'eri&eter of the following sha'es.
a
A= ............................ c&2
P= ............................. c&(5)
A= ............................ c&2
P= ............................. c&( 5)
(Total 10 marks)
,. in% the 'eri&eter an% area of the sha%e% area.
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10 cm
6 cm
4cm
4cm
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P= ............................. c&
A= ............................ c&2
(Total 6 marks)
". $he %iagra& shows a soli% cone.
$he ra%ius of its ase is 3." c& an% the slant height is .3 c&.
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a /alculate the total surface area of the cone.
Give your answer correct to 3 significant figures.
.................................. c&2
(3)
/alculate the volu&e of the cone.Give your answer correct to 3 significant figures.
.................................. c&3
(3)
(Total 6 marks)
2. $he %iagra& shows a 'ris&.
$he cross section of the 'ris& is a rigth angle% triangle.$he lengths of the si%es of the triangle are 3 c&( 4 c& an% 5 c&.
$he length of the 'ris& is " c&.
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a or out the volu&e of the 'ris&.
.................................. c&3
(3)
or out the total surface area of the 'ris&.
.................................. c&2
(3)
(Total 6 marks)
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1". ) cylin%irical tan has a ra%ius of 30 c& an% a height of 45 c&. $he tan contains water to a %e'th of 3, c&.
) &etal s'here is %ro''e% into the water an% is co&'letely covere%. $he water level rises y 5 c&.
/alculate the ra%ius of the s'here.
....................................c&
(Total 6 marks)
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5. or out the area of this sha'e.
c&6(Total 4 marks)
. $he cuoi% shown in the %iagra& hasEF = 4 c&(FG = , c& an%AE = 3 c&.
a/alculate
ithe volu&e of the cuoi%(
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c&
5 c&
4 c&
7iagra& NOTaccurately %rawn
c&
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c&3(2)
iithe surface area of the cuoi%.
c&2(3)
$he cuoi% is %ivi%e% into two equal triangular 'ris&s. 8ne of the& is shown in
the %iagra&.
rite %own the volu&e of the triangular 'ris&.
c&3(1)
9. $he %iagra&s show so&e soli% sha'es an% their nets. )n arrow has een %rawn fro& one soli% sha'e to its net.
7raw an arrow fro& each of the other soli% sha'es to its net.
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(Total 4 marks)
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12. (a) /o&'lete the tale of values fory=x2 ,x! 10
x 0 1 2 3 4 5 ,
y 10
(3)
(b) 8n the gri% %raw the gra'h ofy=x2 ,x! 10
(3)
(c)9se your gra'h to solve the equation x2 ,x! 5 = 0
..............................(3)
(d)rite %own the coor%inates of the &ini&u& 'oint.
..............................(2)
(e)rite %own the equation of the line of sy&&etry.
..............................(2)
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y
x
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7iagra& NOT
accurately %rawnx 5
x! ,
$he %iagra& shows a tra'e:iu&.$he lengths of three of the si%es of the tra'e:iu& arex 5(x! 2 an%x! ,.
)ll &easure&ents are given in centi&etres.
$he area of the tra'e:iu& is 3, c&2.
a Show thatx2x 5, = 0
(4)
i Solve the equationx2x 5, = 0
ii ;ence fin% the length of the shortest si%e of the tra'e:iu&.
c&(4)
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9Art 2ndFinal 2009-10
16.
$he two cylin%ers are &athe&atically si&ilar.
a oth cylin%ers are &a%e of the sa&e &aterial. $he ig one weighs 120g. ;ow &uch %oesthe s&all one weights
(3)
2
30 cmBA 20 cm
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9Art 2ndFinal 2009-10
3