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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