2012 Edexcel Higher a Paper 2

8/12/2019 2012 Edexcel Higher a Paper 2

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Instructions and Information Write your name in the box at the top of the page.

Answer all the questions in the spaces provided. The total mark for this paper is 100. The marks for each question are shown in brackets. Calculators may be used. f your calculator does not have a button! take the value of

to be ".1#$ unless the question instructs otherwise. %uestions labelled with an asterisk & *' are ones where the

quality of your written communication will be assessed.

Advice (ead each question carefully before you start to answer it.

)eep an eye on the time. Try to answer every question. *heck your answers if you have time at the end.

Written by +haun Armstrong

,nly to be copied for use in the purchaser-s school or college

$01$ /A aper $ age 1 *hurchill 2aths 3imited Turn over

4ame *lass

MathematicsPaper 2A (Calculator)

Hi her !ier

!ime " # hour $% minutes

&or 'de cel C '

+ou must have"

(uler! protractor! compasses! pen! pencil! eraser! calculator.

Total 2arks


2/19

GCSE Mathematics

Formulae: Higher Tier

You must not write on this formulae page.

Volume of prism = area of cross section length Area of trapezium =1

2 (a + b)h

Volume of sphere = 43 r 3 Volume of cone = 13 r

2hSurface area of sphere = 4 r 2 Curved surface area of cone = rl

In an triangle ABC !he "uadratic E#uation

The solutions of ax 2 + bx + c = 0here a ! 0" are gi#en $%

x = b b2 4 ac

2 a

Sine $ule a

sin A =b

sin B =

csin C

Cosine $ule a 2 = b2 + c2 & 2bc cos A

Area of triangle =1

2 ab sin C

$01$ /A aper $ age $ *hurchill 2aths 3imited

sectioncross

l e n g t h b

h

a

r

l h

r

c B

C

A

b a


3/19

Answer A%% #uestions.

&rite our answers in the spaces provided.

You must write down all stages in our wor'ing.

( 'ight coins eigh 2* g

,or- out the eight of three coins

........... g

)!otal for "uestion ( is * mar's+

* (a) / $ag of otatoes eighs 2 -g

/ ro imatel% ho much oes the $ag eigh in oun s)(+

.......... oun s

($) ,hich of these istances is the largest

centimetres 3 inches 2 millimetres

' lain %our ans er)*+

............

)!otal for "uestion * is , mar's+

$01$ /A aper $ age " *hurchill 2aths 3imited Turn over


4/19

1 32 4

Total cost( C )

O

20

*0

40

0

100 5artin

6a ri

Time at 7o$ ( t hours)

, 5artin an 6a ri are lum$ers

5artin charges a 2 call8out fee an 20 er hour of or-6a ri oesn9t charge a call out fee $ut charges 30 er hour of or-

(a) alculate ho much less 6a ri charges for a 1 hour 7o$ )*+

...........

The total charge ( C ) for a 7o$ ta-ing t hours is sho n on the gra h $elo for each lum$er

The total that 5artin charges is gi#en $% the formula C = 2 20 t

($) ,rite o n a formula for the total that 6a ri charges)(+

............

$01$ /A aper $ age # *hurchill 2aths 3imited


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(c) ,rite o n the #alue of t at the oint here the t o gra hs intersect)(+

t = ...........

( ) ' lain ho %our ans er to art (c) is useful to someone choosing $et een5artin an 6a ri to o a lum$ing 7o$)(+

...................................

...................................

)!otal for "uestion , is - mar's+

/ Fran ants to sa#e u ; $efore she goes on holi a% on the 1< th une

>he starts sa#ing 0 a a% on the 1 st / ril?n 1* th / ril she increases the amount she sa#es each a% to 0?n 12 th 5a% Fran increases the amount again to 1 20

?n 1 th une" after a ing 1 20 for the a%" she counts her sa#ings

Has Fran reache her target>ho ho %ou eci e

............

)!otal for "uestion / is / mar's+



6/19

- @ha- an has an em t% metal $arrel

The $arrel is in the sha e of a c%lin erThe height of the $arrel is 1 2 mThe iameter of the $ase of the $arrel is 0 cm

@ha- an fills the $arrel ith ater from a taThe ta fills the $arrel at the rate of 1 litre er secon

Fin ho long it ta-es to fill the $arrelAi#e %our ans er to the nearest minute

.......... minutes

)!otal for "uestion - is - mar's+

$01$ /A aper $ age 6 *hurchill 2aths 3imited

1 2 m

0 cm


7/19

0 ?n the gri " ra the gra h of y = x2 + 3

)!otal for "uestion 0 is / mar's+


*

;

amaira as-e 10 families in ifferent to ns to recor the ma imum tem erature eacha% in anuar%

>he then or-e out the mean of these ma imum tem eratures>amaira also as-e the families ho much the% s ent on gas in anuar%The scatter gra h sho s her results

(a) ,hat t% e of correlation oes this scatter gra h sho)(+

............

($) @ra a line of $est fit on the scatter gra h)(+

(c) The mean ma imum tem erature in anuar% in Clla ool as 0 4B

' lain h% it might not $e sensi$le to use %our line of $est fit to estimate thecost of the gas use $% a famil% li#ing in Clla ool

)(+

...................................

...................................



9/19

The ta$le $elo summarises the ma imum tem erature for each a% in anuar% here>amaira li#es

5a imumTem erature (B )

Dum$er of a%s

3 3

4 *

10

* ;

; 4

1

( ) 'stimate the cost of gas use $% >amaira9s famil% in anuar%

)/+

...........

)!otal for "uestion 1 is 1 mar's+



10/19

2 (a)

@iagram 34!accuratel% ra n

The sha e in the iagram a$o#e is ma e u of si i entical isosceles triangles

,or- out the #alue of x),+

x = ...........

($)


The iagram sho s four si es of a regular ol%gon/ otte line is ra n $et een t o of the #ertices of the ol%gon

Fin " in terms of y" an e ression for the num$er of si es of the ol%gon),+

............

)!otal for "uestion 2 is 0 mar's+


32B

xB

yB


11/19

5 / film as sho n se#en times o#er one ee-en at a cinema ith 120 seats

The num$er of tic-ets sol for fi#e of the sho ings ere

*< 10* 1 < ;2

The me ian num$er of tic-ets sol as ;The mean num$er of tic-ets sol as 1

,or- out ho man% tic-ets ere sol at the other t o sho ings of the film

............

an ............

)!otal for "uestion 5 is , mar's+

(6 (a) on#ert 0+* to a fraction)(+

............

($) ,rite the reci rocal of 0 as a ecimal)(+

............

(c) ,or- out the ifference $et een1

0 an 10 &3

)*+

............

)!otal for "uestion (6 is / mar's+



12/19

(( Hafi is la%ing artsHe nee s a score of 1< follo e $% a score of 20 to in a game of roun 8the8cloc-

The ro$a$ilit% that he ill score 1< ith his first art is 0 3The ro$a$ilit% that he ill score 20 ith his secon art is 0 4

(a) ,hat is the ro$a$ilit% that he oes not score 1< ith his first art)(+

............

($) ,hat is the ro$a$ilit% that he gets a score of 1< follo e $% a score of 20)*+

............

)!otal for "uestion (( is , mar's+

(* / ne com an% ha sales of 2 000 in total in its first t o %earsThe ratio of sales in its first %ear to its secon %ear as 2 : 3

The com an%9s rofit as *00 in the first %ear an 1200 in the secon %earFin the ratio of the com an%9s rofit as a ercentage of sales in its first %ear to itssecon %ear

Ai#e %our ans er in its sim lest form

............

)!otal for "uestion (* is - mar's+

$01$ /A aper $ age 1$ *hurchill 2aths 3imited


13/19

(, (a) >ol#e

(i) 4 p & ; = 3;)*+

............

(ii) 3(1 & 2 y) = 1 & 4 y),+

............

($) /nna or ers 2 cu s of coffee an 4 cu s of tea>he is charge 11

,hen /nna loo-s at her recei t she sees that she9s $een charge for 4 cu s ofcoffee an 2 cu s of teaThe cost shoul ha#e $een 10 so she is refun e 1

,or- out the cost of a cu of coffee an the cost of a cu of tea)-+

offee ....... Tea .......

)!otal for "uestion (, is (6 mar's+

$01$ /A aper $ age 1" *hurchill 2aths 3imited Turn over


14/19

(/


The iagram sho s a rism on a 38 imensional griThe oint D is the mi oint of BG

(a) Fin the coor inates of the oints

(i) I ")(+

( .. " .. " .. )

(ii) D)*+

( .. " .. " .. )

1 unit on the gri re resents 1 cm

($) ,or- out the #olume of the rism),+

........... cm 3

)!otal for "uestion (/ is 0 mar's+

$01$ /A aper $ age 1# *hurchill 2aths 3imited

y

x

z

O A

( " *" 0) F

E

C

D

B

(0" 0" )

( " *" 4) I H

G


15/19

(- (a) ' ress4

x 3 +

2

x 1

as a single fraction in its sim lest form),+

............

($) >im lif% full%4 x *

4 x2

2012 Edexcel Higher a Paper 2

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