2012 edexcel higher c paper 1

8/12/2019 2012 Edexcel Higher C Paper 1

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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 must not be used. 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) *+% ,aper 1 ,age 1 - %hurchill aths /imited Turn over

ame %lass

MathematicsPaper 1C (Non-Calculator)

i!her "ier

"ime # 1 hour $% minutes

&or 'de cel C '

+ou must have#

#uler protractor compasses pen pencil eraser.

Total arks


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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 =

bsin B

=c

sin C

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

Area of triangle =1

2 ab sin C

)01) *+% ,aper 1 ,age ) - %hurchill aths /imited

sectioncross

l e n g t h b

h

a

r

l h

r

c B

C

A

b a


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4/21


5/21

- The ta$le gi#es information a$out the eight of some lums*

eight ( w g) >um$er of lums

40 ? w @ .0 1

.0 ? w @ -0 ;

-0 ? w @ ;0 1-

;0 ? w @ ,0 9

,0 ? w @ 90 4

An each art" tic the correct $oB*

(a) The lo est eight coul $e 40 g*

True False


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1 iagram *+!accuratel% ra n

Cen ant 7 Cen ant

The iagram sho s the esigns for t o en ants ma e from a metal sheet*

Cen ant 7 is ma e $% remo#ing , sDuares of si e 1 cm from a rectangle measuring ; cm $% . cm*Cen ant is ma e $% remo#ing 4 triangles from a rectangle measuring - cm $% . cm*

or out the ratio of the area of metal sheet left in esign 7 to the area left in esign *

Ei#e %our ans er in its sim lest form*

,!otal for "uestion 1 is 0 mar's

)01) *+% ,aper 1 ,age 5 - %hurchill aths /imited

1 cm

1 cm

; cm

. cm

1 cm

2 cm

. cm

- cm


7/21

0

1 .

12 miles

-1

2 miles

1

4 mile iagram *+!accuratel% ra n

ill goes to #isit her frien *he al s

1

4 mile to the $us sto *

he then tra#els - 1

2 miles on the $us*

Finall%" she al s 1 .

12 miles to her frien Gs house*

hat fraction of the total istance i she o $% al ing

Ei#e %our ans er in its sim lest form*




8/21

2 Use a ruler and pair of compasses in this question. Leave in your construction lines.

Scale3 )cm represents /4 'm

In the scale ra ing a$o#e" P an Q are air traffic control to ers*ach controls the region of airs ace closer to it than the other to er*

7n aircraft is at the osition la$elle *The aircraft is tra#elling in a straight line*

hen it has tra#elle -0 m from it asses from the control of P to the control of Q*Fin " $% construction" the t o ossi$le ositions it coul then $e in*



P

Q


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5

The iagram sho s a rism of length - cm*

(a) ra a lane of s%mmetr% of the rism on the iagram*,)

($) In the gri $elo " ra a cu$oi ith the same #olume as the rism*,-



- cm


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6 Here are the num$ers of men calling a hel line each a% for three ee s*

32 41 4. .3 4, -2 .9

4; 4- .1 39 42 .- .;

44 40 3- .; 3, -3 .4Here are the num$ers of omen calling the hel line each a% o#er the same erio *

.2 42 .0 3- 49 .0 4,

42 4- 4, 41 3. -1 4.

3; 42 .; .. 4. 42 .3

ra an or ere " $ac Jto $ac stem an leaf iagram sho ing these sets of ata*




11/21

7 (a) ol#ew3

& . = 4

,/

($) B an an sim lif% ( m + 3)( m & ;),/

(c) ol#e 3( x & .) = 11 & 2( x + 3),-

( ) 5a e h the su$ ect of the formula t = 2 h ! ,/




12/21

)4 (a) The nth term of a seDuence is gi#en $% the eB ression 2 n(n & -)*Fin the #alue of the smallest ositi#e term of the seDuence*

,/

($) Here are the first . terms of another seDuence*

11 1. 19 23 2;

Fin an eB ression" in terms of n" for the nth term of this seDuence*,/

,!otal for "uestion )4 is 1 mar's

)) An a game" there are 30 coloure $alls in a $ag*1. of the $alls are orange" 10 are ur le an . are green*

hen it is a la%erGs turn the% ta e one $all at ran om from the $ag an re lace it*The% then ta e a secon $all from the $ag at ran om an re lace it*

Af $oth $alls are the same colour the la%er gets a counter of that colour*The inner of the game is the first la%er to get t o counters of the same colour*

or out the ro$a$ilit% that a la%er gets a counter on their first turn*

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

)01) *+% ,aper 1 ,age 1) - %hurchill aths /imited


13/21

)/ (a) ol#e the ineDualit% - x & ; ? ,,/

( ($)

In the gri " sho the region of oints that satisf% all three of these ineDualities*

y K 0

x ? -

y @ x & 2

La$el the region 6*,1

,!otal for "uestion )/ is 2 mar's


1

2

4

3

.

y

1 2 x &1

&4

&2

&3

&1" 3 4 ;. -


14/21

)- The $oB lot sho s information a$out the mar s stu ents o$taine in a moc eBam*

(a) hat is the interDuartile range of the mar s,)

M

The stu ents all atten e a t oJ a% re#ision course*The% then i a secon moc eBam*

The ta$le summarises their results in the secon moc *

5ar ( m M) >um$er of tu ents

20 ? m @ 30 4

30 ? m @ 40 9

40 ? m @ .0 1;

.0 ? m @ -0 21-0 ? m @ ;0 2.

;0 ? m @ ,0 ,

($) um$er of tu ents

20 ? m @ 30

20 ? m @ 40

20 ? m @ .0

20 ? m @ -0

20 ? m @ ;0

20 ? m @ ,0


5ar (M)20 30 .040 -0 ;0 ,0


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(c) Nse %our ta$le to ra a cumulati#e freDuenc% gra h*,/

The lo est an highest mar s ere 2,M an ;9M res ecti#el%*( ) ra a $oB lot for the secon moc *

,-

O(e)


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)1 This %ear 5att earne 822 000 after taB*

His income as s lit $et een his mortgage" li#ing costs an leisure in the ratio 4 : . : 2

(a) or out ho much 5att s ent per month on his mortgage*

,-

8

5attGs earnings after taB this %ear ere 10M higher than last %ear*

($) or out ho much 5att earne after taB last %ear*,-

8




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)0 (a) Factorise 2 x2 & x & 21,/

($) im lif% full%3 x -

3 &

x 3.

,1




18/21

)2

iagram *+!accuratel% ra n

The iagram sho s a regular heBagon ABC#$% * & is the mi oint of BC *

AB 8 p " A% = #*

(a) B ress %$ in terms of p an #*,)

($) B ress A& in terms of p an #*,/

' is the oint on C# such that A& an %' are arallel*

(c) B ress %' in terms of p an #*,1



#

C

A

$

%

B

&

'

#

p


19/21

)5 The ifference $et een the sDuares of t o consecuti#e o num$ers is a multi le of ,*

For eBam le ; 2 & . . = 24

24 = 3 ,

Cro#e this result alge$raicall%*


)6 y is irectl% ro ortional to x2 an y = 9 hen x = -*

(a) B ress y in terms of x*,-

($) Fin the #alue of y hen x = 10*,)




20/21

)7 iagram *+!accuratel% ra n

B an C are oints on the circumference of a circle" centre A* $ an % are oints on the circumference of a circle" centre # *The straight lines B%( an C($ are tangents to $oth circles an intersect at the oint ( *

(a) Cro#e that angle BAC an angle B($ are eDual*,/

)01) *+% ,aper 1 ,age )0 - %hurchill aths /imited

#

% $

B

A(

C


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($) Cro#e that the line $% eBten e is er en icular to the line BC *,1


!+!A% 9+$ :A:E$ IS )44 MA$;S

2012 edexcel higher c paper 1

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