2012 edexcel higher a paper 1

8/12/2019 2012 Edexcel Higher a 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 thequality 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 1 ,age 1 - %hurchill aths /imited Turn over

ame %lass

MathematicsPaper 1A (Non-Calculator)

i!her "ier

"ime # 1 hour $% minutes

&or 'decel C'

+ou must have#

#uler protractor compasses pen pencil eraser.

Total arks


2/20

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=4

3r3 Volume of cone=

1

3r2h

Surface area of sphere= 4r2 Curved surface area of cone= rl

In an triangle ABC !he "uadratic E#uation

The solutions of ax2+ bx+ c= 0here a! 0" are gi#en $%

x=

bb24 ac 2 a

Sine $ulea

sin A=

b

sinB=

c

sin C

Cosine $ule a2= b2+ c2& 2bccos A

Area of triangle=

1

2 absin C

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

sectioncross

length b

h

a

r

l h

r

c B

C

A

b a


3/20

Answer A%% #uestions.

&rite our answers in the spaces provided.

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

( This con#ersion gra'h can $e use to change $eteen egrees fahrenheit (F) anegrees celsius (*)

(a) ,se the gra'h to change 140 F into egrees celsius)(*

----------- *

($) ,se the gra'h to change .0 * into egrees fahrenheit)(*

----------- F

(c) /ater freees at 0 *t hat tem'erature oes ater freee in egrees fahrenheit

)(*

----------- F

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


40 120.0 10

*

&20

0

40

20

0

.0

F


4/20

, (a) im'lif% 2p& q+ 3p+ 4q),*

------------

($) im'lif% m56 m2

)(*

------------

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

+ Holl% is carr%ing out a sur#e% a$out health% eating

This is one of the 7uestions

Ho man% 'ieces of fruit i %ou eat %estera%

Tic8 one $o9

1 to 2 3 to 4 4 or more

(a) /rite on to criticisms of the response sectionfor this 7uestion),*

First criticism -----------------------------

-----------------------------------

econ criticism ----------------------------

-----------------------------------

Holl% carries out her sur#e% $% as8ing her 7uestions of se#eral grou's of 'eo'lefter as8ing each 7uestion" she goes roun the grou' an recors each 'ersons anser

($) ;i#e one reason h% this is nota goo sur#e% metho)(*

-----------------------------------

-----------------------------------

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

)01) *+A ,aper 1 ,age 3 - %hurchill aths /imited


5/20

- ,se a ruler an 'air of com'asses to construct the $isector of this angle


6/20

0 Here are some 'atterns mae ith ots

?attern 1 ?attern 2 ?attern 3

/or8 out ho man% ots there ill $e in ?attern 0

ho ho %ou o$taine %our anser

------------

)!otal for "uestion 0 is - mar's*



7/20

1 The ta$le shos the 'ro$a$ilit% of a 'erson $eing right@hane" left@hane oram$ie9trous

Aight@hane


8/20

3

(a) En the gri" ra the line y= 2x& 3)+*

($) Fin the e7uation of the line that 'asses through the 'oint (4" 0) an is 'arallel tothe line y= 2x& 3

),*

------------

)!otal for "uestion 3 is / mar's*


1

2

4

3

y

1 2 x&1

&4

&2

&3

&1

O 3 4


9/20

(4 T= (n& m)

(a) Fin the #alue of Then m= &3 an n= 4),*

------------

($) Aearrange the formula to ma8e nthe su$Gect),*

------------

)!otal for "uestion (4 is - mar's*

(( >n a game" to 'la%ers ta8e it in turns to roll to orinar% iceThe ice are fair an num$ere from 1 to

>f" on one turn" the num$er on one of the ice is tice the num$er on the other ice" the'la%er recei#es a $onana car

>n one game" each 'la%er ha 42 turns $efore the game ene/or8 out an estimate for the num$er of $onana cars each 'la%er recei#e in the game

------------

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



10/20

(,

Triangle Ais shon on the gri

(a) Translate triangle Ausing the #ector

1


11/20

(+ (a) /rite 3 as a 'rouct of its 'rime factors),*

------------

Hisham an Iarlon are com'aring ho far the% ste' hen al8ingHishams ste' is 3 cm in length" from the heel of one foot to the heel of the other foot

Hisham an Iarlon start al8ing ith their left heels e9actl% in linefter al8ing 3 metres" one of Hishams heels is e9actl% in line ith one of Iarlonsheels

J ($) The length of Iarlons ste' is an e9act num$er of centimetres $eteen 40 an .0

Fin all the 'ossi$le lengths of Iarlons ste')0*

------------

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


3 cm


12/20

(- Kic8% is ma8ing a 'ath using 'a#ing stones>t is mae u' of octagonal an s7uare stones

The octagonal stones are mae from a s7uare $% remo#ing the four cornersThe imensions are shon $elo

The sie of the s7uare stones is such that the% tesselate ith the octagonal stones

Liagram 67!accuratel% ran

(a) /or8 out the area of this section of 'ath


)/*

----------- cm2

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

10 cm

10 cm

20 cm

20 cm


13/20

Kic8% ecies that the ith of the 'ath is to $e three octagonal stoneshe is not sure ho long the 'ath ill $e $ut there ill $e no s7uare stones on theeges

($) Fin an e9'ression" in terms of nfor the num$er of s7uare stones in the 'ath henit has noctagonal stones

ho ho %ou fin %our anser)+*

------------

)!otal for "uestion (- is 2 mar's*



14/20

(/


The 'oints A" B" C" Dan Elie on the circumference of a circle as shonACis 'arallel to ED

(a) (i) /or8 out the sie of angle a)(*

-----------

(ii) ;i#e a reason for %our anser)(*

---------------------------------

---------------------------------

($) /or8 out the sie of angle b)+*

-----------

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


D

C

A

E

a

B120

b


15/20

(0 (a) Factorise a2& a+ .),*

------------

($) ol#e 2y2+ 5y& 2 = (y+ 2)(y+ ))+*

------------

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

(1 Fin the #alue of

(a)4

1

2

)(*

------------

($) 1

2 2

3

),*

------------

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



16/20

(2 Aesients ho li#e on tratton #enue com'lain of cars ri#ing too fast on their roa>n a stu%" the s'ee of 100 cars is recore an the results are shon in this cumulati#efre7uenc% iagram

The s'ee limit on tratton #enue is 30 miles 'er hour

(a) /hat 'ercentage of the cars in the stu% ere $rea8ing the s'ee limit)(*

----------- M

($) ,se the gra'h to estimate the meian s'ee of the cars in the stu%)(*

---------- m'h

(c) ,se the gra'h to estimate the inter7uartile range of the s'ee of the cars in thestu%

),*

---------- m'h

Folloing the stu%" s'ee cameras are 'ut u' on tratton #enue

secon stu% recors the s'ee of 100 cars one month laterThe results are summarise in the ta$le on the ne9t 'age


'ee (miles 'er hour)

0 10 3020 40 0

*umulati#e

fre7uenc%

0

20

0

40

.0

100

0


17/20

'ee (vmiles 'er hour) Fre7uenc%

0 B vC 10 4

10 B vC 20 1

20 B vC 30 3

30 B vC 40 2.

40 B vC 0 1

0 B vC 0 2

J() ,se the ata an the gri $elo to fin out if the s'ee cameras ha#e ha aneffect

*omment on %our finings)0*

-----------------------------------

-----------------------------------

-----------------------------------

)!otal for "uestion (2 is (4 mar's*



18/20

(3

The gra'h of y= f(x) intersects the x@a9is at (." 0) an the y@a9is at (0" )

(a) /rite on the coorinates of the 'oint here each of these gra'hs intersectsthe y@a9is

(i) y= f(x) + 1)(*

(---" ---)

(ii) y= 2f(x))(*

(---" ---)

(iii) y= f(3x))(*

(---" ---)

($) /rite on the coorinates of the 'oint here each of these gra'hs intersectsthe x@a9is

(i) y= f(x+ ))(*

(---" ---)

(ii) y= f(2x))(*

(---" ---)

(iii) y= f(&x))(*

(---" ---)

)!otal for "uestion (3 is 0 mar's*


x

y

(." 0)

(0" )y= f(x)


19/20

,4


n ornament is in the sha'e of a tetraheronach face is an e7uilateral triangle of sie 4 cm

(a) ho that the surface area of the ornament is 13 cm2)/*

larger #ersion of the ornament is similar in sha'e an has sies of length 12 cm

($) Fin the e9act surface area of the larger ornament),*

----------- cm3

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


4 cm


20/20

,(


The iagram shos triangle OCF

OA = a"OC= 3a"OB = 28anOF9 +8

(a) 9'ressCFin terms of aan 8

)(*

------------

;i#en that CD=1

3CFan that CE=

CF"

($) use #ectors to 'ro#e thatADan BEare 'arallel)/*

)!otal for "uestion ,( is 0 mar's*

!7!A% :7$ ;A;E$ IS (44 MA$

2012 edexcel higher a paper 1

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