MrJacksonMaths Higher Non Calc Paper 1

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Name

For Edexcel

GCSE MathematicsPaper 3A (Non-Calculator)

Higher Tier

Time: 1 hour and 45 minutes

Materials required

Ruler, protractor, compasses,pen, pencil, eraserTracin! paper ma" #e used

Instructions and Information for Candidates

$rite "our name in the #o% at the top o& the pa!eAns'er all the uestions in the spaces proided in this uestion paperThe mar*s &or each uestion and &or each part o& a uestion are sho'n in #rac*etsThe total num#er o& mar*s &or this paper is 1++ There are 4 uestions in this paperCalculators must not be used.

Advice to Candidates

ho' all sta!es in an" calculation$or* steadil" throu!h the paper .o not spend too lon! on one uestion/& "ou cannot ans'er a uestion, leae it and attempt the ne%t oneReturn at the end to those "ou hae le&t out

Written by Shaun Armstrong

Only to be copied for use in the purchaser's school or college

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GCSE Mathematics

0ormulae: i!her Tier

Volume of a rism2 area o& cross section len!th

Volume of shere2

4

3 r3

Volume of cone2

1

3 r

hSurface area of shere2 4r Curved surface area of cone2 rl

In an! triangle A"C The #uadratic Equation

The solutions o& ax bx c2 +'here a +, are !ien #"

x2 bb,4ac

,a

Sine $ulea

sin A2

b

sinB2

c

sin C

Cosine $ule a2 b c bccosA

Area of triangle21

absin C

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sectioncross

len!th

r

l h

r

c B

C

A

b a


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#%

#&

x

CB

A

34

Ans'er A(( T)E*T+ ,-$ questions.

)rite !our ans'ers in the saces rovided.

+ou must 'rite do'n all the stages in !our 'or/ing.

+ou must *-T use a calculator.

%. .ia!ram *-Taccuratel" dra'n

/n the dia!ram,AB2ACand an!leABC2 34

0ind the si7e o& the an!le mar*edx

88888888

0Total 1 mar/s2

&. ole 5p 9 2p 3

p2 88888888

0Total 1 mar/s2

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#1

#3

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1. (a) %press 5; as the product o& its prime &actors

8888888888

0&2

(#) 0ind the i!hest Common 0actor (C0) o& 5; and


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#4

;

4

O

4

;

y

1 1 3 x

4. (a) >n the !rid, dra' the !raph o& y2 x 3

012

(#) ?se "our !raph to sole the euation x 3 2 14

x2 88888888880%2

0Total 3 mar/s2

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#5

5. Tari@s #ic"cle has three !ears

The num#ers o& teeth on the !ears are in the ratio 5 : ; : =

/n total there are 3; teeth on the !ears

(a) $or* out ho' man" teeth are on the middle !ear

88888888012

Tari c"cles 5 *ilometres in + minutes

(#) $or* out his aera!e speed in *ilometres per hour

88888888 *mh0&2

0Total 4 mar/s2

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#6

Mathematical Instruments

+nstrument Set

,-.0 / A1

6.

A set o& mathematical instruments costs B


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+

5

15

1+

+

A!e(da"s)

+ + ;+4+


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#7

#8

N

X

Y

(c) (i) ?se "our !raph to estimate the a!e o& another plant o& the same t"pe 'hen itreached a hei!ht o& 15 cm

88888888da"s

(ii) %plain 'h" it mi!ht not #e sensi#le to use "our !raph to estimate the a!e o&

a plant o& the same t"pe that is 4 cm tall

8888888888888888888888888888888

8888888888888888888888888888888012

0Total 4 mar/s2

8. .ia!ram *-Taccuratel" dra'n

The #earin! o& Y&romXis 115

$or* out the #earin! o&X&rom Y

88888888

0Total & mar/s2

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#%9

#%%

A C

B

%9. $or* out an estimate &or the alue o&91;


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#%&$ei!ht o& potatoes (w*!)

+ +5 151+ + 5 3++

1+

3+

+

4+

0reuenc"

%&. A supermar*et records the 'ei!ht(w*!)o& loose potatoes #ou!ht #" 1++ customersThe results are sho'n in the ta#le

$ei!ht o& potatoes (w*!) 0reuenc"

+5 E w 1+ ;

1+ E w

15 115 E w + 34

+ E w 5 3

5 E w 3+ 1;

(a) $hat percenta!e o& these customers #ou!ht more than 5 *! o& potatoesF

8888888 0%2

(#) >n the !rid, dra' a &reuenc" dia!ram to represent the data in the ta#le

0&2

0Total 1 mar/s2

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#%1

%1. (a) impli&" (a)

888888880%2

(#) impli&"

x5 x,

x3

888888880%2

(c) %pand y(3y )

88888888880%2

(d) ho' that x


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#%3

y

x

A

B

O

y

xO

%3.

The dia!ram sho's a s*etch o& part o& the !raph o& y2 cosx

(a) $rite do'n the coordinates o&

(i) A,

( 88 , 88 )

(ii) B

( 88 , 88 )0&2

(#) >n this cop" o& the dia!ram a#oe, s*etch the !raph o& y2 cos x

0&2

0Total 3 mar/s2

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#%4

#%5

%4. The ta#le sho's some e%pressionsa, b, cand drepresent len!thsand are num#ers 'hich hae no dimensions

ab a

,c,

db3 abc d

d

b4 b(c

d) c3 ab

Tic* () the #o%es underneath the threee%pressions 'hich could represent olumes

0Total 1 mar/s2

%5. P2 r 5r l

Rearran!e the &ormula to ma*e rthe su#Gect

r2 8888888888

0Total 1 mar/s2

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#%6

%6. The a!es o& three sisters arex"ears,x"ears and (3x ) "ears

The total o& the a!es o& the three sisters is 3+ "ears

(a) ho' that x 4x 3 2 +

0&2

(#) 0ind the a!e o& the oldest o& the three sisters

8888888 "ears012

0Total 4 mar/s2

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#%7

#%8

%7. (a) $rite do'n the alue o& 9

1

,

88888888880%2

(#) Rationalise the denominator o&1ne eenin!, Henn" mar*s 1


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#&1

P

R

5 cm

QO

1 cm

&1. .ia!ram *-Taccuratel" dra'n

Pis a point on a circle, centre OThe linePQis the tan!ent to the circle atP

Ris the point on OQsuch that an!le ORP2 9+

(a) Proe that trian!le OPRand trian!le OPQare similar

012

OP2 5 cmPQ2 1 cm

(#) 0ind the e%act len!th o& OR

888888888 cm032

0Total 6 mar/s2

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#&3

x 1

x 1

&3. .ia!ram *-Taccuratel" dra'n

The dia!ram sho's a rectan!le measurin! (x1) cm #" (x 1) cm

The dia!onals o& the rectan!le are each 1+ cm lon!

0ind the area o& the rectan!le

88888888cm

0Total 4 mar/s2

T-TA( ,-$ :A:E$; %99 MA$

MrJacksonMaths Higher Non Calc Paper 1

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Transcript of MrJacksonMaths Higher Non Calc Paper 1