Upload
russell-jackson
View
215
Download
0
Embed Size (px)
Citation preview
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
1/21
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
EH3A 0 !age " # $hurchill %aths &imited
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
2/21
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
EH3A 0 !age # $hurchill %aths &imited
sectioncross
len!th
r
l h
r
c B
C
A
b a
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
3/21
eae
6lan*
#%
#&
x
CB
A
34
Ans'er A(( T)E*T+ ,-$ 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
EH3A 0 !age 3 # $hurchill %aths &imited
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
4/21
#1
#3
eae
6lan*
1. (a) %press 5; as the product o& its prime &actors
8888888888
0&2
(#) 0ind the i!hest Common 0actor (C0) o& 5; and
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
5/21
eae
6lan*
#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
EH3A 0 !age ) # $hurchill %aths &imited
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
6/21
eae
6lan*
#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
EH3A 0 !age * # $hurchill %aths &imited
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
7/21
eae
6lan*
#6
Mathematical Instruments
+nstrument Set
,-.0 / A1
6.
A set o& mathematical instruments costs B
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
8/21
eae
6lan*
+
5
15
1+
+
A!e(da"s)
+ + ;+4+
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
9/21
eae
6lan*
#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
EH3A 0 !age # $hurchill %aths &imited
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
10/21
eae
6lan*
#%9
#%%
A C
B
%9. $or* out an estimate &or the alue o&91;
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
11/21
eae
6lan*
#%&$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
EH3A 0 !age "" # $hurchill %aths &imited
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
12/21
eae
6lan*
#%1
%1. (a) impli&" (a)
888888880%2
(#) impli&"
x5 x,
x3
888888880%2
(c) %pand y(3y )
88888888880%2
(d) ho' that x
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
13/21
eae
6lan*
#%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
EH3A 0 !age "3 # $hurchill %aths &imited
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
14/21
eae
6lan*
#%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
EH3A 0 !age "( # $hurchill %aths &imited
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
15/21
eae
6lan*
#%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
EH3A 0 !age ") # $hurchill %aths &imited
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
16/21
eae
6lan*
#%7
#%8
%7. (a) $rite do'n the alue o& 9
1
,
88888888880%2
(#) Rationalise the denominator o&1ne eenin!, Henn" mar*s 1
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
20/21
eae
6lan*
#&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
EH3A 0 !age 0 # $hurchill %aths &imited
8/21/2019 MrJacksonMaths Higher Non Calc Paper 1
21/21
eae
6lan*
#&3
x 1
x 1
&3. .ia!ram *-Taccuratel" dra'n
The dia!ram sho's a rectan!le measurin! (x1) cm #" (x 1) cm
The dia!onals o& the rectan!le are each 1+ cm lon!
0ind the area o& the rectan!le
88888888cm
0Total 4 mar/s2
T-TA( ,-$ :A:E$; %99 MA$