MathamategMathematics Haen ganolradd papur 1Intermediate tier paper 1 P'M Dydd Mercher, 6 Mehefin 20

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Mathemateg Haen Ganolradd Papur 1 Haf 2001 (2 awr)
Mathematics Intermediate Tier Paper 1 Summer
2001 (2 hours)
NI CHEWCH DDEFNYDDIO CYFRIFIANNELL YN Y PAPUR
HWN CALCULATORS ARE NOT TO BE USED FOR THIS PAPER
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1.Edrychwch ar y rhestr ganlynol o rifau. Look
at the following list of numbers. 20, 21,
22, 23, 24, 25, 26, 27, 28. Gan ddefnyddior
rhifau or rhestr yn unig, ysgrifennwch.Using
only the numbers in the list, write down.(a)
rhif ciwb,(a) a cube number,
(b) rhif cysefin,(b) a prime number,
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2. Darganfyddwch werthFind the value of,(a)
34x 2³
(b) 6.7 3.84
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3. Gall Arwyn brynu planhigion ar hambyrddau
(trays) bach syn dal 4 planhigyn yr un ac ar
hambyrddau mawr syn dal 12 planhigyn yr
un. Arwyn can buy plants on small trays each of
which holds 4 plants and on large trays each of
which holds 12 plants. Maen prynu x o hambyrddau
bach. He buys x small trays. (a)Ysgrifennwch,
yn nhermau x, gyfanswm y planhigion ar yr
hambyrddau bach hyn. Write down, in terms of x,
the total number of plants on these small trays.
(b) Maen prynu 6 yn llai o hambyrddau mawr nag o
hambyrddau bach. ysgrifennwch, un nhermau x,
faint o hambyrddau mawr y mae wedi eu prynu.
He buys 6 less of the large trays than the
small trays. Write down, in terms of x, how many
large trays he has bought.
(c) Ysgrifennwch, yn nhermau x, gyfanswm y
planhigion ar y hambyrddau mawr hyn. Write
down, in terms of x, the total number of plants
on these large trays.
(d) Ysgrifennwch, yn nhermau x, gyfanswm yr holl
blanhigion y mae wedi eu prynu. Rhaid i chi
symleiddio eich ateb gymaint ag syn bosibl.
Write down, in terms of x, the total number of
plants he has bought altogether. You must
simplify your answer as far as possible.
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• 4. (a) Ysgrifennwch 74.8612 yn gywir i 3 ffigur
  ystyrlon.
• Write down 74.8612 correct to 3
  significant figures.

(b) Ysgrifennwch 6.0432 yn gywir i 2 ffigur
ystyrlon. Write down 6.0432 correct to
2 significant figures.
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• 5. Ar droellwr siâp sgwâr maer rhifau 0, 1, 2 a
  3 wediu hysgrifennu. Ar droellwr arall, a siâp
  pentagon rheolaidd, maer rhifau 1, 2, 3, 4 a 5
  wediu hysgrifennu.
• A square shaped spinner has the numbers 0 ,1
  ,2 and 3 written on it. Another spinner, in the
  shape of a regular pentagon, has the numbers 1,
  2, 3, 4 and 5 written on it.

Troellwr pentagon Pentagon spinner
0
2
5
Troellwr sgwâr Square spinner
4
1
1
3
3
2
Mewn gêm, mae chwaraewr yn troir ddau droellwr
ac yn lluosir ddau rif a ddangosir ar y
troellwyr i gael y sgôr ar gyfer y gêm. In a
game, a player spins both spinners and multiplies
the two numbers showing on the spinners to get
the score for the game. Er enghraifft, pe
bair rhif ar y troellwr sgwâr yn 3 ar rhif ar y
troellwr pentagon yn 2, byddair chwaraewr yn
cyfrifo 3x26 a byddain sgorio 6. For
example, if the number on the square spinner is 3
and the number on the pentagon spinner is 2, the
player works out 3x26 and the player scores 6.
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• (a) Cwblhewch y tabl canlynol i ddangos pob sgôr
  syn bosibl.
• Complete the following table to show all the
  possible scores.

Troellwr pentagon Pentagon spinner
(b) (i) beth ywr tebygolrwydd y bydd chwaraewr
yn scorio 0? what is the probability that a
player scores 0?
(ii)Beth ywr tebygolrwydd na fydd chwaraewr yn
scorio 0? What is the probability that a
player dose not score 0?
Mae chwaraewr yn ennill gwobr drwy gael sgôr o 2
neu llai. A player wins a prize by getting a
score of 2 or less. (c) Mae Bethan yn chwaraer
gêm unwaith. Beth ywr tebygolrwydd y bydd hin
ennill gwobr? Bethan plays the game
once. What is the probability that she wins a
prize?
Troellwr sgwâr Square spinner
(d)(i) Mae 600 o bobl yn chwaraer gêm unwaith.
Tua faint ohonynt y byddech chin disgwyl iddynt
ennill gwobr? 600 people each play the
game once. Approximately how many would you
expect to win a prize?
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(ii) Maen costio 30c i chwaraer gêm unwaith. Y
wobr am gael sgôr o 2 neu lai yw 50c. Pe bai pob
un or 600 o bobl yn chwaraer gêm unwaith, tua
faint o elw y byddech chin disgwyl ir gêm ei
wneud? It costs 30p to play the game once.
The prize for getting a score of 2 or less is
50p. If 600 people each play the game once,
approximate how much profit do you expect the
game to make?
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• 6. Darganfyddwch yr onglau x ac yn y diagramau
  canlynol.
• Find the angles marked x and y in the
  following.

x
y
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• 7. Lluniwch dri siâp yn debyg ir un isod, fel
  bor patrwm gorffenedig â chymesuredd cylchdro o
  radd 4 o amgylch O.
• Draw three shapes like the given one, so that
  the completed pattern has rotational symmetry of
  order 4 about O.

O
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• 8. Paralelogram yw ABCD. Mae ei groeslinau yn
  croestorri ym mhwynt E.
• ABCD is a parallelogram. Its diagonals
  intersect at the point E.
• CDB31, DEA67 ac and
  ABC125

Darganfyddwch werth Find the value of (a) DBA
(c) EAB
(b) DBC
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• 9. Dwy o orsafoedd gwylwyr y glannau yw Ardir a
  Phorthle. Mae llomg ar gyfeiriant (bearing) o
  165 (D16Dn) o Ardir ac ar gyfeiriant o 228
  (D48Gn) o Borthle. Lluniwch y cyfeiriannau hyn a
  marciwch safler llong.
• Coatville and Portplace are two coastguard
  stations. A ship is on a bearing of 165 (S15E)
  from Coastville and on a bearing of 228 (S48W)
  from Portplace. Draw these bearing and mark the
  position of the ship.

N
N
Tir Land
Ardir Coastville
Porthle Portplace
Môr Sea
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• 10. Ysgrifennwch, yn nhermau n, yr nfed term ym
  mhob un or dilyniannau canlynol.
• Write down, in terms of n, the nth term of
  each of the following sequences.
• (a) 7 14 21
  28

(b) 3 8 13 18
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• 11.

Pris sêl 15 YN LLAI nar pris a farciwyd Sale
price 15 OFF the marked price
240
Cyfrifwch bris y beic yn y sêl. Calculate the
sale price of the bicycle.
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• 12.Mae rheolwraig uwchfarchnad yn bwriadu cynnal
  arolwg oi chwsmeriaid er mwyn darganfod eu barn
  am y newidiadau y mae hi wedi eu gwneud ir
  uwchfarchnad.
• The manageress of a supermarket intends to
  carry out a survey of her customers in order to
  find out their opinion on the alterations she has
  made to the supermarket
• (a) Un or cwestiynau yn ei holiadur oedd
• One of the questions in her questionnaire
  was
• Beth yw eich barn chi am cyfleusterau
  newydd gwell?
• what do you think of the new improved
  facilities?

Da iawn Very good
Da Good.
Cyffredin Average
Gwael Poor
Beth welwch chi oi le ar y cwestiwn hwn? What do
you see wrong with this question?
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• (b)Cwestiwn arall oedd
• Another of her questions was
• Pa mor aml y byddwch yn dod ir uwchfarchnad?
• How often do you come into the supermarket?

Aml Often
Weithiau Occasionally
Aml iawn Very often
(i) Beth welwch chi oi le ar y cwestiwn hwn?
What do you see wrong with this question?
(ii)Ysgrifennwch well fersiwn or cwestiwn.
write a better version of the question.
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• 13. O wybod bod wd(t-1), darganfyddwch werth w
  pam fo t - 8 a d 25. 3
• given that wd(t-1), find the value of w
  when t - 8 and d 25.
• 3

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14. Mynegwch 108 fel lluoswm rhifau cysefin ar
ffurf indecs. express 108 as a product of
prime numbers in index form.
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• 15. Datryswch yr hafaliadau canlynol.
• Solve the following equations.
• (a)7x 6 10 3x

(b) 4(2x - 5) 2x 1
20
x
16.
Ffens Fence
Lawnt Lawn
x
12
x
15
x
Llwybr path
Maer diagram yn cynrychioli lawnt betryal syn
mesur 15 metr wrth 12 metr. Mae llwybr oi
hamgylch. Lled y llwybr yw x metr. Mae ffens yr
holl ffordd o amgylch ymyl allanol y llwybr. The
diagram represents a rectangular lawn measuring
15 metres by 12 metres, surrounded by a path of
width x metres. There is a fence all round the
outside of the path. (a) O wybod mai 74 metr yw
hyd fens, ysgrifennwch hafaliad y mae x yn ei
fodloni. Given that the length of the fence is
74 metres, write down an equation that x
satisfies.
(b) Datryswch yr hafaliad i ddarganfod gwerth
x. Solve the equation to find the value of x.
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• 17. Mae aloin cael ei wneud drwy ddefnyddio copr
  a sinc yn ôl y gymhareb 17 3.
• An alloy is made by using copper and zinc in the
  ratio 17 3.
• Faint o sinc syn cael ei ddefnyddio i wneud 4kg
  or aloi?
• How much zinc is used to make 4kg of the
  alloy?

(b) Dim ond 1.5kg o sinc sydd ar gael, ond mae
digon o gopr. Faint ywr swm mwyaf or aloi y
maen bosibl ei wneud? There is only 1.5kg of
zinc available, but plenty of copper. What is the
greatest amount of the alloy that can be made?
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18. Mae ci wedii glymu wrth rhaff. Hyd y rhaff
yw 4 metr. Ar ben arall y rhaff mae cylch. Gall y
cylch hwn lithro dros roden (rod), AB, sydd
wedii chysylltu â wal frics. Ni all y cylch
lithro oddi ar y rhoden oherwydd stopwyr yn A a
B. A dog is tied to a 4m length of rope, at the
other end of which is a ring. This can slide over
a rod AB, attached to a brick wall. The ring
cannot slide off the rod due to stoppers at A and
B. Gan ddefnyddior raddfa 1 cm yn cynrychioli
1m, lluniwch ar y diagram isod y rhanbarth lle y
gall y ci symud. Using a scale of 1 cm to
represent 1m, draw on the diagram below the
region in which the dog can move.
A
B
Wal frics
Brick wall
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y
19 (a) Lluniwch ddelwedd y triongl A ar ôl
trawsfudiad o 4 uned ir cyfeiriad x a -2 uned
ir cyfeiriad y. Labelwch y ddelwedd B. Draw the
image of the triangle A after a translation of 4
units in the x direction and -2 units in the y
direction. Label the image B.
5
4
3
2
A
1
1
2
3
4
5
-1
-2
-3
-4
-5
x
0
-1
-2
-3
-4
-5
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y
(b) Cylchdrowch y triongl C trwy 90 yn glocwedd
o amgylch y pwynt (-1, -1). Labelwch y ddelwedd
D. Rotate the triangle C through 90 clockwise
about the point (-1, -1). Label the image D.
5
4
3
2
C
1
1
2
3
4
5
-1
-2
-3
-4
-5
x
0
-1
-2
-3
-4
-5
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20 Dangosodd hap-sampl o bobl mewn gwaith y
wybodaeth ganlynol am y math o swydd oedd
ganddynt au rhyw (gender). A random sample of
people at work revealed the following information
regarding their type of job and their gender.

• Defnyddiwch y wybodaeth hon i amcangyfrif y
  tebygolrwydd mai swydd reoli fydd gan unrhyw
  berson mewn gwaith a ddewisir ar hap.
• Use this information to estimate the probability
  that a randomly chosen person at work is in
  management.

(b) Amcangyfrifwch nifer y bobl â swyddi rheoli
mewn gweithlu o 700 000. Estimate the number of
people in management jobs in a workforce of 700
000.
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21. Datryswch yr hafaliadau cydamserol canlynol
drwy dull algebraidd (nid graffigol). Dangoswch
eich holl waith cyfrifo. Solve the following
simultaneous equations by an algebraic (not
graphical) method. Show all your working.
4 x 2 y 17 5 x 3 y 23
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22. Ffactoriwch Factorise (a) 4x²y 6xy²
(b) x² - 4 x - 12
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23. Gwahoddwyd grwp o 120 o wirfoddolwyr i
gwblhau arbrawf. Nodwyd yr amser roedd pob
gwirfoddolwr yn ei gymryd, wedii fesur ir munud
agosaf. Roedd y canlyniadau fel a ddangosir yn y
tabl canlynol. A group of 120 volunteers were
invited to complete an experiment. The time
taken, measured to the nearest minute, by each
volunteer was noted and the results were as shown
in the following table.

• Cwblhewch y tabl amlder cronnus canlynol.
• Complete the following cumulative frequency
  table.

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(b) Ar y papur graff isod, lluniwch ddiagram
amlder cronnus yn dangos y wybodaeth hon. On the
graph paper below, draw a cumulative frequency
diagram to show the information.
120
(c) Defnyddiwch eich diagram amlder cronnus i
ddarganfod yr amrediad rhyngchwartel. Use your
cumulative frequency diagram to find the
interquartile range.
100
80
60
Amlder cronnus Cumulative frequency
40
20
0
10
15
20
25
30
35
40
45
50
Amser a gymerwyd (ir munud agosaf) Time taken
(nearest minute)
(d) Defnyddiwch eich diagram amlder cronnus i
gwblhaur gosodiad canlynol. Use your comulative
frequency diagram to complete the following
statement. Roedd 80 or gwirfoddolwyr wedi
cymryd llai na munud i gwblhaur
arbrawf. 80 of the volunteers took less than
minutes to complete the experiment.
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B
24.
6cm
Nid ywr diagram wedi ei luniadu wrth
raddfa. Diagram not drawn to scale.
A
C
8cm
E
10.8cm
7.2cm
D
Yn y diagram, mae AB yn baralel i DE, ac maer
trionglau ABC a EDC yn gyflun. In the diagram, AB
is parallel to DE, and the triangles ABC and EDC
are similar. AB 6cm, AC 8cm, DE 7.2 cm a
and CD 10.8cm. Gan ddangos eich holl waith
cyfrifo, darganfyddwch hyd Showing all your
working, find the length of (a) CE,
(b) BC
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25. Ym mhob un or fformwlâu canlynol, mae pob
llythyren yn dynodi mesuriad hyd. Trwy ystyried y
dimensiynau a awgrymir gan y fformwlâu,
ysgrifennwch, i bob un, a allair fformiwla ar
gyfer hyd, arwynebedd, cyfaint neu ddim un or
rhain. Maer cyntaf wedii wneud i chi. In each
of the following formulae, every letter stands
for the measurement of a length. By considering
the dimensions implied by the formulae, write
down, for each case, whether the formulae could
be for a length, an area, a volume or none of
these. The first has been done for you.
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26. Ar y papur graff, lluniwch y rhanbarth syn
bodloni pob un or anhafaleddau canlynol On the
graph paper, draw the region, which satisfies all
of the following inequalities
y
x lt 4 y gt -3 2y x lt - 2
4
2
x
2
4
-2
-4
-2
-4
Gwnewch yn siwr eich bod yn dangos yn eglur y
rhanbarth syn cynrychioli eich ateb. Make sure
that you clearly indicate the region that
represents your answer.