Mathemateg

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Mathemateg Haen Ganolradd Papur 2 Haf 2001 (2 awr)
Mathematics Intermediate Tier Paper 2 Summer
2001 (2 hours)
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1.Ysgrifennwch ddau derm nesaf y dilyniant
canlynol. Write down the next two terms of the
following sequence. 21, 19,
15, 9, ,

2 (a) Symleiddiwch 3x-2y-x 5y
Simplify
3
(b) Expand 5(x-2) Ehangwch 5(x-2)
(c) Darganfyddwch werth 4c-3d pan fo c-2 a d6
Find the value of 4c-3d when c-2 and d6
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3. Gofynnwyd i bumdeg o bobl faint o anifeiliaid
anwes oedd ganddynt. Roedd y canlyniadau fel a
ganlyn. Fifty people were asked how many pets
they owned. The results were as follows.

• Beth ywr tebygolrwydd bod gan berson a ddewisir
  ar hap or grwp hwn 3 anifail anwes yn union?
• What is the probability that a randomly chosen
  person from this group has exactly 3 pets?

(b) Faint o anifeiliaid anwes sydd gan y bobl hyn
i gyd gydai gilydd? How many pets have these
people got altogether?
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• 4. Maer teulu Williams yn mynd ar wyliau i
  Mallorca pan for gyfradd cyfnewid yn 1 286
  peseta.
• The Williams family go on holiday to Mallorca,
  when the exchange rate is 1 286 pesetas.
• Maent yn cyfnewid 350 i besetas. Faint o besetas
  y maent yn eu cael?
• They exchange 350 into pesetas. How many
  pesetas did they get?

Yn ystod eu gwyliau prynon nhw 30 cerdyn post am
85 pesets yr un a stampiau ar gyfer y cardiau
post am 70 peseta am bob cerdyn post. Cyfrifwch
faint gostiodd hyn iddynt mewn punnoedd, yn gywir
ir geiniog agosaf. Whilst on holiday they bought
30 postcards at 85 pesetas each and stamps for
the postcards at 70 pesetas each postcard.
Calculate how much in s, correct to the nearest
penny, this cost them.
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5. Ar y grid isod, lluniwch helaethiad
(enlargement) or siâp a roddir, gan ddefnyddio
ffactor graddfa 3. Draw, on the grid below, an
enlargement of the given shape, using a scale
factor of 3.
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6. Mewn arolwg roedd y math o wres canolog mewn
240 o gartrefi fel y dangosir yn y tabl. In a
survey, the type of central heating used by 240
households was as shown in the table.
Lluniwch siart cylch yn dangos y canlyniadau hyn.
Dylech ddangos sut yr ydych yn cyfrifo onglau
eich siart cylch. Draw a pie chart to illustrate
the results. You should show how you calculate
the angles of your pie chart.
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• 7. Mae tanc dwr o siâp ciwboid yn cynnwys 56
  000cm³ o ddwr. Mae gwaelod y tanc yn mesur 62cm
  wrth 35 cm.
• A water tank, in the shape of a cuboid, contains
  56 000cm³ of water. The base of the tank measures
  62cm by 35cm.
• Cyfrifwch ddyfnder y dwr yn y tanc, mewn cm.
• Calculate the depth, in cm, of the water in
  the tank.

(b) O wybod bod 1 galwyn 4.54 litr, cyfrifwch
nifer y galwyni o ddwr yn y tanc. Given that
1 gallon 4.54 litres, calculate the number of
gallons of water in the tank.
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8. Mae bill nwy Colin am y cyfnod 1af Ebrill hyd
at 30ain Mehefin yn cael ei gyfrifo ar sail y
wybodaeth ganlynol. Colins gas bill for the
period April 1st June 30th is calculated from
the following information. Nifer yr unedau a
ddefnyddiwyd 198 Number of units used Cost pob
uned 43.8c Charge per unit Nifer y dyddiau yn y
cyfnod hwn 91 Number of says in this period Cost
gwasanaeth bob dydd 13.39c Service charge per
day TAW 5 VAT Darganfyddwch gyfanswm cost y
bil, gan gynnwys TAW, am y cyfnod hwn. Dangoswch
eich holl waith cyfrifo. Showing all your
working, find the total cost of the gas including
VAT.
10
9.
26 TAW ar 17 ½ VAT at 17 ½
30 Gan gynnwys Including TAW VAT
Pa bris ywr rhataf a faint yn rhatach ywr pris
hwnnw? Which price offer is the cheaper and by
how much?
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• 10.Mae r graff gyferbyn yn dangos taith Gari yn
  ei gar oi gartref i safle gwasanaethau, lle
  maen aros am gyfnod cyn dychwelyd adref.
• The graph opposite shows Garys journey by car
  from his home to a services area, where he stops
  for a while before returning home.
• Pa mor bell ywr safle gwasanaethau o gartref
  Gari?
• How far is the services area from Garys
  home?

(b) Am faint o amser yr arhosodd Gari yn y safle
gwasanaethau? How long did Gary stop at this
services area?
(c) Defnyddiwch y graff i ddarganfod buanedd
cyfartalog Gari, mewn m.y.a., ar gyfer ei daith
yn dychwelyd iw gartref. Use the graph to find
Garys average speed, in m.p.h., for his return
journey home.
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Pellter o gartref Gari (milltiroedd) Distance
from Garyhome (miles)
70
60
50
40
30
20
10
0
10.00am
11.00am
12.00pm
1.00pm
2.00pm
Amser
Time
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11. Maer asesiad ar gyfer arholiad mathemateg yn
cynnwys dwy ran, sef gwaith cwrs, wedii farcio
allan o 50, a phapurau ysgrifenedig, wediu
marcio allan o 200. Rhoddir marciau deg disgybl
in y tabl. The assessment for a mathematics
exmaination consists of two parts, namely,
coursework marked out of 50, and written papers,
marked out of 200. The marks for ten pupils are
given in the table.

• Ar y papur graff lluniwch ddiagram gwasgariad yn
  dangos y canlyniadau hyn.
• On the graph paper, draw a scatter diagram
  to display these results.

(b) Pa fath o gydberthyniad y mae eich diagram
gwasgariad yn ei ddangos? What type of
correlation does your scatter diagram show?
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180
160
140
120
Papurau ysgrifenedig Written Papers
100
80
60
40
20
Gwaith cwrs Coursework
10
20
30
40
0
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(c) Marc cymedrig y gwaith cwrs ar gyfer y
disgyblion yw 25 a marc cymedrig y papurau
ysgrifenedig yw 98. Tynnwch linell ffit orau ar
eich diagram gwasgariad. The mean coursework
mark for the pupils is 25 and the mean mark for
the written paper is 98. Draw a line of best fit
on your scatter diagram.
(d) Roedd disgybl arall wedi cwblhaur gwaith
cwrs a chael y marc 19, ond roedd yn absennol or
arholiad papurau ysgrifenedig. Defnyddiwch eich
llinell ffit orau i amcangyfrif y marc ar y
papurau ysgrifenedig ar gyfer y disgybl
hwn. Another pupil completed the coursework and
was given a mark of 19, but was absent from the
written papers examination. Use your line of
best fit to estimate the mark of the written
papers for this pupil.
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12. Mesurwyd buanedd 120 o geir ar ran o
draffordd ac fe gafwyd y canlyniadau
canlynol. The speeds of 120 cars on a stretch of
motorway were measured and the following results
were obtained.

• Ysgrifennwch y dosbarth modd.
• Write down the modal class.

(b) Ar y papur graff lluniwch ddiagram amlder
grwp ar gyfer y data. On the graph paper,
draw a grouped frequency diagram for the data.
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50
Nifer y ceir Number of cars
40
30
20
10
0
10
20
30
40
50
60
70
80
90
Buanedd (m.y.a.) Speed (m.p.h.)
(c) Darganfyddwch amcangyfrif ar gyfer buanedd
cymedrig y ceir. find an estimate for the
mean speed of the cars.
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• 13. Maer siâp a ddangosir isod yn cynnwys dau
  hanner cylch.
• Diamedr yr hanner cylch lleiaf yw 8.6cm.
• C yw canolbwynt diamedr yr hanner cylch mwyaf.
• The shape shown below is made up of two
  semicircles.
• The diameter of the smaller semicircle is 8.6cm.
• C is the mid-point of the diameter of the larger
  semicircle.
• Gan nodi unedau eich atebion yn eglur, cyfrifwch
• Stating clearly the units of your answers,
  calculate
• perimedr y siâp, gan roi eich ateb o fanwl
  gywirdeb priodol.
• the perimeter of the shape, giving your answer to
  an appropriate degree of accuracy.

C
(b) arwynebedd y siâp, gan roi eich ateb yn gywir
ir rhif cyfan agosaf. the area of the
shape, giving your answer to the nearest whole
number.
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14. Ar Ebrill 1af roedd gan Owain 250 o ddyled
ar ei gyfrif cerdyn credyd. Maer cwmni cardiau
credyd yn gofyn bod Owain yn talu 10 o leiaf or
gweddill (balance) ar yr 20fed o bob mis. Maer
cwmnin codi llog o 2 ar beth bynnag ywr
gweddill ar yr 28ain o bob mis. Mae Owain yn talu
lleiafswm y taliad (minimum payment) yn brydlon
bob mis. Ysgrifennwch fanylion llawn ei gyfrif
hyd at Fai 31ain. On April 1st Marcus owed 250
on his credit card account. The credit card
company requires Marcus to pay at least 10 of
the balance on the 20th of each month. The
company charges interest at 2 on what the
balance is on the 28th of every month. Marcus
pays the minimum payment on time every
month. Write down full details of his account up
to May 31st. Ebrill 1af April
1st 250 Ebrill 20fed April 20th
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15. (a) Ehangwch Expand 2x(x² 3).
(b) Ehangwch a symleiddiwch Expand and
simplify 4(3x 1) 3(x 5).
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16. Defnyddiwch eich cyfrifiannell i ddarganfod
gwerth v845.6 Use your
calculator to find the value of
253.9 46.74 yn gywir i 2 lle degol. correct
to 2 decimal places.
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• 17. (a) Maer rhifau canlynol wediu hysgrifennu
  yn y ffurf safonol. Ysgrifennwch bob un yn y
  ffurf degol.
• The following numbers have been written in
  standard form. Write each in decimal form.
• (3.7 x 106)

(ii) (8.2 x 10-4)
(b) Darganfyddwch, yn y ffurf safonol,
werth Find in standard form, the value of (i)
(4.2 x 108) x (9.1 x 104)
(ii) (6.2 x 10-9) divide (8.3 x 106)
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53.1cm
18.
Nid ywr diagram wedii luniadu wrth raddfa.
Diagram not drawn to scale.
R
S
24.7cm
16.3cm
Q
P

• Maer diagram yn dangos ciwboid âi hyd yn
  53.1cm. Yn y trawstoriad, PQRS, mae PR24.7cm a
  QR16.3cm.
• The diagram shows a cuboid of length 53.1cm. The
  cross-section, PQRS, is such that PR24.7cm and
  QR16.3cm.
• Cyfrifwch hyd PQ.
• Calculate the length PQ.

(b) Dwysedd y defnydd y maer ciwboid wedii
wneud ohono yw 4.3g/cm³. Cyfrifwch fàs y ciwboid
mewn kilogramau. The density of the material from
which the cuboid is made is 4.3g/cm³. Calculate
the mass of the cuboid in kilograms.
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19. Mae datrysiad ir hafaliad A solution to
the equation x³ - 6x 3 0 iw gael
rhwng 2.6 a 2.7. lies between 2.6 and
2.7. Defnyddiwch y dull profi a gwella i
ddarganfod y datrysiad hwn yn gywir i 2 le
degol. Use the method of trial and improvement to
find this solution correct to 2 decimal places.
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• 20. Mae bag yn cynnwys 7 pêl las a 5 pêl werdd.
  Mae bag arall yn cynnwys 4 pêl las a 6 pêl goch.
  Mae pêl yn cael ei thynnu aar hap or bag cyntaf
  ai lliw yn cael ei nodi. Yna mae pêl yn cael ei
  thynnu ar hap or ail fag ai lliw yn cael ei
  nodi.
• A bag contains 7 blue balls and 5 green balls.
  Another bag contains 4 blue balls and 6 red
  balls. A ball is drawn at random from the first
  bag and its colour is noted. A ball is then drawn
  at random from the second bag and its colour is
  noted.
• Cwblhewch y diagram canghennog canlynol.
• Complete the following tree diagram.

(c) Cyfrifwch y tebygolrwydd bod o leiaf un bêl
yn las. Calculate the probability that at least
one ball is blue
Pêl 1 1st ball
Pêl 2 2nd ball
Glas Blue
Glas Blue
7/12
Coch Red
Glas Blue
Gwyrdd Green
Coch Red
(b) Cyfrifwch y tebygolrwydd bod y ddwy bêl yn
las. Calculate the probability that both
balls are blue.
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21. (a) Symleiddiwch Simplify (5x³)².
(b) Ehangwch y mynegiad canlynol, gan symleiddio
eich ateb gymaint ag syn bosibl. Expand the
following expression, simplifying your answer as
far as possible. (x 7)(x 3)
(c) Gwnewch d yn destyn y fformiwla
ganlynol. Make d the subject of the following
formula. 4(d 2e) 7 3e
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22. Yn y diagram isod, ABC 90, BED 90, AB
17.8m, CD 23.6m, BE 21.4m a BÂC 37. In the
diagram below, ABC 90, BED 90, AB 17.8m,
CD 23.6m, BE 21.4m and BÂC 37.
A
17.8m
Nid ywr diagram wedii luniadu wrth raddfa.
Diagram not drawn to scale
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B
C
23.6m
21.4m
D
E
Cyfrifwch faint BDE Calculate the size
of angle BDE.
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23. Datryswch yr hafaliad canlynol. Solve the
following equation. 3 x 1 2 x 1
3 4 2
4