NI CHEWCH DDEFNYDDIO CYFRIFIANNELL YN Y PAPUR HWN

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Mathemateg Haen Ganolradd Papur 1 Haf 2002 (2 awr)
Mathematics Intermediate Tier Paper 1 Summer
2002 (2 hours)
NI CHEWCH DDEFNYDDIO CYFRIFIANNELL YN Y PAPUR
HWN CALCULATORS ARE NOT TO BE USED FOR THIS PAPER
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• Defnyddiwch y ffaith fod 28 x 49 1372 i
  ysgrifennur atebion ir canlynol.
• Use the fact that 28 x 49 1372 to write
  down the answers to the following
• (a) 2.8 x 4.9

13.72
(b) 14 x 490
6860
(1/2 x 13720)
(c) 137.2 49
2.8
2. Darganfyddwch werth Find the value of (a)
5³ x 2³,
(b) 28.6 12.73
5 x 5 x 5 x 2 x 2 x 2
2 8 . 6 0 - 12 . 7 3 1 5 . 8 7
10 x 10 x 10
1000
3

• 3. Mae Tomos yn teithio ir gwaith sr y trên.
  Maen prynu naill ai tocyn dwyffordd syn 5 neu
  docyn unffordd syn 3.
• Toby travels to work by train. He buys either a
  5 return ticket or a 3 single ticket.
• Dros yr ychydig fisoedd diwethaf prynodd x tocyn
  dwyffordd.
• Over the past few months he bought x return
  tickets.
• Ysgrifennwch, yn nhermau x, gyfanswm cost y
  tocynnau dwyffordd hyn (mewn punnoedd).
• Write down, in terms of x, the total cost
  (in pounds) of these return tickets.

5x
(b) Roedd nifer y tocynnau unffordd a brynodd 9
yn fwy na nifer y tocynnau dwyffordd a brynodd.
Ysgrifennwch, yn nhermau x, faint o docynnau
unffordd a brynodd Tomos. The number of single
tickets he bought was 9 more than the number of
return tickets he bought. Write down, in terms of
x, how many single tickets Toby bought.
x 9
(c) Ysgrifennwch, yn nhermau x, gyfanswm cost y
tocynnau unffordd hyn (mewn punnoedd).
Write down, in terms of x, the total cost (in
pounds) of these single tickets.
3 ( x 9)
(d) Ysgrifennwch, yn nhermau x, gyfanswm gost yr
holl docynnau a brynodd Tomos (mewn punnoedd).
Maen rhaid i chi symleiddio eich ateb gymaint ag
y syn bosibl. Write down, in terms of x, the
total cost (in pounds) of all the tickets Toby
has bought. You must simplify your answer as far
as possible.
8x 27
5x 3(x 9)
5x 3x 27
4
4.Ysgrifennwch y rhifau canlynol yn gywir i 2
ffigur ystyrlon. Write does the following numbers
correct to 2 significant figures. (a) 0.063732
0.064
(b) 7934
7900
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• 5. Mewn gêm, mae chwaraewr yn taflu dau ddis teg,
  y naill yn goch ar llall yn las.
• Y sgôr ar gyfer y tafliad ywr lleiaf or ddau
  rif syn cael eu dangos. Er enghraifft
• os bydd y dis coch yn dangos 5, ar dis glas yn
  dangos 2, y sgôr ar gyfer y tafliad yw 2
• os bydd y dis cosh yn dangos 3 ar dis glas yn
  dangos 3, y sgôr ar gyfer y tafliad yw 3.
• In a game, a player throws two fair dice, one
  coloured red the other blue.
• The score for the throw is the smaller of the two
  numbers showing. For example
• if the red dice shows 5, and the blue shows 2,
  the score for the throw is 2
• if the red dice shows 3 and the blue dice shows
  3, the score for the throw is 3.
• Cwblhewch y tabl canlynol i ddangos pob sgôr syn
  bosibl.
• Complete the following table to show all
  the possible scores.

Dis coch Red dice
Dis glas Blue dice
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Dis coch Red dice
Dis glas Blue dice
11 36
(b) (i) Beth ywr tebygolrwydd y bydd chwaraewr
yn sgorio 1? What is the probability
that a player scores 1?
(ii) Beth ywr tebygolrwydd y bydd chwaraewr yn
sgorio mwy nag 1? What is the probability
that a player scores more than 1?
25 36
Mae chwaraewr yn ennill gwobr drwy gael sgôr o 2
neu lai. A player wins a prize by getting a score
of 2 or less. (c) Mae Gwilym yn chwaraer gêm
unwaith. Beth ywr tebygolrwydd y bydd ef yn
ennill gwobr? William plays the game once. What
is the probability that he wins a prize?
20 36
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(d) (i) Mae 360 o bobl yn chwaraer gêm
unwaith. Tua faint ohonynt y byddech chin
disgwyl iddynt ennill gwobr? 360 people each play
the game once. Approximately how many would
expect to win a prize?
5 x 360 9
5 x 40
200
(ii) Maen costio 1 i chwaraer gêm unwaith. Y
wobr am ennill yw 1.50. Pe bai pob un or 360 o
bobl yn chwaraer gêm unwaith, tuaa faint o elw y
byddech chhin disgwyl ir gêm ei wneud? It costs
1 to play the game once. The prize for winning
is 1.50. If the 360 people each play the game
once, approximately how much profit do you expect
the game to make?
Cost chwarae / cost of playing 360 x 1 360
Enillion / Winnings 200 x 1.50 300
Elw / profit 360 - 300
60
8
6. Barcut yw ABCD. Cyfrifwch faint yr ongl
x. ABCD is a kite. Calculate the size of the
angle marked x.
Nid ywr diagram wedii luniadu wrth
raddfa. Diagram not drawn to scale.
ABC 110 (cymesuredd / symmetry)
110 74 110 x 360
294 x 360
x 360 - 294
x 66
66
X
9
(No Transcript)
10
8 x 2 16cm²
4 x 3 12cm²
12cm
7 cm
10 x 6 60cm²
54 cm
8 2 5 4 7 6 10 12
(b) Cyfrifwch arwynebedd y siâp ABCDEFGH, gan
nodi unedau eich ateb yn eglur. Calculate
the area of the shape ABCDEFGH stating clearly
the units of your answer.
16 12 60
88cm²
11
150
202
x
C
(b) Mae tref arall, C, ir Dwyrain o B ac ar
gyfeiriant o 150 (D30Dn) oddi wrth A. Plotiwch
safler dref hon mor fanwl gywir ag y
gallwch. Another town, C, is due East of B and on
a bearing of 150 (S30E) from A. Plot, as
accurately as you can, the position of this town.
12
10. Mae perchennog siop yn prynu setiau fideo am
160 yr un. Am ba bris y bydd yn rhaid ir
perchennog siop werthur setiau fideo er mwyn
gwneud elw o 30. A shopkeeper buys video
recorders at 160 each. At what price must the
shopkeeper sell the video recorders in order to
make a profit of 30?
Neu or 10 16
Elw 30 x 160 Profit 100
30 3 x 16 48
3 x 16
Pris gwerthu 160 48 Selling Price
48
208
Pris gwerthu 160 48 Selling Price
208
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Often is too vague, no never mentioned. No time
interval given Mae aml yn anelwig. Dim cyfnod
amser wedi nodi.
(ii) Ysgrifennwch well fersiwn or cwestiwn.
Write a better version of the question.
How many times a year do you go to the dentist?
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12. O wybod bod h 12(a 17) , darganfyddwch
werth h pan fo a9 ac m - 4 .
m Given that h 12(a 17) , find the value of h
when a9 and m - 4. m
h 12 ( 9 17) - 4
h 12 x 8 - 4
h 12 x 2
h 24
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13. (a) Mynegwch 700 fel lluoswm rhifau cysefin
ar ffurf indecs. Express 700 as a
product of prime numbers in index form.
700
700 2 x 2 x 5 x 5 x 7
700 2² x 5² x 7
(b) Defnyddiwch eich canlyniad yn rhan (a) i
ysgrifennu lluosrif lleiaf 700 syn sgwâr
perffaith. Use your result in part (a) to write
down the smallest multiple of 700 which is a
perfect square.
(2 x 5 x 7) x (2 x 5 x 7)
70 x 70
4900
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14. Datryswch yr hafaliadau canlynol. Solve
the following equations. (a) 5 x 8 36 2
x
(b) 16 x 5 3 ( 4 x 7)
16x 5 12x 21
5x 2x 36 - 8
16x 12x 21 5
7x 28
4x 26
x 28 7
x 26 4
x 4
x 6 2 4
x 6 ½
17
15.
x
x 6

• Hyd ochrau octagon rheolaidd yw x cm. Mae pob un
  or ochrau pentagon rheolaidd 6cm yn hirach na
  phob un o ochraur octagon. Mae perimedr yr
  octagon 3cm yn hirach na pherimedr y pentagon.
• The sides of a regular octagon are x cm long.
  Each side of a regular pentagon is 6cm longer
  than each side of the octagon. The perimeter of
  the octagon is 3cm longer than the perimeter of
  the pentagon.
• Ysgrifennwch hafaliad y mae x yn ei fodloni.
• Write down an equation that x satisfies.

8x 5(x6) 3
(b) Datryswch yr hafaliad a thrwy hynny
darganfyddwch hyd un o ochraur pentagon.
Solve the equation and hence find the length of a
side of the pentagon.
8x 5(x 6) 3
3x 33
Hyd ochr pentagon Length of side of pentagon 11
6 17 cm
x 33 3
8x 5x 30 3
8x 5x 33
x 11
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• Mae Siwan ac Alun yn buddsoddi arian ac yn rhannu
  unrhyw elw syn cael ei wneud yn ôl y gymhareb
  54.
• Jill and Alan invest some money and share any
  profit made in the ratio of 54.
• Faint fydd Siwan yn ei gael pan fyddant yn gwneud
  elw o 270?
• How much does Jill get when they make a
  profit of 270?

5 4 9 rhan parts
1 rhan part 270 9
30
Siwan yn cael 5 rhan Jill gets 5 parts
5 x 30
150
(b) Ar adeg arall, derbyniodd Alun 136. Faint o
elw roeddent yn ei rannu? On another
occasion, Alan received 136. How much profit
were they sharing?
Alun yn cael 4 rhan 136 Alan gets 4 parts
136
34
1 rhan 1 part 136 4
306
9 rhan parts 34 x 9
19
y
17. (a) Lluniwch y ddelwedd pan gaiff y triongl
ABC ei adlewyrchu yn y llinell y -x. Draw the
image when the triangle ABC is reflected in the
line y-x.
5
A
4
3
B
2
1
1
-3
x
2
3
4
5
-1
-2
-4
-5
0
-1
-2
-3
C
y - x
-4
-5
20
y
(b) Lluniwch y ddelwedd pan gaiff y triongl D ei
gylchdroi trwy 90 yn wrthglocwedd o amgylch
pwynt (1, -1). Draw the image when the triangle
marked D is rotated through 90 anticlockwise
about the point (1, -1).
5
4
3
D
2
1
1
-3
x
2
3
4
5
-1
-2
-4
-5
0
-1
-2
-3
-4
-5
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18. Rhoddodd samol o fechgyn a merched mewn ysgol
y canlyniadau canlynol ar gyfer lliw eu
llygaid. A sample of boys and girls at a school
yielded the following results for their eye
colour.
Mae 930 o fechgyn a 720 o ferched yn yr ysgol.
Defnyddiwch ganlyniadaur sampl ar cyfansymiau
hyn i amcangyfrif cyfanswm y disgyblion yn yr
ysgol sydd â llygaid brown. There are 930 boys
and 720 girls at the school. Use the results of
the sample and these totals to find an estimate
for the total number of pupils in the school with
brown eyes.
40 x 930 30 x 720 100
80
4 x 93 30 x 9
372 270
642
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19. 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. 3 x
4 y 22 2 x 3 y - 8
Lluoswch 1 x 2 a 2 x 3 Multiply eqn 1
x 2 and eqn 2 x 3
Amnewid y -4 yn hafaliad 1 Substitute y -
4 in equation 1
6x - 8y 44
3 x - 4 y 22
6x 9y - 24
3 x 4 x (-4) 22
- 8y - 9y 44 - - 24
3 x 16 22
-17y 68
3x 22 - 16
3x 6
y 68 -17
x 2
y - 4
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20. Ffactoriwch Factorise (a) 3xy² - 6xy,
3xy(y 2)
(b) x² 2x 8.
(Lluosi -8 Swm 2 / 4,
-2) (Multiply -8 Add 2 / 4, -2)
(x 4) ( x 2)
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21. Mesurwyd yr amserau a gymerwyd gan 160 o
ddisgyblion i deithio ir ysgol ac maer
canlyniadau wediu crynhoi yn y tabl
canlynol. The times taken by 160 pupils to travel
to school were measured and the results are
summarised in the following table.

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

12
68
112
132
148
156
160
(b) Ar y papur graff, lluniwch ddiagram amlder
cronnus yn dangos y wybodaeth hon. On the graph
paper, draw a cumulative frequency diagram to
show this information.
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(c) Defnyddiwch eich diagram amlder cronnus i
ddarganfod yr amrediad rhyngchwartel. Use your
cumulative frequency diagram to find the
interquartile range.
Chwartel Uchaf Upper Quartile
33 16 17 mun / min
(d) Defnyddiwch eich diagram amlder cronnus i
gwblhaur gosodiad canlynol. Cymerwch 60 or
disgyblion lai na . munud i deithio ir
ysgol. Use your cumulative frequency diagram to
complete the following statement. 60 of the
pupils took less than minutes to travel to
school.
60
Chwartel Isaf Lower Quartile
27 min
26
A
22.
Nid ywr diagram wedi ei luniadu wrth
raddfa. Diagram not drawn to scale.
6cm
9cm
B
C
3cm
D
E
7.2cm
Yn y diagram, mae BC yn baralel i DE ac maer
trionglau ABC ac ADE yn gyflun. AB9cm, AC6cm,
BD3cm a DE 7.2cm. Gan ddangos eich holl waith
cyfrifo, darganfyddwch hyd In the diagram, BC is
parallel to DE, and the triangles ABC and ADE are
similar. Showing all your working, find the
length of AB9cm, AC6cm, BD3cm and DE
7.2cm. (a) BC
BC 9 x 7.2 12
BC 9 7.2 12
BC 5.4cm
AE 12 x 6 9
AE 8cm
AE 12 6 9
(b) AE.
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23. Ym mhob un or fformiwlâu canlynol, mae pob
llythyren yn dynodi mesuriad hyd. Trwy ystyried y
dimensiynau a awgrymir gan bob fformiwla,
ysgrifennwch, ar gyfer pob un, a allair
fformiwla fod ar gyfer hyd, arwynebedd, cyfaint
neu ddim un or rhain. Maer un 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
each formula, write down, for each case, whether
the formula could be for a length, an area, a
volume or none of these. The first one has been
done for you.
Cyfaint Volume
Hyd Length
Cyfaint Volume
Arwynebedd Area
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24. (a) Ad-drefnwch yr hafaliad 35 3n gt 2n 7
yn y ffurf n lt rhyw rif. Rearrange the inequality
35 3n gt 2n 7 into the form n lt some number.
35 7 gt 2n 3n
28 gt 5n
5n lt 28
n lt 5 3 5
n lt 28 5
(b) O wybod bod n hefyd yn bodlonir anhafaledd
3ngt1 , ysgrifennwch yr holl werthoedd cyfanrifol
n syn bodlonir ddau anhafaledd. Given that n
also satisfies the inequality 3ngt1 , write down
all the integer values of n that satisfy both
inequalities.
a and
n lt 5 3 5
n gt 1 3
n 1, 2, 3, 4, 5