Application of Number Level 2 - Wales Essential Skills · Hawlfraint Tribal Education 2007-2015 1...

Copyright © Tribal Education 2010-2015 1

Application of Number Level 2

Formulae expressed in words

IntroductionA formula is a rule that tells you the relationship between numbers or quantities.

The examples below are all of mathematical formulae expressed in words rather than numbers and symbols.

If you are talking about more than one formula, you can say either formulas or formulae. This activity looks at how to work with formulae that are written in words.

You will learn how to:

n translate word formulae into numbers and symbols

n tackle formulae problems step by step.

n You can use a calculator.

n Read the introduction and the ‘learn about’ examples carefully before you try the practice questions.

n Write down all your working out. If you do not have enough space to do this, ask for extra paper.

n You should show evidence that you have checked your work in your working out.

n You can then give this to your tutor if you are not sure about your answers.

When you have finished, check your answers with the ones provided on page 9.




Learn about simple formulaeWhen you work with a formula that includes words, you need to:

• breaktheformuladownintostepsifneeded

• translateeachstepintonumbersandsymbols

• workouttheanswerstoeachstep.

Look at these examples:

Example A

What is the area of a wall that is 3 m high and 5 m wide?

Answer: The wall has an area of 15 m2.

Example B

You build a square pond in your garden. The length of one side is 1.5 metres. What is the perimeter of the pond?

1.5 m × 4 = 6 m

Answer: The perimeter of the pond is 6 m.

Practice 1

Use the formulae above to help you answer the questions.

a. One side of your square vegetable plot is 6 m. You want to enclose the plot with

border edging. How much border edging do you need to buy?

b. You ask a decorator to paint one wall of your room blue. The wall is 2.3 metres high

and 4 metres wide. What is the area of the wall?

c. You need to put sealant tape round the edge of a square shower tray. How much

tape do you use?




Learn more about simple formulaeNow look at these further examples.

Example A

How much does it cost for seven A4 photocopies?

7 × 8p = 56p

Answer: 7 A4 copies will cost 56p.

Example B

There is a special offer at the Quick Copy Shop: 2p off each A4 photocopy (maximum of 100 copies). What is the cost of 45 A4 copies?

You will need to change the formula before you start to work out the answer.

A4 Photocopies cost 6 pence each for the first 100 copies, and then it is 5 pence each for any further copies.

So the formula becomes:

45 × 6p = 270p (or £2.70)

Answer: 45 copies will cost £2.70.

Practice 2

Use the Quick Copy Shop poster to answer the questions.

a. How much does it cost for 60 A3 photocopies?

b. You need 90 A4 photocopies. What will this cost?

c. The Quick Copy shop has had to increase its prices. Each A4 copy now costs 1p more (any amount of copies). How much will it cost for 21 A4 copies?




Learn about longer formulaeWhen you work with longer word formulae you need to:

• translateeachstepintonumbersandsymbols

• workouttheanswerstoeachstep

• putthestepsinthecorrectorderbeforeworkingoutthefinalanswer.

Example

What is the total preparation time for a rare steak?

This is a two-step problem.

The steak has two ‘sides’ so

Step � 2 × 2 minutes = 4 minutes (cooking time)

Step � 4 minutes + 6 minutes (rest time) = 10 minutes

Answer: It takes 10 minutes to prepare a rare steak.

Practice 3

Use the chef’s formulae above and on page 1 to answer the questions.

a. How long does it take to prepare a medium steak?

b. You have a small 1-kilogram chicken. How long will it take to cook?




Learn about longer formulaeIn this example, the formula uses words, numbers and symbols. If a formula includes brackets, you must work out the answer to what is in the brackets first.

Example

What is the perimeter of a rectangular room that is 4 m long and 3 m wide?

This is a two-step problem.

Step � 4 m + 3 m = 7 m

Step � 2 × 7 m = 14 m

Answer: The room has a perimeter of 14 m.

Practice 4

Use the formula above to help you answer these questions.

a. You want to put a border around the top of your bedroom wall – just below the ceiling.What length of border paper will you need?

b. You put sealant tape round the edges of a rectangular bath. How much tape do you use? Give your answer in metres.




Learn more about longer formulaeNow look at this example.

Example

How much does it cost for 150 A4 copies?

This is a three-step problem.

Step � The first 100 copies will cost 100 × 8p = £8.00

Step � The next 50 copies will cost 50 × 5p = £2.50

Step � So the total cost will be £8.00 + £2.50 = £10.50

Answer: 150 copies will cost £10.50.

Practice 5

Use the Quick Copy Shop poster on this page to answer these questions

a. Calculate the cost of 300 A4 copies.

b. A customer orders 36 A3 copies and 108 A4 copies. What is the total cost?




Apply your skillsIn this section, you will apply what you have learnt to other real-life situations.

Use the formulae above to answer these questions.

a. You hail a cab at 3.30 p.m. for a 5-mile trip. Calculate the fare.

b. How much do Blue Cab charge for a 6-mile trip at midnight?

c. Calculate the cooking time for a large 3.4kg chicken.

d. You have a blocked pipe. The plumber takes 3 hours to fix it. Calculate the cost.




Check your skills

1. Perimeter of a rectangle = 2 × (length + width)

A rectangle is 8 cm long and 13 cm wide. The perimeter is:

a. 34 cm b. 29 cm c. 42 cm d. 23 cm

2. Area of a rectangle = length × width

A rectangle is 45 cm long and 3 cm wide. The area is:

a. 48 cm2 b. 42 cm2 c. 145 cm2 d. 135 cm2

3. Roast beef: cook for 35 minutes per kilogram plus 15 minutes

A 3kg joint of beef will cook in:

a. 50 minutes b. 80 minutes c. 120 minutes d. 105 minutes

4. Emergency electrician: £50 callout charge plus £42 per hour

The electrician stays for 2 hours. The bill is:

a. £92 b. £134 c. £142 d. £ 84

5. Bloxford bus company: a child’s bus fare is half the adult fare plus 20p

An adult fare to Bloxford is £3.28, so a child’s fare to Bloxford is:

a. £1.84 b. £1.74 c. £1.64 d. £3.08




AnswersYou might have the correct answer but used a different method from the one shown in the answers. Talk to your tutor if you are confused.

Practice 1 (page 2)

a. 6 m × 4 = 24 m b. 4 m × 2.3 m = 9.2 m2

c. 80 cm × 4 = 320 cm (or 3.2 m)

Practice 2 (page 3)

a. 60 × 15p = 900p (or £9.00) b. 90 × 8p = 720p (or £7.20) c. 21 × 9p = 189p (or £1.89)

Practice 3 (page 4)

a. (2½ mins × 2) + 4 mins = 5 mins + 4 mins = 9 minutes b. (1 × 45 mins) + 20 mins = 45 mins + 20 mins = 65 minutes

Practice 4 (page 5)

a. (4.2 m + 2.8 m) × 2 = 7 m × 2 = 14 m b. (685 mm + 1685 mm) × 2 = 2370 mm × 2 = 4740 mm = 4.74 m

Practice 5 (page 6)

a. 100 × 8p = £8.00 200 × 5p = £10.00 So total cost = £8 + £10 = £18b. (36 × 15p) + (100 × 8p) + (8 × 5p) = 540p + 800p + 40p = 1380p = £13.80

Apply your skills (page 7)

a. £1.80 + (5 × 90p) = £1.80 + £4.50 = £6.30 b. £2.20 + (6 x £1.30) = £2.20 + £7.80 = £10.00 c. (45 min × 3.4) + 20 min = 153 min + 20 min = 173 minutes d. £40 + (£25 × 3) = £40 + £75 = £115

Check your skills (page 8)

1. c. 2 × (8 cm + 13cm) = 2 × 21 cm = 42 cm 2. d. 45 cm × 3 cm = 135 cm2 3. c. (3 × 35 min) + 15 min = 105 min + 15 min = 120 minutes (or 2 hours) 4. b. £50 + (£42 × 2) = £50 + £84 = £134 5. a. (£3.28 ÷ 2) + 20p = £1.64 +20p = £1.84

Hawlfraint © Tribal Education 2007-2015 1

Cymhwyso rhif Lefel 1

Fformiwlâu wedi’u mynegi mewn geiriau

CyflwyniadRheol yw fformiwla sy’n dweud wrthych beth yw’r berthynas rhwng rhifau neu feintiau.

Isod ceir enghreifftiau o fformiwlâu mathemategol wedi’u mynegi mewn geiriau yn hytrach na rhifau a symbolau.

n Gallwch ddefnyddio cyfrifiannell.

n Darllenwch y cyflwyniad a’r enghreifftiau ‘dysgu am’ yn ofalus cyn i chi roi cynnig ar y cwestiynau ymarfer.

n Ysgrifennwch eich holl waith cyfrifo. Os nad oes gennych ddigon o le i wneud hyn, gofynnwch am fwy o bapur.

n Dylech ddangos tystiolaeth eich bod wedi gwirio eich gwaith wrth gyfrifo’r atebion.

n Yna gallwch roi’r tystiolaeth i’ch tiwtor os nad ydych yn sicr o’ch atebion.

Ar ôl i chi orffen, gwiriwch eich atebion yn ôl yr atebion a roddir ar dudalen 9.

Dwi’n codi £40 am fy ngalw allan a £25 yr awr.

Os byddwch yn sôn am fwy nag un fformiwla, defnyddiwch y gair fformiwlâu. Mae’r gweithgaredd hwn yn edrych ar sut i weithio gyda fformiwlâu a ysgrifennir mewn geiriau.

Byddwch yn dysgu sut i:

n gyfieithu fformiwlâu geriau yn rhifau a symbolau

n delio â phroblemau fformiwlâu gam wrth gam.

Câr am 45 munud y cilo ac 20 munud ychwanegol.

Llungopïau

8 ceiniog yr un am y 100 copi cyntaf

5 ceiniog am unrhyw

gopïau ychwanegol




Dysgu am fformiwlâu symlPan fyddwch yn gweithio gyda fformiwla sy’n cynnwys geiriau, bydd angen:

• symleiddio’rfformiwlaa’irhannu’ngamauosoesangen

• cyfieithupobcamirifauasymbolau

• cyfrifo’ratebibobcam.

Edrychwch ar yr enghreifftiau hyn:

Enghraifft A

Beth yw arwynebedd wal 3 m o uchder a 5 m o led?

Ateb: Arwynebedd y wal yw 15 m2.

Enghraifft BRydych yn adeiladu pwll sgwâr yn eich gardd. Hyd un ochr yw 1.5 metr. Beth yw perimedr y pwll?

1.5 m × 4 = 6 m

Ateb: Perimedr y pwll yw 6 m.

Ymarfer 1

Defnyddiwch y fformiwlâu uchod i’ch cynorthwyo i ateb y cwestiynau.

a. Mae un ochr eich llain tyfu llysiau sgwâr yn 6 m. Rydych eisiau gosod ymylwaith o

gwmpas y llain. Faint o ymylwaith y bydd angen i chi ei brynu?

b. Rydych yn gofyn i beintiwr beintio un wal eich ystafell yn las. Mae’r wal yn 2.3 metr o

uchder a 4 metr o led. Beth yw arwynebedd y wal?

c. Mae angen i chi osod tâp selio o amgylch ymyl gwaelod cawod.Faint o dâp fyddwch

yn ei ddefnyddio?

gwaelod cawod

Sut i gyfrifo perimedr sgwâr

perimedr = unrhyw hyd o x4 ochr

TIPS ADDURNO

Arwynebedd wal betryal mewn metrau sgwâr = lled (mewn metrau) wedi’i luosi â’r uchder (mewn metrau)




Dysgu mwy am fformiwlâu symlYn awr, edrychwch ar yr enghreifftiau hyn.

Enghraifft A

Beth yw cost saith llungopi A4?

7 × 8c = 56c

Ateb: Mae 7 copi A4 yn costio 56c.

Enghraifft B

Mae cynnig arbennig yn y Siop Copïau Cyflym: gostyngiad o 2c ar bris pob llungopi A4 (uchafswm o 100 copi). Beth yw cost 45 copi A4?

Bydd angen i chi newid y fformiwla cyn i chi ddechrau cyfrifo’r ateb.

Mae llungopïau A4 yn costio 6 cheiniog yr un am y 100 copi cyntaf, yna 5 ceiniog yr un am unrhyw gopïau ychwanegol.

Felly’r fformiwla yw: 45 × 6c = 270c (neu £2.70)

Ateb: Mae 45 copi yn costio £2.70.

Ymarfer 2

Defnyddiwch boster y Siop Copïau Cyflym i ateb y cwestiynau.

a. Beth yw cost 60 llungopi A3?

b. Mae arnoch angen 90 llungopi A4. Beth fydd y gost?

c. Mae’r Siop Copïau Cyflym wedi gorfod codi ei phrisiau. Mae pob copi A4 bellach yn costio 1c yn fwy (am unrhyw nifer o gopïau). Beth fydd cost 21 copi A4?

SIOP COPÏAU CYFLYM

Pris llungopïau A4 yw 8 ceiniog yr un am y 100 copi cyntaf ac yna 5 ceiniog yr un am unrhyw gopïau ychwanegol.

Mae llungopïau A3 yn costio 15 ceiniog yr un am unrhyw nifer o gopïau.



Ymarfer 3

Defnyddiwch fformiwla’r cogydd uchod ac ar dudalen 1 i ateb y cwestiynau.

a. Faint o amser mae’n ei gymryd i baratoi stêc canolig?

b. Mae gennych gyw iâr 1-cilogram. Faint o amser bydd yn ei gymryd i’w goginio?


Dysgu am fformiwlâu hirachPan fyddwch yn gweithio â fformiwlâu geiriau hirach bydd angen i chi:

•gyfieithupobcamirifauasymbolau

•cyfrifo’ratebibobcam

• rhoi’rcamauynydrefngywircyncyfrifo’ratebterfynol.

Enghraifft

Beth yw cyfanswm yr amser sydd ei angen i baratoi stêc gwaedlyd.

Mae dau gam i’r broblem hon.

Mae dwy ‘ochr’ i’r stêc felly

Cam � 2 × 2 munud = 4 munud

(amser coginio)

Cam � 4 munud + 6 munud (amser gorffwys) = 10 munud

Ateb: Mae’n cymryd 10 munud i baratoi stêc gwaedlyd.

I baratoi stêc gwaedlyd: coginiwch am ddau funud bob ochr ac yna ei orffwys am chwe munud cyn ei weini.

Stêc canolig: coginiwch am 2½ munud bob ochr ac yna ei orffwys am bedwar munud.

Stêc wedi’i goginio’n dda: coginiwch am 4 munud bob ochr. Nid oes angen ei orffwys.




Dysgu am fformiwlâu hirachYn yr enghraifft hon, mae’r fformiwla yn defnyddio geiriau, rhifau a symbolau. Os yw fformiwla yn cynnwys cromfachau, rhaid i chi gyfrifo’r ateb i’r hyn sydd yn y cromfachau yn gyntaf.

Enghraifft

Beth yw perimedr ystafell betryal 4 m o hyd a 3 m o led?

Mae dau gam i’r broblem hon.

Cam � 4 m + 3 m = 7 m

Cam � 2 × 7 m = 14 m

Ateb: Perimedr yr ystafell yw 14 m.

Ymarfer 4

Defnyddiwch y fformiwla uchod i’ch cynorthwyo i ateb y cwestiynau hyn.

a. Rydych eisiau gosod ymyl o amgylch wal eich ystafell wely – yn union o dan y nenfwd. Beth fydd hyd y papur fydd ei angen arnoch?

b. Rydych yn gosod tâp selio o amgylch ymyl baddon petryal. Faint o dâp fyddwch yn ei ddefnyddio? Rhowch eich ateb mewn metrau.

Gwnewch y swm yn y cromfachau

yn gyntaf.

Sut i gyfrifo perimedr petryal

Perimetr petryal = 2 x (hyd + lled)

Ystafell wely

Baddon




Dysgu mwy am fformiwlâu hirachYn awr, edrychwch ar y enghraifft hon.

Enghraifft

Beth yw cost 150 copi A4?

Mae tri cham i’r broblem hon.

Cam � Bydd y 100 copi cyntaf yn costio 100 × 8c = £8.00

Cam � Bydd y 50 copi nesaf yn costio 50 × 5c = £2.50

Cam Felly cyfanswm y gost fydd £8.00 + £2.50

= £10.50

Ateb: Bydd 150 copi yn costio £10.50.

Ymarfer 5

Defnyddiwch boster y Siop Copïau Cyflym ar y tudalen hwn i ateb y cwestiynau hyn

a. Cyfrifwch beth yw cost 300 copi A4.

b. Mae cwsmer yn archebu 36 copi A3 ac 108 copi A4. Beth yw cyfanswm y gost?

SIOP COPÏAU CYFLYM

Mae llungopïau A4 yn costio 8 ceiniog yr un am y 100 copi cyntaf ac yna 5 ceiniog yr un am unrhyw gopïau ychwanegol.

Mae llungopïau A3 yn costio 15 ceiniog yr un am unrhyw nifer o gopïau.

�

�



Câr am 45 munud y cilo ac 20 munud ychwanegol.

Dwi’n codi £40 am fy ngalw allan a £25 yr awr.


Cymhwyso eich sgiliauYn yr adran hon, byddwch yn cymhwyso’r hyn rydych wedi’i ddysgu i sefyllfaoedd go iawn eraill.

Defnyddiwch y fformiwlâu uchod i ateb y cwestiynau hyn.

a. Rydych yn archebu tacsi am 3.30 p.m. i fynd ar daith 5-milltir. Beth fydd cost y daith?

b. Faint y mae Blue Cab yn ei godi am daith 6-milltir am hanner nos?

c. Cyfrifwch yr amser coginio ar gyfer cyw iâr mawr 3.4kg.

ch. Mae pibell wedi blocio yn eich cartref. Mae’r plymar yn cymryd 3 awr i’w drwsio.

Cyfrifwch y gost.

prisiau Cabiau Glas

Isafswm pris A 90c y filltir ar ben hynny

Isafswm pris £2.20 A £1.00 y filltir ar ben hynny

Isafswm pris £2.20 A £1.30 y filltir ar ben hynny




Gwirio eich sgiliau

1. Perimetr petryal = 2 × (hyd + lled)

Mae petryal yn 8 cm o hyd ac 13 cm o led. Y perimetr yw:

a. 34 cm b. 29 cm c. 42 cm ch. 23 cm

2. Arwynebedd petryal = hyd × lled

Mae petryal yn 45 cm o hyd a 3 cm o led. Yr arwynebedd yw:

a. 48 cm2 b. 42 cm2 c. 145 cm2 ch. 135 cm2

3. Cig eidion rhost: coginiwch am 35 munud y cilogram â 15 munud ychwanegol.

Bydd darn o gig eidion 3kg yn coginio mewn:

a. 50 munud b. 80 munud c. 120 munud ch. 105 munud

4. Trydanwr mewn argyfwng: tâl am ei alw allan £50, ynghyd â £42 yr awr

Mae’r trydanwr yn aros am 2 awr. Y bil yw:

a. £92 b. £134 c. £142 ch. £ 84

5. Cwmni bysiau Bloxford: mae tocyn bws plentyn yn costio hanner tocyn

oedolyn, ac 20c ar ben hynny. Pris tocyn oedolyn i Bloxford yw £3.28, felly

pris tocyn plentyn i Bloxford yw:

a. £1.84 b. £1.74 c. £1.64 ch. £3.08




AtebionEfallai eich bod wedi cael yr ateb cywir ond eich bod wedi defnyddio dull gwahanol i’r un a ddangosir yn yr atebion. Siaradwch gyda’ch tiwtor os ydych wedi drysu.

Ymarfer 1 (tudalen 2)

a. 6 m × 4 = 24 m b. 4 m × 2.3 m = 9.2 m2

c. 80 cm × 4 = 320 cm (neu 3.2 m)


a. 60 × 15c = 900c (neu £9.00) b. 90 × 8c = 720c (neu £7.20) c. 21 × 9c = 189c (neu £1.89)


a. (2½ mun × 2) + 4 mun = 5 mun + 4 mun = 9 munud b. (1 × 45 mun) + 20 mun = 45 mun + 20 mun = 65 munud


a. (4.2 m + 2.8 m) × 2 = 7 m × 2 = 14 m b. (685 mm + 1685 mm) × 2 = 2370 mm × 2 = 4740 mm = 4.74 m


a. 100 × 8c = £8.00 200 × 5c = £10.00 Felly cyfanswm y gost = £8 + £10 = £18b. (36 × 15c) + (100 × 8c) + (8 × 5c) = 540c + 800c + 40c = 1380c = £13.80

Cymhwyswch eich sgiliau (tudalen 7)

a. £1.80 + (5 × 90c) = £1.80 + £4.50 = £6.30 b. £2.20 + (6 x £1.30) = £2.20 + £7.80 = £10.00 c. (45 mun × 3.4) + 20 mun = 153 mun + 20 mun = 173 munud ch. £40 + (£25 × 3) = £40 + £75 = £115

Gwiriwch eich sgiliau (tudalen 8)

1. c. 2 × (8 cm + 13cm) = 2 × 21 cm = 42 cm 2. ch. 45 cm × 3 cm = 135 cm2 3. c. (3 × 35 mun) + 15 mun = 105 mun + 15 mun = 120 munud (neu 2 awr) 4. b. £50 + (£42 × 2) = £50 + £84 = £134 5. a. (£3.28 ÷ 2) + 20c = £1.64 +20c = £1.84

Application of Number Level 2 - Wales Essential Skills · Hawlfraint Tribal Education 2007-2015 1...

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Transcript of Application of Number Level 2 - Wales Essential Skills · Hawlfraint Tribal Education 2007-2015 1...