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Pegasys 2016 National 4 Lifeskills - Numeracy Unit

Homework exercises covering the Unit 3 topics + Answers

CFE ResourcesNational 4 Application of

Mathematics

Unit 3Numeracy

Homework Exercises

N4 Lifeskills Homework - Four Rules with Whole Numbers

1. A golfer plays six rounds of golf. The number of shots he plays for each round is shown below.

78 86 75 82 78 93

How many more shots, in total, did he take to play his last three rounds compared to his first three?

2. A small bag of sand weighs 3 kg.

It has to be divided evenly between 4 buckets.

What weight of sand, in grams, should be in each bucket?

3. Joyce walks to her work and back every day.

The journey takes her, on average, 25 minutes each way.

If she works five days a week, what is her total walking time for a week in hours and minutes?

4. A bottle contains 220ml of medicine.

(a) How many 8ml doses of medicine can you take from this bottle?

(b) How much medicine will be left in the bottle once you have taken as many 8ml dosesas you can?

5. Michael ran a charity disco at his local town hall. After the event he produced the income and expenditure table shown below.

How much profit did Michael make for his charity from this event?


Income 150 tickets sold @ £4 each Raffle tickets sold - £175 Donations - £118

Expenditure Hire of the hall - £60 Cost of disco - £120 Raffle prizes - £53

N4 Lifeskills Homework - Four Rules with Decimals

1. The bookcase shown opposite is made from wooden boards of thickness 14cm.

If the clearance height between each shelf is 218cm, calculate the total height, h, of the bookcase.

2. Susan wants to put some decorative wooden edging around a small rectangular vegetablepatch she has in her garden.

Her rectangular vegetable patch measures 37 metres by 86 centimetres.

She buys 95 metres of edging.

(a) Is this enough edging to surround her vegetable patch? (you must show suitable working)

(b) If so how much edging will she have left? (answer in metres)

3. A dictionary has 14 volumes each 84cm thick. If they are placed side by side on a shelf 17m long, what length of shelf will be left for other books? (answer in centimetres)

4. A box contains 6 identical calculators.

The total weight of the box and calculators is 531g.

If the weight of the empty box is 252g, calculate the weight of a single calculator.

5. A school prints its own yearly newsletter just before xmas.

The cost of running the printing machines is £5.25 per 100 copies. The cost of paper,ink, etc., is an additional 12 pence per copy.

The newsletter is free to all parents and pupils, however, the school charges for localcompanies to advertise in the newsletter.

Last year the school made £241.25 profit from the newsletter.

How much did the school receive for advertisements last year given that it printed 750 newsletters?


218cm

h

N4 Lifeskills Homework - Calculations and Rounding

1. A group of 32 workers win £668 on the lottery. They decide to share the money so that each of them receives a whole number of pounds. They decide that any money left over should goto charity.

How much money did they give to charity?

2. A box of 6 lightbulbs costs £12.28.

Calculate the cost of one lightbulb to the nearest penny.

3. A certain brand of washing powder comes in two different sizes as shown.

(a) Calculate the cost per kilogram of powder for eachbox giving your answers to the nearest penny.

(b) Which box represents the best value for money?

4. A car uses 15 litres of petrol to travel 214 miles.

How far can it travel on one litre of petrol? Give your answer correct to 2 decimal places.

5. How many wavelengths of 00034mm will there be in 10mm? Give your answer tothe nearest 100.

6. An investor changes his clients £245000 investment into euros at the rate of 1278 euros to the pound.

(a) How many euros did he receive?

(b) Two weeks later he changed these euros back into pounds at the rate of 0795 poundsto the euro.

How much profit has the investor made for his client with these two transactions?Give your answer to the nearest pound.


6 kg£10.530

£4.48

N4 Lifeskills Homework - Calculations Involving Fractions

1. Calculate each of the following.

(a) of 280 (b) of 32000 (c) of 140 (d) of £120

(e) of 248kg (f) of 45kg (g) of 52cm (h) of £12.60

2. A small business has 42 employees. Each year all employees must take the company medical test. So far this year of the staff have taken the medical. How many employeeshave still to sit the medical?

3. 60 people were asked to choose, after a taste test, which brand of coffee they preferred, brand A, B or C.

preferred A, chose B and the rest chose C.

(a) How many people chose B?

(b) How many chose C?

4. In a sample of 120 butterflies it is found that of them are multi-coloured and that ofthe multi-coloured butterflies are males.

How many muti-coloured male butterflies are there in this sample?

5. In a group of students were found to be left handed. If 18 students were left handed how many right handed students were in the group?


WHITE HORSE

N4 Lifeskills Homework - Calculations Involving Simple Percentages

1. Calculate each of the following.

(a) 15% of 220 (b) 50% of £4.80 (c) 20% of 40kg (d) 75% of 80p

(e) 10% of £2.60 (f) 40% of £300 (g) 70% of 20cm (h) 33 % of £54

2. The White Horse Building Society pays interest of 4% per annum on savings.

How much interest will Sheila receive on savings of £600 after:

(a) 1 year; (b) 7 months?

3. In a sale everything is reduced by 15%.

How much would you pay in the sale for a mobile phone normally priced at £360?

4. A set of bluetooth speakers are priced at £28.00 + VAT.

What would you pay in total for the speakers if VAT is charged at 20%?

5. 80 people visiting a museum were asked what mode of transport they had used to come to the museum. 15% came by bus, 25% by train and the remainder came by car.

How many of the 80 visitors came by car?

6. Mark and Jade are getting engaged.

They see a ring for Jade that they both like in a local jewellers.

How much would they save if they bought the ring by cash as opposed to paying by instalments?


G. E. Thitched & Sons Pay a deposit of 20% of the normal cash price

then pay 12 monthly instalments of £30or

Pay cash and get a 5% reduction on the normal cash price of £420

Cash price - £420

N4 Lifeskills Homework - Problems Involving Percentages

1. Cal wants to buy a pair of designer sunglasses.He saw the sign opposite in a local shop.

How much will Cal pay for a pair of sunglasses whichcost £86.50 before the sale?

2. Paul buys an antique watch for £2500 as an investment.

He is hoping it will appreciate in value by the rate of 12% per year.

What is he hoping its value might be in 2 years time?

3. Paul buys a jacket from a shop that is having a ‘15% off’ sale.

The original cost is £65 and he is charged £55.50 the checkout.

Paul believes he has been charged wrongly.

Is the sale price correct for the jacket?

Give a reason for your answer.

4. Jane buys a second hand camera online for £140.

She hopes to sell it through a different site and make at least a 20% profit.

She eventually sells the camera for £170.

Did she achieve her hoped for profit? Give a reason for your answer.

5. There are approximately 6 million people in Scotland.

Approximately 32% of these people are aged 50 or over.

Estimate the number of people in Scotland who are under the age of 50. Give your answer correct to the nearest 100 thousand.

6. Every week a salesman is paid a basic wage of £480.

In addition he receives commission of 12% on the first £1000 of his weekly sales and 18% on any additional sales over £1000.

Calculate: (a) his total earnings in a week where his sales totalled £840;

(b) his total earnings in a week where his sales totalled £2200.


SALE16% off all sunglasses

N4 Lifeskills Homework - Problems Involving Time

1. Julie works night shift so she has to sleep during the day.

(a) She sets her alarm clock to go off at 1545. Write this as a 12-hour time.

(b) She goes to bed at 0750. How long is it until her alarm goes off?

2. A film at the cinema has a running time of 100 minutes. The film starts at 7.35 pm.

At what time does the film finish?

3. Jack is flying to Singapore on holiday.

His flight times are shown opposite.

(a) How long will he have to wait in Dubaibefore his flight to Singapore?

(b) What is his total time for the entire journey from Glasgow to Singapore?

4. Barbara and Joe are going on a foreign holiday. Their plane leaves at 0445 on Wednesday.

The journey from their house to the airport takes 1 hour and 25 minutes. Their flight tickets state that they must check in at the airport 2 hours before their flight leaves.

What is the latest time they can leave their house?

5. Susan works a 36 hour week.

From Monday to Thursday she works from 9.00am till 5.00pm taking a 30 minute lunch break each day at 12 noon.

Her lunch breaks are not counted as part of her working hours.

At what time does she finish her work on a Friday if she starts at 9.00am andtakes her usual lunch break?

6. Two coaches per day run from Hamilton to Winchester.They usually have the same journey time.

Unfortunately coach 2 is delayed in a traffic jam adding 55 minutes to its journey.At what time did coach 2 arrive in Winchester?


Depart Glasgow 30/09/06 1320 Arrive Dubai 30/09/06 2340

Depart Dubai 01/10/06 0325 Arrive Singapore 01/10/06 1650

Coach 1 Coach 2

Hamilton 0845 1524

Winchester 1534

N4 Lifeskills Homework - Speed, Distance & Time

1. Ashlyn is training to run her first marathon. One day she planned to run 30km.

She ran for hours at an average speed of 8km/h.

How far did she still have to run so that she completed the 30km?

2. The City Express bus left Edinburgh at 0735 and arrived in Glasgow at 0850.The average speed for the journey was 60km/h.

Calculate the distance from Edinburgh to Glasgow.

3. Josh travelled from town A to town B at an average speed of 56 miles per hour.

The distance between the two towns is 210 miles.

Calculate the time taken to complete the journey.Answer in hours and minutes.

4. The table shows the distances in miles between well known places in Scotland.

(a) Use the table to find the distance from Glasgow to Stranraer.

(b) David is a salesman. He travels by car from Glasgow to Stranraer.

His journey time was 2 hours 30 minutes.

Calculate the average speed for his journey.

5. (a) The Coates family were travelling from Glasgow to Southampton to embark on a cruise.

They left Glasgow at 1020 on a Friday and travelled as far as Coventry, a distance of 500km, at an average speed of 80km/h.

When did they arrive in Coventry?

(b) The next morning they left Coventry at 9.30 am to complete the journey to Southampton.

There were some road works so they only managed to travel at an average speed of 74km/h and got to Southampton at 12 noon.


How far is it from Coventry to Southampton?N4 Lifeskills Homework - Perimeter & Area

1. Carpet costs £14.80 per square metre.

(a) Calculate how much it would cost to carpet the room shown opposite.

(b) Fixing strip for carpets costs £1.60 per metre.

Calculate the cost of the fixing strip to go round the edge of this carpet.

2. The rectangular wooden door shown opposite hasa rectangular glass panel in it.

(a) If decorative edging strip has to be fastenedaround the outside of the door and aroundthe glass panel, calculate the total length ofedging strip needed for the door.

(b) Calculate the surface area of the wood inthe door in square metres.

3. A man decides to paint the four inside walls of his garage and to re-concrete the floor.

The paint costs £1.20 per square metre to apply and theconcrete £6.80 per square metre.

Calculate the total cost of his DIY.

4. The diagram below shows the shape and dimensions of a room.

(a) Calculate the perimeter of the room.

(b) Calculate the area of the room in square metres.


0.8m

20m

02m

16m

86m 5m

3m

6m 3m

window

12m

7m

5m

05m4m

16m

length

breadth

height

N4 Lifeskills Homework - Volume of a Cube & Cuboid

1. Brian is making patterns from his sister’sbuilding blocks. Each cube has a side of length 4 cm.

(a) What is the total volume of the shape he has made?

(b) He rearranges the blocks to form a cuboid with base 12cm by 16cm. How many blocks high will the cuboid be?

2. Lesley wants to make a tank to collect rainwater to use in her garden.

She would like it to be able to hold at least 150 litres of water when full.

Is the tank shown opposite big enough?

Show your working and give a reason for your answer.

3. Jake has 100 cube shaped building blocks of side 5 centimetres which he is tryingto pack into a box measuring 45 cm by 25 cm by 10 cm.

Will all the blocks fit in the box? If not, how many will he be left with.(you must show working with your answer)

4. Two cylinders, each of radius 6 cm and height 10 cm, fit exactly into a rectangular box.

Write down the length, breadth and height of the rectangular box and hence calculate its volume.

5. A truck advertises on its side that it can carry 40 m3.

It is 7∙2m long and 2∙5 m wide.

What is the minimum height of the storage space, correct to 1 decimal place?


35cm

30cm

150cm

4 cm

We carry 40 m3

45 cm

25 cm

10 cm

N4 Lifeskills Homework - Proportion & Ratio

1. A stack of six identical books weighs kg. How much would a stack of 10 books weigh?

2. Fifteen books cost £123. How many books could you buy for £73.80?

3. A Directory Enquiry Call Centre agent can handle 240 calls every 2 hours.

How many calls can the agent handle in 75 minutes?

4. 4 books cost £35.92 and 3 films cost £15.78 to download. Find the total cost of downloading 7 books and 3 films.

5. The scale of a map is 1 cm to 6 miles. What distance on the map would represent a road which is 45 miles long?

6. Graeme and Fred invest £3400 in a new company.

(a) If the money each of them put in was in the ratio 3 : 7 , how much did Fred invest in the new company ?

(b) They decide to split the profits in the same ratio as their investment.If they made £6200 profit, how much of the profit will Graeme get ?

7. Two farmers, Bill and Dan, decided to split a herd of cows in the ratio 5 : 7.

(a) If Dan's share was 42 cows, how many cows did Bill get ?

(b) How many cows were there altogether ?

8. School trips are arranged for teachers, pupils and first aiders.

The ratio of teachers to pupils to first aiders must be 2 : 20 : 1.

(a) 60 pupils want to go on a school trip.

How many teachers must accompany them?

(b) There are enough seats on the bus for 200 people.


£

What is the maximum number of pupils that can go on the school trip?

N4 Lifeskills Homework - Graphs, Charts & Scales

1. Write down the readings indicated by A and B on these two scales:

2. A small company sells a mobile phone cover on the internet.

The cover comes in four different colours.

The bar graph below shows how many covers of each colour the company sold in a one week period.

(a) Which colour was most popular?

(b) How many more Silver covers did they sell over white?

(c) How many covers did they sell altogether in this week?

(d) The cost of each cover is £8.50.

How much money in total did the company make in the week from the covers?


60

76

92

108

124

4oF 8oFA

B

ml

Black White Silver Grey

Numberof cases sold

Colours

72

60

48

36

24

12

0

3. 720 people were surveyed and asked for their favourite take away food.

The results are shown in the pie chart. (a) How many people preferred Indian?

(b) How many more people preferred Chinese to Indian?

4.

Every week Anne goes to visit her Gran and then goes shopping on the way home. The distance/time graph of her journey is shown above.

Answer the following questions from the graph:

(a) How far did Anne travel to her Gran’s house?

(b) How long did she stay at her Gran’s house?

(c) How many kilometres did she travel from her Gran’s house to the shops?

(d) How long did she spend at the shops?

5. A class of 30 pupils was asked how they travelled to school.

The results are shown in the pie chart.

How many more pupils came by bus as opposedto walking?


Italian

ChineseIndian

150o

0900 1000 1100 1200 1300

5

1015

20

2530

35

40

Distancefrom home

(km)

Time

N4 Lifeskills Homework - Probability

1. A letter is chosen at random from the word NOVEMBER.What is the probability that a letter chosen is an E? Give your answer in its simplest form.

2. Anne is looking to buy a new property. She viewed 9 bungalows, 8 flats and 7 detached houses.She bought a property.

What is the probability that the property she bought is a flat?Give your answer as a fraction in its simplest form.

3. A box contains 12 coloured beanbags.

There are 4 yellow beanbags, 5 red beanbags, 2 blue beanbags and a green beanbag.

(a) John takes a beanbag from the box.What is the probability that the beanbag is red?

(b) John puts his beanbag back in the box and takes out the 2 blue beanbags.

Paul now chooses a beanbag from the remaining beanbags. What is the probability that it is yellow?Give your answer in its simplest form.

4. An independent magazine did a survey on the reliability of new low-energy lightbulbs.

They tested three different makes of lightbulbs. The results are shown below.

All three makers claimed there lightbulbs would last for a minimum of 1000 hours

Make A : Out of a sample of 80 lightbulbs 14 failed before 1000 hours of use.Make B : Out of a sample of 65 lightbulbs 11 failed before 1000 hours of use.Make C : Out of a sample of 90 lightbulbs 16 failed before 1000 hours of use.

By considering the probablility of failing before 1000 hours, which make of lightbulb proved to be the closest to the makers claim?

Justify your answer by calculation

5. The probability of a cat having a litter of more than eight kittens is .

(a) What is the probability of a cat having a litter of eight or less kittens?

(b) Out of 75 female cats, how many would you expect to have a litter of more than eight kittens?


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