4b6 National 5 Lifeskills: Revision Questions
1. Do all the questions in this booklet and check the answers. Ask for help as required.
2. Put a star next to all the questions you got wrong or required help (from teachers, friends or the notes) with.
3. Wait a few days and then try the starred questions a second time to see if you can manage them now.
4. If you cannot do them, ask for help again, wait a day or two and then try them again.
5. Repeat until you can do all the questions without needing help.
Topics included in this booklet:
a) Probability
b) Non-calculator skills
c) Rounding
d) Cones, Cylinders, Spheres
e) Standard Deviation
f) Medians and Quartiles and Boxplots
g) Scatter Graphs
h) Money: Foreign Currency
i) Money: Wages
j) Container Packing
k) Time Zones
l) Scale Drawing
m) Task Planning and Activity Networks
n) One-step Pythagoras
o) Money: Best Value
p) Speed, Distance and Time
The following topics have not been covered yet and will not be in the practice exam:
q) More complicated Pythagoras
r) Money: Pay and Tax
s) Money: Savings and Loans
t) Gradient
u) (has been covered, but still not covered in this booklet) Percentage increase/decrease
A) Probability
1) (non-calculator) The table below shows how many flu vaccines were given out at a doctor’s surgery.
Age / GenderMale / Female
5 or under / 4 / 3
6 – 15 / 7 / 8
16 – 59 / 37 / 47
60 or over / 12 / 32
(a) What is the probability that a patient given the flu vaccine was aged 5 or under?
(b) What is the probability that a patient given the flu vaccine was male? Give your answer as a fraction in its simplest form.
2) (non-calculator) The table below shows the number of athletes competing in the Scotland-Ireland athletics championships.
Men / WomenScotland / 28 / 30
Ireland / 32 / 10
a) An athlete is picked at random. What is the probability that the athlete is a man from Ireland?
b) A man is picked at random. What is the probability that the man is from Ireland?
B) Non-calculator skills
3) What is 40% of £75? (Hint: find 10% first)
4) £56·28 – £9·87 – £12·52
5) What is 15% of 400 grams?
6) 4400 ÷ 8
7) 62 × 24
8) £8·60 × 300
9) 2·7 × 20 × 30
10) Do the following sums using π = 3·14:
a) π × 2² × 10
b) π × 3² × 6
c) π × 3³ ÷ 3 × 4 (Hint: don’t try 3·14 × 27 without a calculator. But you could try 3·14 × 3 or 3·14 × 9)
11) Exchange rates: £1 = 2·45 euros, how many euros would you get for £325? (Hint: Work out how many euros you get for £100 first. Then work out how many you would get for £25.)
12) What is 12% of £80?
13) 38 × 47
14) $12600 – 5 × $460 – 3 × $175
15) 843 ÷ 6
16) 9·1 × 200 × 30
17) Exchange rates: £1 = 3·20 krona, how many krona would you get for £750?
C) Rounding
18) Round £2 875 859·24 to the nearest ten thousand pounds.
19) Round 36854·536748 to three significant figures
20) Round £176·925856 to two significant figures
D) Cones, Cylinders, Spheres
21) (past Intermediate 2 exam questions) Find the volume of each of these shapes
a) This child’s toy is made of a cone and a hemisphere.i) find its volume
ii) how many toys can be made out of 30 litres of melted plastic?
/ b) This farm store building is made of a cylinder and a hemisphere:
i) find its volume
ii) there is 5600m³ of grain to be stored. How many of these farm buildings are needed to store it?
22) A cylindrical soft drinks can is 15 centimetres in height and 6·5 centimetres in diameter.
a) Find its volume
b) A new cylindrical can holds the same volume but has a reduced height of 12 centimetres. What is the diameter of the new can? Give your answer to 1 decimal place.
c) How many drinks cans are able to be completely filled from a 200 litre tank?
23) Both of the lengths in the farm building in question 21(a) are measured correct to a tolerance of ±10%. What is the minimum volume of the building?
E) Standard Deviation
24) A cricket team’s scores in January were 125, 163, 142 and 156.
a) Calculate the mean and standard deviation of these scores.
b) In May the same team’s scores had a mean of 131 and a standard deviation of 12·4. Make two appropriate comments comparing the team’s scores in January and May.
25) A new refrigerator is installed in a supermarket. It’s temperature is measured hourly for six hours and is found to be 2·1ºC, 3·4°C, 2·5°C, 2·3°C, 2·5°C and 2·8°C.
For the refrigeration unit to be classed as working properly, it must have a mean temperature of 2·4°C ± 0·25°C and a standard deviation of less than 0·5°C.
Is the refrigeration unit working correctly?
F) Medians and Quartiles and Boxplots
26) The list below shows the ages (in years) of cars in a used-car showroom:
4 / 7 / 2 / 9 / 4 / 7 / 5 / 6 / 76 / 9 / 2 / 4 / 10 / 3 / 5 / 10 / 9
Find the median and quartiles of this data and construct a boxplot.
27) 2008 Intermediate 2 Exam Question: In a survey, the number of books carried by each girl in a group of students was recorded. The results are shown in the frequency table below.
Number of books / Frequency0
1
2
3
4
5
6
7 / 1
2
3
5
5
6
2
1
a) Draw a boxplot for this data.
b) Calculate the semi-interquartile range.
G) Scatter Graphs
28) A guide to used cars shows the engine size (in cc) and the mileage per gallon.
Car / A / B / C / D / E / F / G / H / IEngine size (cc) / 1000 / 1100 / 1300 / 1400 / 1600 / 1900 / 1800 / 2000 / 1600
Mileage per gallon / 40 / 36 / 38 / 34 / 32 / 26 / 20 / 27 / 30
a) Using this data draw a Scatter Graph.
b) Draw a best-fitting line on the graph.
c) One car does not appear to follow the trend. Which one is it? Give a reason for your answer.
Exchange Rates £1 buysJapanese Yen (¥) / 172·419
Euros (€) / 1·2666
US Dollars ($) / 1·6054
Swedish Krona (kr) / 11·5082
Indian Rupee (₹) / 97·9293
Korean Won (₩) / 1712·97
H) Money: Foreign Currency
29) The exchange rates for some currencies are shown in a table on the right.
Valerie is buying a Daewoo car.
· A Daewoo car bought in the UK costs £9460 plus 3·2% tax.
· A Daewoo car bought in Korea costs 16 million Won (₩) plus an extra 300 000 Won to ship it to the UK.
Is it cheaper for Valerie to buy the Volvo in the UK or in Korea? How much cheaper?
30) Jane is going to Switzerland and wants to change £1200 into Swiss francs. Two travel agents offer the following exchange rates. Each also takes off a charge as their own fee.
TravelSun£1 = 2·46 Swiss francs
Charge: 5 francs / Sollair
£1 = 2·51 Swiss francs
Charge: 2·1%
Which agent will give Jane more money, and how much more will she get?
I) Money: Wages
31) (non-calculator) Dave gets paid £5·62 per hour. In one week, he works 30 hours, and he pays £32·17 tax and £6·20 National Insurance. Calculate his take home pay.
32) Danielle gets paid £6·29 per hour. In one week, she works 42 hours, and she pays 20% tax and 3·5% National Insurance. Calculate her take home pay.
J) Container Packing
33) Washing machines are being packed into a lorry.
The lorry measures 6m (height) by 2·5m by 3·2m. Each washing machine measures 95cm (height) by 80cm by 62cm. The washing machines must be packed upright (i.e. the 95cm side must match with the 6m side)
(a) What is the largest number of machines that can fit inside one lorry, and how should they be packed to enable this to happen?
(b) The company has 600 washing machines to send out by road. How many lorries are needed to transport them all?
34) Pencil sharpeners for a school are being packed into a cardboard box.
The cardboard box measures 15cm by 5cm by 4·5cm.
Each sharpener measures 12mm by 6mm by 6mm.
It does not matter which way around the sharpeners are placed. (there are three possible ways)
What is the maximum number of sharpeners that can be fitted into the box? Justify your answer.
K) Time Zones
35) (non-calculator) Las Vegas is 7 hours behind GMT. Sydney is 11 hours ahead of GMT.
Jenny is in Las Vegas and is on the phone to her brother Mark in Sydney. Jenny begins that phone call at 9:45pm and 10 seconds Las Vegas time. The phone call lasts 16 minutes 12 seconds. What time is it in Sydney when the phone call ends?
36) A plane from London to Nairobi flies at an average speed of 450mph.
The distance from London to Nairobi is 6449 miles.
The plane stops off 1 hour 12 minutes in Amsterdam on the way.
a) How long does the entire journey, including the stopover in Amsterdam, last?
The plane takes off in London at 1346GMT on Tuesday.
The time in Nairobi is 3 hours ahead of GMT.
b) What is the local time in Nairobi when the plane lands?
L) Scale Drawing (you will need a ruler and protractor for these questions)
37) A scout troop set off on a walk from a camp. They walk for 15 kilometres on a bearing of 051° to a waterfall, and then 18km on a bearing of 125° to a hill and then they return to camp.
a) Choose a suitable scale and make a scale drawing of this route.
b) Use your scale drawing to find:
(1) The total distance they walked that day
(2) The bearing of the hill from the camp.
(3) The speed they walked at (in kilometres per hour) given that the whole walk took them 11 hours 13 minutes. Round your answer to 2 significant figures.
38) The scale drawing shows the position of two ports, Lubness and Moy.
a) What is the bearing of Moy from Lubness?
b) A boat lies on a bearing of 120° from Lubness and 200° from Moy. Show this on the scale drawing and determine how far the boat is in real life from Moy.
M) Task Planning and Activity Networks
39) (SQP) (non-calculator) Three friends decide to tidy up their garden. The precedence table below shows the tasks that need to be done and their preceding tasks:
a) Complete the chart below by writing the tasks and their times (in minutes) into the boxes.
b) What is the shortest possible time it will take to tidy the garden?
N) One-step Pythagoras
40) The diagram shows a piece of jewellery made from two right-angled triangles. All measurements are in millimetres.
a) Calculate the hypotenuse of the smaller triangle.
b) Calculate the total area of the jewellery
41) A wooden gate is 85 centimetres high and 200 centimetres wide. The gate is made of four horizontal bars strengthened by two diagonal bars which meet half-way across the gate as shown. The ends of each bar measure 15 centimetres.
a) Calculate the length of one of the diagonal bars.
b) The wood for all six bars can be bought in half-metre sections, which can be cut to size and joined together as required. The wood costs £12·04 per half metre. Calculate the total cost of buying the wood for the gate.
O) Money: Best Value
42) Alan and takes his 3 children to the cinema every Saturday afternoon. Adult tickets cost £8·95 and child tickets cost £5·40.
Gold Monthly Family Ticket.Cost £25. / Platinum Monthly Family Ticket.
Cost £15.
40% off all ticket prices
Once you’ve bought more than 10 tickets in a month, any further child tickets are free / Adults pay full price.
65% off all children’s ticket
In March 2015 there are four Saturdays.
Alan has three options:
· Buy all tickets full price
· Buy a Gold Family Ticket to try and save money.
· Buy a Platinum Family Ticket to try and save money.
Which option is cheapest for Alan? If one of the family tickets is the cheapest, how much cheaper is it than full price?
P) Speed, Distance and Time
43) Daniel jogs at a speed of 3·45m/s from 6:48pm until 7:14pm. How far did he jog in total? Round your answer to 3 significant figures.
44) A small plane takes off at 0945 and lands at 1010 at an airfield 78 miles away. What is the speed of the plane in miles per hour? Round your answer to 2 significant figures.
45) (non-calculator) Daniel does a second jog at a speed of 2·98m/s from 9:40pm until 10:10pm. How far did he jog in total? (Hint: remember that to multiply a decimal by 60, multiply by 6 first, then by 10).
46) The world record (in minutes:seconds) for the 3000m in athletics is:
· 7:20·67 minutes for men (Daniel Komen, Kenya)
· 8:06·11 minutes for women (Wang Junxia, China)
What is the difference in speeds between men and women?
47) (non-calculator) A plane flies 2130km at a speed of 300km/h. How long will the journey last in hours and minutes?