Pegasys Educational Publishing
CFE Resources
National 5 Lifeskills
Unit 2
Geometry & Measures
Homework Exercises
 Homework exercises covering
the Unit 2 topics
 + Answers
 Pegasys 2015
National 5 Lifeskills - Geometry & Measures Unit
N5 Lifeskills Homework - Formulae
1.
The following formulae are used in mathematics and science.
Evaluate each formula for the numbers given:
2.
AVt
mT
(a)
h
(b)
s = ut + ½ at2
Find s when a = 0∙2, t = 90 and u = 0∙5
(c)
A =  (R2  r2)
Find A when  = 3∙14, R = 20 and r = 8.
(d)
a=
Find h when A = 6, m = 08, V = 12 , t = 60, T = 20.
b2  c2
Find a when b = 31∙2 and c = 12.
The formula used to calculate the surface area of a sphere is given as
S  4r 2
What radius would give a sphere a surface area of 28274cm2?
Give your answer to 2 significant figures.
3.
A mechanic uses a formula to work out customers' bills for servicing their cars.
The formula is
C  1  2 ( 25 t  P)  32 ,
where £C is the final bill, t is the time in hours to do the job and £P is the
cost of any parts needed.
For a certain customer the final bill for his car service was £363.80 and the job
needed £126.50 worth of parts. Calculate how many hours this service took to complete.
4.
A rectangular metal water tank measures 35 metres long, 15 metres
wide and 18 metres tall.
Estimate how much it would cost to paint the four sides and
the top of the tank if paint costs £7.50 per tin, each tin
can cover 8 square metres and two coats are needed.
Your answer must be accompanied with the appropriate working.
 Pegasys 2015
National 5 Lifeskills - Geometry & Measures Unit
N5 Lifeskills Homework - Scale Drawing
1.
(a)
The diagram shows the logo for a tent company.
Draw an enlargement of this logo.
Make each of its sides twice as long.
(b)
2.
Make an accurate drawing of a reduction of this
logo using a scale factor of 12 .
The delivery chute in a packing factory needs to be replaced.
Make an accurate scale drawing and use it to
estimate the length of the chute.
Use a scale of 1cm to 1m.
40o
75 m
3.
The diagram shows the side view of a panel on a printing machine.
x
The shape of the side view is a trapezium.
The diagram is not drawn to scale.
40cm
(a)
(b)
4.
Using a scale of 1 : 20, make an accurate scale
drawing of the side panel.
Use your diagram to estimate the length of the edge marked x.
120cm
30
o
100cm
Here is part of the map of Normandy in France.
(a)
Using the scale given on the map, estimate
the distance as the crow flies, in kilometres,
from Rennes to Laval.
(b)
A light plane has a maximum speed of
160 km/h, estimate how long it would take,
flying at its maximum speed, to fly the triangle,
Rennes to Fougeres on to Laval and then
back to Rennes?
 Pegasys 2015
National 5 Lifeskills - Geometry & Measures Unit
N5 Lifeskills Homework - Scale Drawing and Bearings
1.
This is Simone's journey to school. Make a scale drawing of her journey using a scale
of 1 cm : 50 m.
Home :
2.
Distance
Direction
200 m
000o
100m
045o
400 m
090o
250 m
000o
: School
N
N
B
N
N
A
C
3.
D
(a)
Draw a table like the one in Q1 to show the distance and direction for each stage of the
journey from A through to D above.
(b)
State the bearing and the distance to return directly from D to A.
A fishing boat sails from harbour H on a bearing of 084o for 340km until it reaches point P.
It then sails on a bearing of 210o for 160km until it reaches point Q.
4.
(a)
Using a suitable scale, construct a scale drawing to represent the fishing
boat's journey.
(b)
Estimate the bearing the boat must sail along to return directly to the
harbour from Q?
(c)
Estimate the direct distance between point Q and the harbour.
Two ships leave Liverpool at the same time. One of them travels north-west at an average speed
of 105 km/h while the other travels at an average speed of 14 km/h on a bearing of 280o.
Using a suitable scale, make a scale drawing, and use it to estimate how far apart the ships are
after 2 hours.
 Pegasys 2015
National 5 Lifeskills - Geometry & Measures Unit
N5 Lifeskills Homework - Stacking, Packing and Filling
1.
The seven boxes below have to be stored on three shelves.
Each shelf can carry no more than 675 kilograms.
Copy and complete the table below to show a way of placing the seven boxes on the
three shelves.
SHELF 3
340 kg
420 kg
SHELF 2
195 kg
390 kg
95 kg
SHELF 1
245 kg
255 kg
Boxes (write down their weights)
Total Weight
SHELF 1
SHELF 2
SHELF 3
2.
The three shelves on Susan's bookcase are 64cm long. The space between each shelf is 20cm.
Susan wants to stack her collection of identical
books so as to get as many books onto the shelves
as possible.
19cm
Each book has dimensions
as shown here.
20cm
3cm
How many more books can she get onto the shelves
if she stacks them upright (as seen on top shelf) as
opposed to longwise (as seen on bottom shelf)?
64cm
 Pegasys 2015
National 5 Lifeskills - Geometry & Measures Unit
3.
Baked beans come in cylindrical tins 11 centimetres high and with diameter 7 centimetres.
The tins are packed into boxes measuring 42 centimetres by 28 centimetres by 35 centimetres.
7 cm
35 cm
11 cm
28 cm
(tin and box not to scale)
42 cm
(a)
One layer of cans is placed (upright) into the bottom of the box above.
How many cans will fit into the bottom layer?
(b)
How many tins can be packed into the box altogether?
(c)
i) Use the formula V  r 2 h to calculate the volume of one can of beans.
ii) Can all the tins in one box be filled from a drum containing 30 litres
of baked beans?
You must show working and give a reason for your answer.
4.
Six delicate glass cylinders, each of radius 8cm and height 12cm, fit exactly into a
rectangular box as shown in the diagram.
(a)
(i)
Write down the length, breadth and height of the box.
(ii)
Find the volume of the box. [ V  lbh ]
The space surrounding the cylinders has to be filled with injected liquid foam to protect
the cylinders.
(b)
Calculate the volume of foam required to completely fill up all the free space in the box.
Round your answer to one decimal place. [ Vcyl  r 2 h ]
 Pegasys 2015
National 5 Lifeskills - Geometry & Measures Unit
N5 Lifeskills Homework - Precedence Tables & Planning Tasks
1.
John and Mark are hoping to be able to clean their dad's car together in less than 1 hour.
The precedence table below shows the tasks they need to complete and how long
they estimate each will take.
Tasks C and D are timed with both boys working together on the same task. The remainder
of the tasks are timed for a single person working.
Task
Activity
Preceded by
Time (mins)
A
Get cleaning materials from garage
-
4
B
Fill buckets one soapy one plain water
-
6
A, B
15
C
2.
Car body is washed with soapy water (both)
D
Car is rinsed with plain water
A, B, C
25
E
Wheels are washed
A, B,C
12
F
Insides of car windows are washed and dried
A, B, C
15
G
Car is dried with clothes (both)
A, B, C, D, E
10
(a)
Draw a network diagram showing which tasks can be done at the same time.
(b)
Use the critical path to decide whether or not John and Mark can complete the
cleaning of the car within one hour.
Shakira has decided to make herself some spaghetti on toast for her lunch.
In the kitchen she has use of a micro-wave a cooker and a small pot.
She notes the following ……..
*
*
*
*
the bread is frozen in the freezer
the spaghetti is in a tin
she wants butter on her toast
she wants a glass of milk with her beans on toast
(a)
Decide on the tasks you think Shakira needs to do to make her lunch.
(b)
Draw and complete a precedence table to show the order of the tasks as you see them
and give an estimated time for each task.
(c)
Use the critical path to work out the minimum amount of time you think she needs to
make her lunch.
 Pegasys 2015
National 5 Lifeskills - Geometry & Measures Unit
N5 Lifeskills Homework - Problems Involving Time Management and Time
1.
Michael owns and hires out a small mini-bus with himself as the driver.
He charges a set fee of £36 for any hire plus a charge of 60p for each mile
travelled. He also charges £4 per quarter of an hour for his own time while
driving with customers on board.
2.
(a)
How much would he charge for a hire which he estimates to be a 68 mile round
trip and will involve him driving with customers on board for an estimated
total time of two and a half hours.
(b)
By only charging for his 'time' when customers are actually in the mini-bus with him,
can you think of any situations, relating to the job he is doing, where he might not be
charging for his 'time' in the most effective way?
John is in Coatbridge and is planning to drive to Aberdeen.
Because of heavy traffic and speed limiting cameras, he reckons
he can average 48 miles per hour.
3.
(a)
How long will his journey take, in hours and minutes, if the distance
between Coatbridge and Aberdeen is 132 miles.
(b)
What is the latest time John should leave Coatbridge if he needs to arrive
in Aberdeen by 13 20?
Bryan had to be at the airport to check in one and a half hours before his flight at 0610.
He lives 90km from the airport and left home at 02 50.
Bryan drove at an average speed of 72km/h.
Once he arrived at the airport it took him 30 mins to park his
car and get to the check-in desk.
Did he make it on time to check in?
You must show all working and give a reason for your answer.
4.
Susan is flying from Glasgow at 22.30 on Wednesday the 4th March to fly to Hong Kong via
London Heathrow.
Her in-flight times and London stop-over time
are shown in the table.
With Hong Kong being + 8 hours GMT, what
will the date and local time be when she arrives
in Hong Kong?
 Pegasys 2015
Flight time Glasgow to London
1h 15m
duration of London stop-over
5h 20m
Flight time London to Hong Kong
11h 35m
National 5 Lifeskills - Geometry & Measures Unit
N5 Lifeskills Homework - Tolerance
1.
(a)
The lifespan of a standard light bulb has a tolerance of (2600  450) hours.
State the minimum and maximum acceptable lifespan.
(b)
A metal punch is designed to punch holes through thin steel plate.
The diameter of any punched hole has a tolerance range of 4285cm to 4.293cm.
Write the diameter of a punched whole in tolerance notation.
2.
A company producing matches sells them in various box sizes.
The largest box they sell has its contents marked on the box as
contents : (240  11) matches
A random sample of boxes is taken and their contents checked. The number of matches in each
box in the sample is shown below.
238
249
241
244
237
228
241
255
240
254
240
236
252
241
248
246
231
237
233
227
229
252
224
230
If more than 20% of the boxes in any sample are either above or below the tolerance limits
then the packing machine needs to be serviced.
Does the packing machine need serviced?
3.
(a)
(b)
4.
(180  002) m
A window frame has dimensions as shown.
Calculate the minimum and maximum
possible areas of the frame.
(156  002) m
Write this minimum and maximum area
in tolerance notation.
A cube has side of length (25  05) cm.
Calculate the difference between its possible minimum and maximum volumes.
 Pegasys 2015
National 5 Lifeskills - Geometry & Measures Unit
N5 Lifeskills Homework - Gradients
1.
A child's chute is deemed to be unsafe if its gradient
is more than 08.
26 m
Is the chute shown opposite safe or unsafe for children?
You must give a reason with your answer.
2.
34 m
In order to test the stability of a bus a tilting platform is used.
This bus will begin to topple when a gradient of 40% is reached.
xm
Calculate the value of x so that the bus just begins to topple.
8m
y
3.
(b)
Calculate the gradients of
the lines (a), (b) and (c) on
the diagram.
(a)
(c)
x
O
4.
Calculate the gradients of the lines joining each pair of points below.
(a) (2, 1) and (6, 3)
5.
(b) (1, 5) and (3, 1)
(c) (1, 2) and (5, 1)
(d) (4, 2) and (4, 4)
A line has a gradient of 2 and passes through the points (1 , 8) and (6 , k).
Find the value of k.
 Pegasys 2015
National 5 Lifeskills - Geometry & Measures Unit
N5 Lifeskills Homework - Composite Shape Problems
1.
Calculate the area of each composite shape below:
(note.... assume right-angles where obvious)
Round your answers to 1 decimal place where necessary.
(a)
(b)
8cm
5cm
3cm
2cm
2.
14mm
10mm
The diagram shows a rectangular lawn measuring 7metres by 4 metres with a circular
flower bed of diameter 4 metres positioned as shown.
7m
lawn
flower
bed
4m
12m
How much would it cost to re-turf the lawn if an online supplier of turf is
quoting £2.60 per square metre for their premier turf?
3.
A Japanese paper fan is fully opened when angle PQR  150o as shown.
Using the dimensions shown in the diagram, calculate
the approximate area of paper material in the fan.
19cm
36cm
P
150o
Q
 Pegasys 2015
R
National 5 Lifeskills - Geometry & Measures Unit
4.
The diagram below shows a lawn (unshaded) surrounded by a concrete path of uniform
width (shaded).
The curved end of the lawn is a semi-circle of diameter 14 metres.
37 m
18 m
lawn
5.
(a)
Calculate the area of the lawn.
(b)
Calculate the area of the path.
(c)
How much would it cost to re-concrete the path if the concrete costs £4.80 per
square metre to lay?
Q
A wafer biscuit for ice cream consists of a sector of a circle with
a triangular part removed as shown in the diagram.
The radius of the circle PQ is 7cm and PS = 2cm.
Wafer
Angle SPT = 90o.
S
P
Calculate the area of the biscuit.
T
R
 Pegasys 2015
National 5 Lifeskills - Geometry & Measures Unit
N5 Lifeskills Homework - Volume of Composite Solids
1.
Calculate the total volume of a factory
unit which is 90 metres long and whose
side view dimensions are shown
opposite.
7m
4m
90m
16m
2.
Two identical solid spheres are packed into the smallest
rectangular box possible.
Calculate the amount of unoccupied space left in the
box given that the radius of each sphere is 20cm.
3
[ Volume of a sphere : V  43  r ]
3.
The prism below was formed by removing a cross-sectional sector from a cylindrical
metal block.
14cm
100o
O
end view
O is the centre of the circular end.
(a)
Given that the original cylinder had a diameter of 8cm, calculate the volume of
the prism in cubic centimetres.
Give your answer correct to 3 significant figures.
(b)
Calculate the mass of this object in kilograms if 1cm3 of the metal
weighs 8∙4 grammes.
 Pegasys 2015
National 5 Lifeskills - Geometry & Measures Unit
4.
Below are two fireworks made by the same company. One is in the shape of a cylinder
and the other a cone.
The two fireworks have the same volume and the same height.
11  5 cm
11  5 cm
6  5 cm
d
Calculate the diameter of the cone, d, correct to 1-decimal place.
[ Volume of a cone : V  13 r 2 h ]
5.
A cone of ice with a base radius of 6cm and a height of 16cm is placed in a
small rectangular glass tank as shown below.
16cm
6cm
13cm
15cm
(a)
Calculate the volume of the cone giving your answer correct
to 3 significant figures.
(b)
If the cone is left to melt away completely, calculate the depth of water
in the tank once all the ice has melted.
 Pegasys 2015
National 5 Lifeskills - Geometry & Measures Unit
N5 Lifeskills Homework - Problems Involving Pythagoras' Theorem
6m
1.
The room shown opposite has two parallel sides.
(a)
Using the given dimensions calculate
the length of the missing side in the room.
(b)
Calculate the perimeter of the room.
3m
46 m
2.
3.
A rhombus has sides of 20cm and its longest diagonal
measuring 34cm.
(a)
Calculate the length of the shorter diagonal.
(b)
Calculate the area of the rhombus
20cm
34cm
T
The pyramid opposite has a rectangular base.
(a)
Calculate the length of the base
diagonal PR.
(b)
Given that edge TR = 18cm, calculate the
vertical height of the pyramid.
(c)
18cm
R
Q
12cm
Calculate the volume of the pyramid.
P
S
16cm
4.
Calculate the length of the banister rail shown in
the diagram if there are 6 stairs, and if each tread
measures 35cm and each riser 20cm.
x
1m
Give your answer in metres.
1m
 Pegasys 2015
National 5 Lifeskills - Geometry & Measures Unit
5.
The shaded shape shown below is constructed from a right-angled triangle and a sector of
a circle.
The sector has an angle of 220o at its centre and the right-angled triangle has two of its
sides measuring 18 centimetres and 16 centimetres as shown.
18cm
220o
(a)
16cm
Calculate the length of the third side of the triangle.
Give your answer correct to 3 significant figures.
(b)
6.
Calculate the area of the shaded shape.
The diagram shows a figure made up from two intersecting circles each with radius 10 cm.
AB is a common chord of both circles.
A
16 cm
B
h cm
10 cm
O
Given that AB = 16 cm, calculate the height, h cm, of the figure.
 Pegasys 2015
National 5 Lifeskills - Geometry & Measures Unit
 Pegasys 2015
National 5 Lifeskills - Geometry & Measures Unit