Maths grade-8

371 Pages·2015·1.05 MB·English

1 MathematMiEPc Y8 Paractilce BoDok A iagrams
1.1 Mileage Charts
In this section we look at mileage charts.
Example 1
Distances in the table below are given in miles.
E
L
P
A
T
S
N
R
A
B OL
T
S
100 RI
B R
E
T
E E
55 84 EX N C
A
Z
N H
108 194 110 PE UT
O
M
Y N
67 125 44 77 PL TO
N
U
A
T
50 51 34 144 75
Using the table, answer the following questions:
(a) How far is it from Taunton to Exeter?
(b) Jerry travels from Barnstaple to Exeter, then from Exeter to Plymouth, and
finally from Plymouth back to Barnstaple.
How far does he travel altogether?
Solution
(a) 34 miles (see table and diagram
opposite). R
E
T
E
X
E
(b) Barnstaple to Exeter: 55 miles
Exeter to Plymouth: 44 miles
Plymouth to Barnstaple: 67 miles N
O
T
N
U
Total distance = 55 + 44 + 67 A
T
34
= 166 miles
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1.1 MEP Y8 Practice Book A
Example 2
10
Devizes
The network diagram opposite shows Upavon
the distances, in miles, between some
towns.
9
14
Copy and complete the following 6
Shrewton
mileage chart to show the shortest Amesbury
distances between these
towns: 11 8
Y
R
U
B Salisbury
S
E
M
A ES
Z
VI Y
E R
D U
B
S
SALI W TO N
E
R
H
S
N
O
V
A
P
U
Solution
Y
R
The direct distances can be completed first: U
B
S
E
M
the shortest route from Amesbury to Devizes A ES
Z
is via Upavon, a total of 19 miles; VI Y
E R
D U
B
the shortest route from Devizes to Salisbury S
is via Shrewton, a total of 25 miles; 8 SALI W TO N
E
R
the shortest route from Salisbury to Upavon H
6 14 11 S
N
is via Amesbury, a total of 17 miles; O
V
A
P
the shortest route from Shrewton to Upavon 9 10 U
is via Amesbury, a total of 15 miles.
Y
R
U
B
S
E
M
A ES
Z
With this information, the table can now be VI Y
19 E R
completed, as shown opposite. D U
B
S
8 25 SALI W TO N
E
R
H
6 14 11 S
N
O
V
A
P
9 10 17 15 U
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MEP Y8 Practice Book A
Exercises
1. Use the table opposite, where the L
L
U
distances are given in miles, to H
S
D
find out how far it is from: E
60 E N
L L R
(a) Leeds to Lincoln, O E
C T
N S
(b) Hull to York, 47 72 LI HE
C
N
A D
(c) Leeds to Manchester, 97 44 85 M L
E
FI
(d) Sheffield to Leeds, EF
H
66 36 47 39 S
(e) Manchester to York. R K
O
Y
38 24 80 71 57
2. Ross travels from Leeds to Manchester, then from Manchester to Sheffield
and finally from Sheffield back to Leeds. Use the table in question 1 to
calculate the total distance he travels.
3. Hannah drives from Bristol to Exeter, continues to Plymouth, on to
Barnstaple and from there back to Bristol. Use the table in Example 1 to
calculate the total distance she drives.
N
O
Ç
N
E
L
A
4. The table opposite gives the S
AI
distances in kilometres 365 AL S
C N
between some towns in A
M
northern France. 49 419 E S
L N
A
E
What is the distance between: L
R
167 433 138 O
(a) Alençon and Paris, RIS
A
220 293 204 135 P
(b) Reims and Orleans,
S
M
(c) Rouen and Calais, EI
355 278 340 270 146 R N
E
U
(d) Paris and Reims, O
R
146 215 199 210 140 284
(e) Le Mans and Rouen?
5. Debbie drives from Calais to Paris and back while she is on holiday. Use the
table in question 4 to calculate how far she travels altogether on this journey.
6. Laura travels from Calais to Paris, on to Alençon and then to Rouen before
returning to Paris. Use the table in question 4 to calculate how far she travels
altogether.
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1.1 MEP Y8 Practice Book A
7. The diagram below shows the distances, in miles, between some junctions
on the M2 motorway:
1 4 4 4 10 2
Jn 1 Jn 2 Jn 3 Jn 4 Jn 5 Jn 6 Jn 7
Copy and complete the chart below to show the shortest distances between
junctions:
1
N
O
TI
C
N 2
U N
J O
TI
C 3
N N
U O
J TI
C 4
N N
U O
J TI
C 5
N N
U O
J TI
C
N 6
U N
J O
TI
N C N 7
U O
J TI
C
N
U
J
8. The following network diagram shows the distances, in miles, between
some towns in Wales:
Lampeter
16
23
Llandovery
4
7
15
Llanwrda
Carmarthen Llandeilo
Use the information in the diagram to complete a copy of the table on the
next page, giving the shortest distances between the towns.
4
MEP Y8 Practice Book A
N
E
H
T
R
A
M
R
A R
C E
T
E
M P O
LA EIL
D Y
N R
A E
L V
L O
D
N A
A D
L R
L W
N
A
L
L
9. The network diagram below shows the distances, in miles, by road between
some towns close to the Scottish border:
Longtown
4
Gretna 9
9
Carlisle 8
Brampton
19
19
Alston
20
N
Penrith O
T
S N
AL O
T
P
M
A
R E
B SL
Use information from the diagram RLI
A
to complete a copy of the table C A
N
T N
opposite, giving the shortest E W
R
G O
distances between the towns. T
G
N
O
L H
T
RI
N
E
P
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1.1 MEP Y8 Practice Book A
10. The diagram below shows stations on the GNER railway:
LONDON STEVENAGE PETERBOROUGH DONCASTER YORK
N
O
D E
Some distances, in miles, are shown N G
O A H
L N G
in the table opposite. E U
V O
E R
(a) Copy the table and fill in 21 ST B O
R R
the missing distances. 68 47 PETE ASTE
(b) What distance is travelled C
N
in a return journey between 188 167 120 D O
London and York? K
R
O
45 Y
1.2 Using Flow Charts to Plan Practical Tasks
A flow chart can be used to organise the instructions for carrying out a task.
Boxes of different shapes are used for particular operations:
START or END POINTS START END
INSTRUCTION BOXES
NO
DECISION BOXES
YES
Each box contains only one instruction.
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MEP Y8 Practice Book A
Example 1
Draw a flow chart to give the instructions for making a mug of tea.
Solution
START
FILL
KETTLE
The flow chart gives the instructions for making
BOIL
KETTLE a mug of tea without sugar.
A mug of tea with sugar, needs this
PUTTEA BAG
IN MUG extra instruction box:
ADD SUGAR
POUR BOILING
WATER INTO
MUG
PUTTEA BAG
Note that the instruction box can go
IN MUG
TAKE OUT
TEA BAG
earlier in the flow chart, for example, immediately
after the START box. The extra box
ADD MILK
ADD SUGAR can also go in various positions: for
PUTTEA BAG
example, before or after the box, or
IN MUG
STIR TEA
before or after the ADD MILK box.
STOP
Example 2
BOIL
The instruction in Example 1 can be broken down into separate
KETTLE
stages.
Draw a flow chart to show this.
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1.2 MEP Y8 Practice Book A
Solution
PLUG IN
KETTLE
SWITCH
ON KETTLE
WAIT
20 SECONDS
IS THE
KETTLE NO
BOILING
?
YES
Example 3
Draw a flow chart showing how to find a programme you would like to watch on
television.
Solution
START
SWITCH ON
THE TV
WATCH THE
PROGRAMME
IS IT HAVE
A GOOD NO YOU TRIED NO CHANGE
PROGRAMME ALL THE CHANNELS
? CHANNELS
?
YES YES
WATCH THE
PROGRAMME
SWITCH OFF AND FIND
SOMETHING ELSE TO DO
STOP
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MEP Y8 Practice Book A
Exercises
1. Draw a flow chart showing how to prepare a drink of blackcurrant squash in
a glass.
2. Draw a flow chart for each of the following:
(a) making a cup of coffee with milk and sugar,
(b) buying a can of drink from a vending machine,
(c) making a telephone call from a pay phone,
(d) shutting down a computer.
3. Draw a flow chart that describes how to cross a road. You should include
decision boxes in your flow chart.
4. Imagine you are driving along a road. You see a 30 mph speed limit sign
and a speed camera. Draw a flow chart that you, as a sensible driver, would
be advised to follow.
5. Jerry needs to work out 4.72 · 11.61 using a calculator.
(a) Draw a flow chart to show how to carry out this calculation on a
calculator.
(b) Redraw the flow chart to include all the following processes:
(i) estimating the answer to 4.72 · 11.61,
(ii) calculating the answer to 4.72 · 11.61
(iii) comparing the answer with the estimate to decide whether the
calculator answer is reasonable.
6. You are playing Snakes and Ladders.
(a) Draw a flow chart to describe how to move your counter for one go.
(b) Describe how you would change your chart when you have an extra
turn after throwing a six.
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MEP Y8 Practice Book A
1.3 Using a Flow Chart for Classification
Flow charts can also be used to sort or classify things.
Example 1
This flow chart can be used to classify angles between 0 (cid:176) and 360(cid:176) . What comes
out at the end points A, B, C, D and E ?
START
IS
ANGLE NO
LESS THAN
90˚
?
IS
YES ANGLE NO
EQUAL TO
90˚
?
IS
YES ANGLE
NO
GREATER
THAN
180˚
?
IS
YES ANGLE NO
EQUAL TO
180˚
?
YES
A B C D E
Solution
A Angles less than 90 (cid:176) ACUTE ANGLES
B Angles equal to 90 (cid:176) RIGHT ANGLES
C Angles greater than 180 (cid:176) REFLEX ANGLES
D Angles equal to 180 (cid:176) ANGLES ON STRAIGHT LINES
E Angles greater than 90 (cid:176) but less than 180 (cid:176) OBTUSE ANGLES
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