INTERMEDIATE 2

1
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
Please decide which Unit you would like to revise
UNIT 1
UNIT 2
UNIT 3
UNIT 4
Calculations using Volumes of Solids Linear
Relationships Algebraic Operations Circles
Trigonometry Simultaneous Linear Equations Graphs,
Charts Tables Statistics
Algebraic Operations Quadratic Functions Further
Trigonometry
Calculations in a Social Context Logic
Diagrams Formulae
EXIT
2
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
Calculations using Percentages
Volumes of Solids
UNIT 1
Linear Relationships
Algebraic Operations
Circles
EXIT
3
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
You have chosen to study
Calculations using Percentages
UNIT 1
Please choose a question to attempt from the
following
1
2
3
4
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4
Calculations using Percentages Question 1

• In 2001, John deposits 650 in the bank at an
  interest rate of 3.5.
• How much is his deposit worth after 1 year?
• In 2002, the interest rate changed to 3.2, and
  in 2003 it changed again to 4.1. Calculate how
  much interest John will have earned at the end
  of 2003.

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5
Calculations using Percentages Question 1

• In 2001, John deposits 650 in the bank at an
  interest rate of 3.5.
• How much is his deposit worth after 1 year?
• In 2002, the interest rate changed to 3.2, and
  in 2003 it changed again to 4.1. Calculate how
  much interest John will have earned at the end
  of 2003.

Reveal answer only
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EXIT
6
Question 1

1. 3.5 of 650 0.035 x 650 22.75

• In 2001, John deposits 650 in the bank at an
  interest rate of 3.5.
• How much is his deposit worth after 1 year?
• In 2002, the interest rate changed to 3.2, and
  in 2003 it changed again to 4.1. Calculate how
  much interest John will have earned at the end of
  2003.

OR 650 x 1.035 672.75
(b) 3.2 of 672.75 0.032 x 672.75 21.53
Value at end of 2002 672.75 21.53 694.28
4.1 of 694.28 0.041 x 694.28 28.47
Value at end of 2003 694.28 28.47 722.75
Begin Solution
Continue Solution
OR 672.75 x 1.032 x 1.041 722.74
Markers Comments
Total Interest 722.74 650 72.74
Calculations using Percentages Menu
7
Markers Comments

1. 3.5 of 650 0.035 x 650 22.75

OR 650 x 1.035 672.75
(b) 3.2 of 672.75 0.032 x 672.75 21.53
Value at end of 2002 672.75 21.53 694.28
4.1 of 694.28 0.041 x 694.28 28.47
Value at end of 2003 694.28 28.47 722.75
Next Comment
OR 672.75 x 1.032 x 1.041 722.74
Calculations using Percentages Menu
Total Interest 722.74 650 72.74
8
Calculations using Percentages Question 2
Joy buys a piano for 350. It depreciates by 15
in the first year and 20 in the second. How
much is the piano worth after 2 years?
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9
Calculations using Percentages Question 2
Joy buys a piano for 350. It depreciates by 15
in the first year and 20 in the second. How
much is the piano worth after 2 years?
238.00
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10
Question 2
15 of 350 0.15 x 350 52.50
Joy buys a piano for 350. It depreciates by 15
in the first year and 20 in the second. How
much is the piano worth after 2 years?
Value after 1 year 350 - 52.50 297.50
20 of 297.50 59.50
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Calculations using Percentages Menu
11
Markers Comments
15 of 350 0.15 x 350 52.50
Value after 1 year 350 - 52.50 297.50
20 of 297.50 59.50
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Calculations using Percentages Menu
12
Calculations using Percentages Question 3

• Joe buys a house for 93,000. Three years later
  it is worth 120,000.
• Calculate the percentage increase in the value of
  Joes house as a percentage of the original
  price.
• Calculate the current value of the house as a
  percentage of the original price.

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13
Calculations using Percentages Question 3

• Joe buys a house for 93,000. Three years later
  it is worth 120,000.
• Calculate the percentage increase in the value of
  Joes house as a percentage of the original
  price.
• Calculate the current value of the house as a
  percentage of the original price.

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14
Question 3

• Joe buys a house for 93,000. Three years later it
  is worth 120,000.
• Calculate the percentage increase in the value of
  Joes house as a percentage of the original
  price.
• Calculate the current value of the house as a
  percentage of the original price.

(a) Increase 120 000 93 000 26 500
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Calculations using Percentages Menu
15
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(a) Increase 120 000 93 000 26 500
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Calculations using Percentages Menu
16
Calculations using Percentages Question 4
Adam puts money into a bank. It increases by 5
and is now worth 596.40. How much money did Adam
originally put in the bank?
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17
Calculations using Percentages Question 4
Adam puts money into a bank. It increases by 5
and is now worth 596.40. How much money did Adam
originally put in the bank?
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18
Question 4
105 596.40
Adam puts money into a bank. It increases by 5
and is now worth 596.40. How much money did Adam
originally put in the bank?
1 5.68
100 568.00
gt 568 invested originally
Begin Solution
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Calculations using Percentages Menu
19
Markers Comments
105 596.40
1 5.68
100 568.00
gt 568 invested originally
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Straight Line Menu
20
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
You have chosen to study
Volumes of Solids
UNIT 1
Please choose a question to attempt from the
following
1
2
3
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21
Volumes of Solids Question 1
A spherical football has a radius of 15 cm. Find
the volume of the football., to 3 significant
figures.
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22
Volumes of Solids Question 1
A spherical football has a radius of 15 cm. Find
the volume of the football, to 3 significant
figures.
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14100 cm³
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23
Question 1
V
A spherical football has a radius of 15 cm. Find
the volume of the football, to 3 significant
figures.
14137.17
14100 cm³
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Volume of Solids Menu
24
Markers Comments
V
14137.17
14100 cm³
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Volume of Solids Menu
25
Volumes of Solids Question 2
A and B are 2 different shaped candles. A is a
cone and B is a cylinder. Both cost 4.00. Which
candle is better value for money? (Justify your
answer.)
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26
Volumes of Solids Question 2
A and B are 2 different shaped candles. A is a
cone and B is a cylinder. Both cost 4.00. Which
candle is better value for money? (Justify your
answer.)
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Candle B because it has a larger volume and
therefore will burn for longer (or similar).
EXIT
27
Question 2
A and B are 2 different shaped candles. A is a
cone and B is a cylinder. Both cost 4.00. Which
candle is better value for money? (Justify your
answer.)
Begin Solution
Continue Solution
Markers Comments
Candle B is better value because it has a larger
volume gt it will burn longer. (Or similar)
Volume of Solids Menu
28
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Next Comment
Candle B is better value because it has a larger
volume gt it will burn longer. (Or similar)
Volume of Solids Menu
29
Volumes of Solids Question 3
A watering trough is shown in diagram A. Diagram
B gives the dimensions of the cross-section.
Calculate the volume of the trough, in litres,
to 2 significant figures.
Diagram A
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800 cm
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Diagram A
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EXIT
30
Volumes of Solids Question 3
A watering trough is shown in diagram A. Diagram
B gives the dimensions of the cross-section.
Calculate the volume of the trough, in litres,
to 2 significant figures.
Diagram A
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800 cm
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Diagram A
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4800 litres
EXIT
31
Question 3
A watering trough is shown in diagram A. Diagram
B gives the dimensions of the cross-section.
Calculate the volume of the trough, in litres, to
2 significant figures.
Begin Solution
Continue Solution
Markers Comments
Candle B is better value because it has a larger
volume gt it will burn longer. (Or similar)
Volume of Solids Menu
32
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Candle B is better value because it has a larger
volume gt it will burn longer. (Or similar)
Volume of Solids Menu
33
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
You have chosen to study
Linear Relationships
UNIT 1
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following
1
2
3
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34
Linear Relationships - Question 1
Draw the graph of
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35
Linear Relationships - Question 1
Draw the graph of
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36
Question 1
Draw the graph of
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37
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Clearly mark at least 3 points on the grid
Extend the line as far as the grid allows
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38
Linear Relationships - Question 2
Find the equation of the straight line shown in
the diagram
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39
Linear Relationships - Question 2
Find the equation of the straight line shown in
the diagram
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40
Question 2
Y-intercept -2
Find the equation of the straight line shown in
the diagram
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41
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Y-intercept -2
Gradient
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Linear Relationships Menu
42
Linear Relationships - Question 3
Does y 3x -2 pass through the point (5,10)?
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43
Linear Relationships - Question 3
Does y 3x -2 pass through the point (5,10)?
y 3x 2 does not pass through (5, 10)
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44
Question 3
Does y 3x -2 pass through the point (5,10)?
At (5, 10), x 5 and y 10
3 x 5 2 13

Therefore y 3x 2 does not pass through (5,
10) as 3 x 5 2 ? 10
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Linear Relationships Menu
45
Markers Comments
At (5, 10), x 5 and y 10
3 x 5 2 13

Therefore y 3x 2 does not pass through (5,
10) as 3 x 5 2 ? 10
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Linear Relationships Menu
46
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
You have chosen to study
Algebraic Operations
UNIT 1
Please choose a question to attempt from the
following
1
2
3
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47
Algebraic Operations - Question 1
Remove brackets and simplify this expression. 6
8(2x -7)
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48
Algebraic Operations - Question 1
Remove brackets and simplify this expression. 6
8(2x -7)
62 16X
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49
Question 1
Remove brackets and simplify this
expression. 6 8(2x -7)
6 8(2x -7)
6 16x 56
62 16x
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Algebraic Operations Menu
50
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6 8(2x -7)
6 16x 56
62 16x
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Algebraic Operations Menu
51
Algebraic Operations - Question 2
The diagram shows a garden with a rectangular
flower bed. (a) Calculate the area of the whole
garden (b) Calculate the area of the flower
bed (c) Calculate the area of the grass
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52
Algebraic Operations - Question 2
The diagram shows a garden with a rectangular
flower bed. (a) Calculate the area of the whole
garden (b) Calculate the area of the flower
bed (c) Calculate the area of the grass
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1. (x 7)(x 8)
2. (x 2)(x 1)
3. 18 (x 3)

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53
Question 2
(a) (x 7)(x 8)
The diagram shows a garden with a rectangular
flower bed. (a) Calculate the area of the whole
garden (b) Calculate the area of the flower
bed (c) Calculate the area of the grass
(b) (x 2)(x 1)
(c) Garden x² 8x 7x 56 x² 15x 56
Flower bed x² - 2x x 2 x² - 3x 2
Begin Solution
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Algebraic Operations Menu
54
Markers Comments
(a) (x 7)(x 8)
(b) (x 2)(x 1)
(c) Garden x² 8x 7x 56 x² 15x 56
Flower bed x² - 2x x 2 x² - 3x 2
Grass Garden Flower bed x² 15x 56
(x² - 3x 2) x² 15x 56 x² 3x - 2)
18x 54 18 (x 3)
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Algebraic Operations Menu
55
Algebraic Operations - Question 3
Factorise (a) 99t 198w (b) 4a² - 36 (c) x ² -
3x -40
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56
Algebraic Operations - Question 3
Factorise (a) 99t 198w (b) 4a² - 36 (c) x ² -
3x -40

1. 99 (t 2w)
2. (2a 6)(2a 6)
3. (x 5)(x 8)

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57
Question 3
(a) 99 (t 2w)
Factorise (a) 99t 198w (b) 4a² - 36 (c) x ² -
3x -40
(b) (2a 6)(2a 6)
(c) (x 5) (x 8)
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Algebraic Operations Menu
58
Markers Comments
(a) 99 (t 2w)
(b) (2a 6)(2a 6)
(c) (x 5) (x 8)
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Algebraic Operations Menu
59
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
You have chosen to study
Circles
UNIT 1
Please choose a question to attempt from the
following
1
2
3
4
5
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60
Circles - Question 1
A pendulum travels along the arc of a circle. It
swings from A to B. The pendulum is 32cm long.
Angle AOB 42º. Calculate the length of the arc
AB. Give your answer to 3 significant figures.
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61
Circles - Question 1
A pendulum travels along the arc of a circle. It
swings from A to B. The pendulum is 32cm long.
Angle AOB 42º. Calculate the length of the arc
AB. Give your answer to 3 significant figures.
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23.5 cm
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EXIT
62
Question 3
A pendulum travels along the arc of a circle. It
swings from A to B. The pendulum is 32cm long.
Angle AOB 42º. Calculate the length of the arc
AB. Give your answer to 3 significant figures.
23.457
23.5 cm (to 3 s.f.)
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Circle Menu
63
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23.457
23.5 cm (to 3 s.f.)
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Circle Menu
64
Circles - Question 2
Find the area of the minor sector AOB of the
circle with radius 8cm and angle AOB 62º.
Give your answer to 1 decimal place.
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65
Circles - Question 2
Find the area of the minor sector AOB of the
circle with radius 8cm and angle AOB 62º.
Give your answer to 1 decimal place.
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34.6 cm
EXIT
66
Question 3
Find the area of the minor sector AOB of the
circle with radius 8cm and angle AOB 62º.
Give your answer to 1 decimal place.
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Circle Menu
67
Markers Comments
Area sector
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Circle Menu
68
Circles - Question 3
If the shaded area 32.6 cm², calculate the
length of the arc.
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69
Circles - Question 3
If the shaded area 32.6 cm², calculate the
length of the arc.
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7.2 cm
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70
Question 3
If the shaded area 32.6 cm², calculate the
length of the arc.
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Circle Menu
71
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Circle Menu
72
Circles - Question 4
Calculate the length AB. O is the centre of the
circle with radius 6 m
A
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O
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6m
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B
8.4 m
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EXIT
73
Circles - Question 4
Calculate the length AB. O is the centre of the
circle with radius 6 m
A
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O
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6m
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B
8.4 m
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10.3 m
EXIT
74
Question 3
Calculate the length AB. O is the centre of the
circle with radius 6 m
If OB 4.3 and OA radius 6 m ? AB 4.3 6
10.3m
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75
Markers Comments
By Pythagoras Theorem OB² 6² - 4.2² 36
17.64 18.36 OB 4.3 m
If OB 4.3 and OA radius 6 m ? AB 4.3 6
10.3m
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Circle Menu
76
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
Trigonometry
Simultaneous Linear Equations
UNIT 2
Graphs, Charts and Tables
Statistics
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77
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
You have chosen to study
Trigonometry
UNIT 2
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following
1
2
3
4
5
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78
Trigonometry Question 1
Calculate the exact value of AC,
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79
Trigonometry Question 1
Calculate the exact value of AC,
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80
Question 1
Calculate the exact value of AC,
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81
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82
Trigonometry Question 2
Calculate the area of ABCD
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83
Trigonometry Question 2
Calculate the area of ABCD
321.63
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84
Question 1
Area of ABD ½ x 21 x 18 x sin 70º
177.60cm²
Calculate the area of ABCD
Area of BDC ½ x 21 x 20.5 x sin 42º
144.03cm²
Area of ABCD 177.60 144.03 321.63 cm²
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85
Markers Comments
Area of ABD ½ x 21 x 18 x sin 70º
177.60cm²
Split the shape into ABD and BDC
Area of BDC ½ x 21 x 20.5 x sin 42º
144.03cm²
Area of ABCD 177.60 144.03 321.63 cm²
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Trigonometry Menu
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86
Trigonometry Question 3
Calculate obtuse angle ABC area of ABCD
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87
Trigonometry Question 3
Calculate obtuse angle ABC area of ABCD
146.86º
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88
Question 1
Calculate obtuse angle ABC area of ABCD
Angle ABC 180 33.14 146.86
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89
Markers Comments
If ABC is obtuse, then it is in 2nd quadrant
Angle ABC 180 33.14 146.86
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90
Trigonometry Question 4
Calculate angle BAC
B
24m
25m
A
C
28m
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91
Trigonometry Question 4
Calculate angle BAC
53.49º
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EXIT
92
Question 1
Calculate angle BAC
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93
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94
Trigonometry Question 5
Calculate angle BAC
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95
Trigonometry Question 5
Find x.
22.50 m
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96
Question 5
Find x.
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97
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98
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
You have chosen to study
Simultaneous Linear Equations
UNIT 2
Please choose a question to attempt from the
following
1
2
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EXIT
99
Simultaneous Linear Equations Question 1
Solve this system of simultaneous equations
graphically
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100
Simultaneous Linear Equations Question 1
Solve this system of simultaneous equations
graphically
x3, y4
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EXIT
101
Question 5
Solve this system of simultaneous equations
graphically
Point of intersection (3,4) So x 3, y4
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102
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Point of intersection (3,4) So x 3, y4
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103
Simultaneous Linear Equations Question 2

• Let x be the cost of a childs ticket for a
  football match. Let y be the cost of an adult
  ticket for the same match.
• 4 adults and 2 childrens tickets cost 115.
  Write this as an equation in x and y.
• 3 adults and 3 childrens tickets cost 103.50.
  Write this as an equation in x and y.
• How much for 5 adults and 2 children?

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EXIT
104
Simultaneous Linear Equations Question 2

• Let x be the cost of a childs ticket for a
  football match. Let y be the cost of an adult
  ticket for the same match.
• 4 adults and 2 childrens tickets cost 115.
  Write this as an equation in x and y.
• 3 adults and 3 childrens tickets cost 103.50.
  Write this as an equation in x and y.
• How much for 5 adults and 2 children?

1. 2x 4y 155
2. 3x 3y 103.5
3. 138

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EXIT
105
(a) 2x 4y 115
Question 5

• Let x be the cost of a childs ticket for a
  football match. Let y be the cost of an adult
  ticket for the same match.
• 4 adults and 2 childrens tickets cost 115.
  Write this as an equation in x and y.
• 3 adults and 3 childrens tickets cost 103.50.
  Write this as an equation in x and y.
• How much for 5 adults and 2 children?

(b) 3x 3y 103.5

• (c) 2x 4y 115 (1)
• 3x 3y 103.5 (2)
• x 3 ? 6x 12y 345 (3)
• x 2 ? 6x 6y 207 (4)
• - (4) ? 6y 138
• y 23
• If y 23 ? 2x 4 x 23 115
• 2x 92 115
• 2x 23
• x 11.50

Begin Solution
? 2x 5y 2 x 11.5 5 x 23 138 ? 2
children and 5 adults costs 138
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106
(a) 2x 4y 115
Markers Comments
(b) 3x 3y 103.5

• (c) 2x 4y 115 (1)
• 3x 3y 103.5 (2)
• x 3 ? 6x 12y 345 (3)
• x 2 ? 6x 6y 207 (4)
• - (4) ? 6y 138
• y 23
• If y 23 ? 2x 4 x 23 115
• 2x 92 115
• 2x 23
• x 11.50

? 2x 5y 2 x 11.5 5 x 23 138 ? 2
children and 5 adults costs 138
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107
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
You have chosen to study
Graphs, Charts and Tables
UNIT 2
Please choose a question to attempt from the
following
1
2
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108
Graphs, Charts and Tables Question 1
200 people are asked about their favourite
holiday destinations. The table summarises their
replies. Draw a pie chart to illustrate these
findings
Destination Europe USA Australia Other
Number of responses 60 80 20 40
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109
Graphs, Charts and Tables Question 1
200 people are asked about their favourite
holiday destinations. The table summarises their
replies. Draw a pie chart to illustrate these
findings
Destination Europe USA Australia Other
Number of responses 60 80 20 40
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110
Question 5
200 people are asked about their favourite
holiday destinations. The table summarises their
replies. Destination Europe USA Australia
Other No of 60 80 20
40 responses Draw a pie chart to illustrate
these findings
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111
Markers Comments
Check all angles add up to 360
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112
Graphs, Charts and Tables Question 2

• A bus company gives its journey times in minutes
  for 1 month.
• 68 62 93 82 63 67 68 70 75 90
  
• Calculate the median of this set of numbers
• Find the upper and lower quartiles
• Draw a boxplot showing this information

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113
Graphs, Charts and Tables Question 2

• A bus company gives its journey times in minutes
  for 1 month.
• 68 62 93 82 63 67 68 70 75 90
  
• Calculate the median of this set of numbers
• Find the upper and lower quartiles
• Draw a boxplot showing this information

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114
Question 2
A bus company gives its journey times in minutes
for 1 month. 68 62 93 82 63 67 68 70 75
90 Calculate the median of this set of
numbers Find the upper and lower quartiles Draw a
boxplot showing this information
(b) Q1 at 3rd position 67 Q3 at 7th
position 82
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115
Markers Comments
State the positions of the median, and the
quartiles
(b) Q1 at 3rd position 67 Q3 at 7th
position 82
Use results to draw a boxplot with an appropriate
scale
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116
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
You have chosen to study
Statistics
UNIT 2
Please choose a question to attempt from the
following
1
2
3
4
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117
Statistics Question 1
Adam works for a fast food company. The number
of burgers he sells each day is logged. Number of
burgers Numbers of days 0 1 5 18 10
28 15 26 20 37

• Calculate
• the median number of
• burgers
• the quartiles
• the semi-interquartile
• range

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118
Statistics Question 1
Adam works for a fast food company. The number
of burgers he sells each day is logged. Number of
burgers Numbers of days 0 1 5 18 10
28 15 26 20 37

• Calculate
• the median number of
• burgers
• the quartiles
• the semi-interquartile
• range

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1. 15
2. 10, 20
3. 5

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119
Cumulative Frequency 1 19 47 73 110
Question 1
Adam works for a fast food company. The number
of burgers he sells each day is logged. Number of
burgers Numbers of
days 0 1 5 18 10 28 15 26 20 37

• Q2 (median) between 55th and 56th position
• 15 burgers

• Q1 at 28th position 10 burgers
• Q3 at 83rd place 20 burgers

Calculate the (i) median number of burgers, (ii)
the quartiles (iii) the semi-interquartile range
(iii) Semi Interquartile range
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120
Cumulative Frequency 1 19 47 73 110
Markers Comments
Know to divide by 4
Find cumulative frequency
State the positions of the median, and the
quartiles
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121
Statistics Question 2

• The price, in pence/litre, of petrol at 10 city
  garages is shown below.
• 84.2 84.4 85.1 83.9 81.0 84.2 85.6
  85.2 84.9 84.8
• Calculate the mean and the standard deviation of
  these prices
• In 10 rural garages petrol prices had a mean of
  88.8 and a standard deviation of 2.4. How do
  rural prices compare with city prices?

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122
Statistics Question 2

• The price, in pence/litre, of petrol at 10 city
  garages is shown below.
• 84.2 84.4 85.1 83.9 81.0 84.2 85.6
  85.2 84.9 84.8
• Calculate the mean and the standard deviation of
  these prices
• In 10 rural garages petrol prices had a mean of
  88.8 and a standard deviation of 2.4. How do
  rural prices compare with city prices?

• 84.3, 1.28
• The average price in the
• city is lower and there is
• less variation in the prices

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123
Question 1
The price, in pence/litre, of petrol at 10 city
garages is shown below. 84.2 84.4 85.1 83.9
81.0 84.2 85.6 85.2 84.9 84.8 (a)
Calculate the mean and the standard deviation of
these prices (b) In 10 rural garages petrol
prices had a mean of 88.8 and a standard
deviation of 2.4. How do rural prices compare
with city prices?
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(b) The average price in the city is lower and
there is less variation in the prices.
Statistics Menu
124
Markers Comments
Know to how to calculate mean
Know how to apply one of the formula for
standard deviation (Note this is one possible
solution)
Make one valid comparison between the two sets of
data.
(b) The average price in the city is lower and
there is less variation in the prices.
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125
Statistics Question 3

• 61 cars are parked in a car park. 26 are
  saloons, 18 are estates and the rest are
  sportscars.
• What is the probability the first car to leave
  the car park is a sportscar?
• The first car to leave is a saloon car. What is
  the probability the second is an estate?

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126
Statistics Question 3

• 61 cars are parked in a car park. 26 are
  saloons, 18 are estates and the rest are
  sportscars.
• What is the probability the first car to leave
  the car park is a sportscar?
• The first car to leave is a saloon car. What is
  the probability the second is an estate?

1. 17/61
2. 3/10

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127
Question 1
(a)
61 cars are parked in a car park. 26 are
saloons, 18 are estates and the rest are
sportscars. (a) What is the probability the first
car to leave the car park is a sportscar? (b) The
first car to leave is a saloon car. What is the
probability the second is an estate?
(b)
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128
Markers Comments
(a)
State formula for probability
Calculate the number of sportscars
Know to divide by the total number of cars
Know to reduce the total number of cars by 1
(b)
Simplify the fraction as far as possible
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129
Statistics Question 4
The number of visitors to a car park each day was
recorded.
Calculate the mean number of visitors to 1
decimal place.
No of visitors No of days
40 11
50 15
60 16
70 13
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130
Statistics Question 4
The number of visitors to a car park each day was
recorded.
Calculate the mean number of visitors to 1
decimal place.
No of visitors No of days
40 11
50 15
60 16
70 13
52.9 visitors
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131
Question 1
No of visitors x No of days
440
600
960
910
Total 2910
The number of visitors to a car park each day was
recorded.
Calculate the mean number of visitors to 1
decimal place.
No of visitors No of days
40 11
50 15
60 16
70 13
mean total number of visitors total number of
days
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132
Markers Comments
No of visitors x No of days
440
600
960
910
Total 2910
Know how to calculate the total number of visitors
Demonstrate how mean is to be calculated
mean total number of visitors total number of
days
Give answer to 1 decimal place as requested
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133
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
Calculations in a Social Context
Logic Diagrams
UNIT 4
Formulae
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134
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
You have chosen to study
Calculations in a Social Context
UNIT 4
Please choose a question to attempt from the
following
1
2
3
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135
Calculations in a Social Context Question 1

• John Stevens works for the sales department of a
  financial company.
• John earns a basic salary of 1800/month plus 9
  of his monthly sales. Calculate his gross salary
  for March when his sales totalled 4632.
• John pays 7 of his gross salary into his
  pension, along with 93.00 for National Insurance
  contributions and 262.86 for Income Tax.
  Calculate his net pay for March.

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136
Calculations in a Social Context Question 1

• John Stevens works for the sales department of a
  financial company.
• John earns a basic salary of 1800/month plus 9
  of his monthly sales. Calculate his gross salary
  for March when his sales totalled 4632.
• John pays 7 of his gross salary into his
  pension, along with 93.00 for National Insurance
  contributions and 262.86 for Income Tax.
  Calculate his net pay for March.

1. 2216.88
2. 1705.84

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137

1. 9 of 4632 0.09 x 4632 416.88

Question 1
Gross monthly salary Basic pay Overtime
Commission 1800 416.88 2216.88
John Stevens works for the sales department of a
financial company. (a) John earns a basic
salary of 1800/month plus 9 of his monthly
sales. Calculate his gross salary for March
when his sales totalled 4632. (b) John pays 7
of his gross salary into his pension, along
with 93.00 for National Insurance
contributions and 262.86 for Income Tax.
Calculate his net pay for March.
(b) 7 of 2216.88 0.07 x 2216.88 155.18
Total deductions NI Tax Pension
93.00 262.86 155.18 511.04
Net pay Gross pay Total deductions
2216.88 511.04 1705.84
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138

• 9 of 4632 0.09 x 4632 416.88
• Gross monthly salary
• Basic pay Overtime Commission
• 1800 416.88
• 2216.88

Markers Comments
Calculate 9 of sales
State how to calculate Gross monthly salary
(b) 7 of 2216.88 0.07 x 2216.88 155.18
Total deductions NI Tax Pension
93.00 262.86 155.18 511.04 Net pay
Gross pay Total deductions 2216.88
511.04 1705.84
Use your answer from (a) to calculate pension
payment
Know how to calculate total deductions
State how to calculate Net pay
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139
Calculations in a Social Context Question 2
Colin is a civil servant. His basic annual
salary is 35042 per annum. His annual tax
allowance is 5125 Calculate his monthly tax bill
using the tax rates given in the table below.
Rates of tax on
First 1920 of taxable income 10
Next 25558 of taxable income 23
All remaining taxable income 40
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140
Calculations in a Social Context Question 2
Colin is a civil servant. His basic annual
salary is 35042 per annum. His annual tax
allowance is 5125 Calculate his monthly tax bill
using the tax rates given in the table below.
Rates of tax on
First 1920 of taxable income 10
Next 25558 of taxable income 23
All remaining taxable income 40
587.16 a month
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141
Taxable Income 35042 5125 29917
Question 2
Colin is a civil servant. His basic annual
salary is 35042 per annum. His annual tax
allowance is 5125 Calculate his monthly tax bill
using the tax rates given in the table below.
Lower rate 10 of 1920 192
Basic rate 23 of 25558 5878.34
(1920 25558 27478) 29917 27478
2439 Higher rate 40 of 2439 975.60
Rates of tax on
First 1920 of taxable income 10
Next 25558 of taxable income 23
All remaining taxable income 40
Annual tax bill 192 5878.34 975.60
7045.94
Monthly tax bill 7045.94/12 587.16/month
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142
Taxable Income 35042 5125 29917
Markers Comments
Find Taxable Income (Gross salary allowances)
Lower rate 10 of 1920 192
Basic rate 23 of 25558 5878.34
Calculate full allowance at lower rate
(1920 25558 27478) 29917 27478
2439 Higher rate 40 of 2439 975.60
Calculate full allowance at basic rate
Calculate remaining taxable income
Calculate higher rate tax on 2439 of taxable
income
Annual tax bill 192 5878.34 975.60
7045.94
Calculate annual tax bill by adding tax at all
bands
Monthly tax bill 7045.94/12 587.16/month
Know to divide by 12 to find monthly tax
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143
Calculations in a Social Context Question 3
Karen wants to borrow 4000 for 3 years with loan
protection. What is the cost of Karens loan?
Loan Amount () With/out Loan Protection WLP/WOLP 12 months 24 months 36 months
1000 WLP WOLP 98.79 92.26 55.39 50.51 41.18 36.76
2000 WLP WOLP 197.42 190.26 102.81 97.53 85.86 78.20
3000 WLP WOLP 296.38 276.77 166.18 151.54 123.56 110.29
4000 WLP WOLP 395.46 387.98 207.45 196.72 193.42 179.76
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144
Calculations in a Social Context Question 3
Karen wants to borrow 4000 for 3 years with loan
protection. What is the cost of Karens loan?
Loan Amount () With/out Loan Protection WLP/WOLP 12 months 24 months 36 months
1000 WLP WOLP 98.79 92.26 55.39 50.51 41.18 36.76
2000 WLP WOLP 197.42 190.26 102.81 97.53 85.86 78.20
3000 WLP WOLP 296.38 276.77 166.18 151.54 123.56 110.29
4000 WLP WOLP 395.46 387.98 207.45 196.72 193.42 179.76
2963.12
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145
36 months 3 years Monthly payment 193.42
Question 2
Karen wants to borrow 4000 for 3 years with loan
protection. What is the cost of Karens loan?
193.42 x 36 6963.12
Total cost of loan 6963.12 4000 2963.12
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146
Markers Comments
36 months 3 years Monthly payment 193.42
Change 3 years into 36 months
Read correct monthly payment from loan repayment
table
193.42 x 36 6963.12
Total cost of loan 6963.12 4000 2963.12
Multiply loan payment by term of loan in months
to calculate total repayment
Subtract original loan from total repayment to
calculate the cost of the loan
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147
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
You have chosen to study
Logic Diagrams
UNIT 4
Please choose a question to attempt from the
following
1
2
3
4
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148
Logic Diagrams Question 1
A fast food company makes different kinds of
burgers, beef or chicken, with or without
lettuce, with or without onions and with or
without ketchup. Draw a tree diagram to
illustrate all the possible combinations of
burgers and use it to calculate the probability a
customer will want a burger with lettuce.
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149
Logic Diagrams Question 1
A fast food company makes different kinds of
burgers, beef or chicken, with or without
lettuce, with or without onions and with or
without ketchup. Draw a tree diagram to
illustrate all the possible combinations of
burgers and use it to calculate the probability a
customer will want a burger with lettuce.
P(Lettuce) 0.5
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150
Question 1
A fast food company makes different kinds of
burgers, beef or chicken, with or without
lettuce, with or without onions and with or
without ketchup. Draw a tree diagram to
illustrate all the possible combinations of
burgers and use it to calculate the probability a
customer will want a burger with lettuce.
Begin Solution
P(Lettuce)
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151
Markers Comments
Calculate number of possible outcomes
Calculate number of outcomes that include lettuce
Simplify probability as far as possible
P(Lettuce)
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152
Logic Diagrams Question 2

1. Draw a network diagram to represent each of the
   maps below. Label the vertices to represent
   places and label the arcs to show distances (in
   miles).
2. Find a route that covers all 127 miles only once
   in Map 1.
3. Is a similar route possible in Map 2? Give a
   reason for your answer.

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153
Logic Diagrams Question 2

1. Draw a network diagram to represent each of the
   maps below. Label the vertices to represent
   places and label the arcs to show distances (in
   miles).
2. Find a route that covers all 127 miles only once
   in Map 1.
3. Is a similar route possible in Map 2? Give a
   reason for your answer.

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MAP2
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(b) B-A-D-E-D-C-B-E (c) No, Map 2 has more than 2
odd vertices and so is not traversable.
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154
Question 2
Draw a network diagram to represent each of the
maps below. (a) Label the vertices to represent
places and label the arcs to show distances (in
miles). (b) Find a route that covers all 127
miles only once in Map 1. (c) Is a similar route
possible in Map 2? Give a reason for your
answer.
(b) B-A-D-E-D-C-B-E
(c) No, Map 2 has more than 2 odd vertices
(Dweep, Lillen and Wull) so it is not traversable.
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155
Markers Comments
2 possib