INTERMEDIATE 2 – ADDITIONAL QUESTION BANK

1
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
Trigonometry
Statistics
UNIT 2
Graphs, Charts Tables
Simultaneous Equations
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INTERMEDIATE 2 ADDITIONAL QUESTION BANK
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Trigonometry
UNIT 2
Please choose a question to attempt from the
following
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3
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6
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TRIGONOMETRY Question 1
Find the area of the following triangle to the
nearest cm2.
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Reveal answer only
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4
TRIGONOMETRY Question 1
Find the area of the following triangle to the
nearest cm2.
What would you like to do now?
2. Always remember to round your answer if the
questions asks you to.
Reveal answer only
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5
TRIGONOMETRY Question 1
Find the area of the following triangle to the
nearest cm2.
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6
Question 1
1. For area of triangles questions where an angle
is present use
Find the area of the following triangle to the
nearest cm2.
Area of ? ½ bcsinA
50 x 40 x sin25 ? 2
422.61
2. Remember to round if asked to.
423 to nearest unit
Area of ? 423cm2
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Markers Comments
Check formulae list for Area of triangle
absinC (Note 2 sides and the included
angle) Relate formula to labels being used.
1. For area of triangles questions where an angle
is present use
Area of ? ½ bcsinA
50 x 40 x sin25 ? 2
422.61
2. Remember to round if asked to.
423 to nearest unit
Area of ? 423cm2
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TRIGONOMETRY Question 1B
Find the area of the following triangle.
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TRIGONOMETRY Question 1B
Find the area of the following triangle.
What would you like to do now?
2. Always remember to round your answer if the
questions asks you to.
Reveal answer only
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10
TRIGONOMETRY Question 1B
Find the area of the following triangle.
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Question 1B
1. For area of triangles questions where an angle
is present use
Find the area of the following triangle.
Area of ? ½ kmsinL
8 x 6.5 x sin150 ? 2
13
Area of ? 13m2
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Markers Comments
Check formulae list for Area of triangle
absinC (Note 2 sides and the included
angle) Relate formula to labels being used.
1. For area of triangles questions where an angle
is present use
Area of ? ½ kmsinL
8 x 6.5 x sin150 ? 2
13
Area of ? 13m2
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13
TRIGONOMETRY Question 2
Two helicopters leave an air base. The first
flies on a bearing of 340 at 160km/hr. The
second flies due east at 200km/hr. How
far apart will they be after 21/2 hours?
Answer to the nearest 10km.
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Reveal answer only
340
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14
TRIGONOMETRY Question 2
Two helicopters leave an air base. The first
flies on a bearing of 340 at 160km/hr. The
second flies due east at 200km/hr. How
far apart will they be after 21/2 hours?
Answer to the nearest 10km.
What would you like to do now?
1. Identify what you need to find and the
information you have to help you.
4. Identify which trig rule to use Two sides
two angles sine rule Three sides one angle
cosine rule
2. Calculate as many of the missing angles as
possible.
3. Make a sketch to clarify matters.
5. Substitute known values, remembering to use
brackets as appropriate.
Reveal answer only
340
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15
TRIGONOMETRY Question 2
Two helicopters leave an air base. The first
flies on a bearing of 340 at 160km/hr. The
second flies due east at 200km/hr. How
far apart will they be after 21/2 hours?
Answer to the nearest 10km.
What would you like to do now?
340
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Distance is 740km
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16
Question 2
1. Identify what needs to be found.
160km/hr.
2. Need distances travelled and angle between
flight paths.
340
d1 speed1 x time 160 x 2.5 400km
How far apart will they be after 21/2 hours?
d2 speed2 x time 200 x 2.5 500km
340 clockwise 20 anti-clockwise
20
Full angle 20 90 110
90
3. Sketch triangle.
200km/hr
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Question 2
4. Apply Cosine rule.
160km/hr.
a2 b2 c2 (2bccosA)
340
5. Substitute known values and remember to use
brackets.
How far apart will they be after 21/2 hours?
4002 5002 (2 x 400 x 500 x cos110)
20
546808.05..
90
a ?546808.05..
739.46....
200km/hr
6. Remember to round answer if asked to.
Continue Solution
740
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Distance is 740km
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Markers Comments
1. Identify what needs to be found.
Note Bearings are measured
clockwise from N.
2. Need distances travelled and angle between
flight paths.
d1 speed1 x time 160 x 2.5 400km
d2 speed2 x time 200 x 2.5 500km
340 clockwise 20 anti-clockwise
Full angle 20 90 110
3. Sketch triangle.
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Markers Comments
Check formulae list for the cosine rule a2
b2 c2 2bc cosA (2 sides and the included
angle) Relate to variables used a2 b2 c2
2bc cosA
4. Apply Cosine rule.
a2 b2 c2 (2bc cosA)
5. Substitute known values and remember to use
brackets.
4002 5002 (2 x 400 x 500 x cos110)
546808.05..
a ?546808.05..
739.46....
6. Remember to round answer if asked to.
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740
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Distance is 740km
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20
TRIGONOMETRY Question 2B
Two ships sail from a port. The first travels
for two hours on a bearing of 195 at a speed of
18mph. The second travels south-east for three
hours at a speed of 15mph. How far apart will
they be?
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Reveal answer only
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21
TRIGONOMETRY Question 2B
Two ships sail from a port. The first travels
for two hours on a bearing of 195 at a speed of
18mph. The second travels south-east for three
hours at a speed of 15mph. How far apart will
they be?
2. Calculate as many of the missing angles as
possible.
What would you like to do now?
1. Identify what you need to find and the
information you have to help you.
3. Make a sketch to clarify matters.
4. Identify which trig rule to use Two sides
two angles sine rule Three sides one angle
cosine rule
Reveal answer only
5. Substitute known values, remembering to use
brackets as appropriate.
Go to full solution
Go to Comments
Go to Trigonometry Menu
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22
TRIGONOMETRY Question 2B
Two ships sail from a port. The first travels
for two hours on a bearing of 195 at a speed of
18mph. The second travels south-east for three
hours at a speed of 15mph. How far apart will
they be?
What would you like to do now?
Go to full solution
Go to Comments
Go to Trigonometry Menu
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23
Question 2B
1. Identify what needs to be found.
How far apart will they be?
2. Need distances travelled and angle between
paths.
d1 speed1 x time 18 x 2 36miles
1350
d2 speed2 x time 15 x 3 45miles
3hr_at_15mph
2hr_at_18mph
NB SE 135
Angle 195 - 135 60
600
3. Sketch triangle.
Begin Solution
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Question 2B
4. Apply Cosine rule.
How far apart will they be?
a2 b2 c2 (2bc cosA)
5. Substitute known values and remember to use
brackets.
1350
3hr_at_15mph
362 452 (2 x 36 x 45 x cos60)
2hr_at_18mph
1701
600
a ?1701
41.243....
41.2
Begin Solution
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Distance is 41.2 miles
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Comments
1. Identify what needs to be found.
Note Bearings are measured
clockwise from N.
2. Need distances travelled and angle between
flight paths.
d1 speed1 x time 18 x 2 36miles
d2 speed2 x time 15 x 3 45miles
NB SE 135
Angle 195 - 135 60
3. Sketch triangle.
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Comments
Check formulae list for the cosine rule a2
b2 c2 2bc cosA (2 sides and the included
angle) Relate to variables used a2 b2 c2
2bc cosA
4. Apply Cosine rule.
a2 b2 c2 (2bc cosA)
5. Substitute known values and remember to use
brackets.
362 452 (2 x 36 x 45 x cos60)
1701
a ?1701
41.243....
41.2
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Distance is 41.2 miles
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TRIGONOMETRY Question 3
In the kite shown below PQ 10cm, QR 15cm
diagonal PR 22cm. (a) Find the size of
angle QPR. (b) Hence find the area of the kite
to the nearest square unit.
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28
TRIGONOMETRY Question 3
In the kite shown below PQ 10cm, QR 15cm
diagonal PR 22cm. (a) Find the size of
angle QPR. (b) Hence find the area of the kite
to the nearest square unit.
1. Identify which trig rule to use Two sides
two angles sine rule Three sides one angle
cosine rule
4. Always remember to round your answer if the
questions asks you to.
What would you like to do now?
2. Substitute known values, remembering to use
brackets as appropriate.
Reveal answer only
Go to full solution
Go to Comments
Go to Trigonometry Menu
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29
TRIGONOMETRY Question 3
In the kite shown below PQ 10cm, QR 15cm
diagonal PR 22cm. (a) Find the size of
angle QPR. (b) Hence find the area of the kite
to the nearest square unit.
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30
Question 3
1. To find angle when you have 3 sides use 2nd
version of cosine rule
(102 222 - 152) ? (2 x 10 x 22)
0.8159
2. Remember to use inverse function to find angle.
(a) Find the size of angle QPR
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Question 3
1. Kite 2 identical triangles. For area of
triangles where an angle is present use
(b) Area ?QPR ½ qrsinP
10 x 22 x sin35.3 ? 2
63.56..cm2
2. Remember to double this and round answer.
Area of kite 2 x 63.56..
(b) Hence find the area of the kite to the
nearest square unit
127.12..cm2
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Markers Comments
Check the formulae list for the second form of
the cosine rule
1. To find angle when you have 3 sides use 2nd
version of cosine rule
( 3 sides)
cosA
(102 222 - 152) ? (2 x 10 x 22)
0.8159
2. Remember to use inverse function to find angle.
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Markers Comments
1. To find angle when you have 3 sides use 2nd
version of cosine rule
(102 222 - 152) ? (2 x 10 x 22)
0.8159
2. Remember to use inverse function to find angle.
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Markers Comments
Note When keying in to calculator work out the
top line and the bottom line before dividing or
use brackets.
1. To find angle when you have 3 sides use 2nd
version of cosine rule
(102 222 - 152) ? (2 x 10 x 22)
0.8159
2. Remember to use inverse function to find angle.
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TRIGONOMETRY Question 3B
The sides of a rhombus are each 15cm while the
main diagonal is 25cm Find the size of angle
EFH and hence find the area of the rhombus to
the nearest square unit.
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Reveal answer only
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36
TRIGONOMETRY Question 3B
The sides of a rhombus are each 15cm while the
main diagonal is 25cm Find the size of angle
EFH and hence find the area of the rhombus to
the nearest square unit.
What would you like to do now?
1. Identify which trig rule to use Two sides
two angles sine rule Three sides one angle
cosine rule
Reveal answer only
4. Always remember to round your answer if the
questions asks you to.
Go to full solution
2. Substitute known values, remembering to use
brackets as appropriate.
Go to Comments
Go to Trigonometry Menu
EXIT
37
TRIGONOMETRY Question 3B
The sides of a rhombus are each 15cm while the
main diagonal is 25cm Find the size of angle
EFH and hence find the area of the rhombus to
the nearest square unit.
What would you like to do now?
Go to full solution
Go to Comments
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38
Question 3B
1. To find angle when you have 3 sides use 2nd
version of cosine rule
(152 252 - 152) ? (2 x 25 x 15)
0.8333
2. Remember to use inverse function to find angle.
(a) Find the size of angle EFH
angleEFH cos-1(0.8333..) 33.6
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Question 3B
1. Rhombus 2 identical triangles. For area of
triangles where an angle is present use
(b) Area ?EFH ½ ehsinF
33.60
25 x 15 x sin33.6 ? 2
207.52....cm2
2. Remember to double this and round answer.
Area of kite 2 x 207.52......
(b) Hence find the area to the nearest square
unit
415.04..cm2
415cm2
Continue Solution
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Markers Comments
Check the formulae list for the second form of
the cosine rule
1. To find angle when you have 3 sides use 2nd
version of cosine rule
( 3 sides)
cosA
(152 252 - 152) ? (2 x 25 x 15)
0.8333
2. Remember to use inverse function to find angle.
angleEFH cos-1(0.8333..) 33.6
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Markers Comments
1. To find angle when you have 3 sides use 2nd
version of cosine rule
(152 252 - 152) ? (2 x 25 x 15)
0.8333
2. Remember to use inverse function to find angle.
angleEFH cos-1(0.8333..) 33.6
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Markers Comments
Check formulae list for Area of triangle
absinC (Note 2 sides and the included
angle) Relate formula to labels being used.
1. Rhombus 2 identical triangles. For area of
triangles where an angle is present use
(b) Area ?EFH ½ ehsinF
25 x 15 x sin33.6 ? 2
207.52....cm2
2. Remember to double this and round answer.
Area of kite 2 x 207.52......
415.04..cm2
415cm2
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43
TRIGONOMETRY Question 4
In triangle TUV, angle U 35, angle T 105,
TV 5.9cm and UV 10cm. Find the perimeter to
one decimal place.
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Reveal answer only
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44
TRIGONOMETRY Question 4
In triangle TUV, angle U 35, angle T 105,
TV 5.9cm and UV 10cm. Find the perimeter to
one decimal place.
3. Identify which trig rule to use Two sides
two angles sine rule Three sides one angle
cosine rule
5. Always remember to round your answer if the
questions asks you to.
What would you like to do now?
1. For perimeter need all three sides. So must
find TU.
2. Calculate unknown angles.
Reveal answer only
Go to full solution
4. Substitute known values, remembering to use
brackets as appropriate.
Go to Comments
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45
TRIGONOMETRY Question 4
In triangle TUV, angle U 35, angle T 105,
TV 5.9cm and UV 10cm. Find the perimeter to
one decimal place.
22.6cm
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46
Question 4

• Perimeter requires all three sides.
• So we need to find TU .

2. Whether you use Sine or Cosine rule need angle
V.
Angle V 180 - 35 - 105 40
400
3. If we use Sine rule
Find the perimeter to one decimal place.
4. Substitute known values
Continue Solution
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Question 4
4. Substitute known values
5. Cross multiply
400
v x sin105
10 x sin40
v 10 x sin40 ? sin105
Find the perimeter to one decimal place.
6.654
6.7cm
6. Answer the question
Continue Solution
Perim of ? (6.7 10 5.9)cm
Comments
22.6cm
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Markers Comments
Since we can pair off two angles with the
opposite sides Sine
Rule

• Perimeter requires all three sides.
• So we need to find TU .

2. Whether you use Sine or Cosine rule need angle
V.
Refer to the Formulae List

Angle V 180 - 35 - 105 40
3. If we use Sine rule
4. Substitute known values
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Markers Comments
4. Substitute known values
Go straight to values

5. Cross multiply
v x sin105
v 10 x sin40 ? sin105
6.654
6.7cm
6. Answer the question
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Perim of ? (6.7 10 5.9)cm
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22.6cm
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50
TRIGONOMETRY Question 5
Lighthouse C is on a bearing of 050 from
lighthouse A and northwest of lighthouse B.
Lighthouse B is 12km due east of lighthouse A.
A ship(S) is sailing directly from lighthouse B
to lighthouse A. How close does it come to
lighthouse C?
Hints
Answer only
Full solution
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51
TRIGONOMETRY Question 5
Lighthouse C is on a bearing of 050 from
lighthouse A and northwest of lighthouse B.
Lighthouse B is 12km due east of lighthouse A.
A ship(S) is sailing directly from lighthouse B
to lighthouse A. How close does it come to
lighthouse C?
2. Identify which trig rule to use Two sides
two angles sine rule Three sides one angle
cosine rule
What would you like to do now?
4. Closest distance perpendicular distance.
Create a right-angled triangle and use SOH CAH
TOA.

• Calculate missing angles.
• (NB. North West 3150)

Answer only
3. Substitute known values, remembering to use
brackets as appropriate.
Full solution
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52
TRIGONOMETRY Question 5
Lighthouse C is on a bearing of 050 from
lighthouse A and northwest of lighthouse B.
Lighthouse B is 12km due east of lighthouse A.
A ship(S) is sailing directly from lighthouse B
to lighthouse A. How close does it come to
lighthouse C?
Closest distance is 5.48km
What would you like to do now?
Full solution
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53
Question 5

• Calculate missing angles.

AngleA 90 - 50 40
NW 3150
angleB 315 - 270 45
950
So angle C 180 - 40 - 45 95
2. Draw a sketch
400
450
b
3. If we use Sine rule
Continue Solution
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Question 5
4. Substitute known values
950
5. Cross multiply
b x sin95
12 x sin45
400
450
b 12 x sin45 ? sin95
8.5176.
8.52km
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Question 5
6. Closest point is perpendicular so sketch right
angled triangle
950
8.52km
400
450
7. Now using SOHCAH TOA
a 8.52 x sin40
5.476.
Continue Solution
5.48
Comments
Closest distance is 5.48km
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Markers Comments
Since we can pair off two angles with the
opposite sides Sine
Rule

• Calculate missing angles.

AngleA 90 - 50 40
NW 3150
angleB 315 - 270 45
Refer to the Formulae List

So angle C 180 - 40 - 45 95
2. Draw a sketch
3. If we use Sine rule
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Markers Comments
Note the shortest distance from a point to a
line is the perpendicular distance.
6. Closest point is perpendicular so sketch right
angled triangle
C
A
B
7. Now using SOHCAH TOA
a 8.52 x sin40
5.476.
Next Comment
5.48
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Closest distance is 5.48km
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58
TRIGONOMETRY Question 6
Two supply vessels are approaching an oil
platform. From the deck of
ship A the angle of elevation of the drill tower
is 2.9 while from the deck of ship B it is 3.8.

The ships are 400m apart. How far from the
platform is each vessel ?
Hints
Answer only
Full solution
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59
TRIGONOMETRY Question 6
Two supply vessels are approaching an oil
platform. From
the deck of ship A the angle of elevation of the
drill tower is 2.9 while from the deck of ship B
it is 3.8.
The ships are 400m apart. How
far from the platform is each vessel ?
4. Then use SOH CAH TOA to find length from rig
to first ship. Second ship is then 400 m further.
2. Identify which trig rule to use to find common
side to both triangles Two sides two angles
sine rule Three sides one angle cosine rule

• Calculate missing angles.

What would you like to do now?
3. Substitute known values, remembering to use
brackets as appropriate.
Answer only
Full solution
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60
TRIGONOMETRY Question 6
Two supply vessels are approaching an oil
platform. From the deck of
ship A the angle of elevation of the drill tower
is 2.9 while from the deck of ship B it is 3.8.

The ships are 400m apart. How far from the
platform is each vessel ?
What would you like to do now?
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Full solution
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ShipA is 1685m away ShipB is 1285m away
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61
Question 6

• Calculate missing angles.

Angle B 180 - 3.8 176.2
Angle D 180 - 2.9 - 176.2 0.9
0.9
2. Draw a sketch
176.2
3. BD is common link to both triangles so find it
using sine rule.
Continue Solution
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62
Question 6
4. Substitute known values
0.9
5. Cross multiply
176.2
a x sin0.9
400 x sin2.9
a 400 x sin2.9 ? sin0.9
1288m to nearest metre
Continue Solution
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Question 6
6. Sketch right angled triangle
0.9
176.2
7. Now using SOHCAH TOA
1285 m
d 1288 x cos3.8
1285m to nearest metre
Continue Solution
OA is 1285m400m 1685m
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Comments
ShipA is 1685m away ShipB is 1285m away
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7. Now using SOHCAH TOA
64
Markers Comments
Since we can pair off two angles with the
opposite sides Sine
Rule

• Calculate missing angles.

Angle B 180 - 3.8 176.2
Angle D 180 - 2.9 - 176.2 0.9
Refer to the Formulae List

2. Draw a sketch
3. BD is common link to both triangles so find it
using sine rule.
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Markers Comments
6. Sketch right angled triangle
Since angle BOD is right - angled use SOHCAHTOA
in triangle BOD
7. Now using SOHCAH TOA
d 1288 x cos3.8
1285m to nearest metre
OA is 1285m400m 1685m
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ShipA is 1685m away ShipB is 1285m away
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66
TRIGONOMETRY Question 6B
Two supply vessels are approaching an oil
platform. From the deck of ship A the angle
of elevation of the drill tower is 27 while
from the deck of vessel B it is 35. The
ships are 80m apart and the height of their decks
is 5m. How high is the drill tower?
Hints
Answer only
Full solution
Comments
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67
TRIGONOMETRY Question 6B
Two supply vessels are approaching an oil
platform. From the deck of ship A the angle
of elevation of the drill tower is 27 while
from the deck of vessel B it is 35. The
ships are 80m apart and the height of their decks
is 5m. How high is the drill tower?
4. Then use SOH CAH TOA to find Height of rig
from deck level. Remember decks are 5m above sea
level.
2. Identify which trig rule to use to find common
side to both triangles Two sides two angles
sine rule Three sides one angle cosine rule

• Calculate missing angles.

What would you like to do now?
3. Substitute known values, remembering to use
brackets as appropriate.
Answer only
Full solution
Comments
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68
TRIGONOMETRY Question 6B
Two supply vessels are approaching an oil
platform. From the deck of ship A the angle
of elevation of the drill tower is 27 while
from the deck of vessel B it is 35. The
ships are 80m apart and the height of their decks
is 5m. How high is the drill tower?
What would you like to do now?
Full solution
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Height of tower is 123m
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69
Question 6B

• Calculate missing angles.

Angle B 180 - 35 145
Angle D 180 - 145 - 27 8
8
2. Draw a sketch
145
3. BD is common link to both triangles so find it
using sine rule.
Continue Solution
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70
Question 6B
4. Substitute known values
8
5. Cross multiply
145
a x sin8
80 x sin27
a 80 x sin27 ? sin8
261m to nearest metre
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71
Question 6B
6. Sketch right angled triangle
8
145
7. Now using SOHCAH TOA
b 261 x sin27
118m to nearest metre
Continue Solution
Height OD deck height 118 5
123m
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Height of tower is 123m
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72
Comments
Since we can pair off two angles with the
opposite sides Sine
Rule

• Calculate missing angles.

Angle B 180 - 35 145
Angle D 180 - 145 - 27 8
Refer to the Formulae List

2. Draw a sketch
3. BD is common link to both triangles so find it
using sine rule.
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73
Markers Comments
6. Sketch right angled triangle
Since angle BOD is right - angled use SOHCAHTOA
in triangle BOD
7. Now using SOHCAH TOA
b 261 x sin27
118m to nearest metre
Height OD deck height 118 5
123m
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74
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
5
Back to Unit 2 Menu
EXIT
75
STATISTICS Question 1
A taxi company was phoned each night of the week
and the response time in minutes of their cars
were noted. They were .
3 5 10 7 7 15 9 (a) Find the mean and standard
deviation for this data. (b) A similar
experiment was conducted with a second
company. The results for this were. mean 12
and standard deviation 1.88 How
does the second company compare to the first?
Go to Comments
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Reveal answer only
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76
STATISTICS Question 1
A taxi company was phoned each night of the week
and the response time in minutes of their cars
were noted. They were .
3 5 10 7 7 15 9 (a) Find the mean and standard
deviation for this data. (b) A similar
experiment was conducted with a second
company. The results for this were. mean 12
and standard deviation 1.88 How
does the second company compare to the first?
Draw a table comparing data to mean. Then square
values.
When comparing data sets always make comment on
the average (which is bigger etc.) and the spread
of the data.
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Reveal answer only
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EXIT
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77
STATISTICS Question 1
A taxi company was phoned each night of the week
and the response time in minutes of their cars
were noted. They were .
3 5 10 7 7 15 9 (a) Find the mean and standard
deviation for this data. (b) A similar
experiment was conducted with a second
company. The results for this were. mean 12
and standard deviation 1.88 How
does the second company compare to the first?
(a) Mean 8

• The second company has a longer average response
  time. The smaller standard deviation means their
  arrival time is more predictable.

Go to Comments
What would you like to do now?
Go to full solution
Go to Statistics Menu
EXIT
78
Question 1

• Calculate mean.

A taxi company was phoned each night of the week
and the response time in minutes of their cars
were noted. They were . 3 5 10
7 7 15 9 (a) Find the mean and
standard deviation for this data.
(a) Mean (351077159)?7 8
So 8 and no.pieces of data n 7
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79
Question 1
2. Draw table comparing data to mean.
A taxi company was phoned each night of the week
and the response time in minutes of their cars
were noted. They were . 3 5 10
7 7 15 9 (a) Find the mean and
standard deviation for this data.
x
3 -5 25
5 -3 9
10 2 4
7 - 1 1
7 -1 1
15 7 49
9 1 1
? (x - )2
90
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80
Question 1
3. Use formula to calculate standard deviation.
A taxi company was phoned each night of the week
and the response time in minutes of their cars
were noted. They were . 3 5 10
7 7 15 9 (a) Find the mean and
standard deviation for this data.
Just found!!
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81
Question 1
1. Always compare mean and standard deviation.
(b) A similar experiment was conducted with a
second company. The results for this
were. mean 12 and standard deviation
1.88 How does the second company compare
to the first?

• The second company has a
• longer average response time.
• The smaller standard deviation means their
  arrival time is more
• predictable.

What would you like to do now?
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82
Comments
Check the list of Formulae for the Standard
Deviation Formula
3. Use formula to calculate standard deviation.
The second formula can be used in the calculator
paper. The calculator must be in Stats. Mode to
allow the data to be entered.
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83
STATISTICS Question 2
Time(s)
Weeks of training
A TV personality takes part in a 20 week training
schedule to copy a 100m sprinter. Her times are
recorded every 2 weeks and plotted in the graph
then a line of best fit is drawn.
Continue question
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84
STATISTICS Question 2
Get hint
Reveal answer only
Time(s)
Go to full solution
Go to Comments
Go to Stats Menu
Weeks of training
(i) Find the equation of the line in terms of T
and W. (ii) Use answer (i) to predict (a)
her time after 12 weeks of training
(b) the week when her time was 11.5secs
EXIT
85
Use your equation and substitute W 12.
Find gradient and note intercept of T axis.
Use your equation and substitute T 11.5
STATISTICS Question 2
Reveal answer only
Time(s)
Go to full solution
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Go to Stats Menu
Weeks of training
(i) Find the equation of the line in terms of T
and W. (ii) Use answer (i) to predict (a)
her time after 12 weeks of training
(b) the week when her time was 11.5secs
EXIT
What would you like to do now?
86
STATISTICS Question 2
What would you like to do now?
Time(s)
Go to full solution
Go to Comments
Go to Stats Menu
Weeks of training
(i) Find the equation of the line in terms of T
and W. (ii) Use answer (i) to predict (a)
her time after 12 weeks of training
(b) the week when her time was 11.5secs
12secs.
EXIT
14 weeks
87
Question 2

• Find gradient and note intercept of T axis.

(i) Find the equation of the line in terms
of T and W.
(a)
-¼

Intercept at 15
Equation is T -¼ W 15
Go to graph
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88
Question 2

• Use your equation and substitute
• W 12.

(ii) Use answer (i) to predict (a) her
time after 12 weeks of training (b) the week
when her time was 11.5secs
(b)(i) If w 12 then T -¼ W 15
becomes T (-¼ x 12) 15
-3 15
12
Time at 12 weeks is 12secs.
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89
Question 2
3. Use your equation and substitute T 11.5
(ii) Use answer (i) to predict (a) her
time after 12 weeks of training (b) the week
when her time was 11.5secs
(b)(i) If t 11.5 then T -¼ W 15
becomes -¼ W 15 11.5
(-15) (-15)
-¼ W -3.5
x (4)
W 14
Reach a time of 11.5sec after 14 weeks.
What would you like to do now?
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90
Comments
To find the equation of a line from the
graph Must Learn y mx c

• Find gradient and note intercept of T axis.

-¼
Intercept at 15
gradient
intercept
Equation is T -¼ W 15
So you need to find these!!
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91
Comments
m

• Find gradient and note intercept of T axis.

-¼
Note Always draw the horizontal before the
vertical
Intercept at 15
horizontal (ve)
Equation is T -¼ W 15
vertical (-ve)
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92
STATISTICS Question 3
A sample of 180 teenagers were asked their
opinions on the TV series the Simpsons the
movie Shrek and their responses were displayed
in the following table

• What percentage liked Shrek but not the Simpsons?
• If someone is picked at random what is the
  probability that
• (i) they liked the Simpsons but not Shrek?
• (ii) they liked neither?

Full solution
Statistics Menu
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Comments
Reveal
93
STATISTICS Question 3
A sample of 180 teenagers were asked their
opinions on the TV series the Simpsons the
movie Shrek and their responses were displayed
in the following table
Remember all entries in table must add to total
sample size
To find probabilities use P no of favourable
/ no of data

• What percentage liked Shrek but not the Simpsons?
• If someone is picked at random what is the
  probability that
• (i) they liked the Simpsons but not Shrek?
• (ii) they liked neither?

What would you like to do now?
Full solution
Statistics Menu
EXIT
Comments
Reveal
94
STATISTICS Question 3
A sample of 180 teenagers were asked their
opinions on the TV series the Simpsons the
movie Shrek and their responses were displayed
in the following table
10

• What percentage liked Shrek but not the Simpsons?
• If someone is picked at random what is the
  probability that
• (i) they liked the Simpsons but not Shrek?
• (ii) they liked neither?

1/12
7/60
Full solution
Statistics Menu
EXIT
Comments
What now?
95
Question 3
1. Use P no of favourable / no of data
NB There are 180 in survey!!

• Like Shrek but not Simpsons
• 180 126 15 21

18
10
18/180 1/10

• What percentage liked Shrek
• but not the Simpsons?

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96
Question 3
1. Use P no of favourable / no of data
(b)(i) Prob 15/180
1/12

• what is the probability that
• they liked the Simpsons but
• not Shrek?

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97
Question 3
1. Use P no of favourable / no of data
7/60
(b)(ii) Prob 21/180
What would you like to do now?
(ii) they liked neither?
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98
Comments
Note To change a fraction to a multiply by
100
1. Use P no of favourable / no of data
NB There are 180 in survey!!
18 180
18 180
x 100

• Like Shrek but not Simpsons
• 180 126 15 21

18
10
18/180 1/10
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99
Comments
To calculate simple probabilities
1. Use P no of favourable / no of data
Probability
(b)(i) Prob 15/180
1/12
Number of favourable outcomes Number of
possible outcomes
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100
STATISTICS Question 4
Get hint
On a college course you have to pick a language
plus a leisure activity from the following lists
Reveal ans
Full solution
Comments
Stats Menu
(a) Make a list of all possible combinations of
courses.

• If a combination is selected at random what is
  the probability that it is

(i) Includes Spanish?
(ii) Includes swimming?
(iii) Doesnt include French but includes music?
EXIT
101
What would you like to do now?
STATISTICS Question 4
On a college course you have to pick a language
plus a leisure activity from the following lists
Reveal ans
Full solution
Comments
Stats Menu
Use a tree diagram branch out with each
language.
(a) Make a list of all possible combinations of
courses.
Now list the pairs of subjects.

• If a combination is selected at random what is
  the probability that it is

Use your list of possible combinations to find
probabilities.
From each language branch out with each
leisure activity.
(i) Includes Spanish?
(ii) Includes swimming?
(iii) Doesnt include French but includes music?
EXIT
102
STATISTICS Question 4
On a college course you have to pick a language
plus a leisure activity from the following lists
Full solution
Comments
Stats Menu
(a) Make a list of all possible combinations of
courses.
CLICK

• If a combination is selected at random what is
  the probability that it is

1/3
(i) Includes Spanish?
(ii) Includes swimming?
1/4
1/6
(iii) Doesnt include French but includes music?
EXIT
103
(a)
Use a tree diagram branch out with each
language.
From each language branch out with each leisure
activity.
Now list the pairs of subjects.
104
Have list of combinations handy.
1/3
4/12
Remember to simplify.
What now?
Comments
1/4
3/12
Stats Menu
What is probability
(i) Includes Spanish?
(ii) Includes swimming?
2/12
1/6

• Doesnt include French
• but includes music?

105
Comments
(a)
No. of possible outcomes 3 x 4 12
To calculate simple probabilities
Probability
Number of favourable Number of possible
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106
STATISTICS Question 5
The delivery times for a fast food company are
shown in the following cumulative frequency
table.
Get hint
Reveal ans
Full solution
Comments
Stats Menu
(a) How many deliveries took longer than 16 mins?
(b) Use the data to construct a cumulative
frequency graph.
(c) Use the graph to find the median and
semi-interquartile range for this data.
107
STATISTICS Question 5
The delivery times for a fast food company are
shown in the following cumulative frequency
table.
For how many greater than 16 find difference
between end value of values up to 16.
What would you like to do now?
Median is middle value- so we want halfway-point
on frequency axis.
Reveal ans
SIQR ½(Q3 Q1) Q1 25 point Q3
75 point
Full solution
Comments
Stats Menu
(a) How many deliveries took longer than 16 mins?
(b) Use the data to construct a cumulative
frequency graph.
(c) Use the graph to find the median and
semi-interquartile range for this data.
108
STATISTICS Question 5
The delivery times for a fast food company are
shown in the following cumulative frequency
table.
Full solution
Comments
Stats Menu
(a) How many deliveries took longer than 16 mins?
7
(b) Use the data to construct a cumulative
frequency graph.
(c) Use the graph to find the median and
semi-interquartile range for this data.
Median 11 mins
SIQR 2.75 mins
109
(a) Deliveries taking longer than 16 mins 60
53
7
¾ of 60 45
Q3
Comments
½ of 60 30
Q2
Stats Menu
¼ of 60 15
What would you like to do now?
Q1
11
8.5
14
(c) SIQR ½(Q3 Q1)
(14 8.5) ? 2
2.75mins
(C) Median 11mins.
110
Comments
Note In a Cumulative Frequency Diagram
Cumulative Frequency
On y-axis (cumulative frequency)
Q1 at 25, Q2 at 50,
Q3 at 75
And read values from the delivery time scale
(x-axis).
Delivery Time
End of Statistics
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111
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
You have chosen to study
Graphs, Charts Tables
UNIT 2
Please choose a question to attempt from the
following
3
4
5
6
1
2
Stem Leaf
Dot Plot
Cum Freq Table
Dot to boxplot
Stem to boxplot
Piechart
Back to Unit 2 Menu
EXIT
112
GRAPHS, CHARTS, TABLES Question 1
The following stem leaf diagram shows the
distribution of wages for employees in a small
factory .. 16 2 3 6 9 17 1 1 1 8 8 9 18 2 3 3
5 6 7 7 19 1 2 8 20 1 5 5 6 n 25 21 8
17 4 174
(a) Use this information to find the (i)
median (ii) lower upper
quartiles (iii) the semi-interquartile range

• What is the probability that someone chosen at
  random earns less than 180?

Go to full solution
Get hint
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Reveal answer
113
GRAPHS, CHARTS, TABLES Question 1
The following stem leaf diagram shows the
distribution of wages for employees in a small
factory .. 16 2 3 6 9 17 1 1 1 8 8 9 18 2 3 3
5 6 7 7 19 1 2 8 20 1 5 5 6 n 25 21 8
17 4 174
Q1 is midpoint from start to median Q3 is
midpoint from median to end
Use median position (n1) / 2 to find median
(a) Use this information to find the (i)
median (ii) lower upper
quartiles (iii) the semi-interquartile range
What would you like to do now?

• What is the probability that someone chosen at
  random earns less than 180?

Go to full solution
Graphs etc Menu
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Reveal answer
114
GRAPHS, CHARTS, TABLES Question 1
The following stem leaf diagram shows the
distribution of wages for employees in a small
factory .. 16 2 3 6 9 17 1 1 1 8 8 9 18 2 3 3
5 6 7 7 19 1 2 8 20 1 5 5 6 n 25 21 8
17 4 174
median 183
(a) Use this information to find the (i)
median (ii) lower upper
quartiles (iii) the semi-interquartile range
Q1 171
What would you like to do now?
Q3 195
12

• What is the probability that someone chosen at
  random earns less than 180?

2/5
Go to full solution
EXIT
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Graphs etc Menu
115
Question 1
1. Use median (n1) / 2 to find median
16 2 3 6 9 17 1 1 1 8
8 9 18 2 3 3 5 6 7 7 19
1 2 8 20 1 5 5 6 n
25 21 8 17 4 174
(a)(i) Since n 25 then the median is
13th value
ie median 183
(NOT 3!!!)
2. There are 12 values before median so Q1
position 13 - (12 1) / 2

• Median
• lower upper quartiles
• (iii) the semi-interquartile range

(ii) Both 6th 7th values are 171 so Q1
171
3. There are 12 values after median so Q3
position 13 (12 1) / 2
Begin Solution
19th is 192 20th is 198 so Q3 195
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116
Question 1
4. Use SIQR ½ (Q3 Q1 ) / 2
(iii) SIQR ½(Q3 Q1)
16 2 3 6 9 17 1 1 1 8
8 9 18 2 3 3 5 6 7 7 19
1 2 8 20 1 5 5 6 n
25 21 8 17 4 174
(195 - 171) ? 2
12

• Median
• lower upper quartiles
• (iii) the semi-interquartile range

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117
Question 1
5. Use P no of favourable / no of data
No of favourable ( under 180) 10
16 2 3 6 9 17 1 1 1 8
8 9 18 2 3 3 5 6 7 7 19
1 2 8 20 1 5 5 6 n
25 21 8 17 4 174
No of data n 25
(b) Prob(under 180) 10/25 2/5 .

• What is the probability that
• someone chosen at random
• earns less than 180?

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118
Comments
Median the middle number in the ordered list.
25 numbers in the list.
1. Use median (n1) / 2 to find median
(a)(i) Since n 25 then the median is
13th value
1 12 13 14 - 25
ie median 183
2. There are 12 values before median so Q1
position 13 - (12 1) / 2
12 numbers on either side of the median
median is the 13th number in order.
(ii) Both 6th 7th values are 171 so Q1
171
3. There are 12 values after median so Q3 13
(12 1) / 2
19th is 192 20th is 198 so Q3 195
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119
Comments
To find the upper and lower quartiles deal with
the numbers on either side of the median
separately.
1. Use median (n1) / 2 to find median
(a)(i) Since n 25 then the median is
13th value
Q1
12 numbers before median. 6 numbers either side
of Q1 is midway between the
6th and 7th number.
ie median 183
2. There are 12 values before median so Q1
position 13 - (12 1) / 2
(ii) Both 6th 7th values are 171 so Q1
171
3. There are 12 values after median so Q3 13
(12 1) / 2
19th is 192 20th is 198 so Q3 195
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120
Comments
To find the upper and lower quartiles deal with
the numbers on either side of the median
separately.
1. Use median (n1) / 2 to find median
(a)(i) Since n 25 then the median is
13th value
Q3
12 numbers after median. 6 numbers either side of
Q3 is midway between the 19th
and 20th number.
ie median 183
2. There are 12 values before median so Q1
position 13 - (12 1) / 2
(ii) Both 6th 7th values are 171 so Q1
171
3. There are 12 values after median so Q3 13
(12 1) / 2
19th is 192 20th is 198 so Q3 195
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121
Charts, Graphs Tables Question 2
The weights in grams of 20 bags of crisps were as
follows 28 29 29 30 31 30 28 30
29 28 29 30 30 28 28 29 29 29
29 28 a) Illustrate this using a dot
plot. b) What type of distribution does this
show? c) If a bag is chosen at random what is
the probability it will be heavier than
the modal weight?
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122
Charts, Graphs Tables Question 2
The weights in grams of 20 bags of crisps were as
follows 28 29 29 30 31 30 28 30
29 28 29 30 30 28 28 29 29 29
29 28 a) Illustrate this using a dot
plot. b) What type of distribution does this
show? c) If a bag is chosen at random what is
the probability it will be heavier than
the modal weight?
Establish lowest highest values and draw line
with scale.
Plot a dot for each piece of data and label
diagram.
For probability use P no of favourable / no
of data
What would you like to do now?
Go to full solution
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Reveal answer
123
Charts, Graphs Tables Question 2
The weights in grams of 20 bags of crisps were as
follows 28 29 29 30 31 30 28 30
29 28 29 30 30 28 28 29 29 29
29 28 a) Illustrate this using a dot
plot. b) What type of distribution does this
show? c) If a bag is chosen at random what is
the probability it will be heavier than
the modal weight?
CLICK
Tightly clustered
3/10
Go to full solution
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124
Question 2
1. Establish lowest highest values and draw
line with scale.

• 29 29 30 31
• 28 30 29 28
• 30 30 28 28
• 29 29 29 29 28

(a) Lowest 28 highest 31.
Illustrate this using a dot plot.
Begin Solution
2. Plot a dot for each piece of data and label
diagram.
Continue Solution
C