Download COS TAN ALL SIN - Millburn Academy

TRIGONOMETRY
Introduction
Knowledge of the sines and cosines of angles other than acute angles is needed within this unit
to allow students to use the Sine and Cosine Rules in obtuse angled triangles.
The tangent is included for completeness.
An investigative approach, using the sine, cosine and tangent graphs, could be taken, though it
should be noted that formal knowledge of the graphs is not required until Mathematics 3.
Exercise 1A takes the students through the drawing of y = sin x°, y = cos x° and y = tan x°.
Exercise 1A may now be attempted.
The class/group should then discuss when graph is positive and when negative. A summary
table of results could then be drawn up, for example:
y = sin x°
positive when
negative when
0 < x < 180
180 < x < 360
y = cos x°
positive when
negative when
0 < x < 90 and 270 < x < 360
90 < x < 270
y = tan x°
positive when
negative when
0 < x < 90 and 180 < x < 270
90 < x < 180 and 270 < x < 360
This should lead to
SIN
ALL
TAN
COS
A class set of graphic calculators will enable students to complete this introduction quickly.
Have students use their trigonometric calculators to look up various trig ratios such as
sin 20°, cos 150°, tan 210° etc, each time checking with their graphs as to the validity of their
results. (i.e the sign each time).
Exercise 1B may now be attempted.
Mathematics Support Materials: Mathematics 2 (Int 2) - Staff Notes
3
B
A. Area of a triangle using trigonometry
Students should be taken through the development
of the formula:
a
h
Area = 1/2 ab sin C
by starting with:
D
C
Area = 1/2 b x h
and showing that in triangle BCD,
=>
=> sin C = h/a
Area = 1/2 b x (a sin C)
=>
=> h = a sin C
Area = 1/2 ab sin C
Go over an example with different named vertices.
=>
Area = 1/2 qr sin P
=>
Area = 1/2 8 x 12 x sin 29°
=>
Area = 23á3 cm2
A
b
R
8 cm
29°
P
12 cm
Q
Exercise 2 may now be attempted
Throughout this unit, students should be encouraged to make effective use of their calculators
and avoid premature rounding.
Mathematics Support Materials: Mathematics 2 (Int 2) - Staff Notes
4
B.
Sine Rule
Students should be encouraged to discuss the restrictions on their present trigonometry. A brief
revision of right angled triangle trigonometry should follow with a few examples ending with
the following:
C
x
10
x = 10 x sin 25°
x = 4á23 cm
sin 25° =
=>
=>
10 cm
x cm
80°
25°
B
A
A slight variation can now be introduced to the above example.
C
Students should realise that the above method
will not work here because it is no longer
a right angled triangle.
10 cm
x cm
25°
B
A
Encourage students to develop the idea of dropping a perpendicular from C to AB, meeting it at
point D and studying the two right angled triangles instead.
Go through this process with the above example and, once accepted, let students attempt Qu
2(a) from Exercise 3 using this method.
C
Develop the Sine Rule with the students.
=>
=>
=>
=>
in triangle ADC
h = b sin A
and in triangle BDC
h = a sin B
combining these 2 results
a sin B = b sin A
a
sin A
=
b
sin B
b
a
h
D
A
=> by symmetry to
B
c
a
sin A
Mathematics Support Materials: Mathematics 2 (Int 2) - Staff Notes
=
b
sin B
=
c
sin C
5
The initial example can now be solved using the Sine rule
to calculate a missing side.
a
b
c
sin A = sin B = sin C
C
10 cm
x cm
=>
=>
x
10
=
sin 25°
sin 80°
x sin 80° = 10 x sin 25°
x = 10 sin 25°
sin 80°
=>
80°
25°
=>
B
A
x = 4á29 cm
Exercise 3, questions 1 to 4, may now be attempted.
Calculating the missing angle using the Sine rule:
Example:
Q
p
sin P
=>
=>
=>
=>
=
q
sin Q
=
r
sin R
12
= 8á5
sin x °
sin 42°
8á5 sin x ° = 12 x sin 42°
8á5 cm
x°
P
12 sin 42°
= 0á945
8á5
x = 70á8°
(remind about the use of sinÐ1)
12 cm
42°
R
sin x =
Exercise 3, questions 5 to 10, may now be attempted.
Mathematics Support Materials: Mathematics 2 (Int 2) - Staff Notes
6
C.
Cosine rule.
C
Students should be given the following example to solve.
They should soon realise it cannot be solved by
use of the Sine rule.
9 cm
x cm
32°
The Cosine rule should now be introduced
10 cm
A
B
C
Define the Cosine rule:
b
a2 = b2 + c2 Ð 2bc cosA
Go over the ÔformatÕ and try to get students
to come up with a similar formula for
a
c
A
B
Note: ÔbracketsÕ could be introduced to prevent mishandling of the values of a, b and c. i.e.
a2 = b2 + c2 Ð (2bc cosA)
Some other named triangles could be presented/displayed and students asked to state the
corresponding formula for any required side.
The initial question can now be solved.
=>
=>
=>
=>
=>
=>
a2
a2
a2
a2
a2
a
= b2 + c2 Ð (2bc cosA)
= 92 + 102 Ð (2 x 9 x 10 x cos32°)
= 81 + 100 Ð (180 x 0á848..)
= 181 Ð 152á64..
= 28á35...
= 5á32 cm
C
9 cm
x cm
32°
10 cm
A
B
Exercise 4A, questions 1 and 2, may now be attempted.
An example involving an obtuse
angled triangle should now be introduced
=>
=>
=>
=>
=>
=>
p2 =
p2 =
p2 =
p2 =
p2 =
p2 =
Q
q2 + r2 Ð (2qr cos P)
72 + 8á52 Ð (2 x 7 x 8á5 x cos 130°)
49 + 72á25 Ð (119 x (Ð0á642...))
121á25 Ð (Ð76á49...)
121á25 + 76á49...
197á7...
=>
p = 14á1 cm
x cm
8á5 cm
130°
P
7 cm
R
Exercise 4A, questions 3 to 6, may now be attempted.
Mathematics Support Materials: Mathematics 2 (Int 2) - Staff Notes
7
Calculating the missing angle using the Cosine rule.
Exercise 4B covers material listed in Helvetica font and is therefore beyond Grade C.
Students should be shown how the formula for
the Cosine rule can be rearranged:
C
a2 = b2 + c2 Ð (2bc cosA)
=>
2bc cos A =
=>
cos A =
Example:
=>
b2
+
c2
Ð
4 cm
5 cm
a2
b2 + c2 Ð a2
2bc
A
b2 + c2 Ð a2
2bc
2
5 + 62 Ð 42
cos A =
2x5x6
B
6 cm
cos A =
=>
=
45
60
= 0á75
A = 41á4°
Students can be asked to define similar formulae for cos B and cos C and for other triangles.
Exercise 4B, questions 1 and 2 may now be attempted.
Now introduce a problem where
the cosine is negative.
=>
=>
2
2
2
cos P = q + r Ð p
2qr
2
2
2
cos P = 8 + 9 Ð 15
2x8x9
cos P =
Q
15 cm
Ð 80
144
9 cm
x°
P
8 cm
R
= Ð0á555...
Students should understand that when the cosine is negative, the angle must be obtuse.
However, not all calculators will give the obtuse angle immediately.
At this point, ask the students to feed in Ð0á555... into their calculators and press Ôcos Ð1Õ
=>
=>
either 123á7° appears and there is no problem
or Ð56á3° appears and the student should be told to simply +180° to get
the correct answer of 123á7°.
Exercise 4B, questions 3 to 6 may now be attempted.
The checkup exercise for Trigonometry may now be attempted.
Mathematics Support Materials: Mathematics 2 (Int 2) - Staff Notes
8
TRIGONOMETRY
By the end of this set of exercises, you should be able to
(a)
calculate the area of a triangle using trigonometry
(b)
solve problems using Sine and Cosine rules.
Mathematics Support Materials: Mathematics 2 (Int 2) - Student Materials
3
TRIGONOMETRY
Introduction: Sine, Cosine and Tangent Graphs
Exercise 1A
1. The Sine Graph
(a) Make a copy of this table and use your calculator to help fill it in, giving each
answer correct to 2 decimal places.
x
sin x°
0°
0á00
x
sin x°
200°
...
20°
0á34
40° 60°
0á64 0á87
220°
...
240°
...
80° 90° 100° 120° 140° 160
0á98 1á00 . . .
...
...
...
260°
...
270°
...
280°
...
300°
...
320° 340°
...
...
180°
...
360
...
(b) Use a piece of 2 mm graph paper to draw a set of axes as illustrated below.
1
0
90
180
270
360
Ð1
(c) Plot as accurately as possible the 21 points from your table.
(d) Join them up smoothly to create the graph of the function y = sin x°.
2. Repeat question 1 (a) to (d) for the function y = cos x°
3. Repeat for the graph of y = tan x° (a different scale will be required for the vertical axis).
(These graphs will be studied later).
Sine, Cosine and Tangents of angles other than acute angles
Exercise 1B
1. Use your calculator to find the following trigonometric ratios.
Give each answer correct to 3 decimal places.
(a) sin 25°
(b) cos 95°
(c) tan 107°
(e) cos 315°
(f) tan 181°
(g) cos 240°
(i) tan 225°
(j) sin 300°
(k) tan 315°
(m) tan (Ð75°)
(n) cos (Ð200°)
(o) sin 360°
Mathematics Support Materials: Mathematics 2 (Int 2) - Student Materials
(d)
(h)
(l)
(p)
sin 200°
sin 330°
cos 500°
cos 360°
4
A . Area of a Triangle using Trigonometry.
Exercise 2
B
1. In this question you are being asked to calculate
the area of triangle ABC, using two methods.
Method 1
(a)
(b)
Method 2
Use basic right angled
trigonometry on triangle
ABP to calculate the
height BP (= h cm).
10 cm
h cm
Now use the formula
72°
Area = 1/2 (base x height)
A
to calculate the area of DABC.
P
C
12 cm
Use the formula:
Area = 1/2 b c sin A
with b = 12 cm, c = 10 cm and angle A = 72°
to calculate the area of triangle ABC.
Did you obtain the same answer? Which method was the faster?
2. Use the formula Area = 1/2 a b sin C to calculate the areas of the following six triangles:
(Give all answers correct to 1 decimal place).
(a)
P
(b)
B
6 cm
C
42°
A
(c)
15 cm
39°
Q
7 cm
R
12 cm
D
M
(d)
9á2 cm
34°
52°
16 cm
L
16 cm
8á5 cm
F
E
N
(e)
(f)
2á1 cm
T
X
S
128°
3á2 cm
13 cm
Y
105°
16 cm
Z
R
Mathematics Support Materials: Mathematics 2 (Int 2) - Student Materials
5
3. Calculate the areas of the following two triangles:
(a)
(b)
8 cm
8 cm
140°
40°
10 cm
10 cm
What do you notice?
4. Calculate the areas of the following two triangles:
(a)
(b)
7 cm
7 cm
127°
53°
6á5 cm
6á5 cm
What do you notice? Can you explain your answers to questions 3 and 4?
5. Shown is a sketch of Farmer GilesÕ
triangular field.
Calculate its area in square metres.
52 m
43°
65 m
6. Calculate the area of this pentagon:
10 cm
6á18 cm
30°
10 cm
15 cm
7. Calculate the areas of the following two parallelograms:
(a)
(b)
14 cm
4 cm
125°
65°
17 cm
8 cm
Mathematics Support Materials: Mathematics 2 (Int 2) - Student Materials
6
B . Sine Rule.
Exercise 3
In this exercise, give all answers correct to 1 decimal place.
C
1. Copy and complete the following:
7á5 cm
a
Sin A
b
=
Sin B
c
= (
)
Sin C
61°
A
a
7á5
=
Sin 61°
Sin 39°
a cm
39°
B
a = 7á5 x Sin 61° =
Sin 39°
=>
cm
2. Use the Sine Rule in each of the following to calculate the size of the side marked x cm.
B
C
(a)
(b)
25 cm
x cm
x cm
72°
B
42°
A
19 cm
84°
A
47°
C
I
Q
(c)
(d)
19 cm
50°
8á6 cm
x cm
110°
24°
K
J
60°
P
R
x cm
E
(e)
T
120°
(f)
40°
x cm
x cm
S
45 cm
x cm
35°
D
70°
9 cm
F
R
Mathematics Support Materials: Mathematics 2 (Int 2) - Student Materials
7
Q
3. (a) Write down the size of Ð PQR.
(b) Use the Sine rule to calculate
the length of the line QR.
80°
P
60°
9 cm
4. In each of the following, calculate the size
of the third angle first before attempting to
calculate the length of the side marked x cm.
(a)
(b)
M
B
R
(c)
J
59°
42°
x cm x cm
26 cm
x cm
52°
A
61°
10á4 cm
C N
6á5 cm
109°
F
72°
P
5. Copy and complete:
a
=
Sin A
C
b
Sin B
= (
c
)
Sin C
8 cm
10 cm
10 =
8
Sin x °
Sin 42°
A
x°
42°
=> 8 Sin x ° = 10 Sin 42°
=>
Sin x
=
=>
x
=
K
10 Sin 42°
8
=
B
0á .....
6. Use the Sine Rule in each of the following to calculate the size of the angle marked x °.
P
(a)
(b)
B
54°
10 cm
30 cm
12 cm
47°
A
x°
Q
C
X
(c)
x°
R
25 cm
M
(d)
75°
12 cm
10 cm
112°
Y
x°
L
3á2 cm
x°
Z
Mathematics Support Materials: Mathematics 2 (Int 2) - Student Materials
8á4 cm
N
8
7. The diagram shows a roof truss.
Calculate the size of the angle marked
x ° between the wooden supports.
3á2 m
2á1 m
x°
34°
8.
N
N
H.M.S. Nautilus lies East of H.M.S. Unicorn.
The diagram shows where an enemy submarine
is in relation to the two ships.
Calculate how far the submarine is from H.M.S.
Nautilus.
35 km
51°
32°
Unicorn
Nautilus
A
9. This is the metal frame used to support and
hold a childÕs swing.
It is in the shape of an isosceles triangle.
30°
(a) Calculate the size of ÐABC.
2á8 m
(b) Use the Sine rule to calculate how
far apart points B and C are.
(Answers to 2 decimal places)
(c) Draw a vertical line through A,
creating two right angled triangles
and use right angled trigonometry
to check your answer to part (b).
2á8 m
C
B
10. Calculate the size of the angles marked x °, y ° and z °. (careful!)
Q
B
108°
x°
R
6á1 cm
9 cm
10 cm
10á6 cm
y°
P
65°
A
C
7á7 cm
U
V
z°
9á8 cm
42°
W
Mathematics Support Materials: Mathematics 2 (Int 2) - Student Materials
9
C . Cosine Rule
Exercise 4A
1. Copy and complete the following:
C
a2 = b 2 + c 2 Ð (2bc cos A)
=>
x2
=> x
=
2
72
82
+
7 cm
Ð (2 x 7 x 8 x cos 25°)
= ... + ... Ð (.....)
x cm
25°
A
=> x 2 = ......
=> x =
8 cm
B
2. Use the Cosine rule to calculate the size of each side marked x cm here.
(a)
(b)
B
R
9 cm
x cm
x cm
12 cm
34°
A
Q
C
10 cm
63°
15 cm
P
(c)
(d)
J
M
51°
29 cm
I
47°
K
x cm
(e)
9á2 cm
x cm
43 cm
G
L
8á7 cm
(f)
34°
7á5 cm
N
Y
7á5 cm
20 cm
x cm
W
15°
18 cm
V
E
F
x cm
Mathematics Support Materials: Mathematics 2 (Int 2) - Student Materials
10
3. Copy and complete the following:
C
a2 = b 2 + c 2 Ð (2bc cos A)
=> x 2 = 8 2 + 6 2 Ð (2 x 8 x 6 x cos 110°)
x cm
=> x 2 = ... + ... Ð (96 x (Ð0á342..))
8 cm
=> x 2 = ...... Ð (Ð32á83..)
=> x 2 = ...... + 32á83..
=> x 2 = ......
=> x =
110°
A
B
(note)
4. Calculate the lengths of the sides marked x cm.
(a)
(b)
17 cm
Q
120°
B
x cm
15 cm
C
9 cm
95°
6 cm
(c)
R
W
x cm
x cm
5á2 cm
7 cm
P
U
A
5. A farmer owns a piece of fenced land which is
triangular in shape.
Calculate the length of the third side and then
write down the perimeter of the field.
D
131°
4á8 cm
V
F
58 m
62 °
71 m
E
6. Two ships leave Peterborough harbour at 1300. The Nightingale sails at 20 miles per hour
on a bearing 042°. The Mayflower II sails at 25 miles per hour on a bearing 087°.
(a) Calculate the size of ÐNMP.
(b) How far apart will the 2 ships be after 1 hour?
(c) How far apart will they be at 1600?
North
042° 087°
N
Nightingale
M
Mayflower II
P
Mathematics Support Materials: Mathematics 2 (Int 2) - Student Materials
11
Exercise 4B
1. Copy and complete the following to find ÐBAC:
C
a2 = b 2 + c 2 Ð (2bc cos A)
=> cos A =
b2+ c2Ð a2
2bc
=> cos A =
6 2 + 7 2 Ð 92
2x6x7
=> cos A =
0á ......
=>
6 cm
9 cm
A
B
7 cm
A =
2. Use this ÔreverseÕ form of the Cosine rule to calculate
the size of each angle marked x° here.
B
(a)
8 cm
cos A =
b2+ c2Ð a2
2bc
R
(b)
15 cm
6 cm
9 cm
A
x°
Q
C
9 cm
x°
J
(c)
13 cm
P
(d)
x°
17 cm
M
18 cm
7á1 cm
7á9 cm
I
x°
K
14 cm
L
8á2 cm
N
G
(e)
(f)
Y
x°
40 cm
6á5 cm
18 cm
6á5 cm
x°
W
36 cm
V
E
5á9 cm
F
Mathematics Support Materials: Mathematics 2 (Int 2) - Student Materials
12
3. Copy and complete the following to find ÐBAC:
C
a2
=
b2
=> cos A =
+
c2
Ð (2bc cos A)
b2+ c2Ð a2
10 cm
2bc
7 2 + 6 2 Ð 102
=> cos A =
2x7x6
=> cos A =
=>
Hint :-
7 cm
x°
Ð0á178..
A
B
6 cm
A = ?????
try finding SHIFT (or INV) cos (Ð0á178..)
if you obtain the correct answer of 100á3°, your calculator can handle negatives.
if you obtain the wrong answer of Ð79á7°, ask your teacher/lecturer for help.
4. Calculate the size of each of the obtuse angles in the following three triangles:
(a)
(b)
(c)
3á5 cm
R
Q
B
9 cm
2á5 cm
66 mm
C
5 cm
5 cm
6 cm
W
41 mm
P
A
5. Two guy ropes are used to
restrain a balloon.
The ropes are 85 metres and
65 metres long, and are tethered
at points 100 metres apart.
Calculate the sizes of the two angles
marked x ° and y °.
U
38 mm
V
P
65 m
85 m
P
y°
x°
Q
100 m
6. This triangular metal plate has its 3 sides as shown.
(a) Calculate the size of the angle marked x °.
(b) Calculate the area of the triangular plate.
23 cm
19 cm
x°
27 cm
Mathematics Support Materials: Mathematics 2 (Int 2) - Student Materials
13
CHECKUP FOR TRIGONOMETRY
1. Write down the values of the following to 3 decimal places:
(a) sin 200°
(b) tan 320°
(c)
cos (Ð265°)
2. Calculate the area of this triangle:
18 cm
29°
21 cm
3. Calculate the area of this parallelogram:
6á5 cm
57°
9á3 cm
4. Use the Sine Rule or the Cosine rule (2 formats) to calculate the value of x each time here:
(a)
(b)
(c)
9á5 cm
115°
x cm
50°
58°
31°
x cm
38°
45°
(d)
22 cm
8á5 cm
x cm
(e)
(f)
13 cm
105°
x cm
58°
15 cm
9á2 cm
9á2 cm
x cm
8 cm
10 cm
61°
x cm
(g)
(h)
(i)
x°
13 cm
7á5 cm
x°
8á7 cm
9 cm
7 cm
11 cm
9á6 cm
x°
11 cm
Mathematics Support Materials: Mathematics 2 (Int 2) - Student Materials
16á5 cm
14
5. The diagram shows the side view of a house
with a sloping roof.
Calculate the size of the angle, x°, between the
two sloping sides of the roof.
x°
4á5 m
3á5 m
6á9 m
North
A
6.
65 km
B
041°
53 km
R
From a radar station at R, signals from
two ships are picked up.
Ship A is on a bearing 041° from R and
is 65 kilometres away.
Ship B is on a bearing 295° from R and
is 53 kilometres away.
Calculate how far apart the two ships are.
295°
tra
ck
44°
far
m
11
B2
7. A farmer owns a triangular piece of land
trapped between 2 main roads and the
farm track.
Calculate the length of the farm track
to the nearest whole metre.
160 m
53°
A74
8. Calculate the shaded area of this
rectangular metal plate with a
triangular hole cut out of it.
7 cm
8 cm
10 cm
52°
14 cm
Mathematics Support Materials: Mathematics 2 (Int 2) - Student Materials
15
ANSWERS TO MATHEMATICS 2 (INT 2)
Trigonometry
Exercise 1A
1. (a)
0á00 0á34 0á64 0á87 0á98 1á00 0á98 0á87 0á64 0á34 0á00
Ð0á34 Ð0á64 Ð0á87 Ð0á98 Ð1á00 Ð0á98 Ð0á87 Ð0á64 Ð0á34 0á00
2.
1
y = sin
x°
90°
180°
270°
1
90°
y = tan x°
360°
180°
360°
Ð1
3.
y = cos x°
180°
270°
90°
360°
270°
Ð1
Exercise 1B
1. (a) 0á423
(f) 0á017
(k) Ð1
(b)
(g)
(l)
Ð0á087
Ð0á5
Ð0á776
(c) Ð3á271
(h) Ð0á5
(m) Ð3á732
(d)
(i)
(n)
Ð0á342
1
Ð0á940
(e) 0á707
(j) Ð0á866
(o) 0 (p) 1
57á06 cm2
Method 2: Ñ> 57á06 cm2
Exercise 2
1. Method :
(a) h = 9á51
(b)
2. (a) 14á1 cm2
(d) 71á6 cm2
(b)
(e)
56á6 cm2 (c)
100á5 cm2 (f)
3. (a) 25á7 cm2
(b)
25á7 cm2
same answer
4. (a) 18á2 cm2
(b)
18á2 cm2
same answer because sin 53° = sin 127°
5. 1152.6 cm2
6.
30á8 cm2
2á6 cm2
117á7 cm2
Exercise 3
1. a = 10á4 cm
2. (a) 17á6 cm (b) 14á0 cm (c) 7á6 cm
3. (a) 40° (b) 13á8 cm
4. (a) 67°; 5á6 cm
(b) 49°; 9á2 cm
5. 0.836, 56á8°
6.
(a) 37á6°
(b)
7. 58á4°
8.
23á9 km 9. (a) 75°
10. (a) x = 60á3
(b) y = 38á8
(c)
7 (a) 215á7 cm2
(d) 8á2 cm
(b) 26á2 cm2
(e) 13á2 cm
(f) 29á8 cm
(c) 29°; 13á3 cm
76á1°
(c) 50á6°
(d)
(b) 1á45 m
(c) 1á45 m
z = 106á3
21á6°
Exercise 4A
1.
2.
3.
5.
x = 3á39
(a) 5á6 cm (b) 14á3 cm (c) 33á5 cm (d) 7á2 cm (e) 4á4 cm
x = 11á5 cm
4.
(a) 11á9 cm (b) 27á7 cm (c) 9á1 cm
67á4 m; 196á4 m
6. (a) 45° (b) 17á8 km (c) 53á5 km
Mathematics Support Materials: Mathematics 2 (Int 2) - Student Materials
(f) 5á3 cm
32
Exercise 4B
1.
2.
3.
4.
5.
87á3°
(a) 40á8° (b) 83á9° (c) 47° (d) 61á7°
100á3°
(a) 109á5° (b) 111á8° (c) 113á3°
x = 40á1°, y = 57á4°
(e) 54á0°
(f) 26á7°
(b) Area = 214á8 cm2
6. (a) x = 56á9°
Checkup for Trigonometry
1. (a) Ð0á342
(b)
Ð0á839
(c)
Ð0á087
2. 91.6 cm2
3. 50á7 cm2
4. (a) 11á4 cm
(f) 22á2 cm
5. 118á7°
6. 94á5 km
7. 199 m
(b) 11á1 cm (c) 12á5 cm (d) 9á3 cm
(g) 80á4°
(h) 72á3°
(i) 131á6°
(e) 8á9 cm
8. 117á9 cm2
Simultaneous Linear Equations
Exercise 1
1. (a) 3
(b) W = 3N
(c) 30kg
(d)(e)
2. (a) 1/10 2/20 3/30 4/40 5/50 6/60 in table
(e) (f)
(b) 10
(c) E = 10P
3. (a) 1/20 2/40 3/60 4/80 5/100 6/120 in table
(b) T = 20W
4. (a) £57 £65
(b) C = 8h + 25
5. (a) 1/12 2/16 3/20 4/24 5/28 in table
(b) C = 4D + 8
(c)
(d) (0,8)
(e) Costs £8 before even paying for any days !!
6. (a) 1/15 2/25 3/35 4/45 5/55 6/65 in table
(b) T = 10W + 5
(c) 105 mins
7. (a) C = 5k + 50 (b) £100 (c)
50
8. (a) W = 10P + 80 (b) £280
(d) 90
(c) 200 mins
8
(c)
80
Mathematics Support Materials: Mathematics 2 (Int 2) - Student Materials
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