The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
Name:
HW1 – Grade B
Bearings
1.
Teacher
Assessment
The diagram shows the positions of three towns, P, Q and R.
Q is 35 km from P on a bearing 100.
R is 42 km from P on a bearing 120.
N
35 km
P
not drawn accurately
Q
42 km
R
Calculate the distance from Q to R.
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Answer...............................................................................................................................km
(Total 4 marks)
The Robert Smyth School
1
The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
2.
Two ships, A and B, leave a port at 1300 hours. Ship A travels at a constant speed of 18 km per
hour on a bearing of 070°. Ship B travels at a constant speed of 25 km per hour on a bearing of
152°.
N
18 km
A
Not drawn accurately
Port
25 km
B
Calculate the distance between A and B at 1400 hours.
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Answer ........................................................... km
(Total 4 marks)
Success:
The Robert Smyth School
Target:
2
The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
HW2 – Grade A
Sine and Cosine Rule
1.
In the diagram, PQ = 14 cm and QR = 8.6 cm.
Teacher
Assessment
Angle PSQ = angle SQR = 90°
Angle PQS = 25°
P
Not drawn accurately
14 cm
S
25°
Q
8.6 cm
R
Calculate angle R.
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Answer ................................................... degrees
(Total 5 marks)
The Robert Smyth School
3
The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
2.
In triangle ABC, AB = 11 cm, BC = 9 cm and CA = 10 cm.
C
Not to scale
10 cm
9 cm
A
11 cm
B
Find the area of triangle ABC.
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Answer ..................................... cm2
(Total 5 marks)
The Robert Smyth School
4
The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
3.
(a)
ABC is a triangle.
AC = 19 cm, BC = 17 cm and angle BAC = 60°
B
Not drawn accurately
17 cm
A
60°
19 cm
C
Calculate the size of angle ABC.
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Answer .......................................................degrees
(3)
(b)
PQR is a triangle.
PR = 23 cm, PQ = 22 cm and angle QPR = 48º
Q
Not drawn accurately
22 cm
P
48°
23 cm
R
Calculate the length of QR.
Give your answer to an appropriate degree of accuracy.
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Answer .......................................................cm
(4)
(Total 7 marks)
The Robert Smyth School
5
The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
4.
The hour hand of a clock is 4.5 cm long.
The minute hand is 6.2 cm long.
Not drawn accurately
6.2 cm
4.5 cm
Calculate the distance between the tips of the hands at 7 o’clock.
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Answer ................................................................... cm
(Total 4 marks)
The Robert Smyth School
6
The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
5.
ABCD is a quadrilateral.
AB = 7 cm, AD = 6 cm and BC = 9 cm.
Angle ABC = 75° and angle ADC = 90°
A
7 cm
B
75°
6 cm
Not drawn accurately
D
9 cm
C
Calculate the perimeter of ABCD.
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Answer ........................................................... cm
(Total 5 marks)
The Robert Smyth School
7
The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
6.
In triangle ABC, AB = 5 cm, BC = 8 cm and AC = 9 cm.
A
9 cm
5 cm
B
8 cm
not drawn accurately
C
Use the cosine rule to show that triangle ABC does not contain an obtuse angle.
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(Total 3 marks)
7.
A shape is made from 6 congruent triangles as shown.
Success:
Not drawn accurately
3 cm
Target:
30°
8 cm
You are given that sin 30° = 0.5
Calculate the area of the shape.
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Answer ………………………………………………
(Total 4 marks)
The Robert Smyth School
8
The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
HW3 – Grade B
Similar Triangles
1.
The triangles A and B are congruent.
Teacher
Assessment
8 cm
B
10 cm
x
A
30°
y
38°
30°
15 cm
(a)
112°
Not drawn
accurately
Write down the values of x and y.
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Answer x =...................... cm, y = ………………… cm
(2)
(b)
Given that sin 30° = 0.5, calculate the area of triangle A.
State the units of your answer.
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Answer ................................................................
(3)
(Total 5 marks)
The Robert Smyth School
9
The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
2.
Triangles ADE and ABC are similar.
DE is parallel to BC.
AD = 4 cm, DE = 6 cm and BC = 9 cm.
A
Not to scale
4 cm
D
B
6 cm
9 cm
E
C
Calculate the length of BD.
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Answer ........................................................... cm
(Total 3 marks)
The Robert Smyth School
10
The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
3.
Triangles ABC and PQR are similar.
AC = 3.2 cm, AB = 4 cm and PR = 4.8 cm.
P
A
Not drawn accurately
4.8 cm
3.2 cm
4 cm
C
(a)
x
B
R
Q
Explain why sin x = 0.8
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(1)
(b)
Calculate the length of PQ.
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Answer .......................................................cm
(3)
(Total 4 marks)
The Robert Smyth School
11
The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
4.
Triangles ABC and APQ are similar.
PQ is parallel to BC.
AQ = 6 cm, QC = 2 cm and BC = 12 cm
A
not drawn accurately
6 cm
Q
P
B
12 cm
2 cm
C
Calculate the length of PQ.
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Answer...............................................................................................................................cm
(Total 3 marks)
The Robert Smyth School
12
The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
5.
A square-based pyramid A is divided into two parts:
a square-based pyramid B and a frustum C, as shown.
Pyramid B
Pyramid A
Frustum C
Pyramid A is similar to pyramid B.
The base of pyramid A is a square of side 10 cm. The base of pyramid B is a square of side 5 cm.
The vertical height of pyramid A is 12 cm.
(a)
You are given the formula
Volume of a pyramid =
1
 area of base × vertical height
3
Calculate the volume of the frustum C.
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Answer .......................................................... cm3
(4)
(b)
Express the volume of the frustum C as a fraction of the volume of the larger pyramid A.
Give your answer in its simplest form.
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Answer ..................................................................
(2) (Total 6 marks)
Success:
The Robert Smyth School
Target:
13
The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
HW4 – Grade A/A*
Trig Graphs
1.
(a)
Sketch the graph of y = sin x for values of x from 0° to 360°.
Teacher
Assessment
y
1
0
0°
90°
180°
270°
360°
x
–1
(1)
(b)
One solution of the equation sin x = 0.92 is x = 67°.
Use your sketch graph to find another solution of this equation.
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Answer ......................................................... degrees
(2)
(c)
Use your sketch graph to work out the value of sin 293°.
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Answer .........................................................
(1)
(Total 4 marks)
The Robert Smyth School
14
The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
2.
The sketch shows the graph of y = sin x for 0°  x  360°
y
2
1
0
90
180
270
360 x
–1
–2
You are given that sin 70° = 0.9397
(a)
Write down another solution of the equation sin x = 0.9397
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Answer ..........................................................degrees
(1)
(b)
Solve the equation sin x = –0.9397 for 0°  x  360°
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Answer .......................................................... degrees
.......................................................... degrees
(2)
The Robert Smyth School
15
The Robert Smyth School
Mathematics Faculty
Y11 Topic 15
Trig 2
Innovation & excellence
(c)
On the axes below sketch the graph of y = sin 2x for 0°  x  360°
y
2
1
0
90
180
360 x
270
–1
–2
(2)
(d)
Hence write down the four solutions of the equation sin 2x = 0.9397
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Answer ..........................................................degrees
.......................................................... degrees
.......................................................... degrees
.......................................................... degrees
(3)
(Total 8 marks)
Success:
The Robert Smyth School
Target:
16