mathematics - · pdf file3.07.2014 · maths department -2- s2 level 3/4 course the...

S2 Level 3/4 Course -1- Maths Department

MA

TH

EM

AT

ICS

Larkhall Academy

Maths Department -2- S2 Level 3/4 Course

The Circle

Exercise 1(A)

Find the circumference ( ) of the following circles

1)

18 cm

2)

12 cm

3)

5 cm

4)

28 m

5)

8 cm

6)

15 m

7) 32 cm·

8)

22 m

9)

52 cm

10)

17 c

m

11)

5 cm

12)

34 m

Exercise 1(B)

Find the circumference ( ) of the following circles

1) d = 2 m 2) d = 20 m 3) d = 54 cm 4) d = 4∙2 m

5) d = 12∙6 cm 6) d = 6∙3 cm 7) r = 2cm 8) r = 6 m

9) r = 50 m 10) r = 3∙2 cm 11) r = 8∙4 m 12) r = 12∙6 cm

13) d = 28 m 14) d = 7∙4 cm 15) r = 19 m 16) r = 264 cm


Exercise 2(A)

Find the area ( ) of the following circles

1)

8 cm

2)

15 m

3) 32 cm·

4)

22 m

5)

18 cm

6)

12 cm

7)

5 cm

8)

28 m

9)

24 cm

10)

17 c

m

11)

5 cm

12)

12 m

Exercise 1(B)

Find the area ( ) of the following circles

1) r = 2 m 2) r = 10 m 3) r = 14 cm 4) r = 4∙2 m

5) d = 8 cm 6) d = 10 cm 7) d = 20 cm 8) d = 6 m

9) r = 50 m 10) r = 3∙2 cm 11) d = 8∙4 m 12) r = 12∙6 cm

13) d = 28 m 14) d = 7∙4 cm 15) r = 19 m 16) d = 264 cm


Exercise 3(B)

Find the area of the following shapes

1)

8 cm

2)

6 cm

3)12 cm

4)1 m

5)

9 m

6)

2 m

7)

5 cm

8)

11 m

9) 0 7 m·

10)20 m

11)

12 cm

12)

13 m

Exercise 3(C)


1)

6 cm45°

2)

10 c

m

45°

3)14 cm

4)

9 m

5)

3 m 120°

6)60°

23 m

7)

8 cm72°

8)

19 m120°


Exercise 4(B)

Find the perimeter of the following shapes

1)

8 cm

2)

6 cm

3)12 cm

4)1 m

5)

9 m

6)

2 m

7)

5 cm

8)

11 m

9) 0 7 m·

10)20 m

11)

12 cm

12)

13 m

Exercise 4(C)


1)

6 cm45°

2)

10 c

m

45°

3)14 cm

4)

9 m

5)

3 m 120°

6)60°

23 m

7)

8 cm72°

8)

19 m120°


Exercise 5(B)


1)

8 cm

4 cm

2)

12

cm

6 cm

3)

4 cm

18cm

4)

3 m

9 m

5)

20 m

8 m

6) 30 m

10

m

Exercise 5(C)


1)

8 cm

4 cm

2)

7 m

11 m

3)

8 cm

4 cm

5 c

m

4)

12 m

7 m

5)

6 m

2 m

6)4 m 4 m


Exercise 6(B)


1)

8 cm

4 cm

2)

12

cm

6 cm

3)

4 cm

18cm

4)

3 m

9 m

5)

20 m

8 m

6) 30 m

10

m

Exercise 6(C)


1)

8 cm

4 cm

2)

7 m

11 m

3)

8 cm

4 cm

5 c

m

4)

12 m

7 m

5)

6 m

2 m

6)4 m 4 m


Exercise 7(C)

Find the total shaded area in each of the following diagrams


Exercise 8(C)

1 A wheel has diameter 80 cm. How far does the wheel travel in one revolution?

2 Repeat Question 1 for the following wheels:

a) Diameter = 1∙2 m b) Diameter = 2∙6 m c) Radius = 3 m

d) Radius = 54 cm.

3 Calculate the diameter of a circle with circumference 40cm

4 Repeat Question 3 for the following circles:

a) Circumference = 82 cm b) Circumference = 160 cm

c) Circumference = 29m.

5 Calculate the diameter of a circle with area 40 cm².

6 Repeat Question 5 for the following circles:

a) Area = 76 cm² b) Area = 15 m²

c) Area = 10km² (d) Area = 300 m²

7 Calculate the area of a circle whose circumference is 70 cm.

8 Calculate the area of a circle whose circumference is 25 m.

9 Calculate the circumference of a circle whose area is 50 cm².

10 Calculate the circumference of a circle whose area is 90m².


Trigonometry

Exercise 1(A)

1 Copy each of the triangles below into your jotter.

On each triangle mark H for the hypotenuse and by looking at the 'marked' angle write O on the opposite side and A on the adjacent side.

2 For the following angles find correct to 3 decimal places

(i) the sine

(ii) the cosine

(iii) the tangent

a) 20° b) 61° c) 9° d) 76.4° e) 27.5°

f) 54.9° g) 5.6° h) 84.3° i) 7.8° j) 29.4°

k) 43.1° l) 36.8° m) 59.2° n) 48.1° o) 71.9°

p) 34.5° q) 89.1° r) 2.5° s) 18.2° t) 37.4°

3 Find the angle (correct to 1 decimal place) which has a tangent of

a) 1.5051 b) 0.7892 c) 0.2314 d) 79.4568 e) 10.2719

f) 2.5124 g) 0.1208 h) 34.5123 i) 1.2769 j) 6.0148


4 Find the angle (correct to 1 decimal place) which has a cosine of

a) 0.1243 b) 0.9271 c) 0.0134 d) 0.5239 e) 0.4531

f) 0.7582 g) 0.2135 h) 0.3985 i) 0.8124 j) 0.0908

5 Find the angle (correct to 1 decimal place) which has a sine of

a) 0.8413 b) 0.7245 c) 0.1324 d) 0.5237 e) 0.4238

f) 0.3901 g) 0.5683 h) 0.2351 i) 0.3987 j) 0.6129

Exercise 2(A)

1 Find the length of the side marked x. (TANGENT)

2 Find the length of the side marked x. (SINE)


3 Find the length of the side marked x. (COSINE)

Exercise 2(B) Find the length of the side marked x. (MIXED)


Exercise 2(C)

Calculate the length of the side marked x in each triangle

1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

17 18 19 20

21 22 23 24

27°

x

A

B

C

12 km Q

P

R

x

8 cm69°

X

Z

Yx

9 cm

17°

E F

G

x

13 m

74°

84°

x

A

B

C

3 cm

E

F

G

x

9 m

40°K

LR

x

20 m 64°

37°

x

L

K

M

4 km

U

V

W

x11 cm

63°

P

VR

x

5 c

m

30° 75°

x

L

D

H

42 m57°

x

V

R

A

17 mls

42°

x

N

K

G

11 m

14°

x

Y

K

N86 m

28°

x

B

A C15 km

68°

x

D

F

E30 km

25°

8 cmA

B

C

xQ

P

R

12 cm

x65°

X

Z

Y

14 cmx

53°

47°42 cm

A

B

C

x

52°

18 cm

A

B

C

x

X

Z

Y

x

24 cm

58°

35°

22 cm

A

B

C

x

X

Z

Yx

19 cm

27°


25 26 27 28

29 30 31

Exercise 3(B)

Find the size of the angle marked x in each triangle

7°

x

K

H

G

540 mls

69°

x

B

AC

25·8 m

21°x

A

B

C

2·6 m70°

x

R

P

Q

36·2 cm

38°

yx

12 cm

24°

42°

yx

29 cm

64°

51°

y

x

36 cm


Exercise 3(C)

Find the size of the angle marked x in each triangle

1) 2) 3) 4)

5) 6) 7) 8)

A

B C

Calculate <ABC

4 mls

17 mls

P

VR

Calculate <RPV

4 c

m

9 cm 18 m

Calculate <DLH

L

D

H

14 m 12 km

Calculate <VRAV

R

A

5 km

12 kmCalculate <KNG

N

K

G

3 km6·7 m

Calculate <YKNY

K

N3·6 m

4·1

1 m

Calculate <ABCB

A C5·72 m

21 m

Calculate <DHL

L

D

H

17 m


Exercise 4(B)

Find the size of x in each triangle.


Exercise 4(C)

1 2

Find YZ Find QR

3 Triangle STV is isosceles 4 Triangle ABC is isosceles

ST = SV AB = AC

Find the lengths of ST and SV. Find the lengths of AB and AC.

5 Find the length of AB and the length of the altitude of triangle XAB through X.

Hence, find the area of triangle XAB.

6 Find the length of PR and the length of the altitude of triangle PQR through Q.

Hence, find the area of triangle PQR.

7 8

Calculate the length of DC Calculate the length of PS

7·5 m7·5 m 110°

RQ

P

50°

V

S

T

20 m

30°

BC

A

2·5 cm

50° 50°BA

X

7 m

18·2 m

25° 25°RP

Q

35° 57°

B

CA D11 cm

26° 48°

Q

RSP

10 cm

5 m

20°

ZY

X

5 m


9 10

Calculate the length of EF Calculate the length of TR

11 12

Find the distance from A to C Find the length of KM

13 14

Calculate the length of AB Find the size of <PRS

Exercise 5(B)

1) A ramp is fitted at a school to allow disabled access to the second floor of the building.

The ramp is 48 m long and is at an angle of 11° to the horizontal.

What is the height of the second floor above the ground?

62° 20°

E

FD G

25 km21°

53°

Q

RP T

8 cm

16° 10°

B

CA D

8·5 m

80° 71°

L

MK N

9 m

30°

20°

D

A

B C

3·7

m

40°

9 cm

4 cmR

S

P

Q

=

=


2) The diagram shows a shop’s ramp for customers who are wheelchair users.

It connects the pavement to the level of the shopping mall.

The ramp is 14 metres long and slopes at an angle of 9°, as shown.

Calculate the difference in height, h metres between the pavement and the shopping mall. Give your answer correct to the nearest metre.

3) The diagram shows a flagpole which is supported by a wire which is fixed to the ground 8∙2 metres from the base of the flagpole.

The wire is 15∙3 metres long.

Calculate the angle between the wire and the ground.

4) Sam is flying a kite.

The string is 48 metres long.

How high is the kite above the ground? (marked x in the diagram)

5) A triangular bracket is designed to support a shelf.

Its length is 10 cm and its height is 7∙5 cm.

Calculate the angle at the base of the bracket, angle B.

15.3 m

8.2 m

x°

75 cm

10 cm

B


6) A ramp has been constructed at a bowling club. It is 3∙5metres long and rises through 0∙3metres.

Calculate the angle, x, that the ramp makes with the horizontal.

7) A boy flying a kite lets out 200 m of string which makes an angle of 72° with the horizontal.

What is the height of the kite?

8) A ladder is 15 m long. The top rests against the wall of a house, and the foot rests on level ground 2 m from the wall.

Calculate the angle between the ladder and the ground.

9) A ladder 12 m long is set against the wall of a house and makes an angle of 75° with the ground.

a) How far up the wall will the ladder reach?

b) How far is the foot of the ladder from the wall?

10) A telegraph pole standing on horizontal ground is 9 m high, and is supported by a wire 10 m long fixed to the top of the pole and to the ground. Calculate:

a) the angle between the wire and the ground.

b) the distance of the point on the ground from the foot of the pole.

VICTORIA BOWLING CLUB

03m

35m

xo


Exercise 5(C)

1) The front of the tent shown below is an isosceles triangle.

The size of the angle between the side and the bottom of the tent is x°.

Calculate x.

2) A television mast is supported by wires.

The diagram below shows one of the wires which is 80 metres long.

The wire is attached to the mast 20 metres from the top and makes an angle of 59° with the ground.

Calculate the height of the mast.

Give your answer to the nearest metre.

3) Alan is standing 30 metres from a tree.

Alan’s height is 150 centimetres.

He measures the angle to the top of the tree to be 32°.

Calculate the height of the tree.


4) The frame of a child’s swing is in the shape of an isosceles triangle.

If the base of the triangle is 1∙9 metres and the sides are at an angle of 65o to the ground, calculate the height of the swing, h.

5) PQRS is a rhombus. It’s diagonals PR and QS are 16 cm and 10 cm long respectively.

Calculate the sizes of the angle of the rhombus.

6) A straight road 350 m long rises 10 m vertically from one end to another.

Calculate the angle between road and the horizontal.

7) A horizontal concrete floor is 30 cm thick.

A small hole is bored through it at an angle of 35o to the horizontal.

Calculate the length of the hole to the nearest cm.

8) The diagram shows a cross section of a valley.

How much higher is C than A?

9) In this figure calculate

a) the angle BAC.

b) the angle CAD.

19 m

h

65o

P

Q

R

S

125 m 190 m

xy

20° 37°

A

D B E

C

A

B C D

3 cm

5 cm

7 cm


10) O is the centre of a circle of radius 8 cm.

PM = 7 cm, angle POQ = 72o.

Calculate the length of QN.

11) It is intended to build a room (DEFG) in a loft of a bungalow.

The roof of the room must not be lower than 2∙4 m.

If the house roof slopes at 40o what is the maximum width of the room?

12) The diagram shows part of the support of a roof.

Find the slope of the roof and the length of the support CD.

M O N

QP

72°

887

A E D C

G

B

F

40°

2·4 m

10 m

B

D

A

C

3 m

2 m


Changing the Subject of a Formula

Exercise 1(A/B)

Make the subject of these formulas.

1) 2) 3) 4)

5) 6) 7) 8)

9) 10) 11) 12)

13) 14) 15) 16)

17) 18) 19) 20)

21) 22) 23)

24) 25) 26)

27) 28) 29)

30) 31) 32)

33) 34) 35)

36)

Exercise 1(C)


1) 2) 3)

4) 5) 6)

7) 8) 9)


10) 11) 12)

13) 14) 15)

16) 17) 18)

Exercise 2(B/C)


1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

11)

12)

13)

14)

15)

16)

Change the subject of each of the following formulae to the variable indicated.

17) 18) 19)

20) 21) 22)

23)

24)

25)

26)

27)

28)

29)

30)

31)


32) 33) 34)

35)

36)

37) The perimeter of a square is . Change the subject to .

38) The area of a rectangle is . Change the subject to .

39) The volume of a cuboid is . Change the subject to .

40) The speed of a train is

. Change the subject to

a) b) .

41) The current in a circuit is

. Change the subject to

a) b) .

42) The area of a triangle is

. Change the subject to .

43) The area of a metal plate is


44) The equation of a straight line is . Change the subject to .

45) The illumination of a lamp is


46) The perimeter of a rectangle is .

a) Change the subject of the formula to .

b) Calculate when .

47) The sum of the numbers in a series cab be given by

.

a) Change the subject of the formula to .

b) Calculate when .


48) The sum of the angles of a polygon with sides is right angles, where .

a) Change the subject to , and find how many sides a polygon has if its angle-sum is 10 right angles.

b) Can a polygon have an angle-sum of 15 right angles?

mathematics - · pdf file3.07.2014 · maths department -2- s2 level 3/4 course the...

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