S3 Pathway 1...S3 PATHWAY 1 October Assessment Revision Mr David Miscandlon [email protected] Question Bank Answers at the back Digital copy is available on FOR REVISION

S3 PATHWAY 1

October Assessment Revision

Mr David Miscandlon [email protected]

Question Bank

Answers at the back Digital copy is available on www.ia-maths.co.uk

TOPICS FOR REVISION

Integers

Algebraic Expressions with Brackets

Equations & Inequalities

Adding, subtracting, multiplying and dividing fractions

Circles (arcs, sectors and geometry)

Trigonometry

Similarity

Sequences & Patterns

Integers

1. Calculate

(a) 20 30 (b) 70 + (20) (c) 50 + 10 (d) 30 40

(e) 18 + 8 (f) 35 40 (g) 27 15 (h) 21 + (37)

2. Calculate :

(a) 4 (5) (b) 7 3 (c) 8 (5) (d) 6 7

(e) 6 (4) (f) 4 (3) (g) 10 (2) (h) 7 (2)

3. Calculate :

(a) (6) 2 (b) 12 (3) (c) 36 (12) (d) (28) 7

(e) 81 (9) (f) (64) 4 (g) 14 (2) (h) 36 (9)

4. Calculate :

(a) 7 + (3) 5 (b) 8 + 9 (2) (c) 2 (4) + (6)

(d) 7 + (9) 2 (e) 5 + (2) 1 (f) 4 + (1) 7

5. Calculate :

(a) 7 (9) (b) 12 (5) (c) 14 (4) (d) (11) (10)

(e) (8) (8) (f) (4) (9) (g) 7 (8) (h) 10 (5)


1. Multiply out the brackets:

(a) 3 (x 5) (b) 5 (y + 7) (c) 8 (a + 6) (d) 6 (3 + t)

(e) x (x + 9) (f) y (3 y) (g) b (b 4) (h) p (5 + p)

2. Expand the brackets:

(a) 4 (2a + 5) (b) 7 (3y 4) (c) 2 (12x + 11) (d) 9 (4c 7)

(e) 2a (a + 3) (f) 5x (x 8) (g) 10y (3 y) (h) 3t (t + 6)

3. Expand and simplify:

(a) 3(3a 1) + 2a (b) 2(5x + 3) 3x (c) 8(b + 2) 9

(d) 4(2h 1) + 7 (e) 5(3 4x) + 11x (f) 3(2c + 1) 8

(g) 2(4t + 3) 10t (h) p(p + q) 3pq (i) 7(1 3c) 10

(j) 3 + 2(2x + 5) (k) 7a + 3(2a 3) (l) 5 2(2x 7)


(a) (x + 2)(x + 3) (b) (y +5)(y +2) (c) (a + 4)(a + 6)

(d) (b + 3)(b + 4) (e) (x + 9)(x +5) (f) (s + 3)(s + 8)


(a) (x 1)(x 5) (b) (c 4)(c 2) (c) (y 3)(y 7)

(d) (b 6)(b 8) (e) (x 5)(x 2) (f) (s 8)(s 5)


(a) (x 1)(x + 5) (b) (a + 3)(a 7) (c) (t 5)(t + 4)

(d) (y + 8)(y 4) (e) (c + 2)(c 7) (f) (x 6)(x + 1)


(a) (x + 3)2 (b) (w 2)2 (c) (a 5)2 (d) (c + 8)2

(e) (y 4)2 (f) (a + 6)2 (g) (b + 1)2 (h) (s + 7)2


(a) (a + b)(c + d) (b) (2 + x)(3 + y) (c) (a + 4)(b + 5)

(d) (p q)(r s) (e) (1 a)(7 b) (f) (c 6)(d + 8)


(a) x(x2 + x 1) (b) 3(2x2 3x + 5) (c) x(3x2 5x + 8)

(d) 2x(x2 + 2x + 3) (e) 5(x2 8x + 2) (f) x(x2 4x 7)

10. Multiply out the brackets and simplify:

(a) (x + 2)(x2 + 3x + 1) (b) (x + 5)(x2 + 4x+ 2)

(c) (x + 1)(x2 + 5x + 4) (d) (x + 3)(x2 + x + 5)

(e) (x + 8)(x2 + 2x + 3) (f) (x + 4)(x2 + 7x + 6)


1. Solve :

(a) 3x 2 = 7 (b) 4x 5 = 11 (c) 2x 9 = 3 (d) 3x 7 = 5

(e) 7a 2 = 12 (f) 5y 3 = 22 (g) 6p 7 = 29 (h) 4c 3 = 29

2. Multiply out the brackets and solve :

(a) 2 (x + 5) = 12 (b) 5 (y + 7) = 45 (c) 3 (a + 6) = 36

(d) 6 (x + 4) = 54 (e) 4 (x + 9) = 48 (f) 3 (c + 8) = 30

3. Solve :

(a) 6y + 3 = y + 18 (b) 5a + 7 = a + 15

(c) 9c + 5 = c + 21 (d) 10x + 1 = 4x + 19

(e) 5b + 3 = 2b + 9 (f) 7n + 6 = 3n + 18

4. Solve :

(a) 6y 3 = 3y + 15 (b) 5a 9 = a + 15 (c) 9c 8 = 4c + 12

(d) 10x 1 = 4x + 5 (e) 5b 3 = 2b + 9 (f) 3n 10 = n + 2

(g) 7x 14 = 3x + 2 (h) 6c 13 = 3c + 59 (i) 7y 16 = 2y + 34

5. Solve :

(a) x + 4 > 5 (b) x + 6 > 9 (c) x + 8 > 12 (d) x + 3 > 7

(e) a + 1 > 4 (f) y + 5 > 8 (g) p + 2 > 11 (h) c + 4 > 5

6. Solve :

(a) x + 5 < 7 (b) x + 1 < 8 (c) x + 3 < 13 (d) x + 5 < 9

(e) a + 3 < 6 (f) y + 5 < 11 (g) p + 2 < 10 (h) c + 1 < 5

7. Solve:

(a) 2x > 6 (b) 5x > 20 (c) 8x > 16 (d) 3x > 27

(e) 4a > 16 (f) 7y > 28 (g) 6p > 18 (h) 5c > 25

8. Solve :

(a) x 3 < 4 (b) x 5 > 1 (c) x 9 > 2 (d) x 2 < 7

(e) a 2 < 4 (f) y 3 > 8 (g) p 7 < 11 (h) c 4 > 5

9. Solve :

(a) 2x + 1 < 5 (b) 4x + 1 > 9 (c) 3x + 3 > 12 (d) 5x + 2 > 12

(e) 2a + 2 < 8 (f) 5y + 3 < 13 (g) 2p + 5 > 21 (h) 3c + 1 < 16

Trickier Equations

1. Solve:

(a) x2 + 2x + 4 = x(x + 6) (b) (x + 3)(x – 2) = x2 – 3

(c) x(2x + 4) = 2x2 + 8 (d) (x + 3)(x + 2) = x2 + 1

2. For each rectangle find a simplified expression for its area:

(a) y + 2 (b) x + 4

10 x - 2

(C) y + 5 (d) 2a + 1

y – 1 a + 3

3. The rectangles below have the same area. Make an equation for each pair and find the length and

breadths of each rectangle.

(a) 2x - 2 2x + 30

x – 10

x

(b) 3x - 3 3x - 8

2x - 2 2x + 2


1. Calculate:

(a) 8

7

7

2

(b) 8

3

5

4

(c) 7

3

9

7

(d) 5

4

8

5

(e) 5

2

8

5

(f) 5

3

6

5

(g) 7

3

9

7

(h) 3

2

8

7

2. Calculate:

(a) 12

52

4

33

(b) 2

12

3

25

(c) 12

11

8

72

(d) 8

58

16

95

(e) 4

31

5

45

(f) 6

51

12

116

(g) 7

11

3

24

(h) 6

11

4

33

3. Calculate:

(a) 5

11

4

13

(b) 3

22

3

11

(c) 2

12

15

11

(d) 5

11

4

33

(e) 5

26

5

25

(f) 7

31

2

11

(g) 2

13

5

14

(h) 9

22

3

21

4. A twenty – one metre length of fabric is cut into 8

5

metre pieces.

(a) How many pieces can be cut?

(b) What length of fabric would be left over?

5. A triangle has base 4

32

cm and height 5

23

cm. Calculate its area.

6. A rectangle measures 4

15

metres by 3

25

metres. Calculate its area.


Working with the arcs and sectors of a circles Exam Questions

Give your answers correct to 3 significant figures unless otherwise stated.

1. Calculate the area of the sector shown in the diagram, given that it has radius 6∙8cm.

2. A table is in the shape of a sector of a circle with radius 1·6m.

The angle at the centre is 130o as shown in the diagram.

Calculate the perimeter of the table.

O

42o

135o

O

42o

130o

1·6m

3. The door into a restaurant kitchen swings backwards and forwards through 110o.

The width of the door is 90cm.

Calculate the area swept out by the door as it swings back and forth.

4. The YUMMY ICE CREAM Co uses this logo.

It is made up from an isosceles triangle and a sector of a circle as shown in the diagram.

The equal sides of the triangle are 6cm

The radius of the sector is 3·3cm.

Calculate the perimeter of the logo.

5. A sensor on a security system covers a horizontal area in the shape of a sector

of a circle of radius 3·5m.

The sensor detects movement in an area with an angle of 105º.

Calculate the area covered by the sensor.

90cm

110o

100o

6cm

105º

P

Q R

S

6. A biscuit is in the shape of a sector of a circle with

triangular part removed as shown in the diagram.

The radius of the circle, PQ, is 7 cm and PS = 1∙5 cm.

Angle QPR = 80o.

Calculate the area of the biscuit.

7. Two congruent circles overlap to form the symmetrical shape shown below. Each circle has a

diameter of 12 cm and have centres at B and D.

Calculate the area of the shape.

Relationship between the centre, chord and perpendicular bisector

1. In each of the diagrams below AB is a diameter. Find the missing angles in each diagram.

(a) (b) (c) (d)

2. Find the length of the diameter AB in each of the circles below, given the other 2 sides of the triangle.

A

B

C

D

ao

bo 45o A B

35o co

do

A

B

A

B

io

27o

j o

ko lo

12o

A

B

47o

eo f o

ho g

o

72o

B 7cm

A

7cm

8cm A

B

3cm

A

B

4cm

5cm

A

B

2cm

9cm

(a) (b) (c) (d)

3. Use the symmetry properties of the circle to find the missing angles in the diagrams below. In each

diagram AB is a diameter.

(a) (b) (c)

4. Calculate the length of d in each diagram.

(a) (b) (c)

6. A cylindrical pipe is used to transport

water underground.

The radius of the pipe is 30 cm and

the width of the water surface is 40 cm.

Calculate the height of the pipe above

the water.

Tangents and angles

1. Calculate the sizes of the angles marked a, b, . . . . .r, in the diagrams below.

(a) (b)

40cm

30cm

A

ao

B

bo

50o co

f o

A

do

57o

eo

B

B

j o

A

io

28o go

ho

k o

lo

mo no

oo

d

9 cm

7 cm

d

12 cm

4 cm

d

7∙5 cm

6 cm

70o ao

bo

co

120o

do

eo

f o

(c) (d)

2. In each of the diagrams below, PQ is a tangent which touches the circle at R.

Calculate the lengths of the lines marked x.

3. In each of the diagrams below, AB is a tangent which touches the circle at C.

Calculate x for each diagram.

Applying Geometric Skills to Sides and Angles of a Shape

Using Parallel Lines, Symmetry and Circle Properties to Calculate Angles PART 2

marks the centre of each circle

1. Calculate the size of each of the angles marked with letters in the diagrams below.

65o 65o

go

ho

no

ko

mo

35o qo

po 45o

r o

B

O

A

C 18 cm

30o

x

Q

(a) (b) (c)

(a)

(b) (c)

A B C

O

18 cm

27 cm xo

O

A

B

C

10 cm

x 55o

x

25 cm 7 cm

x Q P R

O

x

P Q

O

5 cm

12 cm R P R

O

8 cm

10 cm

.

d

64o f

e

. 33o

a

. 72o

b

40o

. c

2. In each of the diagrams below AB is a diameter. Find the missing angles in each diagram.

3. Calculate the sizes of the angles marked a, b, . . . . .n, in the diagrams below.

Circle Exam Questions

1. The diagram shows a section of a cylindrical drain whose

diameter is 1 metre. The surface of the water in the

drain AB is 70 cm.

(a) Write down the length of OA.

(b) Calculate the depth of water in the pipe, d.

(Give your answer to the nearest cm.)

2. The diagram shows a section of a disused

mineshaft whose diameter is 2 metres. The surface of

the water in the shaft, AB, is 140 cm.

(a) Write down the length of OB.

(b) Calculate the depth of water in the pipe, x.

(Give your answer to the nearest cm.)

O

A B

d

O

A B B

x

A

a

b 45o A B

35o

c

d

A

B

A

B

i

27o

j

o l

12o

A

B

47o

e f

h g

72o

70o c a

b

120o

d

e

f

3. A pool trophy is in the shape of a circular disc with

two pool cues as tangents to the circle.

4. A circular bathroom mirror,

diameter 48 cm, is suspended from

the ceiling by two equal wires from

the centre of the mirror, O.

The ceiling, AB, is a tangent to the circle at C. AC is 45 cm.

Calculate the total length of wire used to hang the mirror.

The radius of the circle is 6 cm and the length of the tangent to the point of contact (AB) is 9 cm.

The base of the trophy is 3 cm.

Calculate the total height of the

trophy, h, to the nearest centimetre.

h

6 cm

9 cm

3 cm

O

A

B

8PERF EC T P OOL

A B C

O 48 cm

Trigonometry

1. Calculate the length of the side marked x in these right-angled triangles. You will have to choose which ratio to use.

54 cm

82 cm

68o

43o

x m

x cm

x cm

174 cm

12 m

24m

76o

24o

39o

x cm

x m

x m

83 cm

70 cm

58 m 50o

59o 22o

x cm x m

x cm

19 m

33o

x cm

68 cm 81 m

95 m 35o

58o

57o

x m x m (a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)

2. Calculate the size of the angle marked xo in these right-angled triangles. You will have to choose which ratio to use.

12∙8 cm

6∙5 cm

3 cm

20∙7 cm

9∙3 m 5∙7 m

xo xo

xo

4∙5 cm

4∙9m

13∙3 m

7 cm

1∙8 cm 1∙8cm

xo xo

xo

5∙2 m

3∙8 cm

9∙7 m

7∙8 m

5∙8m

2∙1cm

xo

xo

xo

3∙8 mm

48∙6 m

22∙7 m

6∙9 mm 20∙2 m

25∙8 m xo

xo

xo

29∙4 m 1∙8m 2∙9 m

5∙2 cm

7∙7 cm

xo xo

xo

12∙8 m

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)

(m) (n) (o)

Applying Trigonometric Skills to Right-angled Triangles EXAM QUESTIONS

1. A manufacturer of concrete roof tiles states that to be suitable for concrete tiles the angle of a roof (pitch) must be

greater than 21o.

This roof is symmetrical. Is this roof suitable for concrete tiles?

2.

A ladder 300 cm long rests against a wall at an angle of 80 degrees.

How high up the wall does the ladder reach?

3. The angle of approach, xo, of a plane P as it comes in to land should be between 3o and 5o with the horizontal.

The air traffic controller has to tell the pilot whether he is too high,

too low or on the correct “glide path”.

An incoming plane is 3000 m away from its landing point A and is at a height of 160 m as shown in the diagram.

Is the plane too high, too low or on the correct “glide path”?

4. In triangle ABC, angle BAC is 48o.

Calculate the length of BC.

5. The rim of a rubbish skip is 12 m from the ground.

A workman places a plank 25 m long so that it just reaches

the rim.

What angle, xo, will the plank make with the ground?

P

A

160 m

3000 m

xo

B C

48o

A

20 cm 20 cm

M

25 m 12 m

xo

940 mm

5048 mm

xo

80o

300 cm

6. Craig has put a basketball set on pole

in his garden. To secure the pole he

intends to fix it with a baton nailed

to his garden shed.

The baton makes an angle of 68o with

the pole and is 28 m long.

How far up the pole will the baton reach, x?

7. A firefighter has a 12 metre ladder and needs to reach a window

10 metres from the ground.

What angle, xo, will the ladder make with the building?

8. Steve wants to find the height of a chimney

near his house. He stands at a point 25 m

away and measures the angle to the top of

the chimney as 58o.The height to Steve’s

eye-level is 1∙5 m.

Calculate the height, h, of the chimney.

9. Mr and Mrs Hamilton are building a ramp to allow their daughter easier access to the house.

The ramp has to rise by 08m and has to be 4 metres long.

Planning regulations state that the angle between the ground and the ramp has to be between 10o and 12o.

Would Mr and Mrs Hamilton’s ramp meet these conditions?

Show all working and give a reason for your answer.

18 m

x

68o 28 m

12 m

xo

10 m

08m 4m

h

25 m

58o

1∙5 m

Similarity

1. The diagram below shows two candles. Each candle is in the shape of a cuboid with a square base.

The length of time each candle will burn is proportional to its volume.

The small candle burns for 36 hours.

Nadia reckons that because the large candle’s measurements are double the small candle’s

measurements then the large candle should burn for 72 hours.

Is she correct? [You should show all working and give a reason for your answer]

2. An international perfume manufacturer prices their bottles of perfume by volume.

The two bottles below, although containing different volumes, are mathematically similar in shape.

Their heights and prices are shown.

The larger of the two bottles is for sale in France.

Assuming the smaller bottle to be priced correctly, determine whether or not the larger bottle

has the correct price tag given that the exchange rate is £1 = 110 euros.

20cm

12cm 6cm

10cm

£22.00 8cm 96cm

41.82 euros

3. John is looking to buy a new rug for his main room.

The two rugs below are mathematically similar in shape.

He is hoping that the length of the large rug will be enough to make the area of the large rug at

least 72 square feet.

Does the large rug have the required area?

You must show appropriate working with your answer.

4. In the diagram below triangles ABC and ADE are mathematically similar.

BC 12 cm, DE 9 cm and AE 21 cm.

Find the length of CE.


1. Write down the next 3 terms in each sequence:

(a) 2, 6, 10, 14, … (b) 2, 4, 9, 16, … (c) 3, 8, 13, 18, …

6 ft 72 ft

8 ft

length

A

B

C

D

E 12 cm

9 cm 21cm

2.

3.

ANSWERS

Integers

Check your answers with your teacher


1. (a) 3x 15 (b) 5y + 35 (c) 8a + 48 (d) 18 + 6t

(e) x² + 9x (f) 3y y² (g) b² 4b (h) 5p + p²

2. (a) 8a + 20 (b) 21y 28 (c) 24x + 22 (d) 36c 63

(e) 2a² + 6a (f) 5x² 40 x (g) 30y 10y² (h) 3t² + 18t

3. (a) 11a 3 (b) 7x + 6 (c) 8b + 7 (d) 8h + 3

(e) 15 9x (f) 6c 5 (g) 2t + 6 (h) p² 2pq

(i) 3 21c (j) 13 + 4x (k) 13a 9 (l) 19 4x

4. (a) 652 xx (b) 1072 yy (c) 24102 aa

(d) 1272 bb (e) 45142 xx (f) 24112 ss

5. (a) 562 xx (b) 862 cc (c) 21102 yy

(d) 48142 bb (e) 1072 xx (f) 40132 ss

6. (a) 542 xx (b) 2142 aa (c) 202 tt

(d) 3242 yy (e) 1452 cc (f) 652 xx

7. (a) x ² + 6x + 9 (b) w2 – 4w + 4 (c) a2 – 10a + 25

(d) c² +16c + 64 (e) y2 – 8y + 16 (f) a ² + 12a + 36

8. (a) ac + bc + ad + bd (b) 6 + 3x + 2y + xy (c) ab + 4b + 5a + 20

(d) pr qr ps + qs (e) 7 7a b + ab (f) cd 6d + 8c – 48

9. (a) x3+ x2 x (b) 6x2 9x + 15 (c) 3x3 5x2 + 8 x

(d) 2x3 + 4x2 + 6x (e) 5x2 + 40x 10 (f) x3 4x2 7x

10. (a) x3 + 5x2 + 7x + 2 (b) x3 + 9x2 + 22x + 10

(c) x3 + 6x2 + 9x + 4 (d) x3 + 4x2 + 8x + 15

(e) x3 + 10x2 + 19x + 24 (f) x3 + 11x2 + 34x +24


1. (a) 3 (b) 4 (c) 6 (d) 4 (e) 2 (f) 5

(g) 6 (h) 8 (i) 8 (j) 8 (k) 12 (l) 9

2. (a) 1 (b) 2 (c) 6 (d) 5 (e) 3 (f) 2

3. (a) 3 (b) 2 (c) 2 (d) 3 (e) 2 (f) 3

4. (a) 6 (b) 6 (c) 4 (d) 1 (e) 4 (f) 6

(g) 4 (h) 24 (i) 8 (j) 7 (k) 5 (l) 2∙5

5. (a) x > 1 (b) x > 3 (c) x > 4 (d) x > 4 (e) a > 3 (f) y > 3

(g) p > 9 (h) c > 1 (i) b > 6 (j) q > 0 (k) d > 3 (l) x > 4

6. (a) x < 2 (b) x < 7 (c) x < 10 (d) x < 4 (e) a < 3 (f) y < 6

(g) p < 8 (h) c < 4 (i) b < 5 (j) q < 17 (k) d < 0 (l) x < 5

7. (a) x > 3 (b) x > 4 (c) x > 4 (d) x > 9 (e) a > 4 (f) y > 4

(g) p > 3 (h) c > 5 (i) b < 4 (j) q < 9 (k) d < 10(l) x < 8

8. (a) x < 7 (b) x > 6 (c) x > 11 (d) x < 9 (e) a < 6 (f) y > 11

(g) p < 18 (h) c > 9 (i) b > 16 (j) q < 16 (k) d > 15 (l) x > 7

9. (a) x < 2 (b) x > 2 (c) x > 3 (d) x > 2 (e) a < 3 (f) y < 2

(g) p > 8 (h) c < 5 (i) b > 6 (j) q < 0 (k) d < 10 (l) x > 4

Trickier equations

1. (a) x = 1 (b) x = 3 (c) x = 2 (d) x = -1

2. (a) 10y + 20 (b) x2 +2x – 8 (c) y2 + 4y – 5 (d) 2a2 + 7a + 3


1. (a) 65

56 (b)

47

40 (c)

76

63 (d)

57

40 (e)

9

40 (f)

7

30 (g)

22

63 (h)

5

24

2. (a) 61

6 (b) 8

1

6 (c) 3

23

24 (d) 14

3

16 (e) 4

1

20 (f) 5

1

12 (g) 3

11

21 (h) 2

2

3

3. (a) 39

10 (b) 3

5

9 (c) 2

2

3 (d) 4

1

2 (e)

27

32 (f) 1

1

20 (g) 1

1

5 (h)

3

4

4. (a) 33 (b) 3

8m 5. 4

5

8m 6. 29

3

4m


WORKING with the ARCS and SECTORS of a CIRCLE EXAM QUESTIONS

1. 54·4cm² 2. 6·83m 3. 7770cm² 4. 27cm 5. 11·2m²

6. 33·1cm² 7. 206 cm² x = 37.5 (b) x = -15

RELATIONSHIP between the CENTRE, CHORD and PERPENDICULAR BISECTOR

1. (a) 90o (b) 45o (c) 90o (d) 55o (e) 90o

(f) 43o (g) 90o (h) 18o (i) 90o (j) 63o

(k) 90o (l) 78o

2. (a) 9∙9 cm (b) 8∙5 cm (c) 6∙4 cm (d) 9∙2 cm

3. (a) 40o (b) 40o (c) 50o (d) 33o (e) 33o

(f) 57o (g) 28o (h) 62o (i) 62o (j) 118o

(k) 118o (l) 31o (m) 31o (n) 31o (o) 31o

4. (a) 4∙5 cm (b) 5∙7 cm (c) 7∙2 cm (d) 3 cm (e) 8 cm

(f) 9∙2 cm

6. 37∙6 cm

TANGENTS and ANGLES

1. (a) 90o (b) 20o (c) 110o (d) 90o (e) 60o

(f) 30o (g) 35o (h) 35o (k) 90o (m) 65o

(n) 90o (p) 55o (q) 90o (r) 45o

2. (a) 6 cm (b) 13 cm (c) 24 cm

3. (a) 33∙7o (b) 10∙4 cm (c) 14∙3 cm

Using Parallel Lines, Symmetry and Circle Properties to Calculate Angles

PART 2

1. a = 57o b = 90o c = 18o d = 45o e = 90o f = 26o

2. a = 90o b = 45o c = 90o d = 55o e = 90o f = 43o

g = 90o h = 18o i = 90o j = 63o k = 90o l = 78o

3. a = 90o b = 20o c = 110o d = 90o e = 60o f = 30o

g = 25o h = 25o i = 90o j = 65o k = 90o l = 90o

m = 45o n = 55o

CIRCLE EXAM QUESTIONS

1. (a) 50cm (b) 14cm 2. (a) 100cm (b) 171cm

3. 20cm 4. 102cm

Trigonometry

1. (a) 3∙9cm (b) 13m (c) 5∙2m

(d) 9∙9cm (e) 5m (f) 64∙9cm

(g) 1∙6m (h) 5cm (i) 5∙6cm

(j) 9∙6m (k) 9∙3m (l) 7∙1cm

(m) 26∙5cm (n) 33∙7m (o) 83∙7mm

2. (a) 47∙5o (b) 64∙2o (c) 58∙1o

(d) 38∙2o (e) 58∙5o (f) 24∙8o

(g) 68∙4o (h) 40o (i) 45o

(j) 42o (k) 32∙4o (l) 28∙9o

(m) 27∙1o (n) 62o (o) 33∙4o

Applying Trigonometric Skills to Right-angled Triangles EXAM QUESTIONS

1. No since 20∙4o < 21o 2. 295cm or 2∙95maA

3. Correct since 3o < 3∙05o < 5o 4. 16∙2cm or 16·3cm depending on rounding

5. 28∙7o 6. 2∙85m

7. 33 ∙6o 8. 41∙5m

9. Yes, since 10o < 11∙5o < 12o

Similarity

1. no, will burn for 4 times the time 2. priced correctly

3. rug is too small since 69∙1 < 72 4. 7cm


See your teacher.

Documents

S3 Pathway 1...S3 PATHWAY 1 October Assessment Revision Mr David Miscandlon [email protected] Question Bank Answers at the back Digital copy is available on FOR REVISION