year 8 maths

xii
12 Three construction engineers individually have plans to build the world’s next tallest tower. The
1 Titan Circle tower or write is to down be 1.12 which km mass tall, the measurements Gigan tower are is to the be same. 109500 cm tall and the Bigan tower is to
be a 1210 1 kg, m 100 tall. g, Which 1000 g, tower 10 t will be the tallest?
b 1000 mg, 10 kg, 1 g, 1000 t
13 Steel chain costs $8.20 per metre. How much does is cost to buy chain of the following lengths?
2 a From 1 km options A to F, choose the mass b that 80 cm best matches the given object. c 50 mm
a human hair
A 300 g
14 A house is 25 metres from a cliff above the sea. The cliff is eroding at a rate of 40 mm per year. How
b 10 -cent coin
B 40 kg
many years will pass before the house starts to fall into the sea?
c bottle
C 100 mg
15 Mount d large Everest book is moving with the Indo-Australian 10A plate D Measurement 1.5 at a kg rate of systems of the past and present
about e large 10 bag cm per of sand year. How many years will it take to E move 13 t 5 km ?
f truck
F 5 g
16 A ream of 500 sheets of paper is 4 cm thick. How thick is 1 sheet of
Exercise 10A FRINGE
3 paper, From options in millimetres? A to D, choose the temperature that best matches the description.
UNDERSTANDING a AND temperature FLUENCY of coffee
A 1–815°C
4–9
5–9(½)
17 A snail slithers 2 mm every 5 seconds. How long will it take to
b temperature of tap water
B 50°C
slither 1 m ?
1 Complete c these temperature number of sentences. oven
C −20°C
a Roman 18 Copy d system temperature this chart and in Antarctica fill in the missing information. D 250°C
km
i
Example 16
1
4 Convert to the units shown
=
in
12
brackets.
inches = 16 = m
palms
ii 1 a 2 t (kg) = 1000 paces b 70 kg (g) ÷100
460 b imperial c Chapter system 2.4 g 10 (mg) Measurement and computation of length, d perimeter 2300 mg and (g) area
cm
×10
i 1 foot e 4620 = 12 mg (g) f 21600 kg (t) mm
ii 3 g 0.47 t (kg) = 1 yard
h 312 g (kg)
PROBLEM-SOLVING AND REASONING
10–12, 18 12–14, 18
15–19
19 Many tradespeople measure and communicate with millimetres, 3
iii i 27 mg (g) = 1760 yards
j
4 t (kg) even for long measurements like
10 Arrange timber beams these or measurements pipes. Can you from explain smallest why to this largest. might be the case?
c metric system 1
k
i 1 m = 8 kg (g) cm
10.5 g (kg)
Puzzles and
a 38 cm, 540 mm, 0.5 m b 0.02 km, 25 m, 160 cm, 2100 mm
ENRICHMENT c m 0.003 210 000 km, kg 20 (t) m, 3.1 m, 142 mm n d 0.47 0.001 —
t (kg) km, 0.1 m, 1000 — cm, 10 mm 20
ii 1 cm =
mm
84 Chapter 2 Angle relationships 504
challenges
Chapter 10 Measurement and computation 11 Very of length, Joe o long 592 widens and perimeter 000 short a mg lengths 1.2 (g) m and doorway area by 50 mm . What is the p new 0.08 width kg of (g) the doorway, in centimetres?
iii
km = 1000 m
12 20 Three When construction 1 metre is divided engineers into individually 1 million parts, have each plans part to is build called the a world’s micrometre next tallest (µm). tower. At the The other
1 Without measuring, state which 2 line List looks the longer: units Titan end A of tower or the length B? spectrum, is Then to (e.g. be measure 1.12 a cubit), light km to year tall, from check the is smallest used your Gigan to answer. tower describe to largest, is to be 109 commonly distances 500 cm in tall space. used and in the the Bigan Roman tower system. is to
The perfect billiard ball path
A
be a 1210 State m how tall. many Which micrometres tower will B there be the are tallest? in:
3 List the units of length (e.g. inch), from smallest to largest, commonly used in the imperial system.
When a billiard ball bounces off a straight wall
OR i 1 m ii 1 cm
13 Steel chain costs $8.20 per metre. How much does is cost to buy chain of the following lengths?
(with no side spin), we can assume that the angle
2 You have two sticks of length 34 m and List 5 the m, both units iii
with of 1 length mm
no scales. (e.g. How centimetre), might you mark from a length smallest of 1 to m? largest, iv 1 km commonly used in the metric
9781108466172c10_p448-509.indd a 1 km Page 499 b 80 cm c 50 mm
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at which it hits the wall (incoming angle) is the
b A virus is 0.000312 mm wide. How many micrometres is this?
system.
same as the angle at which it leaves the wall 3 Count squares to estimate the area of these 14 circles, A c house Research where is 25 one the metres grid length square from called a = cliff 1 the cm. above light year. the sea. Explain The cliff what is it eroding is and give at a examples rate of 40 of mm distances per year. using How
(outgoing angle). This is similar to how light a
5 Use the Roman many light years system years, will such to pass state as before to how the the nearest many: house star starts other to fall than into the the Sun. sea?
Example 1
reflects off a mirror.
a feet 15 are Mount in 1 pace Everest is moving with b the feet Indo-Australian are in 1 mile plate at a rate of c palms are in 1 foot
d palms about are in 10 1 cm pace per year. How many e digits years will are it in take 1 foot to move 5 km ? f digits are in 1 pace
Exercise questions categorised by the
working mathematically components
and enrichment
Example references link exercise
questions to worked examples.
Investigations:
inquiry-based activities
Investigation
Puzzles and challenges
6 Use the 16 imperial A ream of system 500 sheets to state of paper how is many: 4 cm thick. How thick is 1 sheet of
b
a inches paper, are in in 1 millimetres? foot b feet are in 1 yard c inches are in 1 yard
d yards are in 1 mile e yards are in 1 chain f rods are in 1 furlong
9781108466172c10_p448-509.indd 17 A snail slithers 2 mm every Page 5 seconds. 460 How long will it take to
29/03/18 1:16 AM
Single bounce
slither 1 m ?
7 wall Use the metric system to state how many:
Use a ruler and protractor to draw a diagram for each part
incoming
outgoing 18 Copy this chart and fill in the missing information.
km
and then answer the questions.
a millimetres are in 1 centimetre
angle centre angle
a Find the outgoing angle if:
angle b centimetres are in 1 metre
m
c metres are in 1 kilometre
÷100
i the incoming angle is 30°
cm
ii the centre angle is 104°
d millimetres are in 1 metre
×10
e centimetres Chapter are in reviews 1 kilometre with multiple-choice, short-answer
mm
b What geometrical reason did you use to calculate the answer to part
506
a ii above?
f Chapter millimetres 10 Measurement and computation of length, perimeter and area
19 Many
are
tradespeople
in 1 kilometre
measure and communicate with millimetres, even for long measurements like
4 A house roof has 500 506 m
Two bounces
2 of area. If there Chapter is and 1 10 mm timber of Measurement extended-response rainfall, beams or how pipes. and much computation Can water, you explain litres, of length, why can questions
be this perimeter might be and the case? area
Example 2 8 Which metric unit would be the most appropriate
collected from the roof?
Two bounces of a billiard ball on a rectangular table are shown here.
for measuring Multiple-choice the following? questions
5 Find the area of the shaded region. 30° a° ENRICHMENT
— —
20
a the Multiple-choice distance
a Find the values of angles a, b, c, d and e , in that order. Give a
b° c° between two questions towns
A drill bit
1 Which of the following is a metric unit of capacity?
b diameter Very long
reason for each.
e°
Chapter summary 505 1 d° Which A cm
of and a small short lengths drill
of the following B
bit
pace is a metric unit of C capacity? digit D yard E litre
c height 20 When of a flag 1 metre pole is divided into 1 million parts, each part is called a micrometre (µm). At the other
b What can be said about the incoming angle on the first bounce and
A cm B pace C digit D yard E litre
7 cm d length
2 Shonali end of a of garden the buys spectrum, 300
hose
cm a light of wire year that is used costs to $2 describe per metre. large How distances much in does space. she pay for the wire?
the outgoing angle on the Units second of area bounce? Give reasons for your Squareanswer.
Parallelogram
2 Shonali A $150 buys 300 cm B of $600 wire that costs $2 C per $1.50 metre. How much D $3 does she pay for E the $6
e width of a a State small how desk many micrometres there are in:
wire?
mm
c Accurately draw the path 2
cm of two bounces using:
3 cm
A = bh
2
A = s 2
A $150 i 1 m B $600 C $1.50 ii 1 cm
2 cm i = 5 an × 2initial incoming mbounce 2
= 9 2 f distance 3 The across triangle a city given has a perimeter of 20 cm . What is the missing
D $3 E $6
of 20 ii 9 an m initial = 81 incoming m 2 bounce of 55° iii 1 mm
iv 1 km
= 10 cm 2 ha
3 base The triangle length? given has a perimeter of 20 cm . What is the missing
6 These two rectangles overlap, as shown. Find the b total A virus area is of 0.000312 the shaded mm region. wide. How many micrometres is this?
5 cm
km 2
1 ha = 10 000 m Triangle
More than two bounces
2 base A 6 length? cm B 8 cm C 4 cm
8 cm
8 cm
c Research the length called the light year. Explain what it is and give examples of distances using
2 m
A D 616 light cm cm
years, such as B E
to 812 the cm cm
nearest star other C 4 than cm the Sun.
8 cm
3 cm
Roman a Draw paths of billiard balls for more than two bounces starting 3 m at the
Rectangle
D 16 cm
1
5 cm
2 cm E 12 cm
16 digits = 12 inches midpoint = 1 foot of one side of a rectangular shape, using the A starting = bh
2 incoming
2 cm
1
?
5 feet = 1 pace angles below.
= × 3 × 2
4 cm
2
1000 paces = 1 mile
= 3 m 4 cm
i 45° A = lb
ii 30°
2
?
9781108466172c10_p448-509.indd 4 The area of a rectangle Page 453 with length 2 m and width 5 m is:
29/03/18 1:16 AM
= 4 × 2
Imperial b Repeat part a but use = different 8 cm 2 starting positions. Show accurate Composite diagrams, figures using the same 4 starting The A 10 area 6 cm m 2 of a rectangle B 5 with m 2 length 2 m C and 5 width m 5 m is: D 5 m 3 E 10 m
18 m
12 inches = 1 foot incoming angle but different starting positions.
10 m 2 B 5 m 2 C 5 m D 5 m 3 E 10 m
10 m
3 feet = 1 yard
8 m 19 m
5 A triangle has base length 3.2 cm and height 4 cm . What is its area?
9781108466172c10_p448-509.indd Page 460
29/03/18 1:16 AM
1760 yards = c 1 mile Summarise your findings of this Area investigation in a report that clearly 1 explains what you have 5 A found. triangle 25.6 cmhas 2 base length B 12.8 3.2 cm cm and height C 12.8 4 cm cm. What 2 is its D area? 6 cm E 6.4 cm 2
A = l × b + bh
2
Show clear diagrams for each part of your report.
1
= 18 × 10 + × 10 × 9
A 25.6 cm 2 B 12.8 cm C 12.8 cm 2 D 6 cm E 6.4 cm 2
2
6 The total area of this composite shape is:
3 km
Units of length
= 225 m 2 6 The A 56 total kmarea 2 of this B composite 45.5 km 2 shape is: C 35 km 2
3 km
10 mm = 1 cm
Measurement
100 cm = 1 m
A D 56 10.5 km km 2 2 E B 45.5 24.5 km 2
C 35 km 2
1000 m = 1 km
Mass
302 Semester
D 10.5 km 2 review 1
5 km
E 24.5 km 2
1 g = 1000 mg
5 km
1 kg = 1000 g
7 km
9781108466172c02_p046-091.indd
Length
Circumference
Page 84 9781108466172c10_p448-509.indd 1 t = 1000 kg Page 504 Two 28/03/18 Semester 2:01 AM reviews per 29/03/18 book 1:20 AM
C = 2πr or πd
7 9 tonnes of iron Chapter ore is being 1: Computation loaded onto with a ship positive at a rate integers of 20 kg per second. How
7 km
many
Perimeter
= 2 × π × 3
3 m
= 6π m 2 7 minutes 9 tonnes will of iron it Multiple-choice take ore to is load being all questions
loaded of the onto 9 tonnes a ship of at ore? a rate Textbooks of 20 kg per second. also How include:
many
2.1 cm
Temperature
minutes A 0.75 will min 1 Using
it take B numerals,
to load 45 min thirty-five thousand,
all of the 9 tonnes C 7.3 two
of min hundred and six
ore? D is: 450 min E 7.5 min
A 350260 B 35260 C 35000206 D 3526 E 35206
3 cm
°C (degrees Celsius)
1.5 cm
8 The
A 0.75
base
min
length of a
B
parallelogram
45 min
is 10
C
cm
7.3
and
min
its area • is 30 Complete D
cm
450 2 . The
min
parallelogram’s answers
E 7.5 min
2 The place value of 8 in 2581093 is:
height
P = 2 × 2.1 + 1.5 + 3
= 8.7 cm
8 is:
A 8 thousand B 80 thousand C 8 hundred D 8 tens The base length of a parallelogram is 10 cm and its area is 30 cm 2 E 8 ones
. The parallelogram’s height
• Index
is: A 10 cm 3 The B remainder 3 cm when 23650 is C divided 30 by cm 4 is: D 3 cm 2 E 10 m 2
A 0 B 4 C 1 D 2
Circular arc
A 10 cm B 3 cm C 30 cm 3 cm 2 E 3
E 10 m 2
is a portion of the circumference
9 What is the exact circumference of a circle with radius 10 cm ?
4 18 − 3 × 4 + 5 simplifies to:
of a circle.
Perimeter of a sector
The arc (l) is subtended by an
9 What A 30 is cm the exact A circumference 65 B 31.4 cm B of 135 a circle C 10π with C cm 11 radius 10 cm D ? 120π cm E 20 E π cm
θ
angle, θ, at the centre of the circle.
P = 360
× 2πr + 2r
10 What
A 30
is
cm 5 800
the exact perimeter
B ÷ 5 × 31.4 4 is the
of
cm same as:
a quadrant
C
cut
10π
from
cm
a circle of
D
radius
20π cm
10 cm ?
E π cm
l
Arc length
r r
A 160 × 4 B 800 ÷ 20 C 800 ÷ 4 × 5 D 40 E 4 × 5 ÷ 800
θ
θ
r
θ
Fraction =
10 What A 50 is cm the exact perimeter of a quadrant B 51.4 cm cut from a circle of radius C 10 (10π cm ? + 20) cm
360
θ
r
l =
360 × 2πr
A D 50 (5π cm + 20) Short-answer cm questions E B 51.4 100π cm cm
C (10π + 20) cm
θ
l = 360
× πd
θ
× 2πr
1 Write the following numbers using words.
360
D (5π + 20) cm
E 100π cm
a 1030 b 13000 c 10300
Chapter summary: mind map of
key concepts & interconnections
9781108466172c10_p448-509.indd Page 505
Cambridge Maths NSW
Stage 4 Year 8 Second edition
Chapter review
Chapter summary
Semester review 1
Short-answer questions
Short-answer questions
d 10 030 e 100 300 f 1 300 000
2 Write the numeral for:
1 Using the metric system, state how many:
a 6 × 10000 + 7 × 1000 + 8 × 100 + 4 × 10 + 9 × 1
1 Using a millimetres the metric in b system, one 7 × centimetre 100 state 000 + how 8 × 100 many: + 5 × 10
c a millimetres 3 in Calculate: one centimetre
b centimetres in one metre
d b square centimetres metres in in one one metre hectare
c millimetres in a one 96481 metre + 2760 + 82 b 10963 −d 4096 square metres c 147 in one × 3 hectare
d 980 × 200 e 4932 ÷ 3 f 9177 ÷ 12
Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party.
29/03/18 1:20 AM
ISBN 978-1-108-46627-1
4
©
State
Palmer
whether each
et
of the
al.
following
2018
is true or false.
a 18 < 20 − 2 × 3 b 9 × 6 > 45 c 23 = 40 ÷ 2 + 3
5 How much more than 17 × 18 is 18 × 19 ?
453