Fill in the blanks.
Range
The range of the scores for Maths is The range of the scores for English
This tells us that the pupils achieved scores in Maths but a
range of scores In English. The teacher can deduce that the
ability of the pupils are about the for Maths, but
for English.
Mean
The Maths scores range
from 74 to 81. These
79 + 79 + 76 + 76 + 74 + 79 4- 81 + 79 + 77 + 80 -
10 scores are close to the
mean.
The mean for Maths is
The English scores range
from 64 to 102. These
67 + 74 + 100 4- 68 + 67 + 83 + 70 + 84 4-102 + 64 ,
scores are not close to the
10
mean.
The mean for English is
Both the means are
But does this mean the pupils scored almost the same marks for both tests?
Are the pupils' individual scores close to the mean? Is the mean a good gauge
for the Maths or the English test?
Median
The median for Maths is The median for English is
74, 76, 76, 77,(^9^ 79, 79, 80, 81 64, 67, 67, 68, (^0^83, 85, 100, 102
median median
The median for the English scores is than the median for the
Maths scores.
Difference between mean and median for Maths =
Difference between mean and median for English =
The larger the discrepancy between the median and mean for the English test
tells the teacher that the mean for English scores is not reliable.
397
Looking at all the measures, the most useful information is obtained by
combining the range and the median.
The median of Maths is and the range is from to
The median of English is and the range is from to
The median divides the scores almost in half. It is a better measure of central
tendency than the mean or the mode for this set of data.
This also shows that overall, the pupils performed better and more consistently
for Maths, than for English.
Spotlight
PM Uyout Formulis
Computer software
A Cut
TietouchtlMS A* *■ ;^WrapTett
programmes such as Excel P*a« Qac<w • ^ ^ • 3- = -= IS IE S Megc & Ctnttt
FonnA Pjintw
have built-in functions Cii0l>o«pd f Aiignniciu
for calculating the mean, =MeD(AN(A2:F2)
median and mode quickly. G H M N
Data Result Formula
Try using it to work out 4 12 20 49 65[ M = MEDIAN (A2:F2)
the measures for the 0 4 12 20 49 65 16 = MEDIAN (A3:F3|
4 12 20 49 65 0 16 = MEDIAN (A4:F4)
Investigate activity.
There were 19 swimmers in a race.
The times clocked by group A swimmers in seconds were:
135, 136, 138, 141, 143, 145, 146, 147, 153, 190
The times clocked by group B swimmers in seconds were:
141, 149, 150, 152, 161, 163, 169, 180, 184
a) Calculate the mean, median, mode and range for each group of swimmers.
b) Which measure of central tendency best represents group A? Explain.
c) Which measure of central tendency best represents group B? Explain.
d) Which measure of central tendency would be best to use to compare the
two sets of data?
lO Journal Writing
L present the data you collected for each class or group as frequency tables.
Using the data you collected for the survey you conducted in Unit 7,
compare the data you have collected for each class or group using the
range and the mode, median or mean.
398 UNIT« Data Handling
In this chapter
CHAPTER 17.2 Pupils should be able to:
• draw and interpret:
o pictograms
o bar-line graphs
o bar charts
o frequency diagrams
for grouped discrete
data
Graphs and charts are visual presentations of information. Data in a frequency o simple pie charts
table can be represented in different ways, such as pictograms, bar charts, • draw cone! usions based
bar-line graphs, frequency diagrams and pie charts. It is often easier to interpret on the shape of graphs
data shown as a graph or chart rather than in a table with many numbers, as we and simple statistics
can see and compare proportions or tell the trend in the data right away.
Pictograms
Mimie wants to find out the day on which she has the most customers, and the
day on which she has the least customers at her cafe. She recorded the number of
customers at her cafe each day for one week in the table below.
^ RECALL
Day Frequency
Monday S
Using a symbol to
Tuesday 20
represent 2 school buses,
Wednesday 8 draw a pictogram to show
Thursday 12 the information below.
Friday 16 • The RE School and
Saturday 32 Artistic School have
Sunday 4 a total of 10 school
buses.
From the table, Mimie can see that she has the most customers on Saturday, and • The number of school
the least customers on Sunday. Mimie then represents the data In the graph buses that the Artistic
the
of
below. School has is |
number of school
Day of the week Number of customers
buses that the RE
Monday IT School has.
• Music Academy has
f ttf i
Tuesday twice the number of
school buses as Artistic
Wednesday If School.
("ifii • The School of
Thursday tlHf Academics has 2 fewer
4 + 4 + 4 + 4 = 16
school buses than the
Friday Titir ' There were 16 Music Academy.
customers on
• The Awesome School
Saturday titll'il'iHr'll' Friday. has 10 more school
buses than the RE
Sunday f School.
Each represents 4 people.
399
Using the pictogram, it is easier to pick out the least number of customers just by
o Spotlight looking at the length of each row being occupied by the icons. We do not need to
go through every single data value to interpret whether the next value is bigger
or smaller.
In the 21'* century,
computers are able to
present data in many m
different types of graphs
and charts. The pictogram shows the distance each pupil ran during a Physical Education
lesson.
- IQ
c Pupil Distance ran (km)
Tia
Sasha
Layla
Suzan
Ml
Hannah
a) If Tia ran 1.6 km, what does each symbol represent?
b) How far did Suzan run?
c) Who ran the furthest? How far did she run?
d) How many pupils ran more than 6 km?
e) How much further than Layla did Sasha run?
f) Change the pictogram to show that Layla ran 7 km instead.
Solution
a) 1.6 km = 1600 m
1600 m -r 8 = 200 m or 0.2 km
Each symbol represents 0.2 km or 200 m.
b) 0.2 X 6 km = 1.2 km
Suzan ran 1.2 km.
c) Hannah ran the furthest. She ran 1.8 km.
d) Four pupils ran more than 0.6 km.
e) Sasha ran 0.2 x 5 = 1 km.
Layla ran 0.2 x 3 = 0.6 km.
1-0.6 = 0.4
Sasha ran 0.4 km further than Layla.
400 UNIT 17
f)
Pupil Distance ran (km)
Jf
Tia
Sasha
Layla Each ^ represents 0.1 km
Suzan
Hannah
A car dealer recorded the number of cars sold over six days.
Draw a pictogram to represent the data in the table.
Day Number of cars sold
Monday 5 b) Use the pictogram to answer the following questions.
Tuesday 40 i) How many cars were sold altogether?
Wednesday 25 ii) On which day was the most cars sold?
Thursday 35 ili) On which day was the least cars sold?
Friday 35 iv) How many more cars were sold on Tuesday than
Saturday 45 on Wednesday?
The number of youths of ages 11-16 who participated in a race are shown
in the pictogram below.
a) How many boys participated in the race?
Age Number of youths
b) How many girls participated in the race?
11
c) Which age group had eight boys and fifteen girls?
mtt
12 d) How many more girls than boys participated in the race?
e) What was the most common age of youths who
un participated in the race?
13
un
14 f) What was the least common age of youths who
participated in the race?
15 g) How many participants were of age 14 years old?
h) How many girls were younger than 13 years old?
16
i) If there were ten 14-year-old boys who participated in
Key:
the race, change the pictogram to show this.
Each^ represents 4 boys.
Each represents 5 girls.
A01
17.2.2 Bar charts
Look at the frequency table for Mimie's cafe on p. 399 again. The same data can
be represented as a bar chart.
A vertical bar chart
bar chart title -Customers visiting Mimie's cafe
^ width
35-
30-
25 n
vertical axis Number of 20-
label customers
15^
10-
5-
The bar chart must
have a title, a label for Monday Tuesday Wednesday Thursday Friday Saturday Sunday
each axis, values on Day •«- — horizontal
one of the axes and a axis label
value or bar label
label for each bar.
frequency
The bars should be of
equal width and the
A horizontal bar chart
gaps between the bars
should be of equal Customers visiting Mimie's cafe
size.
Monday
The bars in a
bar chart can be Tuesday
drawn vertically or
Wednesday
horizontally.
Thursday
bars of equal
width
Saturday
Sunday
T
T
10 15 20
Number of customers
In the vertical and horizontal bar charts, the length of each bar represents the
number of customers that visited the cafe each day. Bar charts are usually more
accurate than pictograms as the axes can be adjusted to different scales to suit the
data values.
^02 UNITTtIB
Data Ha
I
The table shows the number of known moons of the planets in our solar system.
Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune
Number of
0 0 1 2 66 62 27 14
known moons
Present this data as a bar chart. Use a scale of 1 unit to represent 10 moons.
Solution
Known moons in the solar system
The highest bar
70- represents the planet
with the highest known
60-
number of moons.
50-
Number of
known moons ~
30-
20-
Notice that Mercury and Venus
10-
have no known moons. There
are no bars on the graph.
0
Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune
Planets
Bar-line graphs
Bar-line graphs use thick lines instead of bars to represent the data. Bar-line
graphs are similar to bar charts. 1. A bar-line graph
should have a title,
Let us look at the number of customers visiting Mimie's cafe again in a bar-line
a label for each axis,
graph.
values on one of the
axes and a label for
Customers visiting Mimie's cafe
each thick line.
-
2. Lines should be of
equal thickness and
the gaps between
Number of the lines should be of
customers
equal size.
-
- r
[ 1 I
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
Day
403
A survey was done to find out the most popular type of skewer among a group of
pupils. The data was represented in a tally frequency table.
Type of skewer Tally Frequency
Chicken m+mn
Beef -mn
m
Lamb mm
Vegetables ////
a) Complete the table by filling in the third column.
b) Represent the data in a bar-line graph.
c) How many pupils were surveyed?
d) Which type of skewer was most popular?
e) How many more pupils preferred chicken skewers to vegetable skewers
Solutio
a)
Type of skewer Tally Frequency
Chicken mmn 12
Beef mn 7
m
Lamb mm 13
Vegetables //// 4
b)
Types of skewers pupils like
14-
124
10-
Number of 8^
customers
6-
4-
2-
0
Chicken Beef Lamb Vegetables
Types of skewers
c) 12 + 7 + 13 + 4 = 36
36 pupils were surveyed.
d) Lamb skewers were most popular.
e) 12-4 = 8
8 more pupils preferred chicken skewers to vegetable skewers.
^04 UNIT 17^ Data Handling
I
Check My
v*.
U
A school has the following number of teachers.
Subject Number of teachers
Mathematics 8
English 4
History 3
Accountancy 2
Biology 4
Physical Science 5
information Technology 9
a) Draw a vertical bar chart to represent this data.
b) How many teachers are there altogether?
c) How many teachers teach History?
d) Which subject has the least number of teachers?
e) Which subject has the greatest number of teachers?
f) How many more Information Technology teachers are there than Mathematics teachers?
The bar-line graph shows the value of the average monthly sales for 15 companies.
Monthly sales
Value Shop
Sizzling Steaks
Fav Grocery
Saladgo
DIY Homefix
Techno Loop
FF Fashion
Company dreamy Cafe
Babyland
Mrs Heels
Photo Flash
Bloom Laundry
Daily Scoop
Swim Paradise
Charles Burger
$1000 $2000 $3000
Sales value
a) What was the value of the sales of Mrs Heels?
b) Which company had a sale value of $3750?
c) Which two companies had the same sales value?
d) What is the difference between the sales value of Fav Grocery and Swim Paradise?
e) Which company had the lowest value of sales?
f) Which company had the highest value of sales?
g) Which company would you invest in? Explain your answer.
405
17.2.4 Frequency diagrams for
grouped discrete data
This frequency table shows grouped discrete data. The table shows the number of
units in an apartment block and the number of such apartment blocks in a town.
Number of units In an
0-50 51-100 51-100 51-100 51-100
apartment block
Frequency 32 243 521 206 96
This data can be represented as a frequency diagram.
Types of apartment blocks In a town
The most common
number of units
in an apartment
block in this town
is between 101 to
i 200-
150. Recall that this
is the modal class.
0-50 51-100 101-150 151-200 201-250
I Number of units in an apartment block
The number of units in a block There are regular spaces
is discrete. It is not a continuous between the bars.
spectrum of values like time.
A frequency diagram looks similar to a vertical bar chart but there are spaces
between the columns. Frequency diagrams can be used to present grouped data.
A frequency diagram is only used to represent numerical values. For example, a
group of pupils' favourite colours cannot be presented in a frequency diagram
because colours are not a numerical data.
Check My
Unde
The table shows the number of whale sightings per day during an expedition of 27 days.
Number of whales sighted 0-10 11-20 21-30 31-40 41-50
Number of days 3 10 7 4 3
a) Draw a frequency diagram to represent the data.
b) How many days were less than 21 whales sighted?
c) How many days were more than 40 whales sighted?
d) What percentage of the expedition period were more than 30 whales sighted?
e) Estimate the number of whales sighted altogether.
406 UNIT 17
17.2.5 Pie charts
Some data can be represented In a pie chart. A pie chart is a type of graph that is
in the shape of a circle. It is divided into different parts to represent the quantities
of different items.
Aluminium
Steel
Waste material Mass (kg)
Aluminum 12
Steel 15
Pastic
Plastic 42 Paper and
paperboard
Wood 53
Glass 61
Paper and
131
paperboard
The mass of each type of waste The mass of each type of waste
material produced by a company is material produced is also
shown in the table. presented in a pie chart.
The amount of waste material Is it easier to use the table or the
produced is stated in kilograms. pie chart to determine which
Which waste material does the waste material the company
company produce the most of? produces the most of?
A pie chart represents 1 whole or 100%. Each part of the pie chart represents the
quantity of each item in the form of a number, a fraction or a percentage.
The table below shows the quantity of some items in Evan's refrigerator.
' Items in Evan's 1
Vegetables Meat Fish Eggs
refrigerator i There are S + 5 + 2 + 8 = 20
1
Number of items in the refrigerator.
5 5 2 o '
items
We can express the quantity of each type of Item as a fraction of the total number
of items in the refrigerator, then represent the quantities of these items in a pie
chart.
1 of the items in the refrigerator are vegetables.
The total number of items
I of the items in the refrigerator are meat.
Vegetable^ in the refrigerator make
of the items in the refrigerator are fish. up 1 whole.
^ of the items in the refrigerator are eggs.
The angle of each sector is proportional to the fraction
of the data shown.
407
We can also express the quantity of each type of item in Evan's refrigerator as
a percentage.
100%
X
I X 100% = 0.25 X 100% X 100% = 0.1 x 100% |
=
X
100%
0.4
= 25% = 10% = 40%
Each part of the pie chart can represent the quantity
of each item as a number, a fraction or a percentage. Vegetables:
25% &
—
Meat W
Fish 25% ,/
10% a
This pie chart shows the different types of animals on a farm.
There are 20 chickens on the farm. Xchickens
The data is represented as
sectors of a circle. Cows
All the sectors combined
form a complete circle.
a) What fraction of the animals on the farm are sheep?
b) What percentage of the animals on the farm are ducks?
c) How many animals are there on the farm altogether?
Solution
25
a) 25% =
100
_ 1
4
^ of the animals on the farm are sheep.
b) 1 X 100% =0.5 X 100%
= 50%
50% of the animals on the farm are cows.
I X 100% =0.125 X 100%
® = 12.50/0
12.5% of the animals on the farm are chickens.
100% - 50% - 12.5% - 25% = 12.5%
12.5% of the animals on the farm are ducks.
c) 1 of the total number of animals are chickens.
1 -»-20
I —►s X 20 = 160
There are 160 animals on the farm altogether.
It is easy to compare data in a pie chart. In this example, we can easily see that the
majority of the animals on the farm are cows, and the least is chickens.
^08 UNIT 17
Part 1: Draw a pie chart
Use a pie chart to represent the data in the table on the most common eye colour
of pupils in a class.
Eye colour Grey Green Brown Blue
Frequency 12 7 13 4
Solution
First, work out the data.
The fraction^ shows that Add a column to find
12 of the 36 pupils surveyed each sector angle. For each sector, divide the frequency
by the total and multiply by 360°.
This answer is the size of the angle of
Eye colour Frequ^icy Sector angle (°) the sector that represents the pupils
with grey eyes.
Grey 50° = 120° '
Green 7 ^ X 360° = 70°
Think and Share
Brown 13 360° = 130°
1
multiply
Find the Blue 4 ^ X 360° = 40°
sum of the
Total ^"*^36 360°
frequencies.
Then, draw your pie chart. Eye colour
Brown
m
Green
Use a compass to draw your Use a protractor to measure the angle Colour and label your pie chart,
pie chart. of each sector. Pencil in the sectors.
Part 2: Interpret a pie chart
Refer to the pie chart in Part 1.
Which eye colour was the most common?
Which eye colour was the least common?
What percentage of the pupils surveyed had blue eyes?
I
*
^ Challenge Of the 36 pupils surveyed, how many had green eyes?
409
Solution
Brown eyes are the most common. We can see that the sector in the pie chart
representing brown eyes has the largest angle {130°), indicating that the
number of pupils with brown eyes is the greatest.
Blue eyes are the least common. This sector is the smallest with the smallest
angle, 40°.
jq of the pupils have blue eyes. We can also say that 11.1% of the pupils have
blue eyes.
Method 1
We could use the angle size of the sector for pupils with blue eyes to calculate
the percentage.
^ X 100 = 11.1%
Method 2
We could use the number of pupils with blue eyes to calculate the
percentage.
^ X 100 =11.1%
Check your answer by We can use the angle sector size for green eyes to calculate the number of
comparing it with the pupils with green eyes.
data in the frequency ^X36 = 7
table.
7 pupils had green eyes.
I
The table shows the mass of different parts of a human body.
a) Represent the data in a pie chart.
Body part Muscle Fat Bone Other
b) Use the pie chart to answer the following questions.
Mass (kg) 30 14 16 20
i) What fraction of the body Is muscle?
Total
ii) What percentage of the body is fat?
The table shows the water usage by a family over one month.
Water usage Litres of water a) Represent the data in a pie chart.
Shower 3000 b) What does the family use the most water for?
Toilet 1620 c) Calculate the percentage of water that is wasted through
Leaks 320 leaks.
Washing 1000 d) Suggest one way in which the family could reduce their
Cooking 400 water usage.
Other 900
410 UNIT 17i Data Handling'
The pie chart shows the favourite football teams of 100 youths.
Key:
Dribblers
Super Spurs
Football United
Super Scorers
Yellow Dragons
a) Calculate the value of X.
b) What percentage of the youths favoured Football United?
c) What percentage of the youths favoured Yellow Dragons?
d) How many youths indicated the Dribblers as their favourite team?
e) How many less youths indicated Yellow Dragons as their favourite team compared to Super Spurs?
f) What percentage of the youths indicated Super Scorers as their favourite team?
g) Which team is favoured by 25% of the youths?
17.2.6 When to use a bar chart and
a pie chart
The monthly rainfall in Hyderabad is presented as a bar chart and a pie chart.
The same data is used for each chart.
Rainfall in Hyderabad
Rainfall lOO-
(mm)
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
All
Rainfall In Hyderabad
Which chart is better?
I Jan
For each statement, tick the
box indicating where the I Feb
information can be found.
Mar
The month during which
Apr
the highest rainfall was
May
received.
Bar chart □ Pie chart □ Jun
I Jul
The amount of rainfall
received in May. i Aug
Bar chart Q Pie chart □ Sep
The difference in the Get
amount of rainfall received Nov
in April and December.
Dec
Bar chart Q Pie chart Q
The month that received Bar charts show changes over time Pie charts show comparisons between
20 mm of rainfall. more effectively than pie charts. parts of a whole more effectively than
Bar chart Q Pie chart □ Bar charts are useful when specific bar charts. They do not show changes
The trend in rainfall values are required, for example overtime.
received from January to rainfall in millimetres. Pie charts are useful when we want
August. to compare one amount to another in
Bar chart □ Pie chart □ the data set.
Revision
O Journal Writing O Chichi took 7 Mathematics tests. What is the range of her test scores?
Using the data you 87, 75, 86, 93, 89, 78, 94
collected for the survey
conducted in Unit 7, Look at the data below.
select a suitable type 19, 25, 59, 48,35,31,30, 32,51
of chart to present a) Find the range.
your data.
b) Find the mode.
explain why you chose c) Calculate the mean. Round your answer to the nearest 1 d.p.
this type of chart,
d) Find the median.
present your data in
a separate chart for e) Find the new median if 25 is replaced by 52 and 19 is replaced by 29.
each class or group. f) Find the new mean if 25 is replaced by 52 and 19 is replaced by 29.
compare the charts to Round your answer to the nearest 1 d.p.
draw a conclusion that
supports or rejects Q List a set of 5 different numbers where the mean is the same as the median.
your hypothesis. O List a different set of 4 different numbers where the mean is the same as
the mode.
e The data set below is the test scores (out of ICQ) for a Maths test for 20 pupils.
56, 29, 78, 67, 68, 69, 80, 89, 92, 71, 58, 66, 56, 88, 81, 70, 73, 63, 74, 38
a) Construct a tally and frequency table for this data set. Decide what class
intervals would be suitable.
^12 UNIT 17 Data Handiin
I
b) What percentage of the pupils scored 80 marks or more for the test?
c) What percentage of the pupils scored less than 50 marks for the test?
d) Complete the sentence.
More pupils had a test score in the interval than in any other interval.
The number of points scored by the eight winning teams in 17 matches are shown below.
94, 156, 154, 131, 129, 134, 152, 140, 124, 162, 103, 139, 82, 170, 110, 111, 116
a) Construct a frequency table for this data set using a class interval of size 10 starting at 80 points.
b) What is the modal class?
c) How many matches were won with a winning score of 99 points or less?
d) What percentage of the matches had winning scores of 150 points or more?
e) Use the modal class, median and range to describe the distribution of the data.
o A swimming pool has a mean water depth of 130 cm. A boy is 145 cm tall.
Can he stand safely in the pool?
o Explain why you would use the mode, median or mean as the average in each data set.
a) Test results of a group of pupils; AAAABBBCBAAAA
b) Wages of 10 office workers: $ 150, $ 180, $ 170, $ 160, $ 190, $ 165, $ 177
c) The average number of days in a month.
0 The table shows the salaries of the employees in a company.
Employee Annual salary ($)
Technician 27 000
Administrator 1 21 000
Administrator 2 23 000
Finance clerk 28 000
Enaineer 30 000
CEO secretarv 25 000
CEO 89 000
a) Calculate the mean salary of the employees.
b) Calculate the median salary of the employees.
c) Which measure gives more meaningful information about the salary of a employee of this
company? Explain.
® The pictogram shows the number of ice creams sold each week.
Key:
Week 1
represents 16 ice creams.
Week 2
Week 3
Week 4
a) During which week were 32 ice creams sold?
b) How many ice creams were sold in week 2?
c) How many more ice creams were sold in week 3 than week 2?
d) Show that 60 ice creams were sold in week 4.
413
0 The frequency table shows the number of people in certain age categories participating in a Bingo
game in a retirement home.
Age In years 30 5 A- < 40 40£A<50 50sa<60 60 :S A < 70 70 £ A < 80 80 £ A < 90
Frequency 3 6 9 13 7 2
a) Represent the data in a suitable graph. Explain your choice.
b) How many people were surveyed?
c) How many people were in the age range 40-49?
d) Which was the most common age range?
e) How many more people were in the age range 50-59 than in the age range 80-89?
f) Which age range had the lowest frequency?
g) Give a possible reason as to why the frequency of the age range 80-89 is the lowest
The bar chart shows the favourite sport of some pupils in a school.
Favourite sport
Number of 60-
Footba Cricket ice hockey
a) Record the data in a frequency table.
b) Represent the data in a pie chart.
C) What percentage of the pupils prefer squash?
d) Alex wants to know how many more pupils prefer football to ice hockey.
i) Which graph should Alex use to get this information?
ii) Give a reason for your answer.
5
Mathematics Connect
Government planners use statistical data to make
decisions. For example, population statistics such
as birth rates can be used when planning health
amenities, education facilities or ageing population
needs in an estate. Graphs and charts can indicate
trends that help planners to predict how many parks,
schools, hospitals and homes will be needed to meet
the needs of future populations.
UNIT 17
Mean, Median, Mode and Range
First arrange the numbers in order by size.
Example: 3, 5, 5, 6, 8, 10, 12
Mean Median \/'k Range
The average of the The middle value In a The value that occurs The difference between
values in a data set. ranked set of data values. the most. the lowest and the
highest values.
1. Add all the values. The median is the middle Find the value that
value when the odd occurs most often in a Subtract the lowest value
2. Divide the sum of data set.
number of values are from the highest value.
the values by the
arranged in order of size. There may be more
number of values. than one mode.
For an even number of
values, the median is 12-3 = 9
There are two 5s and
3+5+5+6+8+ the average of the two
one of each of the
10+12 = 49
middle values.
other values.
49 + 7 = 7
The middle number is 6.
The mean is 7. The median is 6. The mode Is 5. The range is 9.
V, -2
Statistical
Measures of central tendency —^ Measure of spread
measures
horizontal or vertical representing grouped discrete
numerical data data
.
/ i
can be examples has
useful when type
gaps between
\
ar chart and / bars
bar-line graph Frequency
diagram no gaps between
presented as
to presented as \ bars
useful when
type t
I
show detailed \grouped
specific values
data and changes continuous data
are required a key to describe
in data over time
presented what each sector sectors that
represents
combine to form
presented as ^ complete circle
a
f
uses has
I
symbols instead Pie chart
comparisons between
of numbers to
shows parts of a whole more
represent data
a key to describe useful when effectively than bar
what each symbol charts
represents I
we want to compare
one amount to
another in a data set
415
mK \r.
UNIT 18
You will learn about: Probability Is a number that tells
us the chance or likelihood that
Using probability to describe and Interpret results
something will happen. We use
involving likelihood and chance
probability In many aspects of
The probability scale
life. For example, probability can
Equally likely outcomes be used to predict the chance of
rainfall, the occurrence of natural
Mutually exclusive events
disasters, the chances of you
Probability tree diagrams
winning a raffle or the rate of
Estimating probabilities return on an Investment.
Comparing experimental and theoretical probabilities.
There is a 30% chance
oQ rain on Saturday,
Q0% chance oP rain on Sunday
and a 00% chance oP clear
skies on Monday.
^16 UNIT 18 Probability
CHAPTER 18.1
In this chapter
bability Pupils should be able to:
• use the language of
\ 'FBr
probability to describe
What are your chances? and interpret results
involving likelihood and
chance
• understand and use the
probability scale from
Oto 1
If you do not buy a ticket, If you enter a raffle where If you enter a raffle where
• find probabilities
you have NO CHANCE of there are only two tickets, there are many tickets, based on equally likely
winning a prize in the you have a 50/50 chance you are UNLIKELY to win outcomes in simple
raffle. of winning a prize. a prize. contexts
Using likelihood and chance
^ RECALL
to describe probability
Describe the likelihood of
each of these events as
Q hink and Share certain, impossible, likely,
Tom goes to the store to buy cereal. There are four different types of unlikely or equally likely.
a) Getting a tail when
cereal for him to choose from. tossing a coin
/ / / b) Choosing a King from
a deck of cards
m c) Rolling an even number
d) Having one Wednesday
Cereal A Cereal B Cereal C Cereal D
in this week
There are four possible outcomes for this event.
Tom has no preference for the type of cereal, and picks one at random.
What is the probability that he will pick cereal A?
An outcome is the final result of an activity, action or experiment. Tom has to
choose 1 cereal out of 4 different types of cereal. The chance of Tom picking
cereal A is 1 out of 4. |
Probability is the chance or likelihood that something will happen.
Probability is about how likely something is to happen.
When you think about how likely or unlikely something is to happen, you will use
probability terminology such as impossible, unlikely, equally likely, likely or certain.
Some things will never happen.
If you threw an ordinary die, you will never roll a zero.
It is impossible.
417
9 Somethings always happen.
Think and Share
We say they are certain to happen. If you draw a quadrilateral,
What other property of
quadrilaterals is a certainty? I it has four angles. That is a certainty! four angles
Some things are not certain.
If you toss a coin, it may or may not land heads. It is equally likely to land heads as
to land tails.
18.1.2 Equally likely outcomes
Look at the diagram on the right. Which colour is the pointer
Since each sector of the of this spinner most likely to land on?
spinner is exactly the same
There are 5 possible outcomes: ar^rn, blue, purple, red and
size, the pointer is equally
orange. Each outcome occupies the same area on the circle.
likely to land on any of
We say they have equal chances of occurring. They have equally
the colours.
likely outcomes.
Outcomes that have
an equal chance of The chance of the pointer landing on green is 1 out of 5.
happening are called
The chance of the pointer landing on blue is 1 out of 5.
equally likely outcomes.
The chance of the pointer landing on purple is 1 out of 5.
The chance of the pointer landing on red is 1 out of 5.
9 The chance of the pointer landing on orange is 1 out of 5.
Think and Share
A deck of cards has 52
I
cards. The 52 cards are
divided into 4 suits-2
red suits with hearts and
Suzi has 18 socks in four colours-9 pink, 5 yellow, 3 blue and 1 white. She
diamonds, and 2 black suits
takes one sock from the drawer without looking.
with clubs and spades. Each
suit has 13 cards-A, 2, 3, State whether each of the folllowing statements is true or false. Correct
4, 5, 6, 7, 8, 9, 10, J, Q, K. the false statements.
This means that if you pick a) The sock is most likely white.
a card at random, there are
b) The sock is most likely green.
52 possibilities. What is the
c) The sock is least likely to be white.
chance that you would get
d) The sock is equally likely to be yellow or blue.
a nine of diamonds if you
e) The sock is more likely to be pink than white.
pick a card randomly?
A fair die has 6 faces numbered from 1 to 6. If I throw the die at random,
what is the chance of getting
Randomly chosen objects a) the number 1, b) the number 2, c) the number 3,
are selected by chance or d) the number 4, e) the number 5 and f) the number 6.
without knowing what is
being chosen.
418 UNIT 18 Probability
1
18.1.3 The probability scale
Look at the following events.
Event A: My pet will speak Event B: My teacher Event C: I will continue Event D: will be able
I
to me in English. will not give me any breathing as long as I am to stay up late on a
homework today. alive. school night.
Event A is
impossible. Event B Event C is certain.
is equoliy likely. Event D is unlikely.
We can represent the probability of events on a scale called the probability line,
it shows the chance or likelihood of an event happening.
less likely more likely
impossible unlikely equally likely likely certain
Event A Event D Event B Event C
Let us use numbers on the probability line to describe the probability of an
outcome.
It is impossible to roll a seven on It is certain that we can roll a
an ordinary die. We say that the number less than seven on an
probability of rolling a seven on ordinary die. We say that the
an ordinary die is zero. probability of rolling a number less
than seven on an ordinary die is one.
Probability scale:
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1 I 1 I I I I 1 1 1 1
impossible even chance certain
419
On this probability scale,
• an event that is impossible has a probability of 0.
• an event that is certain has a probability of 1.
• all other probabilities on this scale are between 0 to 1.
Probabilities can also be written as decimals or percentages,
impossible unlikely equally likely likely certain
unlikely
0.25 0.5 0.75
25% 50% 75% 100%
4 ''=1
0 e e
Use the words impossible,
unlikely, equally likely,
likely or certain to describe
the probability of each The table shows a netbal! coach's estimates of the team's chances of winning their
outcome. matches against three schools.
a) The day which follows
School Chance of winning
Wednesday is a Friday.
Rose High 0.1
b) The next 60 babies
born in London will all Crossroads High 90%
be boys. New Horizons High 1
2
The next month will
have at least 28 days. a) Which school is the team most unlikely to beat?
d) I will be 4 metres tall b) Write this probability as a percentage.
next year.
a) Which school is the team almost certain to beat?
e) You will be one year
b) Write this probability as a decimal.
older this time next
year.
a) Which school does the team have an even chance of scoring a win
f) Rolling a number against?
smaller than six on a
b) Write this probability as a percentage.
die.
0 Write this probability as a decimal.
g) Rolling a number
Solution
smaller than seven on a
die. 0 1
h) A coin will land tails if 0% 50% 100%
it is tossed. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
i) A drawing pin will land 1 L _l_ -J I I I I -I
point up if it drops on
the floor.
Rose High New Horizons High Crossroads High
j) It will snow somewhere
a) Rose High School.
in Russia next winter.
The probability of the team beating Rose High School is 0.1. This is close
to 0 on the probability scale which means the team is unlikely to beat
Rose High School.
^20 UNIT 18 robabflity
b) The probability of 0.1 Is 10% as a percentage.
a) Crossroads High School.
The probability of the team beating Crossroads High School is 90%. This
is close to 1 on the probability scale which means the team is likely to
beat Crossroads High School.
b) The probability of 90% is 0.9 as a decimal.
a) New Horizons High School.
The probability of the team beating New Horizons High School is 5. This
is exactly halfway between 0 and 1 on the probability scale which means
the team has an even chance to beat New Horizons High School.
b) The probability of ^ is 50% as a percentage.
c) The probability of 2 is 0.5 as a decimal.
i!
Draw a probability scale and position the following events on the scale.
Events
A 1 can run faster than a cheetah.
B Autumn comes before winter in the same year.
C More people will buy umbrellas on a rainy day.
Match each event with the correct letter on the probability scale.
0 1 1
1 I ^ I I I—I—1—I—I—I
i l i t I t
A C O B E F
a) A triangle will have three sides.
b) The probability of drawing a black card from a pack of 52 playing cards.
c) A number picked from the numbers 0 to 10 will be 12.
d) The probability of drawing a purple ball from a bag containing 9 purple balls and 1 orange
ball.
e) The probability of drawing a green ball from a bag containing 5 blue balls and 5 green balls.
f) The probability of drawing a white ball from a bag containing 3 white balls and 7 yellow balls.
Sam went to a safari. The probability that the first animal he spots is an antelope is 58%, an
elephant is 12%, a lion is 6%, a crocodile is 5% and a zebra is 19%.
a) Draw a percentage probability scale. Mark the position of each animal on the probability scale.
b) Which animal is most likely to be spotted first?
c) Which animal is least likely to be spotted first?
421
CHAPTER 18.2
In this chapter
Pupils should be able to:
• Identify all the possible
mutually exclusive
outcomes of a single
event
Calculating probability
Outcomes which give an event that you are Interested
In are called favourable outcomes for that event.
Remember that In the spinner example earlier, there
are 5 possible outcomes. If you want to know the
probability of the pointer landing on green, then
green is the favourable outcome.
The probability of the pointer landing on green
Is 1 out of 5.
We can also express the
probability as a decimal Only 1 segment satisfies the favourable
and a percentage. This can also be written as 5. outcome green.
1=0.2 There are 5 possible outcomes.
^ X 100% = 20%
To calculate the probability of the favourable outcome, we divided the number of
favourable outcomes by the total number of possible outcomes.
Probability of a favourable outcome = '^^"^ber of favourable outcomes
total number of possible outcomes
Calculate the probability of
a) rolling a 3,
b) rolling an even number,
c) rolling a number less than 6,
d) rolling a number greater than 6 and
e) rolling a number less than 10.
on a die.
Solution
a) Probability of rolling a 3
There Is one 3 on the die.
_ number of favourable outcomes
total number of possible outcomes
There are 6 possible outcomes:
1
- 6 1, 2, 3, 4, 5 and 6.
if*
422 UNIT 18!, Probability
T|
. X P, r . numberof favourable outcomes
b) Probability of rolling an even number = r 2 1
^ tota number of possib e outcomes
3 There are 3 even numbers: 2, 4 and 6.
= 6
1 Express as a fraction in its simplest form.
= 2
0 Probability of rolling a number less than 6 = /mmber of favourable outcomes
' ^ total number of possible outcomes
5 There are 5 numbers less than 6:1, 2, 3, 4 and 5.
- 6
r ... , . .. .. number of favourable outcomes
d) Probability of rolling a number greater than 6 = -r~r-, r t rrn r
j
tota number of possib e outcomes
3
»
0 There are no numbers greater than 6 on this die.
= 6
It Is not possible to roll a number greater than 6.
= 0
.
,
_
numberof favourable outcomes
e) Probability of rolling a number less than 10 = ^tal number of possible outcomes
There are 6 numbers on a die that are
less than 10: 1, 2, 3, 4, 5 and 6.
1
=
It is certain that every roll of the dice
will be a number less than 10.
Check My
I
Under
Look at the spinner.
a) Calculate the probability of the following outcomes,
i) Landing on yellow
li) Landing on a colour
ill) Landing on green
iv) Landing on pink
b) Show the probabilities on a probability scale.
0% 50% 100%
I I ^ I ^ 1 1 ^ ^ \ 1
A spinner is numbered as shown.
What is the probability of getting:
a) a 1?
b) a 2?
c) an odd number?
Write each answer as a decimal.
423
David has a full pack of 52 cards, but he lost the King of Hearts.
There are 52 cards in a
David randomly chooses one card from his incomplete pack. pack divided into 4 suits:
What is the probability that the card is a King? clubs, hearts, diamonds
and spades. There are 13
During a raffle, 600 tickets were sold.
card values per suit: ace,
a) What is the probability of a person winning the raffle if they bought
2, 3, 4, 5, 6, 7, 8, 9,10,
i) 5 tickets? ii) 60 tickets? iii) 100 tickets? Jack, Queen and King.
b) What happens to the probability of winning the raffle as more tickets
are bought? Give your answers in percentages.
182.2 Mutually exclusive outcomes
In a doctor's waiting room, is it possible for patients to be sitting on a chair and
standing up at the same time? Can you sit and stand at the same time? Some
outcomes cannot occur at the same time. We call these outcomes mutually
exclusive outcomes.
p)
An example of an
outcome that is not
mutually exclusive
r is sitting down and
You cannot sit \ . , ^
and stand at the W ' T using your laptop.
, Both can be done at
same time. I \ .
the same time.
A coin is tossed once.
a) List the possible outcomes.
b) Are the outcomes mutually exclusive?
Solution
a) H - heads and T-tails
b) The outcomes are mutually exclusive. The coin cannot land on heads and
tails at the same time.
A die is rolled.
a) List all the possible outcomes.
b) State whether the following outcomes are mutually exclusive:
i) Rolling a number that is odd and divisible by two.
ii) Rolling a number that is greater than zero and less than six.
Solution
a) 1,2, 3,4, 5 and 6.
b) i) This Is a mutually exclusive outcome. A number that is odd is not
divisible by two.
^24 UNIT 18
ii) This Is not a mutually exclusive outcome Any number that is rolled
will be greater than 0 and less than 6.
j
State whether each of the following pairs of events is mutually exclusive or not.
a) Losing a football match and winning the same football match
b) Catching the bus and missing the bus
c) Being asleep and being awake
d) Randomly choosing an object from this bag that is:
i) round and blue ii) round and red iii) square and blue iv) blue and red
An 8-sided die shows the 18.2.3 Probability tree diagrams
numbers 1 to 8.
June wants to compare the probability of a 6-sided die landing on 5 to the
probability of an 8-sided die landing on 5 when each die is rolled once.
She uses probability tree diagrams to show the possible outcomes.
The probability of each branch The outcome is written at
probability outcomes
is written on the branch. the end of the branch.
probability outcomes
1
8-sided die
6-sided die
Each number has an
equally likely chance of
being rolled.
There are 6 possible outcomes. The sum There are 8 possible outcomes. The sum
of the probabilities of all the possible of the probabilities of all the possible
outcomes must add up to 1. outcomes must add up to 1.
1 1 1 1 1 1 1 1 1 1 . 1
i
6 + 6 + 6 + 6 + ^=1 8 + S"*" 8 + 8 + 8 + 8 + 8 s =
All the possible outcomes of an event form the sample space.
425
The favourable outcome is rolling a 5 on each die.
Probability of rolling a 5 on a 5-sided die = number of favourable outcomes
total number of possible outcomes
= ^ or 0.167 or 16.7%
number of favourable outcomes
Probability of rolling an 8 on an 8-sided die =
total number of possible outcomes
= ^ or 0.125 or 12.5%
The probability of June rolling a 5 on a 6-sided die is higher than rolling a 5 on an
8-sided die. This means that June is more likely to roll a 5 on a 6-sided die than on
an 8-sided die.
It is useful to use a probability tree diagram in situations where the number of
possible outcomes is not clear.
A 4-slded die shows the
numbers 1 to 4.
I
Why do we say that this
die has rolled a 4?
Discuss with a partner.
Tim rolls a 4-sided die.
a) Draw a probability tree diagram to show all the possible outcomes.
b) List the possible outcomes.
c) Calculate the probability of Tim rolling:
I) a 4, ii) an even number and iii) a zero.
A bag contains 4 yellow balls, 3 blue balls and 1 pink ball. One ball is
selected.
a) Draw a probability tree diagram to represent the sample space.
b) List all the possible outcomes.
c) Calculate the probability of selecting a yellow ball.
Anni, Kati, Patty and Lee are going to the movies. There is only one ticket
left for the movie that they all want to watch. They decide to write each
of their names on a separate piece of paper to randomly choose who will
watch the movie.
a) Draw a probability tree diagram to show all the possible outcomes in
the sample space.
b) What is the probability that Lee will watch the movie?
c) If Patty decides to give her movie ticket to Lee if her name is selected,
what is the probability of Lee watching the movie?
d) If Patty decides not to enter her name in the draw, what is the
probability of Lee watching the movie?
e) Compare your answers in parts (b), (c) and (d). Under what
circumstances does Lee have the best chance of watching the movie?
^26 UNIT 18 Probability
CHAPTER 18.3 in this chapter
Pupils should be able to:
• compare experimental
and theoretical
probabilities in simple
contexts
• use experimental
data to estimate
probabilities
183.1 Theoretical probability
Recall that probabilities we have calculated earlier are based on equally likely ^ RECALL
outcomes. They are theoretical probabilities.
For example, there are two possible outcomes with this spinner - orange or blue. A coin is tossed 20
times. A head is
We would expect these two outcomes to be equally likely because each colour
recorded 14 times,
sector is of the same size.
and a tail 6 times.
Find the experimental
and theoretical
The theoretical probability of
probabilities of
each outcome is 5 or 50%.
getting a head.
A dice is thrown
5 times. It gives a
However, these two outcomes may or may not be equally likely in a real-life
'four' 3 times. Find
situation. the experimental
and theorectical
18.3.2 Experimental probability probabilities of
getting a 'four'?
Max did an experiment to investigate whether the number of times the arrow
landed on the blue sector is equal to the number of times the arrow landed on
the orange sector.
Each time Max spins the
Max spun the spinner 40 times. He conducted 40 trials. spinner is called a trial.
He recorded his results on where the arrow landed.
Sector Frequency Experimental probability Frequency refers to the
number of times the
Orange 26
i =0.65 arrow lands on a colour
The experimental
sector.
Blue 14 ^ =0.35 probability should
add up to 1 or 100%
Total 40 1 * in percentage form.
In this experiment, the experimental probability tells us that the arrow landed on
the orange sector in 65% of the trials and on the blue sector in 35% of the trials.
Experimental probability = nomber of favourable outcomes
total number of trials
427
According to the theoretical probability, Max expected the probability of the
spinner landing on the orange sector to be 2, same as the probability of landing
on the blue sector. But the experimental probability is different from the
theoretical probability.
Max decided to increase the number of trials in the experiment. His results are
recorded in the table below.
Experimental
Sector Frequency
probability
The experimental
Orange 510
1000 =0.51 probabilities: 0.51 and 0.49
are closer to the theoretical
Blue 490 490
1000 = 0.49 probability of 0.5 when the
number of trials is increased.
Total 1000 1
As the number of trials in an experiment increases, the experimental probability
becomes closer to the theoretical probability.
GROUP WORK
List all the possible outcomes for rolling a 6-sided fair die.
Calculate the theoretical probability of each outcome.
Roll the same die 100 times.
Use the table below to record your experimental data. Use tally marks to
record the number obtained each time.
Experimental probability
can be referred to as Number Tally of the number of times the Relative
Frequency
relative frequency. on dice number appeared frequency
' •
i' "•
i
Spotlight
•
:
;
: •
' •
A biased die is also called
'• •
''
i
a loaded die. This die ' •
•
is made to land on one
I •
side more often than
the other sides. This is f •
•
: •
usually done by adding
an additional weight to What are some precautions you can take to make sure the experiment is
one or more sides of the as fair as possible?
die. The probabilities
Check your experimental probabilities with another group. Do you have
of the outcomes of an
the same experimental probabilities?
experiment using a
Compare your results and discuss the difference from the theoretical
loaded die will not be
probabilities. Are your results close to the theoretical probabilities?
equal.
How can you find out if this die is a fair or biased die?
i28 UNIT 18
The more times this experiment is conducted, the more accurate the estimated
probability of rolling each number will be. If the experimental probabilities of
every group are far from what you would expect, then you can say that the
die may be biased.
J
A spinner is divided into 5 equal sectors. Theo spun the spinner 50 times
and recorded the outcomes in the frequency table below.
Colour Frequency a) Calculate the theoretical probability of the
spinner landing on each colour sector.
Red 6
b) Calculate the experimental probability of the
Green 15 spinner landing on each colour sector.
Blue 8 c) Based on the experimental probabilities that you
have calculated, which colour sector is the spinner
Yellow 11
i) most likely to land on?
Pink 10 ii) least likely to land on?
Sue took part in a bowling game. There were 10 bowling pins to knock over in each round. She
recorded the number of pins she knocked over with each bowl. She bowled 50 times.
a) Calculate the theoretical probability of knocking over each
Number of pins
Frequency number of pins if all pins are equally likely to be knocked
knocked over
over.
0 '
1
b) Calculate the experimental probability of each number of
2 2 pins knocked over by Sue.
Based on the experimental probabilities that you have
3 5
calculated, which number of pins did Sue
4 7
i) most likely knock over?
5 2 ii) least likely knock over?
6 4 d) Sue is good at 10-pin bowling. Why would you not expect
the theoretical probability to match the experimental
7 8
probability?
8 6
9 11
10 5
*Cha!len9G!
A spinner is divided into 8 equal sectors. It is spun 120 times.
The arrow lands on the purple sectors 30 times. How many times
should the arrow have landed on the purple sectors for the
experimental probability to equal the theoretical probability?
429
Estimating probabilities
Freya wants to find the probability that it will rain on any one day in September.
So, she records the weather over 15 days in September in the bar chart below.
Weather over 15 days In September
Number of
days 4_
3-
2-
I
1 -
Sunny Cloudy Rainy
Weather
Using the information Freya recorded, we can find the experimental probability
hink and Share that it will rain on any one day in September.
Number of favourable outcomes = 5 days
Can Freya calculate the
theoretical probability that Total number of days = 15 days
it will rain on any one day Experimental probability that it will rain on any one day in September = ^
in September? Why or why
1
not? - 3
The experimental probability that it will rain on any one day in September is 3.
Sometimes, it is not possible for us to know the theoretical probabilities of the
outcomes. We can use the experimental probabilities to estimate the probability
of an outcome.
When your favourite sports team plays a match, there are three possible
outcomes.
The team loses Your team draws The team wins
You would not know what the outcome will be. You check the previous scores of
30 matches played by each team.
Experimental
Team Matches won in the past year Frequency
probability
Your team 22 30 =0.73
Opposing
i - 0-27
team
^30 UNITir^l Probability
Estimate the probability that your team will win.
Sokitioii
Your team won 22 out of 30 of their previous matches. The experimental
probability of your team winning is about 0.73.
The opposing team won 8 out of 30 of their previous matches. The experimental
probability of the opposition team winning is about 0.27. Based on this data, you
can estimate that it is more likely that your team will win.
A spinner, with 5 equal sectors is spun 100 times.
The results of the experiment are provided in the
table below.
f •
Colour red green pink blue orange
Frequency
20 17 10 35 18
Use the data to estimate the probability of the spinner landing on each
colour sector. Write the estimated probability in decimal form.
A coin is tossed 50 times. It lands on 'heads' 20 times.
a) Estimate the probability of the coin landing on heads.
b) Estimate the probability of the coin landing on tails.
c) Is this a fair coin? Explain.
A survey was conducted to find out which car colour was most popular at
a promotion fair. The number of cars sold during the fair was recorded in
the table below.
Colour Frequency
Red 9
Green 7
Blue 25
Black 33
White 108
Silver 18
a) How many cars were sold altogether at the fair?
b) Estimate the percentage probability of the next car being sold is white.
c) If you were to guess the colour of the car least likely to be bought by a
customer, what colour would you guess? Use the data to explain your
answer.
431
Revision
Describe the likelihood of the following events.
a) The sun will rise in the west.
b) Tomorrow will be Monday if today is Sunday.
c) You have a bag with 9 red balls and 1 white ball.
i) You draw a white ball. ii) You draw a red ball. ii) You draw a green ball.
There is a hot drink vending machine in an office. A survey was
Drink Frequency^.^
conducted to find the probabilities of an employee choosing
each type of drink. Each employee could only choose one drink. coffee 0.5
Draw a decimal probability scale. Mark the probability of each 1
tea
4
drink being chosen on the probability scale.
a) Which drink is most likely to be chosen? hot chocolate 20%
b) Which drink is least likely to be chosen? cappuccino 0.05
c) Show this data on a probability tree diagram.
5 dominoes are placed face down. Sarah randomly
chooses one domino. What is the probability that
Sarah will pick up a domino with
•
•
a) a blank on it?
•
•
b) five dots on it?
•
•
c) seven dots in total?
•
•
This spinner is used in a game.
The spinner is spun once. The arrow indicates the score achieved.
a) Use a probability tree diagram to show all the possible scores.
b) What is the most likely score?
c) What is the probability of getting a score of 1 ?
A company manufactures batteries. They want to know how
long the batteries can last. They tested a sample of 100 batteries.
The results are in the table below.
Battery life (h) Frequency
Less than 10 h 4
From 10 h to less than 20 h 46
From 20 h to less than 30 h 39
30 h or more 11
Estimate the probability of a battery chosen at random lasting
a) less than 10 hours.
b) more than 10 hours and less than 30 hours.
c) more than 30 hours.
Help
Sheet
Probability of a favourable outcome
number of favourable outcomes
total
' number of possible outcomes
Calculate probability
The measure of the likelihood
that an event will occur. Probability tree diagram
Heads 2
defined as
used to
represented
Probability as
based on
Probability scale
Outcome
A possible result of a Probability is measured from 0 to 1.
probability experiment.
can be A probabilty of 0 means the event is impossible.
A probabilty of 1 means the event is certain.
Probabilty is written as a fraction, decimal or percentage.
can be
impossible unlikely equally likely likely certain ,u.
*
1 3 1
2 4
Mutually exclusive Equally likely
0.5 0.75 1
50% 75% 100%
Events which cannot Events which have
occur at the same time. the same theoretical
probability of occuring. 0 © e
based on
Theoretical probability Experimental probability
Calculating the probability of an event occuring Can be referred to as relative frequency.
without experimental values. It can be written as Represented as a ratio of the number of
the ratio of the number of favourable outcomes times a favourable outcome occurs to the
to the number of positive outcomes. number of trials in the experiment.
433
Mathematics Connect 4
Flooding is a common natural disaster
in the United States. The name
'100-year flood' can be confusing
because it makes us think that a river
will flood only once every hundred fliisstrsfimS
years. This is not necessarily the
case. The 100-year flood describes
the estimated probability of a 1%
chance that this flood will happen in
any given year. Even if the flood just
happened last year, it might happen
again the next year. The chance of
l.'tOl _ li)'Ung
an occurrence of the next flood is
-ll.SKacn
independent of the previous flood. In
ISWU _ -I0.3nti
fact, there is a 63% probability that 1
or more such flood could occur within
a period of 100 years.
_
Similarly, a 10-year flood will have a
Sfdi-tBarta
10% chance of occurring in any given aioso-iu;
IS99__I.13fW
year or a 500-year flood will have a
0.2% chance of occurring in any given
year.
18J»3_ iliig
In the 1960s, the United States 2002 13. jiuii
government decided to use the 1 %
figure as an indicator for the size of
the flood where the citizens can be
protected via insurance against the
n)2o_ _ S Sflrt
perils of flood damage. For some
people who are staying in an area
where there is a high risk of flooding,
it may be compulsory for them to buy
such an insurance. The 100-year flood
will then be a useful indicator to the
authorities to decide if a coastal area
is 'high risk' or not.
Find out more on this link.
The Passau flood scale
^3i> UNIT 18
probability
ANSWERS
Check My Understanding (Pg 15)
Unit 1
1. a)15 b)4 0)5 d)4 e)2
2. 8
Recall {Pg 4)
1.8) 15,30,45 b)20, 40, 60
Recall (Pg 16)
0)25,50,75 d)50, 100, 150
1. 0, 2, 4. 6 or 8; 2 2. 1,3, 5, 7, 9; 2
2. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Check My Understanding (Pg 21)
Check My Understanding (Pg 5)
1.2- A number is divisible by this number if the last
1. a) 1,3, 9 b) 1, 2, 4, 8, 16
digit is an even number
0)1,2,3, 4, 6,8,12, 16, 24, 48
3 - A number is divisible by this number If the sum of
d) 1. 3, 9, 11, 33, 99 e) 1,7, 49 f)1,13
its digits is a multiple of 3
2. a) 1 X 12, 2 X 6, 3 X 4 b) 1 x 7
4 - A number is divisible by this number if the number
0)1 X 16, 2 X 8,4 X 4 d) 1 x 21,3 x 7
formed by its last two digits is divisible by 4
e) 1 X 50, 2 X 25, 5 x 10
5 - A number is divisible by this number if its last digit
f) 1 X 48, 2 X 24, 3 X 16, 4 X 12, 6 X 8
is 0 or 5
3. a) Inoorreot: 4 b) Inoorreot: 2, 7 6 - A number is divisible by this number if It is
o) Inoorreot: 5 d) Inoorreot: 15 divisible by 2 and also by 3
4. a) false b) true o) false d)true 8 - A number is divisible by this number if the number
formed by its last three digits Is a multiple of 8
Check My Understanding (Pg 6)
9 - A number Is divisible by this number if the sum of
1. 7, 11. 19
its digits is a multiple of 9
2. Prime Number - A number that has exactly two factors:
10 - A number is divisible by this number if Its last digit
1 and itself
is 0
Factor - A number which divides into another number
100 - A number is divisible by this number if its last two
exactly without leaving a remainder
digits are 00
Product - The result obtained when two or more
2.
numbers are multiplied
3. 2 and 13 are prime, 8, 25 and 70 are composite. 357 3
432 2, 3. 4, 6, 8, 9
Check My Understanding (Pg 9) 2362 2, 6
1. a)1,3, 5, 15 b) Any multiple of 15.
5681 None
2. a) 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99
18 303 3
b) 1, 3, 9
58 475 5
0)9
d) i) false, 9 Is a multiple of 9 400 005 3, 5, 9
ii) false, 3 is not a multiple of 9 782 300 2, 4. 5, 10, 100
III) false, 3 Is a prime number 7 421 894 2
iv) false, 27 has other factors like 27 7 762 342 2
3. a) 9. 18, 27, 36, 45 b) 24, 30, 36, 42
4. a) true 3.2,3,4,6.8 4.2
b) false, 0 Is not a multiple of 6
o) false, 32 is not a multiple of 10 Recall (Pg 23)
5. 8 1. a) 1 b)4 0)9 d) 25
2. 36, 49, 64, 81, 100
Recall (Pg10)
1. 36 2. 48 3. 90
Check My Understanding (Pg 25)
1. 16, 25, 36,49, 64, 81. 100, 121, 144, 169, 196, 225,
Check My Understanding (Pg 11)
256, 289, 324, 361, 400
a) 35 b)30 o) 12 d) 14
2. a) Draw a 7 by 7 dot pattern
e)132 f) 180 g)150 h)72
b) Draw a 9 by 9 dot pattern
Check My Understanding (Pg 13)
Check My Understanding (Pg 26)
1. a) 1. 2, 3. 4, 6, 9, 12, 18, 36
1. Draw a 2-by-2 square grid, 3^ = 9, = 4, Draw a 5 by 5
b) 1, 2, 3, 4, 6, 8, 9 ,12, 18, 24, 36, 72
square grid. Draw a 6 by 6 square grid, V36 = 6, 7^ = 49
0) 1, 2, 4, 5, 8, 10, 16, 20, 80
Draw a 7 by 7 square grid
2. a) 23 X 32 X 52 b) 22 X 3 X 52
2. 8)10 b)9 0)12 d)20
e)19 f)21 g)26 h)14 4.
Check My Understanding (Pg 14)
3. Top to Bottom;
1. a) 30 b)48 o)60 d)672 e)80
- sixteen, = ten, = fifty, - fourty, = eleven, = one, = zero
2. 120
Left to Right:
- two, - twenty, - fifteen, - thirty, = nine, - eighty
4. a) true
b) false, a square root is obtained when the number is Check My Understanding (Pg 39)
divided by itself 1. a)-23 b)-10 c)-11 d)-11 e)-7
c) true f)-9 g)8 h)12 i)-5 i)-13
d) false, the square root of 4 is 2 k)-9 l)-18 m)-8 n)2 0)2
p)3 q)-20 r)-21 s) 0 t)0
Revision (Pg 28)
2. 41 m below sea level
1. a) 1,2, 3, 4. 6, 12 b) 12. 24, 36, 48. 60
3. ire
c) 1,2, 3, 6, 9, 18 d)26. 45,54, 63, 72 4. Bangkok = -150 cm, Kolkata = 914 cm.
e) 1, 17
Difference = 1064 cm
2. a) 1,6, 10, 15, 30 b) 1.2, 3 5
3. a) false, any even natural number is a multiple of 2 Check My Understanding (Pg 41)
b) true 1. a) 4 b)2 c)-2 d)-4 e) 4
c) false, 7 is a factor of 49 f)-2 9)-29 h)30 0-29 j)-32
d) false, 1 is a factor of every natural number 2. a) 5 b) 14 c)-17 d)0 e)-2
e) false, there is only one even number that is a prime
f)-6 9)0 h)-13
number 3. Basement 1
4. a) 24 b)77 c) 60 d)156 4. a)-3 b) 13 c) -9 d)-10 6)0
5. a) No b) There are infinite multiples of 7 f)1 9)16 h)50 1)0 j)-7
6. a) 81 b)72 c) 60 d) 81 e)17 k)-9 1) 16 m) -8 n)-33 0) 30
7.2 P)25 q)-9 r) -15 s)0 t)1
8. 72 5. a) 9 b) 23 c) -6 d)-18 e)-11
9. 2 hot dogs, 1 8-roll and 1 12-roll f)5 9)^ h)-2 i)5 j)0
10. a) Check if the number is even and then check if the 6. 24°C
sum of the digits is divisible by 3 7. a) Subtract 27 from 13 using an integer ruler, answers
b) Check if the last two digits of the number is divisible may vary
by 4 b) Temperature calculation
11. 9042 is divisible by 2, 3, 6
76 543 is not divisible by any of the numbers Speed Challenge (Pg 42)
124 800 is divisible by 2, 3, 4. 5, 6, 8, 10, 100 I.-23 2.-11 3.-7 4.8 5. -5
12. a) 36 b)121 c) 1 d)81 e)225 6.-9 7.-8 8.2 9.-10 10. -11
f)0 g)11 h)8 i)7 j)17 II.-9 12. 12 13.-13 14.-18 15.2
k) 35 I) 20 16.3 17.-7 18.2 19.6 20. 2
13.29 14. 1 15.3
Revision (Pg 43)
1. a) Anchorage, Buffalo, Albany, Reno
Unit 2
b)18°C 0)10^ d)5^C
2. a)-$34 b)$65 c) Withdrawal of $90
Check My Understanding (Pg 35)
d) Deposit of $70
Use the integer ruler to count if you are stuck
a)
3. a)-4 b)-18 c) 4 d)-9 '537
f) -28 g) -50 h)69 1)11
Try and Apply (Pg 35) 23
k)^ I)-4
Russia, Iceland, United Kingdom, India, South Africa
4. a) 8 b)-21 c) 91 d)-12 e)101
Check My Understanding (Pg 36) f) 187 g)-40 h)-88 i)8 j)3
k) 12 0-17
1. a) < b) > c) > d) > e)<
5. a)-61 b) -278 c) -30 d)79 e)-93
g)> h)< i)> j)<
>
k)> 1) < m) n)< 0) = f) -25 9)23 h) 14 1)41 j)^5
k)9 i)-10
Check My Understanding (Pg 36) 6. 10
1.d 7. a) 9
2. a)-4,-3, 2 b)-4,-2,-1 b)
c)^, -1, 0, 4 d)-8,-3, 0, 6
-3 4 8
e)-9, -6, -5,0, 1 f)-12,-12, 10, 12, 13
3. a)4, 2,-1,-4 b) 5, 1,-3,^
14 3 -8
c) 6,-2,^,-6 d) 9, 6, -1,-3, -8
e)10, 6, -6, -12,-20 f)7, 5, 2,0,-3,-4 -2 2 9
4. a) 0,-2,-4,-6 b)-15,-25, -35, ^5
c) 12, 17, 23, 30 d)2. 6, 10, 14
e)-11,-17,-24,-32 f) 0, 5, 11, 18 Units
5. a) A is -20, B is -13 and C is 1
Recall (Pg 46)
b) C, 8, A
Pentagon -
4
6. ^0°C, -45"C
6
Heart -
Try and Apply (Pg 38)
Check My Understanding (Pg 50)
47 m
1. a)m + 3 b)m-7 c) 4m
Answers
25 Check My Understanding (Pg 60)
n +7
a) 6a b)4ib c) 6a + 4ib
a) X + 4 b)x-1 Check My Understanding (Pg 62)
a) iv b) ii c) iv 1. a) 3 b) 19 c)41 d)27 e)-1 f)5
a) 10x + 6y b) 2{p + 15) 2. a) 6 b)90 c)1
c)15{x+ y)-z d) + 1 3. a) 4 b)50 c)3
a)x-22 b)x- 15 4. a) 9, 10, 14 b) 6, 15, -6
5. a) X 6 b)-5
Recall (Pg 51) 6. a) 8, 60, 102 b) 18, 8, 39, 25 c) 2, 11,7, 23
Check My Understanding (Pg 65)
Check My Understanding (Pg 52) 1. a) No b) Yes c) No
1. a) false, 7a b) true d) Yes e) No f) Yes
c) true d)false. 21f-5 2. a) 11 b) V c) ill d) iv
e) false, 2a + 3b f) true 3. a) 4 b)5 c)2 d)9
2. a) 9a b) 5d c) 2a + 35
d)8(a + 1) e)6W f) 5(3/ +2s) Check My Understanding (Pg 66)
g) 4(4g + k) h) 15a + 1 i)-3a(1 -65) 1. a)43 b)9 c)10 d)15 e)26 f)15
]) 5xy + 2x + y + 8 k) 25c + 55 + 9 2. a) 6 b)24 c) 3 d) 84 e) 4 f) 200
I) xyz + 9y + 7 m) mn + 12m + 2n + 15 3. a) 15 b)17 c)10 d) 8 e) 35 f) 72
n)75xyz + 35xy + 20 9)9 h)50
3. a) 6x + 4y b) 3x + 5y c) 5x + 2y + 5 4. x + 5= 14, 9
4. a)7a, 5a, 3a b) 23y. 12y, 7y 5. 6x = 42, 7
c) 13a + 145, 5a + 95, 8a + 55 6. X- 14 = 18, 32
d) 10x + 23, 8x + 22, 2x+ 1 7.1= 12. 96
5. Accept any answers that equate to 6x + 5y
6. 9a + 55 + 4, 3a + 9, 4a + 45 + 6. a + 5 + 6, 2a - 5 + 3, Check My Understanding (Pg 68)
1. a) 2 b) 3 c)3 d)4 e)3| f)2
a+ 25 + 11
9)8 h) 12 i)150 j)2 k) 33 0-3
Check My Understanding (Pg 55) 2. a) 6 b)8 C)-3 d)8
ii
a) b) iv c) ill d) 3. a) 4 b)7 c)21 d)2 e) 14
1
a) 2x + 6 b) 35 + 15 c)-i2-6y d)6x-6 f) 13 9)16 0
e)-18 + 9c f)60-5/< g)-8xy-8 h)-12c + 6 4. a) 15 b)2 c) 3 d)8 e) 19 f)6
a) 6a + 95 + 12 b)12x + 8y + 4 5. a) 2
c) -8m - lOn + 6 d)30x-20y-35 b) 4x - 84, 21 cm
e) 35a-215 +35c f) -42c- 125+ 24/ c)5
4. a) 13m+ 21 b) 485 + 32 c) 12y-3 d)17 = 2 + 5x, 3
d)-2x+13 e)10x + 3 f)21a + 6
Revision (Pg 70)
Check My Understanding (Pg 56) 1. a)8 b)24 c)2 d)18 e)18 f)-12
1. a) 12 b)2 c)21 d) 29 8)6 2. a) 5c b)18a5 c) 3(3m + 2p)
f) 56 9)1 h)-3 d) 9xy + 4x + 6 e) c5 + 1
2. a) 8 b) 18 c) -4 d)0 e) 4 f) 3xyz + 8xy + 8z + x + 3
f)0 9)2 h)-63 3. a) 4a5 b) 4a + 5 c)0
3. a) 7 b) 19 c) 4 d)2 e)10 d)5(5 + 3) e)5x-12 f) 4a(3 + 25)
f)6 9)2 h) 10 4. a)7x b)75a c)100y d)x-y e)2x + 3y
4. a) 120 b)30 0) 60 d)36 5. a) 9 b)3 c)15 d)15 e) 3 f) 45
5. a) b)3 c)y = 5 ,x=1 9)15 h)26 i)8 j)7
ii
6. a) yz + 4 b) yz + 2y c) yz +, z + y 6. a) 10 b)6
7. a) Not equal unless x = | b) Not equal unless x 7. X + 7, 2x + 14, 2x + 8, X + 4 , 4
8. Across: 14, 2, 12, 14, 16. 15, 23. 12, 55. 26
= 0 or 2 c) Not equal unless x =0
Down: 15, 24, 20. 35, 13, 18, 25, 22. 16
Check My Understanding (Pg 58)
a) 72 b) 168 c) 24a Unit 4
a) 73 b) 245 c) 13x + 60y
a) 2 b)5 c)| Recall (Pg 74)
a) 5 = 245 b) 336 h 1. 5,0.6,0.03 2. 0.36 3. $3.45
a)c=fl b) 10 cm
Check My Understanding (Pg 75)
a) p = 2{l + w) b) 18
1. a) true b) true c) false d) false e) false
b) 8 m/s 2. a) tenths b)hundredths c) tenths
8. a) k = 3s b) 45 km d) thousands e) thousandths f) tens
9. a)7x + 5 b) 27X-28 c) 23X-22 g) tenths
d)21x-11 3. a) 0.4 b)0.04 c) 0 d) 1000 e) 0.003
10.a) 3y + 4x + 2 b) 26 c) The 2x + 3 side f) 0 g) 0.04
Recall (Pg 77) e) 4 f)3 g) 0.304 h) 0.509
1. 1.93 i) 1.53 j) 0.2651 k) 0.10314 I) 0.0304
2. 2.44 2. a) 10 b) 100 c)1 d)1000
e) 10 f) 10 g)100 h)100
Check My Understanding (Pg 78)
3. 2.1
1. a) 3.3 kg b) 38.9 g c) 109.9 g d)5.75g 6) 7.03 g 4. $29
f) 0.55 kg 9) 7.52 g h) 3.91 kg
2. a) $0.30 b)$1.67 c) $0.80 d) $20.01 e) $3.31 Recall (Pg 86)
f)$0.88 g)$1.82 h)$0.82 4.8
3.8)14.21 b) 10.19 0)6.649 d) 6.213 e) 5.00
f)9.81 g)1.32 h) 3.193 1)0.45 j)3.02 Check My Understanding (Pg 87)
k)9.8 1)14.63 m)6.32 n)4.27 0) 5.100 1. a)4.3 b)2.1 c)2.2 d) 1.1 e)7.1 f)0.3
p) 20.78 q)1.82 r) 31.33 s) 0.45 t) 7.00 9)0.5 h)0.1 i) 0,9 j)0.7
4. a) 9.09 b)9.58 0)8.181 d) 2.241 e) 14.861 2. a) 2.34 b) 1.16 c) 1.01 d)0.09 e)1.07 f)2.07
f) 6.786 g) 1.515 h)0.09 i) 1.04 j) 0.54
5. a) 6 b)0 0)2,2 d) 3 e)2 f)6,3 3. a) 0.1 b) 9.18 c) 0.06 d)2.05 e) 4.545 f) 3.03
6. a)0 b) 0,1,2 0)0,2,8 g) 7.02 h) 5.15 1) 0.04 j) 18.23
7. 13.31, add the respeotive plaoe values 4. a) 4.88 b)4 c)2 d) 9.3 e)12.8 f)26.4
5. 8.75 cm
Speed Challenge (Pg 79) 6. 3.23 kg
1. (1)36.5 (2) 11.1 (3) 5.3 (4) 45.3 7. $16.95
(5)-0.5 (6) 86.3 (7)0.4 (8) 95.7 8. 15 160 9
(9) 114.7 (10) 93.52. 9. a) 6 m b) 30 m
2. (1)79.13 (2)47.41 (3) 88.21 (4) 84.55 10. 0.23 m
(5) 83.92 (6) 22.73 (7) 49.6 (8) 83.65 11. Cleo is correct
(9) 62.65 (10) 84.53
3. (1)0.91 (2)43.78 (3) 95.76 (4) 52.83 Check My Understanding (Pg 90)
(5) 36.84 (6) 2.37 (7) 93.13 (8) 70.86 1. a) 0.38/, 1.203/, 2.741 /, 4.321 I
(9) 32,22 (10) 101.56 b) 1.201 /. 1.279 /, 1.729 /, 1.9/
c) 4.102 /, 4.192 /, 4.2 /, 4.291 I
Check My Understanding (Pg 80) d) 3030 ml, 10.13 /, 10.31 /, 13030 ml
1. 0.181 kg 2. a) 0.1 kg. 0.25 kg, 0.6 kg, 0.9 kg
2.315.94 kg b)0.8 t, 3.6 t, 3.61 t,4t
3. 21.56 c) 1.066g, 2.439, 2.5 9,2.7 g
4. a) 5 b) Pentagon d)Og, 10.1 9, 10.78 g, 10.87 9
e) 2.07 kg, 2.172 kg, 2.70 kg, 2.71 kg
Check My Understandlng(Pg 82) 3. a) 1.6 km, 1.35 km, 1 km, 0.16 km
1.a)32 b)9 o)160 d) 232 e) 0.4 f) 3 b) 2,51 m, 2.5 m, 2.2 m, 2.01 m
g)30.4 h)509 i)153 j) 2600 k)20 1) 1040 c) 0.18 km, 0.108 km, 0.081 km, 0.8 km
2. a) 10 b)100 o)10 d)100 e) 1000 f) 1000 d) 20.32 mm, 20.3 mm, 2.32 mm, 2.23 mm
9)100 h)10 e) 6.51 cm, 6.15 cm, 6.05 cm, 60.1 mm
3. a) 2399 b) 23 990 4. 0,1297, 2.3579, 0.1137, 0.0028, 0.0224
4. 18 5. 6.015
5. a) Answers may vary. Accept all answers that follow
condition stated, Check My Understanding (Pg 91)
b) Answers may vary. Accept all answers that follow a) 0.285 m b) 170.6 cm
condition stated.
6. The owl reading the book is correct Check My Understanding (Pg 92)
1. a) 1250g, 0.55 kg, 0.525 kg, 250 9
Recall (Pg 83) b) 250 /, 2,5 /, 250 ml, 25 ml
63.2 c) 3.251 km, 3.25 km, 325 m. 3251 cm
d) 320 mm, 302 mm, 0.3 m, 0.03 m
Check My Understanding (Pg 83) e) 101 cm, 0.99 m, 0.98 cm, 909 mm
1. a)2.3 b) 12.6 c) 1 d)0 e) 15.6 2. B, C. D,A
f)7.6 9)15.9 h)8.1 i) 17.6 j)80.1 3. 0, D,A, B
2. a) 2.38 b)8,64 c)2.04 d)0.21 e) 15.76 4. A. C, D, B
f)7.74 9)30.18 h)5.28 i) 16.24 j) 161.1
3. a) 5.6 b)20.1 c)39 d) 10.8 e) 0.64 Recall (Pg 93)
f) 18.18 9)31.5 h)91.15 1)69.21 j)105 1. a) 600 b)1200
4. a) 2 b)3 c)4 d)1.11 e)3.2 f) 2.45 2. a) 4.50 b)31.0
5. Sue is correct
Check My Understanding (Pg 96)
Check My Understanding (Pg 86) 1. a) 1430, 1400, 1000, 1432, 1432.3
1. a)3.2 b)0.09 c) 16 d) 0.0232 b) 650, 600, 1000, 646, 645.5
c) 940, 900, 1000, 937, 937.1
Answers
d) 790, 800, 1000, 787, 787.2 g) 7 cm h) 1.81 cm i) 6.4 cm
e)7850, 7800, 8000. 7848, 7847.9 j) 6.0 cm k)49.8 cm 1) 0.07 cm
f) 1010, 1000, 1000, 1010, 1010 3. a) 4000 mm b) 1600 mm c) 15 200 mm
2. b)Incorrect, the digit in the units column is more than 5 d) 350 mm e) 175 mm f) 6 mm
thus it would become 130 g) 540 mm h) 0.5 mm i) 1 600 000 mm
c) Incorrect, the digit does not change j) 16 000 000 mm k) 500 000 mm 1) 50 000 mm
d)Correct, 1 is added to the digit in the tenths column if 4. a) 1.6 km b) 9.53 km c) 14.6 km
the hundredths column is more than 5 d)0.35 km a) 0.095 km f) 0.005 km
3. a)41 b) 16.6 s c) 24.00 s d) 2000 ml g) 0.05 km h) 0.5 km
e)500 cm f) 7000 m g)4000g h) 4.7 kg 5. a) 55 cm b) 550 mm
4. a)2 m b) 180 mm c) 400 ml d)590g 6. 22 cm
/
e)7:00 a.m. f)90°C 7. a) 3/ b) 5 c) 50 / d) 3.765/
e) 0.406 / f) 0.5 / g) 0.25/ h) 0.098/
Check My Understanding (Pg 100) 8. a) 6000 ml b) 40 000 ml c) 360 000 ml d) 1000 ml
1. a) 19.6596 b) 7.057142... c)2.588907. e)7560 ml f) 10 100 Til g) 540 ml h)400 ml
t
2. a) 20 b)7 c) 3 9. 8
3. a) 32.43 b) 4.104 c)25.3 10. 0.75/
4. a) Using estimation, we would arrive at 60. 11. a)1 kg b) 8 kg c) 70 kg d) 54 kg
b) 58.48, Harry moved one decimal point too far e) 0.768 kg f) 0.23 kg g)0.1 kg h) 0.098 kg
12. a) 1000 g b)6000 g c) 40 000 g d) 74000 g
Check My Understanding (Pg 101)
e)88100g f) 650 g g)500g h)54g
1. $22.05 13. a) 1 t b)6t c) 50 t d)34t
2. 17m
e) 0.128 t f) 0.566 t g) 0.399 t h) 0.076 t
3. 15 14. 5568 g
15. 270
Revision (Pg 102)
16. 1875 g
I. a) 50, 0, 0, 50, 49.6 b) 30. 0. 0, 30, 29.7
17. a) > b)> c)< d)< e) > f) <
c)2, 0,0, 0,2.0 d)0, 0,0, 0,0.1
g)= h)> i)>
e) 340, 300,0, 340, 340.1
f) 1790, 1800, 2000, 1794, 1794.3 Recall (Pg 112)
g) 600, 600, 1000, 600, 600.3
1. Barrel
2. a) 4 b)0.8 c)5 2. Kilometres
3. 23.4
4. a) 13.08 s. 13.69 s, 13.95 b) 0.87 s Check My Understanding (Pg 112)
5. 25.7 1. a) 12 cm b) 3 mm c) 3000 mm d) 250 ml
6. a) i) 1.52 il) 0.245 iii) 0.3021 e) 900 g f) 30 g g) 0.005 I
b)i)4.8 11)9.6 iii) 12.0 2. Car length - metres
c) i) X 3 ii) X 3 iii) X 3 Mass of a cell phone - grams
a) i) 1 m
7. a) ii) 6.75 m iii) 6.2 m Amount of water in a bathtub - litres
b) They are reasonable Length of a pencil tip - millimetres
c) $15.25 Amount of water in a raindrop - millilitres
8. a) 7.88 h b) 63.04 h
9 a) 0.7 kg b) 0.82 kg c) 6.56 kg Recall (Pg 115)
10. a) 15 X 6 = 90, Correct 1. 2 cm
b) 30 X 3 = 90, Incorrect 2. 650 g
c) 20 -5- 4 = 5, Incorrect
Check My Understanding (Pg 116)
II. 21
1. 5.4 cm
Unit 5 2. 80 ml
3. 75 g
Recall (Pg 106) 4. a) 79.8 cm b) 12.4 cm
1. 0.105 m 2. 0.706 km 3. 0.875 kg 5. 44.301 I
4. 3.008 kg 5. 0.98/ 6. 12.059/ 6. a) 162 kg b) 105 kg c)53kg
7. a) Arrow exactly halfway between 3 and 4
Check My Understanding (Pg 107) b) Arrow 3 small markings to the left of 0
1. millimetre, centimetre, decimetre, metre, kilometre c) Arrow exactly halfway between 1 and 2
2. kilogram, hectogram, gram, centigram, milligram 8. a)70km/h b) No c) 117 569 km
3. millilitre, decilitre, litre, decalitre , kilolitre
Revision (Pg 118)
Check My Understanding (Pg 110) 1. a) 23 m b) 0.155 m c) 0.001 m
1. a)3000 m b)4200 m c) 12 500 m 2. a) 392 cm b) 10.2 cm c) 0.001 cm
d)500 m e) 3 m f) 5.5 m 3. a) 28 mm b) 5 000 000 mm c) 1 060 000 mm
g) 0.58 m h) 15m i) 4 m 4. a) 0.254 km b) 0.03421 km
j) 6.85 m k) 0.035 m 1)0.008 m 5. a) 0.6/ b) 0.06 /
2. a) 600 cm b) 820 cm c) 1680 cm 6. a)4500 ml b) 80 ml
d) 56 cm e) 6 cm f) 1 cm 7. a) 1.496 kg b)0.01 kg
8. a) 6876 g b) 3
g
9. a) 5.619 t b) 0.009 t e)
10. a) < b)> c)<
11. Mass of this book - kilograms
Mass of a truck full of sand - tonnes
Mass of a packet of crisps - grams
12. Measure 6150 ml containers then measure 425 ml
containers and add them together
13. 1200 ml
14. 6.70 km
15. a) 44 mm b)45g c) 170 ml
d) 4.2 kg e) 30 ml f) 32 t
2. a
Unit 6
Recall (Pg 121)
a) 48' b)125'
Check My Understanding (Pg 122)
1. a) Reflex b) Acute c) Acute d) Reflex
e) Reflex f) Obtuse g) Reflex
2. a) reflex ... 360° b) 90° c) right
d)180° e)360° f) 90° . 180°
a) from left to (I) from right
b) from left to (IV) from right
c) from left to (V) from right
d) from left to (VI) from right
e) from left to (111) from right
f) from left to (II) from right
Recall (Pg 123)
Recall (Pg 131)
1. Students are to give a rough estimate
c/ = 52°
2. a) Acute, p = 45° < 90°
b) Right angle, q = 90°
Check My Understanding (Pg 132)
c) Obtuse, r = 118° > 90°
1. a) 90° b)44° c) 99° d) 56' e)8r
Check My Understanding (Pg 126) f) 129° 9)105 h) 72° i) 14° j) 32°
k) 60° 1)73° m) 103' n)25'
1 (I)obtuse
.
o) 45°
(II) full
Conclusion: 180
(III) right
(IV) reflex
Recall (Pg 134)
a) from left to I from right
b) from left to (I) from right a) Equilateral triangle
c) from left to (IV) from right b) Isosceles triangle
c) Scalene triangle
d) from left to (II) from right
2. a)Acute, 44° b) Acute, 67° c) Obtuse, 94' Check My Understanding (Pg 134)
a)
d) Obtuse. 172° e) Obtuse, 164° f) Reflex, 343° 1. a)60° b)130° c)40° d) 40° e)44'
g) Reflex, 268° h) Reflex, 205° f)29°, 58*
2. a) 51 b)24 c) 20 d)22.5 e)e = 40. f=55
3. a) 60° b) 50° c) 80° d) 20° 144' f) 118°
4. a) 276° b)216° c) 300° d) 340' 242' f)310' Check My Understanding (Pg 136)
1. 22
Check My Understanding (Pg 130)
2.45
1. a) b)
3. 60°
4. Angle AMB = 72°, Angle BMC = 72°, Angle CMD = 72°,
Angle AMD = 144°
Speed Challenge (Pg 137)
c)
Level 1
A. 230° B. 290° 0. 320° D. 260° E. 245° F. 305
Level 2
A. 306° B. 109° C. 53° D.309° E. 214° F. 227'
Level 3
A. 134° 8. 112° C. 175° D. 241° E. 144° F. 200'
Level 4
A. 215° B. 58° 0. 58° D.44° E. 186° F. 217'
E
Answers
Check My Understanding (Pg 139) 9. ^8 = 40° ^5 = 68° ^c = 72° Ad = 45°
1. 100° 2.25° 3.37° 4.45 5. 31 Ze = 63° /If =45° Lg = 15° ^5 = 105°
Ai= 108° /.;■= 108°
Check My Understanding (Pg 139)
10. ^p = 65° = 65° Ar=60° As = 35°
1. 8)27° b)27°
2. 8)151° b)29° 11. ^8 = 80° zl5 = 80° Ac= 100° /.d= 100'
3. 8 = 10,5 = 25 ^e = 90° ^7=62°
12. Za = 58° /15 = 77° Ac = 45° Ad =77°
Check My Understanding (Pg 141) ^e = 45° /if =58°
1.54° 2.209° 3. 112'
13. ^8 = 88° /i5 = 73° Ac=G2°
^c/=92° zle = 88° Af=73°
Try and Apply (Accept any possible pairs)
14.
Check My Understanding (Pg 146)
1. 138° 2.25° 3.23° 4. 74°
Check My Understanding (Pg 151)
1. 8)90° b)45° c)90° d)45°
2. 8)90° b)72° c)54° d) 108'
3. 8)117° b)63° 15. They are paraliel to each other.
4. 123°
5. a) a = 60° 5 = 30° b) 20° c) 10 mm Unit?
d) 5 mm e) 30 mm
6. a)ZCED = ZCDE=47° b) 5 cm Check My Understanding (Pg 162)
7. 8= 115 5 = 35° 1.8)
8. 8)70° b)5 Colour Tally Total
c) 70° + 110° + 110° + 70° = 360° Red
Blue
Revision (Pg 153) White
1. AABC = 45° ABCD =^48° Silver
^ ODE =46° zlDEF=120°
b) Make of cellphone Tally Total
^EFG=66° ZFGH= 122°
Apple
^GH/=77° zlH/J=67°
Samsung
^/JK=129° ZJK/.= 124°
2. 8) \ b) C) Mode of transport Tally Total
Bus
Car
Walk
Bicvcle
c) d)
d) Reading Watching TV
Tally
Total
e) Separate Do not separate
Tally
Total
(Accept any other possible answers)
2. a) The total for Tuesday is 6. b)4
c) 10 d) Text Message e) Video Call
f) 9 g) Thursday h) Friday
h)
Check My Understanding (Pg 165)
1. a)
3. 8)62° b)25° c)20° d) 15° Colour of Car Tally Frequency
e)a = 25°, c=17.5°, d=20°
Red tttt tttt ll 12
f)x = 23°, 8=111°, 5 = 69°
Mil llll
4. 8)60° b)50° c)105° d)80° e)137°f)13° Blue TTTttm 10
9) 113° h)99° 1) Rhombus, 3m. 3m j) 109° Green 1111 4
5. a) 90° b) 90° c) 90° d) 45°
6. 8)90° b)110° c) 70° d) 35° White Iftfllll 9
7. 8)123° b)57° Silver 1111 4
8. 52°
Black 1 1
b)
b)10 c) 0 d) Black e) Red
Points Tally Frequency
f) Simone will be able to keep track of all the different
colours and the number of them. Therefore, it Is easier 1-3 1 1
for comparison. (Accept any other possible answers) 4-6 1 1
CO
2. a)
7-9 4
1 nil
Number o Tally Frequency 10-12 nil 4
1 nil 4 13-15 nil 4
2 tttt 5 16-18 nil 4
3 M 5 19-21 tttt i 6
4 3
III 22-24 tttt 5
5 tttf 5 25-27 IIII nil 10
ittt tttt
6 Hit III 8 28-30 1 1
Ungrouped because the range of possible v£ c) The frequency table with 6 class intervals is better
small. (Accept any other possible answers) because it has a suitable range for each Interval of
c) 5 rather than a range of 3 for the frequency table
with 10 class intervals. (Accept any other possible
Number Tally Frequency
answers)
2 11 2
3 1 1 Revision (Pg 168)
1.
4 3
III
5 7 Type of music Tally Frequency
tttt II
6 4 Jazz
nil
7 tttt i 6 Classical
8 1 1 (Accept any other possible answers)
9 II 2 2. 3)4
b) 14
10 2
II
c) Delayed at previous delivery
11 1
1 d) 3 e) 3 f) Friday 9)2
12 3. a)a) Open-ended
1 1
d) Ungrouped because the range of possible values is b) Closed
small. (Accept any other possible answers) 4. a) Would you rather have a four-door car or a two-door
e) Grouped because the range of possible values is car? (Accept any other possible answers)
from 5 to 30. (Accept any other possible answers) b) How many times in a week do you eat fish? (Accept
any other possible answers)
3.
5. Suggest a solution to reduce the problem of litter in the
Range of angle Tally Frequency school playground. (Accept any other possible answers)
1 -10 6. Are you going to study after school?
nil 4
Are you going to watch a movie after school?
11 -20 tttt 5
Are you going to play after school?
21-30 tttt 5 Are you going to sleep after school?
tttt III 8 Are you going to watch TV after school?
(Accept any other possible answers)
Total 22
0 7.
Points Tally Frequency Number of qoals Frequency
0 3
1-5 II 2
1 4
6-10 tttt 5
2 6
11 -15 tttt II 7 3 5
16-20 tttt ill 8 4 1
21 -25 tttt tttt III 13 5 1
26-30 tttt 5
B
Answers
1
8. a) 5. a)^ b)^ .,2
Mass (kg) Tally Frequency
Check My Understanding (Pg 181)
6-7 nil 4 (Nim
a) I b)^ c) 39 e)|
till MM MM 1 8
8-9 ITTT tttt ittT 1 16 OC
17
10-11 ttflll 7 "lO 9'l ^>5 i)¥ j)¥
12-13 III 3
Check My Understanding (Pg 183)
Total 30
1. a)ll b)2l c)33 d)ll e)3l
b)8.8 c) 12.5kg d) 6.9kg
f)3l 9)23 h)2| i)lf
b)26 f)27 g)3, $300
9. a a) 2. a) 3 b)13 0^ d)U e)f
10
Duration (min) Tally Frequency
3. a)li b)2| c)ll d)2l e) 1 3 f)2|
81 -90 Mil 7
91 -100 tttt nil 9 Recall (Pg184)
101 - 110 tttt II 7 2. ^ ± ± 3.
n
10 • 10 10
111 - 120 III 3
Check My Understanding (Pg 187)
121 - 130 tttt III 8
131 - 140 III 3 1- a)3 b)| c)f d)| Of
141 - 150 0 2. a)< b)> c)> d) = e)> f)<
151 -160 II 2 9)< h)> i)< j)<
19
161 -170 1 1 3.
10
I I I
b)40 c)89min d)164min e) 83 min f) 14 g) 6
10. She could change the class interval range to be 5
instead of 10. Therefore, the class intervals will be 0-5,
greatest.
is
6-10, 11-15, 16-20, 21-25, 26-30, 31-35, 36-40, 4. Yg is the smallest. |
the
41-45, 46-50, 51-55, 56-60.
5.1 Is the smallest. |
greatest.
the
is
Units 6 1 i 19 5
3 ' 12 24 6
n
n
Recall (Pg174)
11 2 6 4
a) 5 b)5 c)7 d)4 7. 15 ' 7 • 5 '
3
all 5 2
8 8. 3)2-8M b)l,|,1
Check My Understanding (Pg 175)
n
1. a)2 b)l d)l e)l 9- a) T 3. 25 b)i 3 13
5' 23
50
9_ 10
g)^ in all 12^ 11 ' 12
6'9' 10
4. # ft 7 us 28 543 280 150
e-TT
50 • 800 ' 400 ' 200
r\ 9222 13790 34820 17500
8. 8
' 15000' 20000' 45000' 18000
11. 3)1,1,6, 1,0
Try and Apply (Pg 175)
1.3=1, b=^C=l US 115 482 60 103
'' 125' 1250' 250' 500
^s 2500 6000 11500 7650
' 3825' 11475' 22950' 15300
Check My Understanding (Pg 179)
1. a) 2 b)21 c) 25 d) 20 e)12 f)35
13. Adam's father
2. c)^ d)3 e)3 14. Sheila
g) 1 h)3 i)? i)i Check My Understanding (Pg 190)
3. a)l b)l c)| d)l e)f 1. a)| b)U
9)i b)il i)T5 2. 8)1 b) 1
4. a)§ ")§ 0)^ d)3 e)^ "i 3. a) 1 1 b)4
9)2 h)^ "is 4. a)2§ b)2l
Check My Understanding (Pg 194)
1. a) 1 b)1 0)2 d)l denominators are the same, we can just compare
the numerator. 18 is greater than 17, therefore, 2 4
2. a) 2 0)2 d)2 is greater.
e; 12 g)i^ 7. a) 3 b)33
12
3. a) 1 1 C)1| d)l| 8. a)^ b)47 47
1411 659 437 271
9.
6000' 3000' 2000' 1259
4. a)5| b)i^ c)10i 10.a) 4 of 24 b) ^ of 45 c) I of 40
f)3| CO h)H 11. c)| d)l
Check My Understanding (Pg 196)
12. a) $750 b) $437.50
13. a) False. ^ is more than one-half
13
1. 16h 2.
20 b)True
3.8^/ 4. 16l kg c) True
d) False. If you add 1 to the denominator, you make the
5. a) I b)i fraction smaller.
e) True
Try and Apply (Pg 196)
a) 2, 3, 4, 5, ll
Unit 9
b) 34, 212, 3, 134. 12
c) 112, 234, 314, 114, 134 Check My Understanding (Pg 207)
1. a) The rule is "multiply each term by 2 to get the next
Check My Understanding (Pg 198) term". Next two terms are 32 and 64.
1. a)5 b)7 c) 4 d)4 e)4 f)5 b) The rule is "add 5 to each term to get the next term".
2. a) 2 sweets b) 25 m c)$20 d)12m Next two terms are 30 and 35.
e) 15 min f) 30 s g) 1 mm h) 16 i) 16 kg c) The rule is "multiply each term by 5 to get the next
3. a) 15 pencils b) 18 eggs c) 30 bananas d) 10 sweets term". Next two terms are 3125 and 15625.
e) 36 apples f) $8 g) 7 plates h) 210 cents 2. a) The rule is "add 2 to each term to get the next term".
i) 6 days j) 75 cm k) 12 cm 1) 18 s Next two terms are 15 and 17.
4. 6 boys b) The rule is "add 3 to each term to get the next term".
5. 12 red balls Next two terms are 21 and 24.
6. 42 nuts c) The rule Is "add n to each term to get the next term
7. 3)3 b) $24 where n increments by 1 for each term". Next
8. 5 sweets two terms are 20 and 26.
d) The rule is "subtract 1 or 3 from each term to get the
Try and Apply (Pg 199)
next term. Subtract 3 if 1 was subtracted to a
1. 27 cm achieve the previous term. Subtract 1 if 3 was
2. 36 animals subtracted to achieve the previous term". Next two
terms are 91 and 88.
Revision (Pg 200)
e) The rule is "add 13 to each term to get the next
1. The shape that is colored is a triangle that does not
term". Next two terms are 82 and 95.
have the same height as the length of the rectangle The rule is "subtract 3 from each term to get the next
or the same base length as the width of the rectangle. f)
term". Next two terms are 85 and 82.
Therefore, John is not correct. (Accept any other g) The rule is "subtract 7 from each term to get the next
possible answers)
term". Next two terms are -13 and -20.
h) The rule is "subtract 4 from each term to get the next
1
b)4 term". Next two terms are -27 and -31.
3. a) 12 b) 72 i) The rule is "add 5 to each term to get the next term".
Next two terms are 27 and 32.
4. a)l b)| d) j) The rule is "subtract 2 from each term to get the next
13
term". Next two terms are -8 and -10.
18 k) The rule is "multiply each term by 3 to get the next
24
term". Next two terms are 2916 and 8748.
lA- 4, B- 0- 4,D- 4.E- 11 F- 4
4 G-i- I) The rule is "divide each term by 2 to get the next
20 f,K term". Next two terms are 20 and 10.
6- 3. a) 13, 15. 17 b)31, 36,41 c)11.0, 11.2, 11.4
b) 2 4 is greater. 2 4 in mixed fraction is ^-24 j d) 68. 60. 52 e)-4, -11,-18 f) 36, 49, 64
in
which
Since
188.
mixed fraction is | the 4. a)12, 3,-3 b)41, 59, 77 c)118, 82, 73
is
also
Answers
5. a) 5x, 6x b) X + 9, X + 11 Revision (Pg 218)
c) 2x + 8, 2X + 10 d)15x-1,18x-1 1. a) Next two terms are 28 and 35. The term-to-term
e) 25xy, 36xy f)125a6, 216ab rule is "start at -7 and add 7".
6. a) 13, 16, 19 b) Next two terms are 105 and 101. The term-to-term
b) 15, 22, 29. 36, 43 rule is "start at 125 and subtract 4".
c) 30, 57, 84 c) Next two terms are 75 and 86. The term-to-term
7. a) 38.5, 37, 35.5 b) 80, 70, 60 rule is "start at 20 and add 11".
c) 11, 9, 7, 5, 3, 1,-1 d)-8,-14,-20 d) Next two terms are 37 and 44. The term-to-term
8. a) 18, 22, 18. 22 b) 22 rule is "start at 2 and add 7".
e) Next two terms are -11 and -14. The term-to-term
Check My Understanding (Pg 211) rule is "start at 4 and subtract 3".
1. i) The rule is "add 2 to each term to get the next term", f) Next two terms are -3 and 1. The term-to-term rule
T^ = 2n, 150 is "start at -23 and add 4".
11) The rule is "multiply each term by 2 to get the next g) Next two terms are 43 and 34. The term-to-term rule
term", T„ = 2", 2" = 3.777.... x 10^^ is "start at 88 and subtract 9".
ill) The rule is "multiply each term by 3 to get the next h) Next two terms are 1 and The term-to-term rule
term", T^ = 3", 3^^ = 6.08.... X 10^5 is "start at 8 and divide by 2".
iv) The rule is "add 8 to each term to get the next term", i) Next two terms are 121 and 169. The term-to-term
T„ = 8n, 600 rule is "start at 1, add 2 and square the sum".
v) The rule is "multiply each term by 8 to get the next j) Next two terms are 28 and 40. The term-to-term rule
term", T^ = 8", 8^5 = 5.39.... x 10^^ is "start at -2, and add x where x starts at 2 and 2 is
vi) The rule is "multiply each term by 10 to get the next added to x after each term".
term", T^ = 10", 1 X 10^^ 2. 3)0,4,8,12 b)243, 81,27, 9
2. a) 4 b)29 c) 11, 11.5, 12, 12.5 d) 1, 0.5, 0.25, 0.125
3. 3)4,5,6,7,8 b)1,3, 5, 7, 9 3. a)T^ = 3{n + 1), 603 b) T„ = 9n-4, 1796
c)2, 13,24, 35,46 d) 0, 3,6, 9, 12 c)T||=2n + 8,408 d) T^ = n + 24, 224
e)9, 11, 13, 15, 17 f)-6,-2, 2, 6, 10 e) tI = 40000 f) T„ = + ,
4. a) 64, 81
Check My Understanding (Pg 213) b)T„ = (/7 + 2)^
a)T„ = 2n + 8, 208 b) T^ = 5n + 4, 504 c) 1024
c)T" = 4n +12,412 d) T„ = 11n + 2, 1102
e) / = 4n - 1, 399 f) T„ = 4n - 2, 398 5. a) Diagram show 3 pieces of wood added to the side of
the previous one
g) t" = 4n + 1, 401 h) T^ = 5n + 2, 502
b)4, 7, 10, 13, 16
i) en - 4, 596
The term-to-term rule is "start at 4 and add 3".
c) Number of pieces of wood: 4, 7, 10, 13, 16
Check My Understanding (Pg 216)
Multiples of 3: 3, 6, 9, 12, 15
1. 3)14,18,22
Multiples of 3 + 1 : 4, 7, 10, 13, 16
b)6, 10, 14, 18,22
T^ = 3n + 1
The term-to-term rule is "start at 6 and add 4".
d)64, 121, 334
c) Number of people: 6, 10, 14, 18, 22
6. a) Diagrams show 1 light globe added to the top and
Multiples of 4: 4, 8,12, 16, 20
right side.
Difference: 2, 2, 2, 2, 2
T^ = 4n + 2 b) Height of L: 2, 3, 4, 5, 6
Number of globes: 3, 5, 7, 9, 11
d)302
2. a) Diagrams drawn show 3, 4 and 5 section of the fence The term-to-term rule is "start at 3 and add 2".
c) Height of L: 2, 3, 4, 5, 6
interconnected.
Number of globes: 7,9, 11
b) 5, 9, 13, 17,21
Multiples of 2: 2, 4, 6,8,10
The term-to-term rule is "start at 5 and add 4".
Difference : 1, 1, 1, 1, 1
c) Number of pieces of wood: 13, 17, 21
T„=2n+1
Multiples of 4 : 12, 16, 20
Multiplesof4 + 1 : 13, 17, 21 d) 239 globes
T =4n + 1
n
di)201 pieces of wood
Unit 10
dil) 206 sections
3. a) Diagram shows number of tiles at the each sides Recall (Pg 222)
increasing by 1. Parallelogram, Rectangle, Equilateral Triangle, Kite,
b) 5, 9, 13, 17, 21 Right-Angled Triangle, Square, Trapezium, Rhombus,
The term-to-term rule is "start at 5 and add 4". Quadrilateral, isosceles Triangle, Trapezium, Triangle
c) Number of tiles: 13, 17, 21
Multiples of 4: 4, 8, 12, 16,20
Multiples of 4 + 1 : 5, 9, 13, 17, 21
T^ = 4n + 1
d) 209 tiles
Check My Understanding (Pg 226) 2. Cube - fourth net
1. a) Correct if the triangle is repiicated correctly in Cuboid - third net
different orientations Triangular Prism - sixth net
b) Correct if the rectangle is replicated correctly in Cylinder - second net
different orientations Pentagonal Prism - first net
c) Correct if the hexagon is replicated correctly in Pyramid - fifth net
different orientations 3. Equilateral Triangle, 3, 3
d) Correct if the pentagon is replicated correctly in Infinity Symbol, 2, 2
different orientations Yen Symbol, 1, 1
e) Correct if the octagon is replicated correctly in Regular Hexagon, 6, 6
different orientations Dollar Symbol, 0, 2
2. a) Rhombus b) Trapezium Extinction Symboi, 2, 2
c) Parallelogram d) Kite 4. Answers may vary, accept all symmetrical answers
Check My Understanding (Pg 228)
1. a) Cube, 6, 12. 8 b) Cuboid, 6, 12, 8 Unit 11
c) Cylinder, 2, 2, 0 d)Cone, 1,0, 1
Recall (Pg 244)
e) Sphere, 1, 0, 0
1. Describe an object using (X-Axis, Y-axis)
2. a) No
Check My Understanding (Pg 232)
b) Mark an X on points (1,1), (2,5), (4,1) and label them
1. a) Pyramid, 5, 5, 8
accordingly
b) Cube, 6, 8, 12
c) Pentagonal Prism, 7, 10, 15
d) Cuboid, 6, 8, 12 B
e) 6-Sided Pyramid, 6, 7, 12
f) Trapezoid Prism, 6, 8, 12
2. a) Triangular Prism, 5, 9, 6
b) Pyramid, 4, 6, 4
A
c) Pentagonal prism, 7,10, 15
1 2 3 4 5
Recall (Pg 233)
c) Mark an X on points (0,4), (3,1), (5,3) and label them
1. Circle the second, third and fourth shape
2. Circle the first, third and fifth shape accordingly
Draw 2 lines, 1 connecting (0,4) and (3,1) and 1
Check My Understanding (Pg 234) connecting (4,4) and (5,3)
1. a)1 b)4
2. a) yes b) no
5 k
Check My Understanding (Pg 235)
Colour in the symmetrical shapes with similar colours and
design a pattern with symmetry
Check My Understanding (Pg 237)
1. Only H and S have an order of 2
1 2 3 4 5
2. Oval has order of 2
Check My Understanding (Pg 248)
Plus-sign has order of 4
1.
Arrow-plus-sign has order of 4
Dual-triangles has order of 2
3. a) Shade the uppermost right square B
b) Line of symmetry is horizontal A
r.
c) Shade the uppermost left square
d) Line of symmetry is diagonal from left to right
e) Shade the uppermost middle square D
4. Replicate the figure but flip it so the white part looks like g' k /
an "S" /f
5. a) 1, 1 b)1,1 c)3, 3 d)4, 4 e) 2, 2 f) 0, 2
g)2,2 h)0. 1 1)1, 1 j)5,5 k)6,6 1)8,8
n 5 - 4 -3 - ? _ U
.-,1..
Revision (Pg 239)
The shape is a heptagon.
1. a) Correct if the cross is replicated correctly in different
orientations
b) Correct if the arrow is replicated correctly in different
orientations
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Math Smart - 7
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