Volume of a
Rectangular Prism
Quick Review
You can use a formula to find the volume of a rectangular prism.
The volume is the product of the prism’s length, width, and height.
Volume = length X width X height
V=€ X wxh
This rectangular prism is 7.0 cm long,
3.5cm wide, and 2.3 cm high.
Volume = 7.0 cm X 3.5 cm X 2.3 cm
2 X 2.3 cm
= 24.5 cm
3
= 56.35 cm
2.3cm
7.0 cm
.
3
The volume of the prism is 56.35 cm
These
a
a
ii
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.
.
.
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a
a
•
•
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ma
a
am....
1. Find the volume of each rectangular prism.
c)
b)
a)
cm
0.5 cm
3.0 cm
1.5 c
1.5 cm
4.0 cm
e)
d)
1.5 cm
f)
1.2 cm
2.0 cm
6cm
3.0 cm
0.5 cm
6 cm
I
86
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____________
L!1IT_7
____________
Using a Questionnaire
to
Gather
Data
Quick Review
Here are some guidelines for writing questions for a questionnaire.
The question should be understood in the same way by all people.
Instead of asking: Do you play video games a lot? D Yes C No
Ask: How many hours a week do you spend playing
video games?
>
Each person should find an answer he would choose.
Instead of asking: What’s your favourite subject? C Math C Science
Ask: What’s your favourite subject?
C Math C Science C Other
The question should be fair. It should not influence a person’s answer.
If it does, it is a biased question.
Instead of asking: Do you prefer boring documentaries or hilarious
sitcoms?
Ask: What kind of TV shows do you prefer? C Documentaries
C Sitcoms C Dramas C Reality Shows C Other
TryThese
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1. Write better questions.
a) Do you get a lot of sleep on school nights?
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C Yes C No
b) What is your favourite reality show? C Survivor C The Amazing Race
c) Do you prefer greasy potatoes or healthy carrots?
88
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UNIT 7
Conducting Experiments
to Gather Data
Quick Review
>
m)
Solomon wanted to answer this question:
Is a thumbtack more likely to land
pointed end up or pointed end sideways?
To find out, Solomon
dropped 10 thumbtacks
a total of l0times.He
recoided the results in
a tally chart.
(
Th
)
Pointed End Up Pointed End Sideways
fffH++F ffl+H+FfH+fFF
fFFfH+fHHH +fH+fH+R
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From the data, Solomon concluded that a thumbtack is more likely to
land with the pointed end up than with the pointed end sideways.
Try These
q
4
1. a) Repeat Solomon’s experiment.
Record your results in the
Pointed End Up Pointed End Sideways
tally chart.
b) How do your results
compare with Solomon’s?
2. Is a penny more likely to come up heads
or tails?
Flip a penny 30 times. Record the results in
the tally chart.
What conclusion can you make?
90
Heads
Tails
Graphs
Interpreting
Quick Review
Number of Students at Elm School
This graph is a series of points
that are not joined.
It shows discrete data.
There are gaps between values.
Usually, discrete data represent
things that can be counted.
5OO
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Growth of Sunflower
> This graph shows consecutive points
r
--t---oD-
joined by line segments.
This is called a line graph.
It shows continuous data.
Continuous data can include any
value between data points.
Time, money, temperature, and
measurements are continuous.
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Try These
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1. Would you use a series of points or a line graph to display each set of data?
a) the diameter of a maple tree over 10 years
b) the number of hot dogs sold on Hot Dog Day
C)
the length of a snake as it grows
d) the population of Richmond, BC, from 2005 to 2008
92
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UNIT 7
4
Drawing Graphs
(
Quick Review
This table shows the changes
in temperature from 8:00 am
to 12:00 pm on Jake’s
birthday.
.
4±,,
Temperature (°C)
14
15
17
18
20
Time
8:00am
9:00am
10:00am
11:00am
12:00pm
Temperatures on
Jake’s Birthday
To display these data:
• Draw and label 2 axes.
• Choose an appropriate scale for each axis.
• Mark points for the data.
• Both time and temperature are continuous.
So, join consecutive pairs of points.
• Give the graph a title.
z1JH±hE::
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TryThese
p
1. Eric jogged every day from Monday to Friday.
He recorded the distances in a chart.
Display these data in a graph.
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Distance (km)
1.0
1.5
2.0
2.5
3.5
p
p
•
*
Distances Eric Jogged
4
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UNIT
7
Choosing an
Appropriate Graph
(*.3’
Quick Review
When you decide which type of graph to use, choose a graph that best
represents the data.
How We Get to School
Refreshment Sales
14
12
10
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Method
of Travel
-
Double Bar Graph
Bar Graph
Our Car Trip
Favourite Kinds of TV Shows
Comedy
Sports
o]I1aFe
RiIl
Reality
Drama
iiiei
ó
10votes
Pictograph
Line Graph
S
•
•
•
*
9
*
9
0
1. Draw a graph to display these data.
Our Favourite Seasons
Number
Number
Season
of Girls
of Boys
Spring
6
4
Summer
9
12
Fall
6
7
Winter
5
6
96
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_________
Theoretical Probability
Quick Review
This table shows the possible
outcomes when 2 dice are
rolled and the numbers
are added.
56
4
3
2
1
234567
1
8
7
6
5
4
3
2
9
8
7
6
5
4
3
10
9
8
7
6
5
4
9 10 11
8
7
56
7- -8— 9 l0 11 12..
6
+
From the table:
There are 36 possible outcomes.
18-outcomes are odd sums.
18 outcomes are even sums.
•
—‘
We say:The probability of getting an odd sum is 18 out of 36.
We write the probability of an odd sum as a fraction:
This probability is a theoretical probability.
Number of favourable outcomes
Number of possible outcomes
=
Theoretical probability
The probability of an odd sum is
Since
=
.
The probability of an even sum is
the probability of getting an odd sum or an even sum is
equally likely.
TryThese
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.
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,
a
a.
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a
a...
1. A bag contains 10 white marbles and 8 black marbles.
A marble is picked at random.
What is the probability
that a black marble is picked?
2. 16 girls and 13 boys put their names in a bag.
One name is drawn from the bag. What is the probability
that a boys name will be drawn?
98
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______
______
______
______
______
______
______
______
Experimental
Probability
Quick Review
Saul spun the pointer on this spinner 10 times.
The theoretical probability of landing on the letter A is
Here are Saul’s results.
Letter
Number of Times
B
1
A
6
C
2
,
or
D
1
The experimental probability is the
likelihood that something occurs based on the
results of an experiment.
Experimental probability
=
Number of times an outcome occurs
Number of times the experiment is conducted
The experimental probability of landing on the letter A is
This is different from the theoretical probability.
-,
or
> Saul combined the results from 10 experiments.
Letter
Numberof Times
A
B
C
51
19
8
D
22
The experimental probability of landing on the letter A is
The experimental probability is close to the theoretical probability.
The more trials we conduct, the closer the experimental probability
may come to the theoretical probability.
Try These
.
*
.
.
a
a
1. Look at the table of Saul’s individual results.
What is the experimental probability of landing on:
i) B?
ii) C?
iii) D?
iv) B or C?
2. Look at the table of Saul’s combined results.
What is the experimental probability of landing on:
I) B?
100
ii) C?
iii) D?
iv) B or D?
v) A or D?
.
a
a
_________
UNIT 8
RN? 1%
4
Drawing Shapes on a
Coordinate Grid
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Quick Review
To describe the position of a shape
on a grid, we use ordered pairs.
The numbers in an ordered pair
are called coordinates.
The first coordinate tells
how far you move right.
The second coordinate tells
how far you move up.
The point A has coordinates (4,6).
We write: A (4,6)
Try These
1. Match each ordered pair with a letter on the grid.
a) (20,15)
b) (25,30)
c) (5,5)
---i!
- 10
d) (20,0)
e) (20,25)
2. a) Plot each point on the grid.
A(2,3)
B(5,7)
C(7,7)
D(8,5)
E (6, 2)
0
8
7
E
20i 23 4 567
b) Join the points in order.Then join E to A.
What figure have you drawn?
102
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8.
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5 1015.O2530
UNIT
Transformations on a
Coordinate Grid
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2
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Quick Review
4)
We can show transformations on a coordinate grid.
104
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>
Rotation
Reflection
) Translation
10
9
F’
E
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t1E
21
1D
12345678910
Horizontal axis
12345678910
Horizontalaxls
1 2345678910
Horizontal axIs
—
Quadrilateral DEFG was Quadrilateral JKLM was
reflected in a horizontal
translated 4 squares
right and 5 squares up. line through the
vertical axis at 5.
Try These
•
4
1. a) Identify this transformation.
b) Write the coordinates of the
vertices of the quadrilateral and
its image.
I
t
Triangle PQR was
rotated 900
counterclockwise
about vertex R.
—
10
Kj/L
9’
8’
7.
6
5.
4.
3.
2
0’
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1234 5 6 7 8 9 10
Horizontal axis
104
3
UNIT 8
---
Successive
Transformations
‘41
I
Quick Review
1’•
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ml
The same transformation can be applied to a shape more than once.
>
When a shape is transformed 2 or
more times, we say the shape
undergoes successive transformations.
Quadrilateral A”B”C”D” is the image
of Quadrilateral ABCD after 2
successive translations.
/-
D
___________
12345678
Horizontal xls
The same is true for rotations and reflections.
Try These
1. Make 2 successive translations of
3 squares right and 1 square up.
“It
A
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q
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‘-F
2. Rotate Trapezoid PQRS 1800 about
vertex Q.
Then rotate the image 180° about
vertex S
Draw and label each image.
J
106
-a
UNIT 8
Combining
Transformations
Quick Review
A combination of 2 or 3 different types of transformations can be
applied to a shape.
To identify the transformations, we can work backward.
> Can you find a pair of transformations
that move Trapezoid DEFG to its
final image?
1 2345678 91G
Horizontal axis
1. D’E’FG’ is a reflection in a vertical line
through 5 on the horizontal axis.
2. D”E”FG” is a rotation of 900 clockwise
about vertex F.
j
12345678910
Horizontal axis
Try These
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t
1. Describe a pair of transformations that
8
7
move LLMN to its image.
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t
3
>
2
N
lmage
4
1 2 3 4 5 6 7 8 9 10
Horizontal axis
108
4
4
Creating Designs
We can use transformations of one or more shapes to create
a design.
> Start with Hexagon A.
Translate the hexagon 1 square right
and 3 squares down to get Image B
-
Translate Image B 2 squares left to get
ImageC.
Translate Image C 1 square left and
3 squares down to get Image D.
Translate Image D 2 squares right to
get Image E.
Translate Image E 2 squares right to
get Image F.
-
—
ro
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Try These
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110