Download Chapter 10 - Haese Mathematics

10
E
Chapter
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Positive and
negative numbers
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Contents:
A Opposites
B Combined effects
C The number line
D Addition and subtraction with negative numbers
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POSITIVE AND NEGATIVE NUMBERS (Chapter 10)
Opening problem
In indoor cricket, 5 runs are subtracted when a wicket
is lost.
Blake had only scored 3 runs when he lost his wicket.
Things to think about:
a What operation would you need to find Blake’s
score?
b Is it possible to subtract 5 from 3?
c What number can we use to display Blake’s score?
d Suppose Blake scored 6 runs on the next ball. What would his new score be?
E
Suppose Amanda has 5 cupcakes and eats 3 of them.
The number of cupcakes remaining is 5 ¡ 3 = 2.
SA
M
PL
?
Now suppose Adam has 5 cupcakes, and he wants to
eat 7. This is impossible, because once Adam has eaten
5 cupcakes, zero cupcakes remain, and there are no
more left to eat. It does not make sense to say the
number of cupcakes remaining is 5 ¡ 7 because we
cannot have less than zero cupcakes.
However, there are many situations where it does make sense to talk about numbers less than zero.
For example, suppose the temperature at Cradle Mountain,
Tasmania, is 5± C at 8 pm. Between 8 pm and midnight,
the temperature falls by 7± C. The temperature at midnight
is given by 5 ¡ 7. The answer is less than zero, so we
call it a negative number.
A
OPPOSITES
Many mathematical problems use opposites.
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² earning money is the opposite of spending money
² going up is the opposite of going down
² getting warmer is the opposite of getting cooler.
For example:
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POSITIVE AND NEGATIVE NUMBERS (Chapter 10)
Example 1
213
Self Tutor
Write the opposite of:
a winning by 7 points
b travelling 10 km north.
a The opposite of winning by 7 points is losing by 7 points.
b The opposite of travelling 10 km north is travelling 10 km south.
Instead of using words to describe opposites, we can use positive and negative numbers.
POSITIVE NUMBERS
Positive numbers are numbers which are greater than zero.
E
The positive whole numbers are 1, 2, 3, 4, 5, ....
SA
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They can be written with a positive sign (+) before the number, but we normally see them without
the positive sign and assume the number is positive.
NEGATIVE NUMBERS
Negative numbers are numbers which are less than zero.
They are written with a negative sign (¡) before the number.
¡1 is read as
“minus one” or
“negative one”.
The negative whole numbers are ¡1, ¡2, ¡3, ¡4, ¡5, ....
WORDS INDICATING POSITIVE AND NEGATIVE
Some common uses of positive and negative signs are listed in
the table alongside.
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For example, we could write “a profit of $5” as +5. The
opposite statement “a loss of $5” is written as ¡5.
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Positive (+)
Negative (¡)
above
over
increase
profit
below
under
decrease
loss
right
left
faster
win
north
east
slower
lose
south
west
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POSITIVE AND NEGATIVE NUMBERS (Chapter 10)
EXERCISE 10A
1 Write the opposite of:
a winning $20
b being 10 minutes early
c moving 2 steps to the right
d being 6 m above sea level.
2 Copy and complete the following table:
Statement
Number
a
losing by 3 points
¡3
b
c
d
e
a clock is 5 minutes fast
4 m above the water
2± C below zero
an increase of 6 kg
Opposite of statement
Opposite number
3 If north is the positive direction, write these positions as positive or negative numbers:
b 12 km north
c 15 km south
E
a 7 km south
Discussion
SA
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4 If temperatures above zero are positive, write these temperatures as positive or negative
numbers:
a 7± C below zero
b 32± C above zero
c 40± C below zero
Why do you think we choose:
² north to be positive and south to be negative
² east to be positive and west to be negative?
B
COMBINED EFFECTS
In situations where two things happen in opposite directions, we can use a diagram to help find
the combined effect.
Example 2
Self Tutor
Find the combined effect of travelling:
a 5 km north and then 1 km south
b 2 km north and then 7 km south.
a
b
1 km
5 km
2 km
N
W
4 km
E
N
7 km
5 km
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The combined effect is travelling
5 km south.
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The combined effect is travelling
4 km north.
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POSITIVE AND NEGATIVE NUMBERS (Chapter 10)
215
EXERCISE 10B
1 Henry is travelling in a lift. Find the combined effect
of going:
a up 3 floors and then down 1 floor
b up 4 floors and then down 5 floors
c down 2 floors and then up 6 floors
d down 3 floors and then down 4 floors
e down 8 floors and then up 5 floors.
Draw a diagram so
you can picture the
situation.
2 Find the combined effect of travelling:
a 10 km east and then 6 km west
b 7 km east and then 9 km west
c 4 km west and then 5 km east
d 11 km west and then 3 km east.
N
E
W
S
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E
3 Boris checks the temperature in his bedroom on a
regular basis. Find the combined effect if his bedroom
gets:
a 5± C warmer, then 2± C cooler
b 1± C warmer, then 6± C cooler
c 4± C cooler, then 11± C warmer
d 8± C cooler, then 7± C warmer.
4 Find the combined effect of:
a earning $50 and then spending $20
b earning $5 and then spending $15
c spending $10 and then earning $30
C
d spending $40 and then earning $40.
THE NUMBER LINE
We have seen previously that we can place positive
numbers on a number line.
0 +1 +2 +3 +4 +5
We can also place negative numbers on a number line
by extending the number line to the left:
negative whole
numbers
The number line
continues forever
in both directions.
positive whole
numbers
-5 -4 -3 -2 -1
0
1
2
3
4
5
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Zero is neither positive nor negative.
The negative whole numbers, zero, and the positive whole numbers are together known as the
integers.
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POSITIVE AND NEGATIVE NUMBERS (Chapter 10)
In the same way that earning $5 and spending $5 are opposites, we say that +5 and ¡5 are
opposites. They are the same distance from 0, but on opposite sides of 0.
Example 3
Self Tutor
Write the opposite of:
a +6
b ¡3
a The opposite of +6 is ¡6.
b The opposite of ¡3 is +3.
Discussion
Does zero have an opposite?
E
We can use a number line to compare the sizes of different numbers and arrange them in order.
SA
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As you move along the number line from left to right, the numbers increase. The number furthest
to the right is the greatest number.
numbers increase
-6 -5 -4 -3 -2 -1
0
1
2
+2 is greater than ¡3 because it is further to
the right on the number line.
3
As you move along the number line from right to left, the numbers decrease in size. The number
furthest to the left is the least number.
numbers decrease
-6 -5 -4 -3 -2 -1
Example 4
0
1
2
¡5 is less than ¡3 because it is further to the
left on the number line.
3
a Place ¡7 and ¡2 on a number line.
a
Self Tutor
b Which of these numbers is larger?
-2
-7
-10
-5
0
5
b ¡2 is further to the right on the number line, so ¡2 is larger than ¡7.
EXERCISE 10C
1 State whether the following integers are positive, negative, or neither:
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f 0
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POSITIVE AND NEGATIVE NUMBERS (Chapter 10)
217
2 Write the opposite of:
a +7
b ¡1
c 2
d ¡4
e +11
f ¡13
3 Write the values of A, B, C, and D:
D
B
-10
C
A
-5
0
5
10
4 Place the following numbers on a number line. Use a different number line for each part.
a 2, ¡5, 1, ¡3
c ¡2, 0, 7, ¡4
b ¡8, 4, ¡1, 6
d ¡9, 3, ¡7, ¡6, 5
5 For each pair of values:
i place the values on a number line
a 2 and ¡1
ii determine which value is larger.
b ¡6 and ¡3
c ¡5 and 3
d ¡5 and ¡8
E
6 Consider the numbers 4, ¡8, 0, ¡2, ¡5, and 1.
a Place the numbers on a number line.
b Use the number line to write the numbers in order of size, from smallest to largest.
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7 The table alongside shows the elevation above sea level
of various locations.
a Place these values on a number line.
b Which of these locations are below sea level?
c Which of these locations has the:
i highest elevation
ii lowest elevation?
D
Location
Brisbane
Lake Eyre
Elevation
15 m
¡16 m
Hobart
New Orleans, USA
4m
¡2 m
Wellington, NZ
3m
ADDITION AND SUBTRACTION WITH
NEGATIVE NUMBERS
We can use a number line to perform additions and subtractions involving negative numbers.
² To increase a number, we move right along the number line.
² To decrease a number, we move left along the number line.
Example 5
Self Tutor
Use a number line to find:
a 5¡8
b ¡7 + 3
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a We start at 5, and move
8 units to the left.
So, 5 ¡ 8 = ¡3
b We start at ¡7, and
move 3 units to the right.
So, ¡7 + 3 = ¡4
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Subtracting 8 means we
decrease the number by
8. We move to the left.
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POSITIVE AND NEGATIVE NUMBERS (Chapter 10)
EXERCISE 10D.1
1 Use
a
e
i
a number line to find:
3¡5
b ¡1 + 4
¡4 ¡ 4
f 7 ¡ 12
1¡9
j ¡5 + 5
2 Use a number line to find:
a 2+3¡6
d 3 ¡ 10 + 1
c 0¡6
g ¡3 + 0
k ¡11 + 7
d ¡9 + 2
h ¡8 ¡ 5
l ¡6 ¡ 7
b ¡7 + 4 ¡ 2
e ¡8 + 6 ¡ 7
c ¡5 + 8 + 3
f ¡9 ¡ 5 ¡ 2
Example 6
Self Tutor
A lift started 2 floors above ground level. It travelled down 5 floors, then up 1 floor.
How many floors above or below ground level is the lift now?
E
The lift starts at +2 or just 2. We therefore
need to find 2 ¡ 5 + 1.
Using a number line, 2 ¡ 5 + 1 = ¡2.
0
SA
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-5 -4 -3 -2 -1
1
2
3
) the lift is now 2 floors below ground level.
3 A lift started 1 floor below ground level. It travelled 4 floors up, then 6 floors down.
How many floors above or below ground level is the lift now?
4 At midnight, the temperature in Canberra was ¡3± C. Between midnight and 9 am, the
temperature dropped by 4± C, then rose by 6± C. What was the temperature at 9 am?
5 A football team was 13 points ahead at quarter time.
They lost the 2nd quarter by 20 points, won the 3rd
quarter by 10 points, and lost the 4th quarter by
7 points.
a By how many points was the team winning or
losing at:
i half time
ii three quarter time?
b Did the team win or lose the game? By how
much?
ADDING A NEGATIVE NUMBER
Freddy the frog is sitting on the number line. He is performing an addition, so he
faces the right.
0
1
2
3
4
5
6
7
8
9 10
DEMO
To find 5 + 3, Freddy starts at 5 then hops 3 units
forwards, to the right.
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So, 5 + 3 = 8.
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POSITIVE AND NEGATIVE NUMBERS (Chapter 10)
Freddy can use the same approach to find 5 + ¡3.
He again starts at 5, facing the right. To add
negative 3, he hops 3 units backwards. He ends
up 3 units to the left of his starting point.
0
1
2
3
4
5
6
7
8
9 10
7
8
9 10
So, 5 + ¡3 = 2.
Notice also that 5 ¡ 3 = 2.
Adding a negative number is the same as subtracting its opposite.
For example, 1 + ¡4 is the same as 1 ¡ 4.
SUBTRACTING A NEGATIVE NUMBER
To perform a subtraction, Freddy faces the left.
0
1
2
3
4
5
6
E
To find 7 ¡ 2, Freddy starts at 7 then hops 2 units
forwards, to the left.
SA
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So, 7 ¡ 2 = 5.
To find 7 ¡ ¡2, Freddy starts at 7, again facing
the left. To subtract negative 2, he hops 2 units
backwards. He ends up 2 units to the right of his
starting point.
0
1
2
3
DEMO
4
5
6
7
8
9 10
So, 7 ¡ ¡2 = 9.
Notice also that 7 + 2 = 9.
Subtracting a negative number is the same as adding its opposite.
For example, 6 ¡ ¡3 is the same as 6 + 3.
Example 7
Self Tutor
Simplify and then find:
a 3 + ¡7
b 3 ¡ ¡7
3 + ¡7
=3¡7
= ¡4
a
c ¡3 + ¡7
3 ¡ ¡7
=3+7
= 10
b
c
¡3 + ¡7
= ¡3 ¡ 7
= ¡10
d ¡3 ¡ ¡7
d
¡3 ¡ ¡7
= ¡3 + 7
=4
EXERCISE 10D.2
1 Simplify and then find:
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c ¡6 + ¡2
g ¡5 + ¡9
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b 6 ¡ ¡2
f 5 ¡ ¡9
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a 6 + ¡2
e 5 + ¡9
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d ¡6 ¡ ¡2
h ¡5 ¡ ¡9
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POSITIVE AND NEGATIVE NUMBERS (Chapter 10)
2 Simplify and then find:
a 10 + ¡4
e ¡9 ¡ ¡6
i ¡4 + ¡5
b 1 ¡ ¡7
f ¡4 + ¡9
j 2 ¡ ¡11
c ¡3 + ¡5
g 0 ¡ ¡5
k ¡3 + ¡4
d ¡8 ¡ ¡14
h ¡11 ¡ ¡18
l ¡12 ¡ ¡4
3 Simplify and then find:
a 2 + 7 + ¡3
d ¡3 + ¡8 ¡ ¡5
b 8 ¡ 5 + ¡4
e 7 + ¡11 + ¡1
Example 8
c 10 ¡ ¡6 ¡ 8
f ¡5 + 14 + ¡9
Self Tutor
Find the difference between:
a 2 and ¡6
b ¡11 and ¡1
The difference between two
numbers is the greater number
minus the lesser number.
SA
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E
a 2 is to the right of ¡6 on the number line, so 2 is greater
than ¡6.
The difference between 2 and ¡6 = 2 ¡ ¡6
=2+6
=8
b ¡1 is to the right of ¡11 on the number line, so ¡1 is
greater than ¡11.
The difference between ¡11 and ¡1 = ¡1 ¡ ¡11
= ¡1 + 11
= 10
4 Find the difference between:
a 3 and ¡4
d 0 and ¡6
g ¡4 and 10
b ¡7 and 2
e 11 and ¡8
h ¡7 and ¡5
c ¡4 and ¡8
f ¡13 and ¡9
i 5 and ¡7
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5 A seagull is flying 5 metres above sea level, a
kayaker is paddling at sea level, a snorkeller is
swimming 2 metres below sea level, and a dolphin
is 6 metres below sea level.
a Write an integer to describe the height above
sea level of each person or animal.
b Find the distance between the:
i kayaker and the diver
ii seagull and the dolphin
iii dolphin and the kayaker
iv diver and the dolphin.
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POSITIVE AND NEGATIVE NUMBERS (Chapter 10)
6 Write the following statements using directed numbers and calculate the resulting quantity:
a
b
c
d
e
f
g
spending $50 then spending $40
a fall in temperature of 20± C followed by a rise of 13± C
a profit of $310 followed by a loss of $97
a fall in temperature of 5± C followed by a fall of 8± C
a journey 21 km north followed by a journey 29 km south
winning by 13 points in the 1st half then losing by 17 points in the 2nd half
a loss of 3 kg in weight followed by a loss of 2 kg in weight.
Team A
¡50
400
900
Team B
810
140
¡300
E
7 Team A is playing Team B in the card game canasta. This
table shows the number of points scored by each team for
Hand 1
the first three hands.
Hand 2
a Find the difference in points scored by the teams in:
Hand 3
i hand 1
ii hand 2
iii hand 3.
b Find the total number of points scored by each team so far.
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8 This table shows the minimum and maximum temperatures in Mount Hotham, Victoria, during
a week in July 2012:
Minimum temperature
Mon
¡5± C
Tue
¡2± C
Wed
¡3± C
Thu
¡7± C
Fri
¡5± C
Sat
¡4± C
Sun
¡3± C
Maximum temperature
1± C
¡1± C
¡2± C
¡1± C
1± C
0± C
4± C
a Which day had the:
i warmest maximum temperature
ii coolest maximum temperature
iii warmest minimum temperature
iv coolest minimum temperature?
b Find the difference between the minimum and
maximum temperatures on:
i Monday
ii Thursday
iii Saturday.
9 Steve, Paul, Peter, and William played together in the first round of a
golf tournament.
Each player’s score shows how many shots above or below the ‘par’
score they obtained. In golf, a lower score is better.
a Rank these players in order, from best to worst.
b Find the difference between:
i Steve’s score and Paul’s score
ii Paul’s score and Peter’s score.
Player
Score
Steve
Paul
Peter
William
+2
¡3
¡1
+5
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c In the next three rounds, William scores ¡4, ¡3, and +1. Find William’s combined score
for the tournament.
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POSITIVE AND NEGATIVE NUMBERS (Chapter 10)
10 The children at a party are trying to guess how many lollies are in a jar. The results of the
game are shown below. A positive number means that the child guessed too high, and a
negative number indicates that the child guessed too low.
Child
Max
Xavier
Lauren
Molly
Result
+30
¡12
¡4
+21
Claire
Jack
Gabrielle
Luis
Kevin
+3
¡24
+9
¡13
¡7
a
b
c
d
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E
How many children guessed too low?
How many children were within 10 of the correct answer?
Which child’s guess was the closest?
Find the difference between:
i Xavier’s guess and Kevin’s guess
ii Gabrielle’s guess and Luis’ guess.
e Jack’s guess was 50 lollies.
i How many lollies were in the jar?
ii What was Molly’s guess?
Investigation
Calculator use
We can use our calculator to perform operations with negative numbers. We use the
+/¡
or
(¡) button to write negative numbers.
For example, to find ¡3 ¡ ¡2, press
+/¡
3 ¡
+/¡
2 = .
What to do:
1 Use your calculator to find:
a ¡10 + 8
d ¡31 + 49 + ¡60
b 23 ¡ 48
e 19 ¡ ¡83 + ¡43
c ¡57 + 39
f ¡124 + ¡71 ¡ ¡94
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2 Use your calculator to solve the following problems:
a Los Angeles has an altitude of 113 m, and the Dead Sea has an altitude of ¡423 m.
Find the difference between their altitudes.
b Harry’s credit card balance was ¡$347 at the start of the month. During the month
he bought a dishwasher for $549, then made a credit card repayment of $250. What
is his credit card balance now?
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POSITIVE AND NEGATIVE NUMBERS (Chapter 10)
223
Game
This game can be played by 2 or more people.
You will need: Two sets of cards with the numbers ¡15 to 15 written
on them (62 cards in total). You can make your own, or
print them off by clicking on the icon alongside.
¡15 ¡14 .... ¡1
0
1
....
14
15
¡15 ¡14 .... ¡1
0
1
....
14
15
PRINTABLE
CARDS
What to do:
1 Shuffle the cards, then deal 6 cards to each player. Place the remaining cards face down
in a pile.
¡8
12
¡4
and
7
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Examples of sets include
E
2 Select a player to go first. The player takes a card from the top of the pile. The player
then looks at his cards, and tries to form a set of 3 cards which sum to zero.
¡7
0 .
3 If the player can form a set, the player puts the cards to one side, and then takes another
turn. If not, play passes to the next player.
4 Play continues until all of the cards in the pile have been taken. The winner is the player
with the most sets.
KEY WORDS USED IN THIS CHAPTER
² integer
² number line
² negative number
² opposite
² negative sign
² positive number
Review set 10
1 Write the opposite of:
a travelling 10 km south
b getting 3 cm shorter.
2 Find the values at point A, B, and C.
C
A
-10
-5
0
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b ¡4 + 7
e ¡8 ¡ 3 + 7
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
4 Use a number line to find:
a 6 ¡ 10
d 5 ¡ 10 + 3
5
5
a Place the values ¡7 and ¡5 on a number line.
b Determine which of the values in a is larger.
3
cyan
B
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AUS_06
224
POSITIVE AND NEGATIVE NUMBERS (Chapter 10)
5 Isabella ran a lemonade stall at a school festival.
She made a $10 profit in the first hour, a $25 loss
in the second hour, and a $7 profit in the third hour.
Find the total profit or loss made by Isabella over
the three hours.
6 Simplify and then find:
a 3 + ¡8
d 9 + ¡9
b 5 ¡ ¡5
e 11 + ¡7 ¡ ¡1
c ¡6 ¡ ¡13
f 2 + ¡10 ¡ ¡4
Multiple Choice
E
Practice test 10A
1 What is the combined effect of losing $40 and then winning $30?
B losing $20
C losing $10
D winning $10
E winning $70
SA
M
PL
A losing $70
2 Which of the following integers is negative?
A 1
B +5
C 0
D ¡3
E 2
3 Which number is indicated by point X on this number line?
X
-10
-5
A 7
0
B 8
5
C ¡7
10
D ¡9
E ¡8
C 0
D 3
E ¡7
C ¡2
D 4
E 18
4 Which of the following numbers is the largest?
cyan
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50
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
6 The scores of three contestants at the end
of a game show are given alongside.
What is the difference between Phil’s score
and Janice’s score?
A 70
B 15
C 55
D ¡15
E ¡55
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Y:\HAESE\AUS_06\AUS06_10\224AUS06_10.cdr Wednesday, 20 March 2013 1:33:56 PM BRIAN
PIERRE
PHIL
JANICE
55
-15
40
95
5 The value of ¡3 ¡ 11 + 10 is:
A ¡24
B ¡4
100
B ¡6
75
A 4
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AUS_06
POSITIVE AND NEGATIVE NUMBERS (Chapter 10)
Practice test 10B
225
Short response
1 Find the combined effect of:
a going up 5 floors and then down 7 floors
b travelling 8 km east and then 2 km west
c getting 3± C warmer and then 9± C cooler.
2 Write the opposite of:
a +5
b ¡8
c 12
3 Place the following numbers on a number line: ¡9, 4, 0, ¡2, 8.
4 Find:
a 11 + ¡1
b 3 ¡ ¡9
c ¡10 ¡ ¡10
5 Find the difference between:
a 4 and ¡4
b ¡9 and ¡2
d ¡4 + 13 + ¡8
E
c ¡3 and 0
SA
M
PL
6 In a spelling quiz, students were awarded points
for answering questions correctly, and they lost
points for answering questions incorrectly. Nick
scored 7 points, Teresa scored 12 points, and Brett
scored ¡4 points.
Find the difference between:
a Teresa’s score and Brett’s score
b Brett’s score and Nick’s score.
Practice test 10C
Extended response
1 The top of a tree is 5 metres above ground level.
A bird in the tree is 3 metres above ground level,
the tree’s roots are 1 metre below ground level,
and a pipe is 2 metres below ground level.
a Write a positive or negative number to
describe the height above ground level of
each object.
b Find the difference in height between the:
i tree top and the roots
ii bird and the pipe
iii roots and the pipe.
cyan
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Y:\HAESE\AUS_06\AUS06_10\225AUS06_10.cdr Wednesday, 20 March 2013 1:42:49 PM BRIAN
95
100
50
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75
25
0
5
95
100
50
75
25
0
5
95
100
50
Find the value of ¡4 + ¡4 + ¡4.
Explain why ¡4 + ¡4 + ¡4 is the same as 3 £ ¡4.
Use a and b to find the value of 3 £ ¡4.
Write a rule which describes how to multiply a positive number by a negative number.
Use your rule to find 5 £ ¡7. Use your calculator to check your answer.
75
25
0
a
b
c
d
e
5
95
100
50
75
25
0
5
2
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226
POSITIVE AND NEGATIVE NUMBERS (Chapter 10)
3 Suppose A owes B $11, B owes C $13, and C owes A $5.
a Use positive and negative numbers to complete this table:
Amount B owes A ¡$11
Amount B owes C
Amount A owes B $11
Amount A owes C ¡$5
Amount C owes A
Amount C owes B
b Find the sum of each column to find the total amount owed by:
i A
ii B
iii C.
c Explain how all three debts can be repaid in only two payments.
Game
Lucky Dip
Lucky Dip is a game for two people.
E
How to play:
1 Each player prints a grid like the ones alongside.
This sheet represents their Lucky Dip box
containing 16 small bags. Each player marks any
3 squares with the numbers 2, 4, and 5.
2 represents a bag containing $2, 4 represents
a bag containing $4, and 5 represents a bag
containing $5. All the other bags are empty.
Joanne
A
B
E
F
I
J
M
N
O
D
A
G
H
E
K
L
I
J
M
N
SA
M
PL
5
Troy
C
2
P
4
4
B
F
2
C
D
G
H
K
L
O
P
5
2 Players take turns to pick a bag from their opponent’s Lucky Dip box, by calling the letter
of a square.
3 If a player does not get a bag containing money, then he or she loses $2. If a bag containing
money is selected, then that amount is gained.
4 The player with the most money after 8 rounds each is the winner, unless one player has
gained all of the opponent’s money in less than 8 rounds. Each player must have the same
number of selections.
Sample game:
Consider the Lucky Dip boxes for
Joanne and Troy above.
Joanne
Selection Score
C
¡2
J
¡4
K
¡6
A
¡2
H
3
N
1
F
3
Round
1
2
3
4
5
6
7
The game ends after 7 rounds, with
Joanne winning.
PRINTABLE
GAME
Troy
Selection
G
P
L
A
N
M
B
Score
¡2
2
0
¡2
¡4
¡6
¡1
cyan
magenta
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Y:\HAESE\AUS_06\AUS06_10\226AUS06_10.cdr Wednesday, 3 April 2013 5:27:10 PM BRIAN
95
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
95
100
50
75
25
0
5
Print two pages and play against a partner!
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AUS_06