17-apr-15created by mr. lafferty maths dept ordering integers integers add / sub mathematically...
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
Ordering integers
IntegersIntegersw
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Add / Sub Mathematically
Letters and Numbers
Multiplying Integers
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Dividing Integers
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
Starter QuestionsStarter Questionsw
ww
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.com 30% of £ 270 = £ 81Q1. Explain why
Q2. How many Euros do I get for £20 if exchange rate is £1 1.5 €
Q3. The answer to the question is 90. What is thequestion.
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Deptww
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1.1. To be put integers in To be put integers in order of size.order of size.
1. To understand how to add positive and negative numbers using the thermometer as an aid.
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IntegersIntegers
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Deptww
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IntegersIntegersS33
Definition : An INTEGER is a negative or positive whole number, including 0.
e.g. -2, -1, 0, 5, 100
Note : -2.5, -1.2, 23.5 Are NOT INTEGERS
Write down 3 places where negative numbers are used
Temperature Sea Level
Coordinate Grid
Profit and Loss
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Deptww
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1
4
1211
10
7
98
65
32
0-1
-4
-12
-11-10
-7
-9-8
-6-5
-3-2
Negaive -
Positive +
12 > 4
-2 > -3
-4 < -1
Integers can be representedon a thermometer or number line.
IntegersIntegersS33
The further to the top a number isthe bigger it is.Greater
than
Less than
-3.5 < -2.8
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Deptww
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1 32 540
1
3
2
5
4
1 32 40
-2
1
-1
32
Plot the point(3,2)
(-2,2)x - axis
y - axis
x-coordinate is 3
y-coordinate is 2origin
-3
-4 -2-3 -1
Plot the point that makesshape a parallelogram.
Coordinate Grid
(-4,-2)
IntegersIntegersS33
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 2.1
Ch2 (page 23)
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IntegersIntegersS33
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
Starter QuestionsStarter Questionsw
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Q2. How many euros do I get for £10 if exchange rate is £1 1.4 €
Q3. The answer to the question is 30. What is thequestion.
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Deptww
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1.1. To be able to write down To be able to write down mathematically the mathematically the addition and subtraction addition and subtraction of both positive and of both positive and negative integers.negative integers.
1. To explain how to write down mathematically addition and subtraction of negative integers.
Negative Negative NumbersNumbers
Addition & SubtractionS33
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
NegativeNumbers
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1
4
1211
10
7
98
65
32
0-1
-4
-12
-11-10
-7
-9-8
-6-5
-3-2
(a) 12 + 4 =
(b) 10 + ( - 8) =
(c) -7 – (- 10) =
2
3
16
Start at 12
Go up 4
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replace by single “-”
“- -” side by side
replace by single “+”
10 - 8 =
-7 + 10 =
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
= -4
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(1) 3 - 7
(2) 4 + (-9)
(3) -7 – (- 8)
(4) -2 + (-12)
(5) -5 – (-25)
(6) 8 + (-9)
Examples
= -5
= 1
= -14
= 20
= -1
Negative Negative NumbersNumbers
Remember
“+ -” = -
“- -” = +
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Ex 3.1 to 4.2
Ch2 (page 26)
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IntegersIntegersS33
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
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-2
1. 21% of £ 300
2. True or f alse :
(a) -1 - (-1) = 2 (b) - 3 - (5 - (-4)) = - 6
(c) - 6 + 10 - ( - 3) = 7
3. Does 3.5 10 = 0.35
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18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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2.2. Solving expressions Solving expressions showing working.showing working.
1. To explain the process of working out expressions by substitution method.
1.1. Understand process of Understand process of substitution.substitution.
SubstitutionSubstitutionS33
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
1 If a = 2 and b = 14 evaluate
a + b
2 +14=
= 16
Sub in a=2Sub in b=14
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SubstitutionSubstitutionS33
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
If a = 3 and b = -9 evaluate
a - bRemember “- -” replace by “+”
3 - (-9)=
= 3 + 9
2
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SubstitutionSubstitution
= 12
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18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
3 If a = 3 and b = 9 evaluate
b2 – a2
Remember b2 means b x b
9x9 – 3x3
81
- 9== 72
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SubstitutionSubstitutionS33
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
If a = 5 and b = 6 evaluate1. a + b2. ab
3. 3a
4. b - a
5. 4b
6. 3ab
=11=30=15
=1
=24=90w
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SubstitutionSubstitutionS33
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
Now try Exercise 5.1
Ch2 (page 28)Q1 – Q4
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SubstitutionSubstitutionS33
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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2.2. Be able to tidy up like Be able to tidy up like terms.terms.
1. To explain the process of tidying up expressions.
1.1. Understand the term like Understand the term like terms.terms.
Tidying Up Like TermsTidying Up Like TermsS33
18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Tidying Termsw
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1, 3 , 5, -6, 8 are like terms simple numbers
x, 3x , -2x are like terms in x
x2, 3x2, -2x2 are like terms in x2
x is NOT the same as x2
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18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Tidying Termsw
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3a2 – 2a2 =a2
3x – 4y – x – 2y =2x – 6y
4x2 – x – y + 6x2 = 10x2 – x - y
Examples
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6p2 – q – 3q + 6p2 =12p2 – 4q
18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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1 3 11
2 4 4
1. Share 36 in the ratio 3:9
1 12. Calculate of
2 2
3. Does Explain ?
4. Explain how we solve - 3x +9 27
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. Explain how to multiply positive and negative integers.
1. Understand how to multiply positive and negative integers.
IntegersIntegersMultiplication
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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IntegersIntegers
1 1 xx (-2) = (-2) =
Multiplying Integers
5 5 x x (-8) =(-8) =
(-3) (-3) xx 3 = 3 =
(-4) (-4) xx 5 = 5 =
(-2) (-2) xx (-1) = (-1) =
(- 2) (- 2) xx (-5) = (-5) =
(-5) (-5) x x (-5) =(-5) =
(-4) (-4) xx (-8) = (-8) =
Rules
+ve x -ve = -ve -ve x +ve = -ve
Multiplying Integers
Multiplication
-ve x -ve = +ve +ve x +ve = +ve
-2-2
-20-20
-9-9
-40-40
22
1010
2525
3232
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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IntegersIntegers
1 1 ++ (-2) (-2) xx (-10) = (-10) =
Multiplying Integers
5 5 x x (-2)(-2)22 + 5 - 19= + 5 - 19=
8 – (-3)8 – (-3)22 = =
3 + (-5)3 + (-5)22 = =
Rules
+ve x -ve = -ve -ve x +ve = -ve
Multiplying Integers
Multiplication
-ve x -ve = +ve +ve x +ve = +ve
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2828
-1-1
66
Remember BODMAS
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try MIA Ex 6.1Ch2 (page 31)
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IntegersIntegersMultiplication
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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× =
1 3 16
3 7 21
2
1. Share 63 in the ratio 2:5
2. Decide which are true or f alse
(a) a a = 2a (b) 3b 5f = 8bf
(c) 2w w = 2w (d) 2xy 4y 8 xy
3. Does Explain ?
4. Write in sc
ientifi c notation and to 2 sig. fi g.
(a) 0.03465 (b) 4960000
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. Explain how to divide positive and negative integers.
1. Understand how to divide positive and negative integers.
IntegersIntegersDivision
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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IntegersIntegers
8 8 ÷÷ (-4) = (-4) =
Dividing Integers
16 16 ÷ ÷ (-2) =(-2) =
(-3) (-3) ÷÷ 3 = 3 =
(-24) (-24) ÷÷ 6 = 6 =
(-22) (-22) ÷÷ (-2) = (-2) =
(- 56) (- 56) ÷÷ (-7) = (-7) =
(-15) (-15) ÷ ÷ (-5) =(-5) =
(-4) (-4) ÷÷ (-8) = (-8) =
Rules
+ve ÷ -ve = -ve -ve ÷ +ve = -ve
Multiplying Integers
Division
-ve ÷ -ve = +ve +ve ÷ +ve = +ve
-2-2
-4-4
-1-1
-8-8
1111
88
33
0.50.5
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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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IntegersIntegers
1 1 ++ (-20) (-20) ÷÷ (-10) = (-10) =
Division Integers
-48 -48 ÷ ÷ (6 - 2)(6 - 2)22 + 5 = + 5 =
100 - 36 100 - 36 ÷÷ (-3) (-3)22 = =
100 100 ÷÷ (-5) (-5)22 = =
Rules
+ve ÷ -ve = -ve -ve ÷ +ve = -ve
Multiplying Integers
Division
-ve ÷ -ve = +ve +ve ÷ +ve = +ve
33
44
9696
22
Remember BODMAS
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