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Unformatted text preview: Algebra
General Tidying Up Terms www.mathsrevision.com Multiplying Terms Removing Brackets & Simplifying Solving Simple Equations ( x+1=5 ) Harder Equations ( 2x+1=9 ) Solving Equations ( brackets) Solving Equations (terms either side) Inequalities
13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
General 1. A TV has been reduced in t he sale by 20%. I t was 250. How much is it now. www.mathsrevision.com 2. 3. 30% of 300 Tidy up t he expression 5y + 3d + 4d + 10y
2cm 6cm 3cm 2cm 4. Explain how do f ind t he area and perimet er of t he shape.
Created by Mr. Lafferty Maths Dept. 13 Feb 2012 General Multiplying Terms
Learning Intention Algebra
Success Criteria 1. Understand the term `like terms'. www.mathsrevision.com 1. To explain how to gather `algebraic like terms'. 2. Gather like terms for simple expressions. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Tidying Terms
General First Row : www.mathsrevision.com 2c
2nd Row : + + + + c + + +
2d =
4c = 7c =
3d = 7d 13 Feb 2012 2d Created by Mr.Lafferty Maths Dept + Tidying Terms
General 3rd Row : www.mathsrevision.com +
3f +
f =
2f = 6f
CANNOT TIDY UP ANYMORE + + In Total we have WE CAN ONLY TIDY UP "LIKE TERMS"
13 Feb 2012 Created by Mr.Lafferty Maths Dept 7c + 7d + 6f Tidying Terms
General WE CAN ONLY TIDY UP "LIKE TERMS" www.mathsrevision.com Tidy up the following: Q1. 2x + 4x + 5y 3y + 18 = Q2. 4a + 3b + 5a + 6 b = 13 Feb 2012 Created by Mr.Lafferty Maths Dept 6x + 2y + 18 9a + 2b + 6 General Simplifying Algebraic Expressions Algebra www.mathsrevision.com Now try Exercise 1 Ch7 (page 85) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
General 1. Find t he per imet er . www.mathsrevision.com 5d 4d
2 . C a lc ula t e ( a ) ( 3 a ) + ( 4 b ) +2 a + 3 b 3. Find all t he missing angles. 120 40
o o 13 Feb 2012 Created by Mr. Lafferty Maths Dept. General Multiplying Terms
Learning Intention Algebra
Success Criteria 1. Understand the key steps of multiplying terms. 2. Apply multiplication rules simple expressions. for www.mathsrevision.com 1. To explain how to multiply out algebraic terms. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. General Simplifying Algebraic Expressions Algebra www.mathsrevision.com We can only add and subtract " like terms " Reminder ! x + x + x + x = 4x 9p 7p = 2p 3a + b  a + 6b = 2a + 7b 10 + 6 w  1 = 9 + 6w 2 2 2 2 x + x + x = 3x
13 Feb 2012 Created by Mr. Lafferty Maths Dept. General Simplifying Algebraic Expressions Algebra www.mathsrevision.com Reminder !
Multiplying terms 7 a = 7a w 5 = 5w 2 b b = b ( NOT 2b ) 2 2m 4m = 8m ( NOT 8m )
13 Feb 2012 Created by Mr. Lafferty Maths Dept. General Simplifying Algebraic Expressions Algebra www.mathsrevision.com Now try Exercise 2 Ch7 (page 86) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
General 1. Find t he per imet er and ar ea of t he shape. www.mathsrevision.com 2a
2 . C a lc ula t e ( a ) ( 3 m ) x ( 4 m ) ( b ) ( 2 b ) x ( 3 a ) 3. Find all t he missing angles. 6h 100
13 Feb 2012 Created by Mr. Lafferty Maths Dept. o 60 o General Removing brackets
Learning Intention Algebra
Success Criteria 1. Understand the key steps in removing brackets. 2. Apply multiplication rules for integers numbers when removing brackets. www.mathsrevision.com 1. To explain how to multiply out simply algebraic brackets. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. General Removing a Single Bracket
Example 1 www.mathsrevision.com 3(b + 5) = 3b + 15
Example 2 4(w 2) = 4w 8
Feb 13, 2012 Created by Mr. [email protected] General Removing a Single Bracket
Example 3 www.mathsrevision.com 2(y 1) =
Example 4 2y 2 7(w 6) = 7w 42
Feb 13, 2012 Created by Mr. [email protected] General Removing a Single Bracket
Example 5 www.mathsrevision.com 8(x + 3) = 8x + 24
Example 6 4(3 2m) =
Feb 13, 2012 Created by Mr. [email protected] 12 8m General Removing a Single Bracket
Example 7 Tidy Up www.mathsrevision.com 7 + 3(4 y) =
Example 8 7 + 12 3y = 19 3y Tidy Up 9 3(8 y) =
Feb 13, 2012 Created by Mr. [email protected] 9 24 + 3y = 15 + 3y Removing Two Single Brackets
General Example 9
www.mathsrevision.com Tidy Up 4(m 3) (m + 2) =
Example 10 4m 12 m 2 = 3m 14
Tidy Up 7(y 1) 2(y + 4) =
Feb 13, 2012 Created by Mr. [email protected] 7y 7 2y 8 = 5y 15 General Removing brackets Algebra www.mathsrevision.com Now try Exercise 3 Ch7 (page 86) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
General 1. S im p lif y 3 x + x  6 + x + x  3
www.mathsrevision.com 2. S im p lif y 7( p +1)  3 3. Find 15% of 1500
13 Feb 2012 Created by Mr.Lafferty Maths Dept Equations
General Solving Equations
Learning Intention Success Criteria 1. Know the process of the `Balancing Method'. 2. Solving simple algebraic equations. www.mathsrevision.com 1. To solve simple equations using the `Balancing Method'. 13 Feb 2012 Created by Mr.Lafferty Maths Dept 13 Feb 2012 Created by Mr Lafferty Maths Dept Balancing Method
General Kirsty goes to the shops every week to buy some potatoes. She always buys the same total weight. One week she buys 2 large bags and 1 small bag. The following week she buys 1 large bag and 3 small bags. If a small bags weighs 4 kgs. How much does a large bag weigh? 4 4 What instrument measures How can we go about solving balance this using balance ? www.mathsrevision.com 4 4 13 Feb 2012 Created by Mr Lafferty Maths Dept Balancing Method
General www.mathsrevision.com Take a small bag away from each side. Take a big bag away from each side. We can see that a big bag is equal to 4 + 4 = 8 kg 4 4 4 4 13 Feb 2012 Created by Mr Lafferty Maths Dept Balancing Method
General What symbol should we use for the scales ? Let's solve it using maths. www.mathsrevision.com Let P be the weight of a big bag. We know that a small bag = 4 2P + 4 = P + 12
4 4 P P 4 P 4 4 4 Subtract 4 from each side Subtract P from each side 2P = P + 8
P P=8 P Balancing Method
General 13 Feb 2012 www.mathsrevision.com It would be far too time consuming to draw out the balancing scales each time. We will now learn how to use the rules for solving equations. Created by Mr Lafferty Maths Dept Equations
General Solving Equations The method we use to solve equations is www.mathsrevision.com The Balancing Method +
x
13 Feb 2012 Write down the opposite of the following : opposite is opposite is opposite is opposite is +
x Created by Mr.Lafferty Maths Dept Simple Equations
General Example 1
www.mathsrevision.com ( 3) x + 3 = 20 x = 20 3 x = 17 Feb 13, 2012 Created by Mr. [email protected] Simple Equations
General Example 2
www.mathsrevision.com (+ x) ( 8) 24 x = 8 24 = 8 + x 24 8 = x 16 = x x = 16
Created by Mr. [email protected] Feb 13, 2012 Simple Equations
General Example 3
www.mathsrevision.com ( 4) 4x = 20 x = 20 4 x = 5 Feb 13, 2012 Created by Mr. [email protected] Simple Equations
General Example 4
www.mathsrevision.com ( 8) 8x = 28 x = 20 8 x = 3.5 Feb 13, 2012 Created by Mr. [email protected] Simple Equations
General www.mathsrevision.com Now try Exercise 4 Ch7 (page 87) 13 Feb 2012 Created by Mr.Lafferty Maths Dept Starter Questions
General www.mathsrevision.com Q1. Solve for x 2x + 3 = 15 Q2. 14% of 700
Feb 13, 2012 Created by Mr. [email protected] Equations
General Learning Intention Harder Equations
Success Criteria 1. Know the process of Method'. `Balancing www.mathsrevision.com 1. To solve harder equations using the rule `Balancing Method'. repeatedly. 2. Solving harder algebraic equations by using rule repeatedly. 13 Feb 2012 Created by Mr.Lafferty Maths Dept 13 Feb 2012 Created by Mr Lafferty Maths Dept Balancing Method
General www.mathsrevision.com Group of 5 adults and 3 children go to the local swimming. Another group of 3 adults and 8 children also go swimming. The total cost for each group is the same. A child's ticket costs 2. 2
If a child's ticket costs 2. How much for an adult ticket ? 2 a a a a a 2 2 2 2 2 a 2 2 a a 2 2 Let a be the price of an adult ticket. We know that a child price = 2 13 Feb 2012 Created by Mr Lafferty Maths Dept Balancing Method
General For balance we have www.mathsrevision.com 5a + 6 = 3a + 16
6 3a 6 Subtract 3a from Subtract 6 from each side
a a a a a 2 2 2 2 2 2 2 a 2 2 a a 2 2 1 5a = 3a + 10
3a 2a = 10 a= 5 Divide each side by 2 Adult ticket price is 5 13 Feb 2012 Created by Mr Lafferty Maths Dept Balancing Method
General www.mathsrevision.com It would be far too time consuming to draw out the balancing scales each time. We will now learn how to use the rules for solving equations. Equations
General Level E Harder Equations The rule we use to solve equations is www.mathsrevision.com The Balancing Method +
x
13 Feb 2012 Write down the opposite of the following : opposite is opposite is opposite is opposite is +
x Created by Mr.Lafferty Maths Dept Equations
General Example 1
www.mathsrevision.com ( 4) (2) 2x + 4 = 22 2x = 18 x = 9 Feb 13, 2012 Created by Mr. [email protected] Equations
General Example 2
www.mathsrevision.com (+ 5) (9) 9x 5 = 40 9x = 45 x = 5 Feb 13, 2012 Created by Mr. [email protected] Equations
General www.mathsrevision.com Now try Exercise 5 Ch7 (page 88) 13 Feb 2012 Created by Mr. [email protected] Starter Questions
General Q1. www.mathsrevision.com Solve for x (a) Q2. x + 3 = 8 (b) 2x 14 = 50 Is this statement true (x 1) 3(x + 1) = 2x Feb 13, 2012 Created by Mr. [email protected] Equations and brackets
General Learning Intention Success Criteria 1. Be able to multiply out brackets and solve equations. www.mathsrevision.com 1. To show how to solve equations that have bracket terms. Feb 13, 2012 Created by Mr. [email protected] Equations and brackets
General Multiply out the bracket first and then solve. www.mathsrevision.com Example 1 (+15) (5)
Feb 13, 2012 5(x 3) = 25 5x 15 = 25 5x = 25 + 15 = 40 x = 40 5 = 8
Created by Mr. [email protected] Equations and brackets
General Multiply out the bracket first and then solve. www.mathsrevision.com Example 2
(+3)
Feb 13, 2012 (3) 3(g 1) = 9 3g 3 = 9 3g = 9 + 3 = 12 g = 12 3 = 4
Created by Mr. [email protected] Equations and brackets
General www.mathsrevision.com Now try Exercise 6 Ch7 (page 89) 13 Feb 2012 Created by Mr. [email protected] Starter Questions
General Q1. Solve for x
www.mathsrevision.com (a) x + 7 = 29 (b) 2x 5 = 21 Q2. Is this statement true (x + 1) 2(x + 1) = x Feb 13, 2012 Created by Mr. [email protected] Equations and brackets
General Learning Intention Success Criteria 1. Be able to solve equations with terms on both sides. www.mathsrevision.com 1. To show how to solve equations with terms on both sides. Feb 13, 2012 Created by Mr. [email protected] Equations and brackets
General Example 1
www.mathsrevision.com ( x) (+3) (5) x + 7 6x 3 = 5x 3 = 7 5x = 7 + 3 = 10 x = 10 5 x = 2 Feb 13, 2012 Created by Mr. [email protected] Equations and brackets
General Example 2
www.mathsrevision.com ( 5y) (1) (2) 5y + 7 8y + 1 = 3y + 1 = 7 3y = 6 y = 2 Feb 13, 2012 Created by Mr. [email protected] Equations and brackets
General www.mathsrevision.com Now try Exercise 7 Ch7 (page 89) 13 Feb 2012 Created by Mr. [email protected] Starter Questions
General 1.
www.mathsrevision.com Simplif y 7 a  4a  9b +11b + ab  3 2 . Find t wo num b e r s t h a t a d d t o g ive 10 a nd m ult ip ly t o g ive 2 4 3.
13 Feb 2012 Find LCM of 4 qand 7
Created by Mr.Lafferty Maths Dept Inequalities
General Learning Intention Success Criteria 1. Know rule the 4 symbols for inequalities. 2. Solving simple inequalities equations. www.mathsrevision.com 1. To explain the various symbols for inequalities. 13 Feb 2012 Created by Mr.Lafferty Maths Dept Inequalities
General The equations you were solving were called equations because they contained an "=" sign. www.mathsrevision.com There are 4 other Mathematical symbols They are called inequalities : > <
13 Feb 2012 greater than less than greater than or equal to less than or equal to
Created by Mr.Lafferty Maths Dept Inequalities
General www.mathsrevision.com 5 > 3 Arrow ALWAYS points to the smallest Examples : Write in words what each mean. number means 5 is greater than 3 7 < 6 means 7 is less than 6 means x can take the value 2 or greater means y can take the value 5 or less x 2
y 5
13 Feb 2012 Created by Mr.Lafferty Maths Dept Inequalities
General Examples : Write out an inequality for the numbers www.mathsrevision.com (a) (b) (c) (d) 14 and 6 2 and 1 3 and 7 34 and 35 14 > 6 2 < 1 3 > 7 34 > 35 13 Feb 2012 Created by Mr.Lafferty Maths Dept Inequalities
General Examples : Choosing from 3, 2, 1, 0 , 1, 2, 3 www.mathsrevision.com (a) (b) (c) (d) y < 0 y > 2 y 2 y > 3 3, 2, 1 3 3, 2 No solution 13 Feb 2012 Created by Mr.Lafferty Maths Dept Inequalities
General www.mathsrevision.com The Good News
Same rule as solving equations The Balancing Method
13 Feb 2012 Created by Mr.Lafferty Maths Dept Inequalities
General Example 1
www.mathsrevision.com ( 4) (2) 2x + 4 30 2x 26 x 13 Feb 13, 2012 Created by Mr. [email protected] Inequalities
General Example 2
www.mathsrevision.com (+ 5) (6) 4x 5 19 4x 24 x 6 Feb 13, 2012 Created by Mr. [email protected] Inequalities
General www.mathsrevision.com Now try Extension Booklet 8E (page 27) 13 Feb 2012 Created by Mr.Lafferty Maths Dept ...
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This note was uploaded on 02/13/2012 for the course HUM 400 taught by Professor Hum during the Spring '11 term at University of Phoenix.
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