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## Algebra

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**MTH 3-14a**MTH 3-15a MTH 3-15b Algebra Tidying up terms Number Machine Working with Expressions Solving Simple Equations www.mathsrevision.com Solving Harder Equations Understanding Inequalities Solving Simple Inequalities Created by Mr.Lafferty Maths Dept**MTH 3-14a**MTH 3-15a MTH 3-15b Starter Questions Q1. Calculate Q2. Convert 60% to fraction and simplify. to a percentage. Q3. Convert www.mathsrevision.com Q4. What is the time difference 09:28 and 10:50 Q5. The answer to the question is 90. What is the question. Created by Mr.Lafferty Maths Dept**MTH 3-14a**MTH 3-15a MTH 3-15b Aim of the Lesson Tidying Terms a+2b+3a+b • Tidying up expressions. • Show steps when tidying up. www.mathsrevision.com Created by Mr.Lafferty Maths Dept**Tidying Terms**MTH 3-14a MTH 3-15a MTH 3-15b + + = First Row : + + 2c c 4c = 7c www.mathsrevision.com + + = 2nd Row : + + 2d 2d 3d = 7d Created by Mr.Lafferty Maths Dept**Tidying Terms**MTH 3-14a MTH 3-15a MTH 3-15b + + = 3rd Row : + + 3f f 2f = 6f CANNOT TIDY UP ANYMORE www.mathsrevision.com In Total we have 7c + 7d + 6f WE CAN ONLY TIDY UP “LIKE TERMS” Created by Mr.Lafferty Maths Dept**Tidying Terms**MTH 3-14a MTH 3-15a MTH 3-15b WE CAN ONLY TIDY UP “LIKE TERMS” Tidy up the following: Q1. 2x + 4x + 5y -3y + 18 = Q2. 4a + 3b + 5a + 6 – b = 6x + 2y + 18 www.mathsrevision.com 9a + 2b + 6 Created by Mr.Lafferty Maths Dept**Tidying Terms**MTH 3-14a MTH 3-15a MTH 3-15b Your turn ! Page 46 Exercise 1 Q1 and Q2 www.mathsrevision.com Created by Mr.Lafferty Maths Dept**MTH 3-14a**MTH 3-15a MTH 3-15b Starter Questions Q1. Tidy up the expression Q2. Calculate Q3. Round to 1 decimal place. www.mathsrevision.com (a) 2.34 (b) 10.25 (c) 3.23 Q4. 12.5 % as a fraction Created by Mr.Lafferty Maths Dept**MTH 3-14a**MTH 3-15a MTH 3-15b Aim of the Lesson Number Machine • To build simple expressions. • To UNDO simple expressions. www.mathsrevision.com Created by Mr.Lafferty Maths Dept**4a**7m Number Machine MTH 3-14a MTH 3-15a MTH 3-15b To build an expression from the number machine simply follow the rules given: www.mathsrevision.com Created by Mr.Lafferty Maths Dept**Number Machine**MTH 3-14a MTH 3-15a MTH 3-15b To build an expression from the number machine simply follow the rules given: 20 23 www.mathsrevision.com 3b 3b+9 Created by Mr.Lafferty Maths Dept**Number Machine**MTH 3-14a MTH 3-15a MTH 3-15b Your turn ! Page 93 Exercise 2 Q1 www.mathsrevision.com Created by Mr.Lafferty Maths Dept**UNDO**UNDO Number Machine MTH 3-14a MTH 3-15a MTH 3-15b To UNDO the number machine simply do the opposite of the rules given: +8 x2 18 36 www.mathsrevision.com Created by Mr.Lafferty Maths Dept**UNDO**UNDO Number Machine MTH 3-14a MTH 3-15a MTH 3-15b To UNDO the number machine simply do the opposite of the rules given: -9 x4 5 20 www.mathsrevision.com Created by Mr.Lafferty Maths Dept**Number Machine**MTH 3-14a MTH 3-15a MTH 3-15b Your turn ! Page 93 Exercise 2 Q3 and Q4 www.mathsrevision.com Created by Mr.Lafferty Maths Dept**MTH 3-14a**MTH 3-15a MTH 3-15b Starter Questions www.mathsrevision.com Created by Mr.Lafferty Maths Dept**Substitution**MTH 3-14a MTH 3-15a MTH 3-15b Learning Intention Success Criteria • To explain the process of working out expressions by substitution method. • Understand process of substitution. • 2. Solving expressions showing working. www.mathsrevision.com Created by Mr.Lafferty Maths Dept**Substitution**MTH 3-14a MTH 3-15a MTH 3-15b 1 If a = 3 and b = 9 evaluate a + b www.mathsrevision.com Sub in a=3 = 3 + 9 Sub in b=9 = 12 Created by Mr.Lafferty Maths Dept**Substitution**MTH 3-14a MTH 3-15a MTH 3-15b 2 If a = 3 and b = 9 evaluate ab a x b Remember ab means a x b www.mathsrevision.com Sub in a=3 = 3 x 9 Sub in b=9 = 27 Created by Mr.Lafferty Maths Dept**Substitution**MTH 3-14a MTH 3-15a MTH 3-15b 3 If a = 3 and b = 9 evaluate 4b 4 x b Remember 4b means 4 x b www.mathsrevision.com = 4 x 9 Sub in b=9 = 36 Created by Mr.Lafferty Maths Dept**Substitution**MTH 3-14a MTH 3-15a MTH 3-15b If a = 5 and b = 6 evaluate 1. a + b =11 4. b - a =1 2. ab =30 5. 4b =24 www.mathsrevision.com 3. 3a =15 6. 3ab =90 Created by Mr.Lafferty Maths Dept**Substitution**MTH 3-14a MTH 3-15a MTH 3-15b If a = 5 and b = 3 evaluate 4 2a + 4b 2xa + 4xb = Remember 2a means 2 x a Sub in a=5 4x 3 = 2x 5 + www.mathsrevision.com Sub in b=3 = 10 12 + = 22 Created by Mr.Lafferty Maths Dept**Substitution**MTH 3-14a MTH 3-15a MTH 3-15b 5 If a = 5 and b = 3 evaluate a 2 a x a = Remember a2 means a x a www.mathsrevision.com Sub in a=5 = 5 x 5 = 25 Created by Mr.Lafferty Maths Dept**Remember a means a ÷ b**b Substitution MTH 3-14a MTH 3-15a MTH 3-15b 6 If a = 15 and b = 3 evaluate a 15 = b 3 www.mathsrevision.com Sub in a=15 = 5 Sub in b = 3 Created by Mr.Lafferty Maths Dept**6) b**a Substitution MTH 3-14a MTH 3-15a MTH 3-15b If a = 2 and b = 6 evaluate 1) 4a + 3b =26 4) 5b – 3a =24 2) a2 =4 5) 4a2 =16 www.mathsrevision.com 3) b2 =36 =3 Created by Mr.Lafferty Maths Dept**Substitution**MTH 3-14a MTH 3-15a MTH 3-15b Your turn ! Page 94 Exercise 3 www.mathsrevision.com Created by Mr.Lafferty Maths Dept**MTH 3-14a**MTH 3-15a MTH 3-15b Starter Questions www.mathsrevision.com Created by Mr.Lafferty Maths Dept**MTH 3-14a**MTH 3-15a MTH 3-15b Level E Solving Equations Equations Learning Intention Success Criteria • To solve simple equations using the rule • ‘change side change sign’. • 1. Know rule • ‘change side change sign’. • 2. Solving simple algebraic equations. www.mathsrevision.com Created by Mr.Lafferty Maths Dept**Equations**MTH 3-14a MTH 3-15a MTH 3-15b Level E Solving Equations The rule we use to solve equations is The rule “change side change sign” Write down the opposite of the following : + + - - www.mathsrevision.com opposite is opposite is x x ÷ ÷ opposite is opposite is Created by Mr.Lafferty Maths Dept**Check to see if correct !**Check to see if correct ! Equations MTH 3-14a MTH 3-15a MTH 3-15b Level E Solving Equations The rule “change side change sign” +8 opposite is -8 -5 opposite is +5 Examples www.mathsrevision.com Created by Mr.Lafferty Maths Dept**Check to see if correct !**Check to see if correct ! Equations MTH 3-14a MTH 3-15a MTH 3-15b Level E Solving Equations The rule “change side change sign” times by 8 opposite is divide by 8 times by 3 opposite is divide by 3 Examples www.mathsrevision.com Created by Mr.Lafferty Maths Dept**Equations**MTH 3-14a MTH 3-15a MTH 3-15b Level E Solving Equations Now try Exercise 4 Ch8 (page 96) www.mathsrevision.com Created by Mr.Lafferty Maths Dept**MTH 3-14a**MTH 3-15a MTH 3-15b Starter Questions www.mathsrevision.com Created by Mr.Lafferty Maths Dept**MTH 3-14a**MTH 3-15a MTH 3-15b Level E Harder Equations Equations Learning Intention Success Criteria • To solve harder equations using the rule • ‘change side change sign’. • repeatedly. • 1. Know rule • ‘change side change sign’. • 2. Solving harder algebraic equations by using rule repeatedly. www.mathsrevision.com Created by Mr.Lafferty Maths Dept**Equations**MTH 3-14a MTH 3-15a MTH 3-15b Level E Harder Equations The rule we use to solve equations is The rule “change side change sign” Write down the opposite of the following : + + - - www.mathsrevision.com opposite is opposite is x x ÷ ÷ opposite is opposite is Created by Mr.Lafferty Maths Dept**Check to see if correct !**Equations MTH 3-14a MTH 3-15a MTH 3-15b Level E Harder Equations The rule “change side change sign” +1 opposite is -1 Examples times by 2 opposite is divide by 2 www.mathsrevision.com Created by Mr.Lafferty Maths Dept**Check to see if correct !**Equations MTH 3-14a MTH 3-15a MTH 3-15b Level E Harder Equations The rule “change side change sign” -6 opposite is +6 Examples times by 4 opposite is divide by 4 www.mathsrevision.com Created by Mr.Lafferty Maths Dept**Equations**MTH 3-14a MTH 3-15a MTH 3-15b Level E Harder Equations Now try Exercise 5 Ch8 (page 97) www.mathsrevision.com Created by Mr.Lafferty Maths Dept**MTH 3-14a**MTH 3-15a MTH 3-15b Starter Questions www.mathsrevision.com Created by Mr.Lafferty Maths Dept**MTH 3-14a**MTH 3-15a MTH 3-15b Level E Solving Inequalities Inequalities Learning Intention Success Criteria • To explain the various symbols for inequalities. • Know rule the 4 symbols for • inequalities. • 2. Solving simple inequalities equations. www.mathsrevision.com Created by Mr.Lafferty Maths Dept**Inequalities**MTH 3-14a MTH 3-15a MTH 3-15b Level E Solving Inequations The equations you were solving were called equations because they contained an “=“ sign. There are 4 other Mathematical symbols They are called inequalities : www.mathsrevision.com greater than or equal to greater than less than or equal to less than Created by Mr.Lafferty Maths Dept**Inequalities**MTH 3-14a MTH 3-15a MTH 3-15b Arrow ALWAYS points to the smallest number Level E Solving Inequalities Examples : Write in words what each mean. 5 > 3 means 5 is greater than 3 -7 < -6 means -7 is less than -6 means x can take the value 2 or greater x ≥ 2 www.mathsrevision.com y ≤ -5 means y can take the value -5 or less Created by Mr.Lafferty Maths Dept**Inequalities**MTH 3-14a MTH 3-15a MTH 3-15b Level E Solving Inequalities Examples : Write out an inequality for the numbers (a) 14 and 6 14 > 6 (b) -2 and 1 -2 < 1 www.mathsrevision.com (c) -3 and -7 -3 > -7 (d) 34 and -35 34 > -35 Created by Mr.Lafferty Maths Dept**Inequalities**MTH 3-14a MTH 3-15a MTH 3-15b Level E Solving Inequalities Examples : Choosing from -3, -2, -1, 0 , 1, 2, 3 (a) y < 0 -3, -2, -1 (b) y > 2 3 www.mathsrevision.com (c) y ≤ -2 -3, -2 (d) y > 3 No solution Created by Mr.Lafferty Maths Dept**Inequalities**MTH 3-14a MTH 3-15a MTH 3-15b Level E Solving Inequalities Now try Exercise 6 Ch8 (page 99) www.mathsrevision.com Created by Mr.Lafferty Maths Dept**MTH 3-14a**MTH 3-15a MTH 3-15b Starter Questions www.mathsrevision.com Created by Mr.Lafferty Maths Dept**MTH 3-14a**MTH 3-15a MTH 3-15b Level E Inequalities Inequalities Learning Intention Success Criteria • To solve simple inequalities using the same rules as for equations • ‘change side change sign’. • 1. Know rule • ‘change side change sign’. • 2. Solving simple inequalities equations. www.mathsrevision.com Created by Mr.Lafferty Maths Dept**Inequalities**MTH 3-14a MTH 3-15a MTH 3-15b Level E Inequalities The Good News Same rule as solving equations www.mathsrevision.com The rule “change side change sign” Created by Mr.Lafferty Maths Dept**Check to see if correct !**Check to see if correct ! Inequalities MTH 3-14a MTH 3-15a MTH 3-15b Level E Solving Inequalities The rule “change side change sign” +10 opposite is -10 -9 opposite is +9 Examples www.mathsrevision.com Created by Mr.Lafferty Maths Dept**Check to see if correct !**Check to see if correct ! Inequalities MTH 3-14a MTH 3-15a MTH 3-15b Level E Solving Inequalities The rule “change side change sign” times by 9 opposite is divide by 9 times by 7 opposite is divide by 7 Examples www.mathsrevision.com Created by Mr.Lafferty Maths Dept