S4 Credit 23-Jun-16 Created by Mr. Equations and Inequations Reminder of Solving Equations 1 Inequalities Reminder of Solving Equations 2 Equations with Fractions More Equations with Fractions Solving Inequalities

S4 Credit 23-Jun-16Created by Mr. Starter Questions Q1.Is the following true or false (A)(-3a) x 5a = -15a (B) (-6x) x (-7y) =-42xy Q2.Are the 2 answers the same ? (a)(-3h) 2 =(b)-(3d) 2 = Q3.Spilt £64 pounds into the ratio 7:9 Q4.Explain why is equal to 6.75 x 10 -2

S4 Credit 23-Jun-16Created by Mr. Learning Intention Success Criteria 1.To remind pupils on how to solve various types of equations 1.Understand the process of solving equations using “ the balancing method ” Reminder on Solving Equations

S4 Credit 5(x - 3) = 25 5x Example 1 23-Jun-16Created by Mr = 25 Multiply out the bracket first and then solve. 5x = x = 40 ÷ 5 = 40 = 8 Reminder on Solving Equations Substitute value into original equation to check answer

S4 Credit 6(x - 2) = 3(x + 1) 6x Example 2 23-Jun-16Created by Mr = 3x = x – 3x -12 3x -12 = 3 3x = = 15 x = 15 ÷ (3) = 5 Solve as normal Substitute value into original equation to check answer 18 Reminder on Solving Equations

S4 Credit -3(2 + 2y) = 6 – (y + 2) -6 Example 3 23-Jun-16Created by Mr. - 6y = 6 Equations and brackets = 4 - y - y – 6y y + y = 4 -6 – 5y = 4 – 5y = 10 y = 10 ÷ (-5) = -2 Tidy up RHS Solve as normal Substitute value into original equation to check answer 6 6

S4 Credit 23-Jun-16Created by Mr. Now try Ex 2.1 Ch5 MIA (page 99) Reminder on Solving Equations

S4 Credit 23-Jun-16Created by Mr. Starter Questions Q1. Explain why the following are True or False (a)-3y x 5y =-30y (b)-6q x (-4q) = 24q 2 Q2. Is the following true -2a( b – a) = -2ab +4a Q3.Write down the two numbers that multiply to give 8 and subtract to give 2.

S4 Credit 23-Jun-16Created by Mr. Learning Intention Success Criteria 1.To remind pupils on how to solve equations containing square terms. 1.Understand the process of solving equations with square terms using “ the balancing method ” Reminder on Solving Equations

S4 Credit (x + 2) 2 = x (x + 2)(x + 2) Example 1 23-Jun-16Created by Mr. = x Multiply out the bracket first and then solve. Equations and brackets x 2 + 4x + 4 4x = 60 x = 60 ÷ 4 = 15 FOIL = x x + 4 = 64 Substitute value into original equation to check answer 289

S4 Credit m(m + 2) = m m 2 + 2m Example 2 23-Jun-16Created by Mr. = m Multiply out the bracket first and then solve. Equations and brackets 2m m = 10 ÷ 2 = 5 = 10 Substitute value into original equation to check answer 35

S4 Credit Solve in the usual way A = (x + 7)(x – 2) Example 5 : The two areas are equal. Find the value of x. 23-Jun-16Created by Mr. (x + 7) (x – 2) (x + 2) A = (x + 2) 2 (x + 2) 2 = (x + 7) (x - 2) x 2 + 4x + 4 x = 18 Foil Equations and brackets = x 2 + 5x x + 4= 5x = x - 14 Substitute value into original equation to check answer 400

S4 Credit 25 Equations & Pythagoras Using Pythagoras find the length of all sides of the triangle. x + 3 cm 3cm x + 2 cm (x + 3) 2 = (x + 2) x 2 + 6x + 9 x = 2 = x 2 + 4x x + 9= 4x x= 4 25 Foil Balancing Method Lengths are 3, 4 and 5 cm 4 5 Check ! Example

S4 Credit 23-Jun-16Created by Mr. Now try Ex 2.2 Ch5 MIA (page 101) Equations and brackets

S4 Credit 23-Jun-16Created by Mr. Starter Questions Q1.Multiply out. (a)3y(x - y) =(b)6q 2 (2 - 4q) = Q2.Explain your working to show that if we split 24 into the ratio 1:5 the answer is 4:20 Q3.Writing out in full 5.2 x to get Is the correct?

S4 Credit 23-Jun-16Created by Mr. Lafferty Maths Dept. Equations & Fractions Learning Intention Success Criteria 1. To show how to solve fractional equations using all the rules learned so far. 1. Apply Balancing Method to solve fractional equations. Fractional Equations with Brackets

S4 Credit 23-Jun-16Created by Mr. Lafferty Maths Dept. Process of solving equations with fractions 1.Remove any fraction by multiplying. 2.Remove any fractions. 3.Simply each side of the equation if possible. 4.Carry out balancing method to solve equation. Equations & Fractions

S4 Credit 23-Jun-16Created by Mr. Lafferty Maths Dept. Multiply EVERY term by 5 Equations with Fractions Equations & Fractions

S4 Credit Multiply EVERY term by 3 Equations with Fractions Remove brackets Balancing Method Equations & Fractions

S4 Credit Multiply EVERY term by 4 Equations with Fractions Tidy up Balancing Method Equations & Fractions

S4 Credit 23-Jun-16Created by Mr. Now try Ex 3.1 Ch5 MIA (page 103) Equations & Fractions

S4 Credit 23-Jun-16Created by Mr. Starter Questions Q1.Find the area of the second shape given the first has area 7w - 14 Q2.Split 48 into the ratio 1:3 Q3.In standard form is 1.8x10 7 is the correct? (w - 2) 7 (w – 5) 3

S4 Credit 23-Jun-16Created by Mr. Learning Intention Success Criteria 1.To remind pupils on how to solve equations containing fraction terms. 1.Understand the process of solving equations with fraction terms using “ the balancing method ” Equations & Fractions

S4 Credit 23-Jun-16Created by Mr. Lafferty Maths Dept. Multiply EVERY term by LCM 12 Equations with Fractions Tidy up Balancing Method Equations & Fractions

S4 Credit 23-Jun-16Created by Mr. Lafferty Maths Dept. Multiply EVERY term by LCM 6 Equations with Fractions Tidy up Balancing Method Equations & Fractions

S4 Credit 23-Jun-16Created by Mr. Lafferty Maths Dept. Equations with Fractions Balancing Method Equations & Fractions

S4 Credit 23-Jun-16Created by Mr. Now try Ex 4.1 Ch5 MIA (page 106) Equations & Fractions

S4 Credit 23-Jun-16Created by Mr. Starter Questions Q1.Solve for x (a)x + 3 = 8(b)2x – 14 = 50 Q2.Is this statement true (x – 1) – 3(x + 1) = -2x Q3.

23-Jun-16Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1. To show how we can solve inequalities using the same rules we use for equations. 1. Understand the term inequality. 2. Solve inequalities using the same method as equations. Solving Inequalities Equations & Inequalities

23-Jun-16Created by Mr. Lafferty Maths Dept. Inequalities are similar to equations except we replace the “=“ with one of the following symbols : Solving Inequalities Less than or equal to Greater than or equal to Greater than Less than The Good News Equations & Inequalities

S4 Credit 23-Jun-16Created by Mr. Now try Ex 5.1 Ch5 MIA (page 108) Removing a Single Bracket

S4 Credit 23-Jun-16Created by Mr. Starter Questions Q1.Does = 5.793x10 5 Q2.Explain why the answer to 4(w + 2) = 6(w + 1) is w = 1 Q3.

23-Jun-16Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1. To show how we can solve inequalities using the same rules we use for equations. 1. Understand the term inequality. 2. Solve inequalities using the same method as equations. Solving Inequalities Equations & Inequalities

23-Jun-16Created by Mr. Lafferty Maths Dept. Inequalities are similar to equations except we replace the “=“ with one of the following symbols : Solving Inequalities Less than or equal to Greater than or equal to Greater than Less than The Good News Equations & Inequalities

23-Jun-16Created by Mr. Lafferty Maths Dept. Solving inequalities is almost identical to solving equations : Solving Inequalities x is any value less than 4 Even Better News ! Equations & Inequalities Balancing Method Add 1 to both sides Tidy up Divide by 2 both sides

23-Jun-16Created by Mr. Lafferty Maths Dept. Solving inequalities is almost identical to solving equations : Solving Inequalities x is any value greater than or equal to 5 Equations & Inequalities Multiply out brackets Add 6 to both side Subtract x from each side. Divide both sides by 3

S4 Credit Solving Inequalities Inequalities The only one to watch out for is when you are dividing by a negative Example 1 8 – 3m < 2 -3m < -6 m Subtract 8 from each side Divide across by -3 and change the Sign So m > 2 >

S4 Credit 23-Jun-16 Solving Inequalities Inequalities Example 2 5( x – 1 ) - 8x ≥ x – 5 – 8x ≥ x - 5 ≥ x ≥ - 12 x ≤ So x ≤ 4

S4 Credit 23-Jun-16Created by Mr. Now try 6.1 & 6.2 Ch5 MIA (page 110) Inequalities