Mathematics Algebra and Indices Class 9

Can you: If not you need Simplify linear expressions Use brackets in Algebra Try a test Understand the rule of indices Use substitution in expressions TOP 1: Review 1 - collecting like terms Practice 1: Multiplying a bracket by a whole number or letter Practice 2: Expand the brackets and simplify the expression by collecting the like terms TAIL 1 Practice 3: Multiplying and dividing indices in algebra TOP 2: Review 2 – substituting numbers for letters TAIL 2 If not you need

Are you ready for the answers ? TOP 1: Simplify (i) 3g + 5g (ii) 3x + y - x + 2y (2) (b) 4a + 9b – 3a – 5b (1) (c) 3p + q – 2p – 2q 2w – 4v –3w + 2v 3x² - 2x + x² + x (1) (Total 7 marks) 8g 2x + 3y a + 4b p - q -2v -w 4x² - x Lesson

Are you ready for the answers ? Practice 1: Expand the brackets: (a) (i) 7(n – 3) (ii) 4(2x – 3)   (iii) p(q – 2p)   Multiply out: (3) 5(2y – 3) (1) (c) x(2x +y) (2) 7n - 21 8x -12 pq – 2p² 10y - 15 2x² + xy Lesson

Are you ready for the answers ? Practice 2: Expand and simplify: (i) 4(x + 5) + 3(x – 7) (2) (ii) 5(3p + 2) – 2(5p – 3) (iii) (t + 4)(t – 2) (iv) (x + 3y)(x + 2y) 4x + 9 + 3x -21 = 7x - 12 15p + 10 - 10p + 6 = 5p +16 t² - 2t + 4t -8 = t² + 2t -8 x² + 2xy + 3xy + 6y² = x² + 5xy + 6y² Lesson

1 2 3 4 5 6 7 8 9 10 TAIL 1 Are you ready for the answers ? e + f + e +2f 2x² + 2x + 3x² - x 2(a + b) 5(2d + 2e) x(x + y) a(3a + 2b) 3(x + y) + 2(x – 2y) 5(3x + 2) – 3(4x – 3) (x + 3)(x - 2) (2a + b)(3a – 2b) Answers

TAIL 1 1 2 3 4 5 6 7 8 9 10 e + f + e +2f 2e + 3f 5x² + x 2x² + 2x + 3x² - x 2(a + b) 2a + 2b 5(2d + 2e) 10d + 10e x(x + y) x² + xy a(3a + 2b) 3a² + 2ab 5x - y 3(x + y) + 2(x – 2y) 5(3x + 2) – 3(4x – 3) 3x + 19 (x + 3)(x - 2) x² + x - 6 Lesson (2a + b)(3a – 2b) 6a² - ab –2b²

Can you remember the rules of indices (or powers) Can you remember the rules of indices (or powers)? When MULTIPLYING, you ADD the powers. e.g. 3¹ X 3² = 3³ When DIVIDING, you SUBTRACT the powers. e.g. 4³ ÷ 4² = 4¹ .. and for few more click mouse… Anything to the POWER 1 is just ITSELF. e.g. 5¹ = 5 x¹ = x Anything to the POWER 0 is just 1. e.g. 6º = 1 xº = 1 When RAISING one power to another, you MULTIPLY the powers. e.g. (3²)³ = 36 (45)² = 4¹0 Now try some questions

Can you Simplifying indices? Are you ready for the answers ? Write down your solutions to: 1. k³ ÷ k² 2. p² × p3   p² + p² + p² x8 × x³ x6 x4 a7 x a3 x² x x³ x² (7) Are you ready for the answers ? k¹ p5 3p² x¹¹ x² a¹º x³ Lesson

Are you ready for the answers ? By using substitution answer the following questions: (i) Work out the value of 2a + ay when a = 5 and y = –3   (2) (ii) Work out the value of 5t² - 7 when t=4 Work out the value of 5x + 1 when x = –3 (iv) Work out the value of D when: (4) D = ut + 2kt If u = 5 t = 1.2 k = –2 (3) Are you ready for the answers ? -5 73 -14 1.2 Lesson

TAIL 2 Are you ready for the answers ? Simplify 3p + q – p +2q 2p + 3q Simplify 3y² - y² Simplify 5c + 7d – 2c – 3d Simplify 4p x 2q Simplify x³ + x³ 2p + 3q 2y² 3c + 4d 8pq 2x³ Some more questions

Are you ready for the answers ? Can you work out the answers to these? 1. 3¹ 2. 8º 3. (2³)4 4. (4² x 4¹) ÷ (2³ x 2²) 3 1 2¹² 2 Lesson