1. Mathematics
Algebra and Indices
Class 9

2. 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

3. 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

4. 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

5. 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 x = 7x - 12
15p p = 5p +16
t² - 2t + 4t = t² + 2t -8
x² + 2xy + 3xy + 6y² = x² + 5xy + 6y²
Lesson

6. 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

7. 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

8. 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 = x¹ = x Anything to the POWER 0 is just 1. e.g. 6º = xº = 1
When RAISING one power to another, you MULTIPLY the powers. e.g. (3²)³ = 36 (45)² = 4¹0
Now try some questions

9. 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

10. 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

11. 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

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