Targeting Grade C

Unit 1

Algebra 1

GCSE Mathematics

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

Can you:

• •Simplify linear expressions
• •Use brackets in Algebra

Try a test

• •Understand the rule of indices
• •Use substitution in expressions

Try a test

If not you need

TOP 1: Simplify

(i) 3g + 5g

(ii) 3x + y - x + 2y

(2)

(b) 4a + 9b – 3a – 5b

(1)

(c) 3p + q – 2p – 2q

(2)

• (d)2w – 4v –3w + 2v

(1)

• (f)3x² - 2x + x² + x (1)

(Total 7 marks)

Lesson

8g

2x + 3y

a + 4b

p - q

-2v -w

4x² - x

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)

• (a) 5(2y – 3)

(1)

(c) x(2x +y)

(2)

Lesson

7n - 21

8x -12

pq – 2p²

10y - 15

2x² + xy

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)

(2)

(iii) (t + 4)(t – 2)

(2)

(iv) (x + 3y)(x + 2y)

(2)

Lesson

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

Are you ready for the answers ?

e + f + e +2f

Answers

1

2

3

4

5

6

7

8

9

10

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)

TAIL 1

Are you ready for the answers ?

e + f + e +2f

1

2

3

4

5

6

7

8

9

10

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)

2e + 3f

5x² + x

2a + 2b

10d + 10e

x² + xy

3a² + 2ab

5x - y

3x + 19

x² + x - 6

6a² - ab –2b²

TAIL 1

Lesson

Can you remember the rules of indices (or powers)?When MULTIPLYING, you ADD the powers. e.g. 3¹ X 3² = 3³When 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 = xAnything 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?

Write down your solutions to:

1. k³ ÷ k²

2. p² × p3

• 3.p² + p² + p²
• 5.x8 × x³
• 7.x6

x4

• 9.a7 x a3
• 11.x² x x³

x²

(7)

Lesson

k¹

p5

3p²

x¹¹

x²

a¹º

x³

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

• (iii)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 = 1.2k = –2

(3)

Lesson

-5

73

-14

1.2

Are you ready for the answers ?

TAIL 2

• (a)Simplify 3p + q – p +2q
• (b)Simplify 3y² - y²
• (c)Simplify 5c + 7d – 2c – 3d
• (d)Simplify 4p x 2q
• (e)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)

Lesson

3

1

2¹²

2

Are you ready for the answers ?