Transcript Document

GCSE
Mathematics
Targeting Grade C
Unit 1
Algebra 1
Can you:
If not you need
•Simplify linear expressions
TOP 1: Review 1 - collecting like
terms
Practice 1: Multiplying a bracket by
a whole number or letter
•Use brackets in Algebra
Try a test
•Understand the rule of indices
•Use substitution in expressions
Try a test
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
TOP 1:
Are you ready for
the answers ?
Simplify
(i)
3g + 5 g
8g
(ii)
3x + y - x + 2y
2x + 3y
(b)
(c)
4a + 9b – 3a – 5b
3p + q – 2p – 2q
a + 4b
p-q
(2)
(1)
(2)
(d)
(e)
2w – 4v –3w + 2v
3x² - 2x + x² + x
Lesson
-2v -w
4x² - x
(1)
(1)
(Total 7 marks)
Are you ready for
the answers ?
Practice 1:
Expand the brackets:
(a)
(i)
7(n – 3)
(ii)
4(2x – 3)
8x -12
(iii)
p(q – 2p)
pq – 2p²
Multiply out:
(a)
(c)
7n - 21
(3)
5(2y – 3)
x(2x +y)
10y - 15
2x² + xy
(1)
(2)
Lesson
Practice 2:
(i)
4(x + 5) + 3(x – 7)
4x + 9
(ii)
+ 3x -21
= 7x - 12
(2)
5(3p + 2) – 2(5p – 3)
15p + 10
(iii)
Are you ready for
the answers ?
Expand and simplify:
- 10p + 6
= 5p +16
(2)
(t + 4)(t – 2)
t² - 2t + 4t -8
= t² + 2t -8
(2)
(iv)
(x + 3y)(x + 2y)
x² + 2xy + 3xy + 6y²
Lesson
= x² + 5xy + 6y²
(2)
Are you ready for
the answers ?
TAIL 1
1
2
3
4
5
6
7
8
9
10
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
Lesson
1
2
3
4
5
6
7
8
9
10
e + f + e +2f
2e + 3f
2x² + 2x + 3x² - x
5x² + x
2(a + b)
2a + 2b
5(2d + 2e)
10d + 10e
x(x + y)
x² + xy
a(3a + 2b)
3a² + 2ab
3(x + y) + 2(x – 2y)
5x - y
5(3x + 2) – 3(4x – 3)
3x + 19
(x + 3)(x - 2)
x² + x - 6
(2a + b)(3a – 2b)
6a² - ab –2b²
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
Anything to the POWER 0 is just 1. e.g. 6º = 1
x¹ = x
xº = 1
When RAISING one power to another, you MULTIPLY the
powers.
e.g. (3²)³ = 36 (45)² = 4¹0
Now try some questions
Are you ready for
the answers ?
Can you Simplifying indices?
Write down your solutions to:
1.
k³ ÷ k²
k¹
2.
p² × p3
p5
3.
p² + p² + p²
3p²
4.
x8 × x³
x¹¹
5.
x6
x4
a7 x a3
x²
x² x x³
x²
x³
6.
7.
a¹º
(7)
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
-5
73
(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:
If
u=5
t = 1.2
k = –2
(2)
-14
D = ut + 2kt
(4)
1.2
(3)
Lesson
Are you ready for
the answers ?
TAIL 2
(a)
Simplify
3p + q – p +2q
2p + 3q
(b)
Simplify
3y² - y²
2y²
(c)
Simplify
5c + 7d – 2c – 3d
(d)
Simplify
4p x 2q
8pq
(e)
Simplify
x³ + x³
2x³
3c + 4d
Some more questions
Are you ready for
the answers ?
Can you work out the answers to these?
1.
3¹
3
2.
8º
1
3.
(2³)4
2¹²
4.
(4² x 4¹) ÷ (2³ x 2²)
2
Lesson