Targeting Grade C

1
GCSE Mathematics
Targeting Grade C
Unit 2 Algebra 2
2
Top Review 1 - How much do you know? Practice
1 Solving equations with the unknown on one side
Practice 2 Solving equations with the unknown
on both sides TAIL 1 Practice 3 Writing the
expression in a different form using
brackets Practice 4 Forming equations TAIL 2

• Can You ?
• Solving simple linear equations
• Unknowns on both sides of the equation
• Try
  a test
• Factorising an expression
• Form equations
• 
  Try a test

If not you need
3
Are you ready for the answers ?

• TOP How much do you know?
• Solve the following
• (i) x 5 16
• (ii) 3x 4 19
• (2)
• (b) 6y 9 45
• 
  
• (1)
• (c) 2x 5 -1
  
• (2)
• 4(x 3) 20
• 
  (1)
• 29 9x - 7
  
  
  (1)
• (Total 7 marks)

x 11
x 5
y 6
x 2
x 2
x 4
4
Are you ready for the answers ?

• Practice 1 Solve
• (a) (i) 4x 2 18
• (ii) 8x 5 19
•   (iii) 7 3y - 8
•  
• Multiply out the brackets first
  
• 2(x 3) 16
• (1)
• (c) 3(2x 3) 9
• (2)

x 4
x 3
y 5
x 5
x 3
Lesson
5
Are you ready for the answers ?

• Practice 2 Solve
• (i) 2x 3 x 7
• (2)
• (ii) 8r 3 5r 12
• (2)
• (iii) 9x 14 4x 11
• (2)
• (iv) 20y 16 18y - 10
• (2)

x 4
3r 9 r 3
5x 25 x 5
2y 6 y 3
Lesson
6
Are you ready for the answers ?
TAIL 1
1
2
3
4
5
6
7
8
9
10
3x 5 10
5y 6 21
2(x 4) 12
5(y - 3) 4
8x 12 20
4x 5 2x 9
3y 2 2y 8
5t 8 t 16
15x 6 7x - 2
20y 16 18y - 10
Next
7
Are you ready for the answers ?
TAIL Answers
1
2
3
4
5
6
7
8
9
10
x 3
3x 5 10
y 3
5y 6 21
2(x 4) 12
x 2
5(y 3) 5
y 4
x 1
8x 12 20
4x 5 2x 9
x 2
3y 2 2y 8
y 10
5t 8 t 16
t 6
15x 6 7x - 2
x -1
Lesson
20y 16 18y -10
y 3
8
This is the exact reverse of multiplying out the
brackets.
Putting brackets in
Factorising means...
This is what you have to do...

Take out the biggest number that goes into all
the terms
Take out each letter that will go into every term
the highest power
Factorise 3x 6 3 divides into
3 and 6 3(x
2)
Multiply out the brackets to check... 3(x 2)
3x 6
For more click here
9
Look at these examples

• 5x² 15x 5 divides
  into 5 and 15
• x
  divides into x² and x
• 5x(x 3)
• Multiply out the brackets to check
• 
  5x(x 3) 5x² 15x
• 4x² - 8xy 4 divides
  into 4 and 8
• x
  divides into x² and x
• 4x(x 2y)
• Multiply out the brackets to check
• 
  4x(x 2y) 4x² - 8xy

For more practice click here
10
Are you ready for the answers ?

• Can you factorise these?
• Write down your solutions to
• 1. 9x 12
• 2. 10x - 6
  
•  
• 9 3x
  
• 3x 5xy
• x² - 9x
  
• x² x
  
• 3x² 6xy
• p² 6p

3(3x 4)
2(x -3)
3(3 x)
x(3 5y)
x(x 3)
x(x 1)
3x(x 2y)
p(p 6)
4x(2x x)
ax(x 1)
Lesson
11
Have a go at...
Forming equations
1. Mr Smith owns minibuses and coaches. Each
minibus has 12 seats. (a) Write an expression, in
terms of m, for the number of seats in m
minibuses. (1) Each coach has 48
seats (b) Write an expression, in terms of m and
c, for the number of seats in m minibuses and
c coaches. (2) (Total 3 marks)
12m
12m 48c
Are you ready for the answers ?
More practice
12

• Lisa packs pencils in boxes.
• She packs 12 pencils in each box.
• Lisa packs x boxes of pencils.
• Write an expression, in terms of x, for the
  number of pencils Lisa packs.
• .................................
• (1)
• Lisa also packs pens in boxes.
• She packs 10 pens into each box.
• Lisa packs y boxes of pens.
• (b) Write down an expression, in terms of x and
  y, for the total number of pens and pencils Lisa
  packs.
• .................................
• (2)
• (Total 3 marks)

12x
10y 12x
Are you ready for the answers ?
More practice
13
The diagram represents a garden.All measurements
are given in metres.The garden has a flowerbed
in one corner.The flowerbed is a square of side
x. (a) Write down an expression, in terms of x,
for the shortest side of the garden. .............
........................ (1) (b) Find an
expression, in terms of x, for the perimeter of
the garden.Give your answer in its simplest
form. ..................................... (2) T
he perimeter of the garden is 20 metres. (c) Find
the value of x. (2) (Total 5 marks)
x 2
4x 14
Are you ready for the answers ?
4x 14 20 4x 6 x 6/4 1½
More practice
14

• The cost, in pounds, of hiring a car can be
  worked out using this rule.
• (a) Work out the cost of hiring a car for 4
  days.9
• (2)
• Bishen hired a car.
• The cost was 120
• (b) Work out the number of days for which Bishen
  hired the car.
• ..

Add 3 to the number of days hire Multiply your
answer by 10
Are you ready for the answers ?
70
9
10(n3)
More practice
15

• The width of a rectangle is x centimetres.The
  length of the rectangle is (x 4) centimetres.
• Find an expression, in terms of x, for the
  perimeter of the rectangle.Give your expression
  in its simplest form
• .
• (2)
• The perimeter of the rectangle is 54
  centimetres.
• Work out the length of the rectangle.

4x 8
4x 8 54 4x 46 x 46/4 11½
The length must be 11½ 4 15½ cm.
15½
Are you ready for the answers ?
16
TAIL 2
Are you ready for the answers ?
1.
5(3x 1)

• Factorise 15x 5
• Factorise 6y² - 3y
• Factorise a² a
• Factorise 18x² 12x
• Simplify xy² - xy

3y(2y 1)
a(a 1)
6x(3x 2)
xy(y 1)
Click for the next question
17

TAIL 2
Jennifer made x cakes. She put 4
sweets on top of each cake. (a) Write down an
expression, in terms of x, for the number of
sweets she used. .. (1) Paul made 3
more cakes than Jennifer. (b) Write down an
expression, in terms of x, for the number of
cakes Paul made. .. (1) Paul also put
4 sweets on each of his cakes. (c) Write down an
expression, in terms of x, for the number of
sweets Paul used. .. (1) (Total 3
marks)
2.
4x
x 3
4(x 3)
Are you ready for the answers ?
Click for next question
18
Eggs are sold in boxes. A small box holds 6
eggs. A large box holds 12 eggs. Hina buys x
small boxes of eggs. Hina also buys 4 less of
the large boxes of eggs than the small
boxes.(a) Find, in terms of x, the total number
of eggs in the large boxes that Hina buys.


..........................


(1)(b) Find, in terms of x, the total number of
eggs that Hina buys. Give your answer in its
simplest form.



..........................

(2)

(Total 3
marks)
TAIL 2
12(x 4)
12(x 4) large eggs and 6x small eggs 12x 48
6x 18x - 48
18x - 48
Are you ready for the answers ?
Click for the next question
19
4. The perimeter of this triangle is 19 cm. All
lengths on the diagram are in centimetres.
Work out the value of t.

t

(Total 3 marks)
Are you ready for the answers ?
4?
3t 6 19 3t 13 t 13/3 4?
Lesson