Transcript Targeting Grade C GCSE Mathematics Unit 2

GCSE
Mathematics
Targeting Grade C
Unit 2
Algebra 2
Can You ?
If not you need
•Solving simple linear equations
•Unknowns on both sides of the equation
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
Try a test
TAIL 1
•Factorising an expression
Practice 3: Writing the expression
in a different form using brackets
•Form equations
Practice 4: Forming equations
Try a test
TAIL 2
Are you ready for
the answers ?
TOP
How much do you know?
Solve the following
(i)
x + 5 = 16
x = 11
(ii)
3x + 4 = 19
x=5
(b)
(c)
6y + 9 = 45
2x – 5 = -1
y=6
x=2
(2)
(1)
(2)
(d)
4(x + 3) = 20
x=2
(1)
(e)
29 = 9x - 7
Lesson
x=4
(1)
(Total 7 marks)
Are you ready for
the answers ?
Practice 1:
Solve:
(a)
(i)
4x + 2 = 18
x=4
(ii)
8x – 5 = 19
x=3
(iii)
7 = 3y - 8
y=5
Multiply out the brackets first:
(a)
2(x + 3) = 16
x=5
(1)
(c)
Lesson
3(2x – 3) = 9
x=3
(2)
Practice 2:
(i)
Are you ready for
the answers ?
Solve:
2x + 3 = x + 7
x=4
(ii)
8r + 3 = 5r + 12
(2)
3r = 9
r=3
(iii)
9x – 14 = 4x + 11
(2)
5x = 25
x=5
(iv)
20y – 16 = 18y - 10
2y = 6
y=3
Lesson
(2)
(2)
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
TAIL Answers
Lesson
1
2
3
4
5
6
7
8
9
10
Are you ready for
the answers ?
3x – 5 = 10
x=3
5y + 6 = 21
y=3
2(x + 4) = 12
x=2
5(y – 3) = 5
y=4
8x + 12 = 20
x=1
4x +5 = 2x + 9
x=2
3y – 2 = 2y + 8
y = 10
5t – 8 = t + 16
15x + 6 = 7x - 2
20y – 16 = 18y -10
t=6
x = -1
y=3
Putting
brackets in
Factorising
means...
This is the exact reverse of multiplying out the brackets.
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
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…
For more practice click here
4x(x – 2y) = 4x² - 8xy
Are you ready for
the answers ?
Can you factorise these?
Write down your solutions to:
1.
9x + 12
3(3x + 4)
2.
10x - 6
2(x -3)
3.
9 – 3x
3(3 – x)
4.
3x + 5xy
x(3 + 5y)
5.
x² - 9x
x(x – 3)
6.
x² + x
x(x + 1)
7.
3x² + 6xy
8.
p² + 6p
p(p + 6)
9.
8x² + 4x
4x(2x + x)
10.
ax² + ax
3x(x + 2y)
ax(x + 1)
Lesson
(10)
Have a go at...
1.
Forming equations
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.
12m
………………………………
(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.
12m + 48c
………………………………
(2)
Are you ready for
the answers ?
(Total 3 marks)
More practice
Lisa packs pencils in boxes.
She packs 12 pencils in each box.
Lisa packs x boxes of pencils.
(a)
Write an expression, in terms of x, for the number of pencils Lisa
packs.
12x
.................................
(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.
10y + 12x
.................................
(2)
Are you ready for
(Total 3 marks)
the answers ?
More practice
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.
2
Flowerbed
5
Diagram NOT
accurately drawn
x
x
(a)
Write down an expression, in terms of x, for the shortest side of the
garden.
x+2
.....................................
(1)
(b)
Find an expression, in terms of x, for the perimeter of the garden.
Give your answer in its simplest form.
4x + 14
.....................................
(2)
The perimeter of the garden is 20 metres.
(c)
Find the value of x.
4x + 14 = 20
4x = 6
More practice
x = 6/4 = 1½
Are you ready for
the answers ?
(2)
(Total 5 marks)
The cost, in pounds, of hiring a car can be worked out using this rule.
Add 3 to the number of days’ hire
Multiply your answer by 10
(a)
Work out the cost of hiring a car for 4 days.9
Bishen hired a car.
The cost was £120
(b)
Work out the number of days for which Bishen hired the car.
(c)
The cost of hiring a car for n days is C pounds.
Write down a formula for C in terms of n.
Are you ready for
the answers ?
70
£……………………
(2)
9
……………………..
(2)
10(n+3)
……………………..
(3)
(Total 7 marks)
More practice
The width of a rectangle is x centimetres.
The length of the rectangle is (x + 4) centimetres.
(a)
(b)
Find an expression, in terms of x, for the perimeter of the rectangle.
Give your expression in its simplest form
The perimeter of the rectangle is 54 centimetres.
Work out the length of the rectangle.
4x + 8
…………………….
(2)
4x + 8 = 54
4x = 46
x = 46/4 = 11½
The length must be
Lesson
11½ + 4 = 15½ cm.
Are you ready for
the answers ?
15½
…………………cm
(3)
(Total 5 marks)
Are you ready for
the answers ?
TAIL 2
1.
(a)
Factorise
15x + 5
5(3x +1)
(b)
Factorise
6y² - 3y
3y(2y – 1)
(c)
Factorise
a² + a
(d)
Factorise
18x² + 12x
6x(3x + 2)
(e)
Simplify
xy² - xy
xy(y – 1)
a(a + 1)
Click for the next question
2.
(a)
used.
Jennifer made x cakes.
She put 4 sweets on top of each cake.
TAIL 2
Write down an expression, in terms of x, for the number of sweets she
4x
……………………………..
(1)
Paul made 3 more cakes than Jennifer.
(b)
made.
Write down an expression, in terms of x, for the number of cakes Paul
x+3
…………………………..
(1)
Paul also put 4 sweets on each of his cakes.
(c)
used.
Write down an expression, in terms of x, for the number of sweets Paul
4(x + 3)
……………………………..
Are you ready for
the answers ?
(1)
Click for next question
(Total 3 marks)
3.
Eggs are sold in boxes.
A small box holds 6 eggs.
A large box holds 12 eggs.
Hina buys x small boxes of eggs.
TAIL 2
Hina also buys 4 less of the large boxes of eggs than the small boxes.
(a)
(b)
Find, in terms of x, the total number of eggs in the large boxes
that Hina buys.
12(x – 4)
..........................
(1)
Find, in terms of x, the total number of eggs that Hina buys.
Give your answer in its simplest form.
12(x – 4) large eggs and 6x small eggs
12x – 48 + 6x = 18x - 48
Are you ready for
the answers ?
Click for the next question
18x - 48
..........................
(2)
(Total 3 marks)
4.
The perimeter of this triangle is 19 cm.
All lengths on the diagram are in centimetres.
(t + 4)
(t + 3)
Are you ready for
the answers ?
(t – 1)
Work out the value of t.
3t + 6 = 19
3t = 13
t = 13/3 = 4⅓
Lesson
4⅓
t = ……………………………
(Total 3 marks)