1. Year 8 Mathematics Algebraml
Algebra

2. Expressions
A Mathematical uses numbers and letters to represent numbers
Expressions are used to solve problems
Example:
We represent the following as 4a + 3c. (4 apples and 3 cars)

3. Simplifying Expressions
Can you write an expression for the following:
5a + 6c (5 apples and 6 cars)

4. Simplifying Expressions
Can you write an expression for the following:
3a + 2c – 1c – 2a (3 apples add 2 cars minus 1 car minus 2 apples)
Can you simplify the expression?
1a + 1c or a + c
+ – –

5. Harder examples Simplify 2a + a - a + c - 2c - a = 2s -s + r + 3r =
2g + 3k - g + 2k - k =
5t2 + 2t – 2t2 + 4t

6. Summary
We can simplify expressions by collecting terms with the same letters together.
Terms with the same letter are called LIKE TERMS.
E.g. Simplify :
2a + a - a + c - 2c - a =
2s -s + r + 3r =
2g + 3k - g + 2k - k =

7. Perimeter
Write an expression for the perimeter of the following shape: a a a a

8. Write the Perimeter of these Shapes
p-y 3y
2y - p 4p
p+y x x y y 2y

9. Multiplication in Algebra
We else can write ?
Lets look again at the perimeter of a shape.
How many sides does the shape have?
How long is each side?
How can you calculate the perimeter of the shape?
In Algebra we don’t write the ‘x’ sign.
We write 4 x a as

10. Making Formulas
A Pencil costs x pence and a Pen costs y pence. Write in algebra the cost of:
(i) Crayons if they are 3p more than pens?
(ii) A sharpener if it is 4p less than pencils?
(iii) A book if it costs the same as a pencil and a pen together?
(iv) What is the total cost of a pencil and a pen?
(v) What is the total cost of Crayons and a book?

11. Some More! A box of roses contains n chocolates.
(i) How many chocolates are there if 4 are eaten?
(ii) A boy buys 3 boxes of chocolates. How many chocolates does he buy altogether.
(iii) Miniature heroes have 10 more chocolates in a box than roses. How many are in a box of miniature heroes?
(iv) How many chocolates are in 2 boxes of miniature heroes?
(v) How many chocolates are left if 5 chocolates are eaten out of a box of miniature heroes?

12. Meanings
Write out the meanings of the following: 3a xy
2pq r3 d 2 3b 4

13. Algebraic Pyramids To find the next term, ADD the two bricks below it

14. Harder Pyramids
a + b
2a + b b x 2y 7x

15. Substitution
We can find the value of an algebraic expression by substituting in values for the letters.
E.g. Find the value of the following expressions if a = 1 b = 4 and c = 10
a + 6
9 – b
c – a – b
7 + b – a 9a
5b + 2c2

16. Harder Substitution
Find the value of the following expressions if p=2 q=18 and r=20 4p
2r - q P 9 2r 10 p2

17. Forming Expressions A bus can hold x people.
A school trip needs 4 full buses.
How many people go on the trip?
Going home only half of the buses are needed, how many people travel home?
On another school trip there are only three buses needed and there are 5 free seats.
How many people travel on the buses this time?

18. More Expressions A farmer has m cows
He has the same number of pigs as cows. How many pigs has he?
He has 100 more sheep than pigs. How many sheep has he?
He has twice as many chickens as cow. How many chickens?

19. Summary
The three strips of wood have lengths as shown. Write expressions for the following situations:
The length of the new strip if the first two strips were joined together.
The length of the new strip if the last two strips were joined together.
The length of the new strip when the last strip is sawn off the first.
The length of the new strip when 2 of the first strip are joined together.
x cm
3 cm
2 cm

20. Summary 2 A box contains 24 books How many books are there in n boxes?
How many books are there in n boxes and half a box?
24 Books

21. Ages and Ages
An algebraic expression can be formed from a given word problem.
1. Charlotte is x years old. How old will she be in:
(a) 6 years time. (b) 12 years time. (c) another x years time
2. Simon is y years old.
(a) How old was he: (b) 3 years ago. (c) 7 years ago.