1. Getting Used to Algebra
Algebra is where you use letters to represent numbers
Aims:
To get to grips with the algebra idea
To solve simple algebraic problems
Monday, 24 April 2017

2. Example
Alex has some sweets, we do not know how many sweets Alex has…. so we can say ‘Alex has x sweets’ If Alex is given 5 more sweets, how many sweets has he got? x + 5
Monday, 24 April 2017

3. Example
Bob has some toys, we do not know how many toys he has…. so we can say ‘Bob has m toys’ If Bob buys 6 more toys, how many toys has he now got? m + 6
Monday, 24 April 2017

4. Another Example
Bill catches y fish. Ben takes 3 away from him. How many fish does Bill now have? y - 3
Monday, 24 April 2017

5. A Third Example
Fred has x DVDs Frank has y DVDs How many DVDs do they have altogether? x + y
Monday, 24 April 2017

6. Questions Use algebra to write: 2 less than w 3 more than d
5 together with c
f more than g
p less than q
m less than 7
w – 2
d + 3
c + 5
f + g
q - p
7 - m
Monday, 24 April 2017

7. Adding and Subtracting with Letters
a + a + a = b + b + b + b + b = c + c – c + c = 3a 5b 2c
Monday, 24 April 2017

8. Questions
1) a + a = 2) c + c + c + c = 3) p - p + p = 4) v + v + v + v - v + v = 5) b + b + b – b = 6) n - n + n + n + n - n + n = 7) h - h = 8) g + g + g - g 2a 4c p 4v 2b 3n 2g
Monday, 24 April 2017

9. Adding Expressions & Terms
2a + 4a = 6a – 5a = 7a – 4a + 10a = 6a a
13a
Monday, 24 April 2017

10. Questions 7w
1) 5c + 7c 2) 9d – 4d 3) 2s + 12s 4) 13a – 5a 5) 4e – e + 3e 6) 6e – 2e + 5e 7) 12e – 10e 8) 3h – 2h + h 9) 4r – r + 5r
12c
10) 3w + 9w – 5w 11) 2g + 5g – 3g 12) 7f – 4f + 9f 13) 5b + 50b 14) 75j – 43j 15) 34p + 12p – 5p 16) 3m – m + m + 5m 17) d – d + d - d 18) 4f + 10f - 13f 5d 4g
14s
12f
55b 8a 6e
32j 9e
41p 2e 8m 2h f 8r
Monday, 24 April 2017

11. Going Negative 3a – 5a = 5p + 4p – 12p = -5a + 2a – 7a = -2a -3p -10a
Monday, 24 April 2017

12. Working with Algebra Aims:
To be able to collect like terms in order to simplify algebraic expressions
To be able to multiply terms together and expand the brackets from an expression
Monday, 24 April 2017

13. Example 1
3a + 4b + 2a + 6b = firstly collect like-terms… 3a + 2a + 4b + 6b = 5a + 10b
Monday, 24 April 2017

14. -3a + 2b – 4a + 6b collect like-terms -3a – 4a + 2b + 6b -7a + 8b
Example 2
-3a + 2b – 4a + 6b collect like-terms -3a – 4a + 2b + 6b -7a + 8b
Monday, 24 April 2017

15. -4a + 9b + 3a - 12b collect like-terms -4a + 3a + 9b – 12b - a – 3b
Example 3
-4a + 9b + 3a - 12b collect like-terms -4a + 3a + 9b – 12b - a – 3b
Monday, 24 April 2017

16. Aims
To be able to simplify expressions (including expressions with indices)
To be able to expand brackets and simplify
To be able to understand the 3 laws of indices
Monday, 24 April 2017

17. Simplify each expression…
5a – 4y – 11a + 2y
2) -4f + 6g – 7f – 3g
3) 4m + 9n – 6m - 14n
4) -4t + 7y – 10t + 5y
5) 1 + 2r – 7 – 7r
6) 3d – 5e – 4d + 2e 7) p + 8r – 7p + 2r + 3p 8) 9x + 3x – 8 - 2x + 3 9) a – 6b + 2a + 3b - 3a 10) 3g + 2h – 3h + 2g
-d – 3e
-6a - 2y
-11f + 3g
-3p + 10r
-2m – 5n
10x – 5
-14t + 12y
-3b
-6 – 5r
5g – h
Monday, 24 April 2017

18. Harder Simplification… (remember, a, a2 and a3 are completely different terms)
4a – 5a2 + 2a + 3a2 =
2) 5h2 + 2h3 – 10h2 – 3h3 =
3) 3x2 – 4x – 5x2 + x =
4) -4t2 + 7t – 10t2 + 5t3 =
5) r2 + 2r – 7r2 – 7r2 – 2r =
-5h2 –h3
– 3x-2x2
7t -14t2 + 5t3
-13r2
Monday, 24 April 2017

19. Multiplying Terms Together
When two terms in algebra are being multiplied together, they are simply written next to each other. e.g. 3a means 3 x a and efg means e x f x g
Monday, 24 April 2017

20. Multiplying Terms Together
Simplify: 2a x 4b = 10c x 2de = 3w x 4y x 5z =
8ab
20cde
60wyz
Monday, 24 April 2017

21. Questions – simple multiplication
1) 7ab x 8pq 2) 3f x 2h x 5a 3) 3abc x 4def 4) 5g x 25 5) 5mn x 2pq x 4 6) 5f x g x h x 2j 7) 3w x 4d x 2h x yz 8) 7pqr x 4abc x 2h
56abpq
30afh
12abcdef
125g
40mnpq
10fghj
24dhwyz
56abchpqr
Monday, 24 April 2017

22. Questions – reverse multiplication
1) 7ab x ___ = 70abc 2) 3f x ___ x 5h = 60fgh 3) 3abc x ___ = 3abcd 4) 5g x ___ = 20g 5) 5mn x ___ x 4 = 20mnp 6) 5f x ___ x 2g = 40fgh 7) 3w x ___ x 2v x yz = 24vwyz 8) 4bc x ___ x 2ad = 80abcde
10c 4g d 4 p 4h 4
10e
Monday, 24 April 2017

23. Dividing Algebraic Terms
Simplify: 8a ÷ 4 = 10ab ÷ 2a = 20pq pq = 2a 5b 20
Monday, 24 April 2017

24. Powers
Aims: To remember how to work out the HCF & LCM from any given pair of numbers To be able to understand how indices (powers) work in algebra To be able to manipulate the powers in an expression in order to simplify it
Monday, 24 April 2017

25. Powers Rules
a x a = a x a x a x a = But, what is a2 x a4? It’s (a x a) x (a x a x a x a) = What did you do with the powers? You added them! a2
Rule 1:
When you multiply powers of the same letter or number you add the indices… a4 a6
Monday, 24 April 2017

26. a3 x a6 x a2 = c3 x c5 x c = 2y2 x 4y5 = 3m3 x 4m5 =
Indices Questions
a3 x a6 x a2 = c3 x c5 x c = 2y2 x 4y5 = 3m3 x 4m5 =
a11 c9 1
8y7
12m8
Monday, 24 April 2017

27. Harder Indices Questions
2a3b6 x a6b2 = 3c5d4 x 5c2d4 = 2ab4 x 4a2b3 = 3mnp3 x 4mn2p5 =
Q1.
2a9b8
Q2.
15c7d8
Q3.
8a3b7
Q4.
12m2n3p8
Monday, 24 April 2017

28. Powers
a x a x a x a x a = a x a x a = But, what is a5 a3? It’s (a x a x a x a x a) (a x a x a) = What did you do with the powers? You subtracted them! a5
Rule 2:
When you divide powers of the same letter or number you subtract the indices… a3 a2
Monday, 24 April 2017

29. Indices Questions a6  a2 = c3  c5 = 3y2 x 4y5 = 2y3 a4 c-2 6y4
Monday, 24 April 2017

30. Harder Indices Questions
4a6 x 8a2 = 2a9 30y2 x 4y5 = 6 x y4
Q1.
16a-1
20y3
Q2.
Monday, 24 April 2017

31. Powers a x a x a = What do you think is… (a3)2 = a3 x a3 = a3 a6
Rule 3:
When you raise a power by another power (separated by brackets) you multiply the indices… a6
what did you do with the powers here?
multiplied them!
Monday, 24 April 2017

32. (a2)4 x (a3)2 = 4(a2)3 = (4a2)3 = (5ab3)2 =
Indices Questions
(a2)4 x (a3)2 = 4(a2)3 = (4a2)3 = (5ab3)2 =
Q1.
a14
Q2.
4a6
Q3.
64a6
25a2b6
Q4.
Monday, 24 April 2017

33. Have you really understood indices??
We’ll see… Simplify this…
Monday, 24 April 2017

34. Expanding the Brackets
Expand these expressions: 3(a + b) = 4(y + 6) = 2(2a + 3b – 4c) =
3a + 3b
4y + 24
4a + 6b – 8c
Monday, 24 April 2017

35. Expand the brackets…
1) 4(2p – 12) = 2) 5(2a + 4b) = 3) 3(4c – 4b) = 4) 7(3e + 2f – 4g) = 5) 9(6w + 2y – 7z) = 6) 10(3b – 9m) = 7) 6(-6j – 7m) = 8) 5(4a – 3b) =
8p - 48
10a + 20b
12c – 12b
21e + 14f – 28g
54w + 18y – 63z
30b – 90m
-36j – 42m
20a – 15b
Monday, 24 April 2017

36. Factorising
Aims:
To remember how to expand brackets, including expressions with indices
To learn what the process factorising is and be able to apply it to any expression
Monday, 24 April 2017

37. Factorising
Reminder of how to expand brackets: 4(2m – 5) = What is factorising then? Q1. 8m – 20 =
8m - 20 4 ( 2m - 5 )
Monday, 24 April 2017

38. Factorising Q2. 25a – 30b = Q3. 40a + 6a2 = 5 ( 2m - 5 ) 2a ( 20 + 3a
Monday, 24 April 2017

39. Adding Bracketed Expressions
Aims:
To be able to multiply out the brackets from expressions…
… and then collect like-terms and simplify
Monday, 24 April 2017

40. Adding Bracketed Expressions
4(a + 5b) + 3(7a – b) = 4a + 20b + 21a – 3b = 25a + 17b
Monday, 24 April 2017

41. Adding Bracketed Expressions
2(7a – 6b) + 6(3a + b) = 14a – 12b + 18a + 6b = 32a – 6b
Monday, 24 April 2017

42. Questions
1) 7(2a – 4b) + 2(2a + b) 2) 2(3y – w) + 3(2y + 5w) 3) 4(p + q) + 5(2p – 3q) 4) 6(2n + m) + 2(n – m) 5) 2(4s + r) + 7(2s – 3r)
18a – 26b
12y + 13w
14p – 11q
14n + 4m
22s – 19r
Monday, 24 April 2017

43. Subtracting Bracketed Expressions
3(2a – 4b) – 2(a + 2b) =
Monday, 24 April 2017

44. Subtracting Bracketed Expressions
3(2a – 4b) – 2(a + 2b) = 6a – 12b – 2a – 4b =
Monday, 24 April 2017

45. Subtracting Bracketed Expressions
3(2a – 4b) – 2(a + 2b) = 6a – 12b – 2a – 4b = 4a – 16b
Monday, 24 April 2017

46. Subtracting Bracketed Expressions
3(2p + 3q) – 4(p – 2q) =
Monday, 24 April 2017

47. Subtracting Bracketed Expressions
3(2p + 3q) – 4(p – 2q) = 6p + 9q - 4p + 8q =
Monday, 24 April 2017

48. Subtracting Bracketed Expressions
3(2p + 3q) – 4(p – 2q) = 6p + 9q - 4p + 8q = 2p + 17q
Monday, 24 April 2017

49. Invisible 1
7(m – 2n) – (m – 3n) =
Monday, 24 April 2017

50. 7(m – 2n) – (m – 3n) = 7m – 14n – m + 3n =
Invisible 1
7(m – 2n) – (m – 3n) = 7m – 14n – m + 3n =
Monday, 24 April 2017

51. 7(m – 2n) – (m – 3n) = 7m – 14n – m + 3n = 6m - 11n
Invisible 1
7(m – 2n) – (m – 3n) = 7m – 14n – m + 3n = 6m - 11n
Monday, 24 April 2017

52. Questions
1) 3(4n + 5m) – 5(2n – 4m) 2) 5(n – 2m) – (m + 2n) 3) 3(2n + 6m) – 6(n – 2m) 4) 2(3n – m) – 7(n – 5m) 5) 8(5n – m) – 2(2n + m)
Monday, 24 April 2017

53. Questions
1) 3(4n + 5m) – 5(2n – 4m) 2) 5(n – 2m) – (m + 2n) 3) 3(2n + 6m) – 6(n – 2m) 4) 2(3n – m) – 7(n – 5m) 5) 8(5n – m) – 2(2n + m)
Monday, 24 April 2017