1. Expanding

2. 101 11 1001 Area=101×11 100×111×11 = (100+1) × 11 = 100×11+1×11

3. ab 2a 2b 2 (a + b) × c = a × c + b × c

4. a3 b 2 ab 3b 2a6 (a+3) × (b+2) = ab + 2a + 3b + 6

5. (a+3) × (c+2) = ac + 2a + 3c + 6 = 2a + 3c + 6 + ac = 3c + 6 + ac + 2a = 6 + ac + 2a + 3c a3 c 2 ac 3c 2a6

6. (a+3)(b+2)= ab (a+3)(b+2)= ab +2a +3b +6 +2a+3b

7. Linear Equations

8. Have one variable and one solution. Ex. 3x+5=11 x=2 Equations can sometimes be solved by working out the answer mentally. Ex. 5-x=3 x=? The aim when solving an equation is to get the variable (x) on one side of the equation. To remove a term from one side of an equation, carry out the opposite operation to both sides of the equation. Ex x-5=3 x-5+5=3+5 x=8 Remember: + and - are opposite operations. × and ÷ are opposite operations. The answer should then be checked by substituting the answer back into the equation to make sure that both sides have the same value.

9. Linear Equation Application Mind reader: I think of a number, multiply it by 5 and then take away 4. The result is 31. What is the number I’m thinking of?

10. How many girls are there in this class? I add 2 to the number of girls then multiply it by 3. It is the same as the number of girls plus 26. What is the number of girls in this class?

11. How old am I? My mom’s age is twice my age. The sum of our age is 72. How old am I?

12. A helicopter costs 450000 times of a lollipop. The cost of a Helicopter and 100 lollipops is 562600 times the cost of a lollipop. How much are the lollipop and the helicopter?

13. Simulation Equaitions

14. Simultaneous Equation Andrew buys 1 apple and 1 banana for $4. How much does each apple and banana cost? Matt buys 1 apple and 2 bananas for $6. How much does each apple and banana cost? The difference is 1 banana. So 1 banana costs 6-4=2 dollars!

15. + + = = 8 6 = 2 = 1

16. 3a+2b=8 a+2b=6 2a=2 a=1 Substitute a=1 into a+2b 1+2b=6 2b=6-1 2b=5 b=2.5 5a+11b=8 2a+11b=2 3a=6 a=2 Substitute a=2 into 2a+11b=2 2×2+11b=2 4+11b=2 11b=2-4 11b=-2 b=-2 4a-3b=10 2a-3b=6 2a=4 a=2 Substitute a=2 into 2a-3b 2 × 2-3b=6 4-3b=6 -3b=2 b=2/-3

17. Maths starter

18. += += 50 20 Double it!!! + = 40 10 =

19. 2x+3y=6 1 x+y=1 2 2 ×2 2x+2y=2 3 1 - 3 3y-2y=6-4 y=2 Substitute y=4 into 2 x+4=1 x=1-4 x=-3 Can cancel out 3y by 2 ×3, but in this case easier to cancel out 2x y=-3 y=2 10x+3y=1 1 2x+2y=3 2 2 × 5 10x+10y=15 3 3-13-1 10y-3y=15-1 7y=14 y=2 Substitute y=2 into 2 2x+2 × 2=3 2x+4=3 2x=3-4 2x=-1 x=-1/2 y=2

20. Geese and Pigs There are a total of 50 geese and pigs. There are 140 legs altogether. How many geese and how many pigs are there? Let x=the number of geese y=the number of pigs x+y= 50 2x+4y=140

21. Jonathan x+y=8 1 x-y=2 2 Oh no… Simultaneous Equations!!! Don’t worry Jonathan. Ms Li taught us how to do it! Opps I think I was talking to Nick when she was explaining it… She said we need to find out the difference of the two equations! Equation 1 – Equation 2 X will be canceled out! We then get y-(-y)=8-2 2y=6 y=3 Then you subsititute y=3 into x+y=8 You get x=5! y-(-y)????? That’s too hard for me!!! Blake Corne You don’t have to make it this hard!! Look! +y and –y!! If you add Equation 1 and Equation 2 +y and –y will be canceled out! You would have x+x=8+2 2x=10 x=5 If you substitute x=5 into x+y=8 You get y=3! It’s the same answer as Blake’s!!

22. Quadratic equations

23. 0 × any number = 0

24. If 4×x=0 What can you say about x? x=0 If 5×y=0 What can you say about y? y=0 If x × y = 0 What can you say about x and y? Either x=0 or y=0 If (x-2)(x+3)=0 What can you say about x -2 and x+3? Either x-2=0 or x+3=0 What can you say about x? x=2 or x=-3

25. Summary

26. Solving Equations Step 1: Bracket Step 2: + and – Step 3: ÷ and × When a term is moved. Change it to the opposite sign. ÷  × +  -

27. End of the year revision

28. Revision 1)Expanding (a+b)(a+2b)= (a-b)(2a+b)= 3(a+b)+2(a-2b)= 2) Factorise a 2 + ab= a 2 + 3a + 2= a 2 -2a-15= 2a 2 +4a+2= a 2 – 9=

29. Exponents 2a 2 ·3a 3 = (2a 3 ) 2 = 6a 2 b 3 = ab 3ab 2 = 6b 3 ×+×+ power  × ÷-÷-

30. Equations Linear Equations 9x-5=-2 -3x+9=2 4(x+2)=-24 3(2x-1)=12 (2x+3)(x-5)=0 (3x-2)(x+3)=0 Simultaneous Equations: 2x + 3y = 6 2x + 5y = 10 3x+2y=8 -3x+5y=6 2x+3y=10 3x+y=3

31. Changing subject Backtracking rule or flowchart a= 34bc 2 + 4d (b as subject) a=42b 2 c (c as subject) d

32. Pattern What’s the nth term? (linear) 2,6,10,14…… 3,6,9,12 What’s the nth term? (quadratic)

33. 2006 Merit

34. One integer is 5 more than twice another integer. The squares of these two integers have a difference of 312. Write at least ONE equation to describe this situation, and use it to find the TWO integers.