1. 𝐴

2. 2. B

3. 𝐴′

4. 𝐵′

5. (A ∪𝐵)

6. (A ∩𝐵)

7. (A ∩𝐵)′

8. (A 𝑈𝐵′) This is quite complex
Watch

9. Quadratics Solve this equation 𝑥 2 +4𝑥=12 by all the methods
Factorisation
( ) ( )=0
x= ___ or x=___
Use the formula
𝒂 𝒙 𝟐 +𝒃𝒙+𝒄=𝟎 𝒙= −𝒃± 𝒃 𝟐 −𝟒𝒂𝒄 𝟐𝒂
Complete the Square
(𝑥+?) 2 −?+?=0
(𝑥+𝑎) 2 +b=0
Graphically
(need to make a table and plot

10. Complete this table

12. Directly/ inversely proportional
Inverse Proportion 1:
𝑡 is inversely proportional to 𝑛.
When 𝑛=2, 𝑡=108.
(a) Find an equation linking 𝑡 and 𝑛.
(b) When 𝑛=6 find the value of 𝑡
(c) When 𝑡=24 find the value of 𝑛
(b) When 𝑛=6
𝑡= 216 𝑛
𝑡= 216 6
𝑡=36
Box It
Up!
(a) 𝑡∝ 1 𝑛
𝑡= 𝑘 𝑛
108= 𝑘 2
108×2=𝑘
216=𝑘
𝑡= 216 𝑛
Inversely proportional
General equation
(c) When 𝑡=24
𝑡= 216 𝑛
24= 216 𝑛
24𝑛=216 𝑛=
𝑛=9
substitution
constant
Final equation
Key Words
Directly/ inversely proportional
square
cube
root
equation
substitute
variable
constant

13. Directly/ inversely proportional
Inverse Proportion 2:
𝑥 is inversely proportional to 𝑦 2 .
When 𝑥=5, 𝑦=4.
(a) Find an equation linking 𝑥 and y.
(b) When 𝑦=2 find the value of 𝑥
(c) When 𝑥=5 find the value of y
(b) When 𝑦=2
𝑥= 80 𝑦 2 𝑥=
𝑥=20
(a) 𝑥∝ 1 𝑦 2
𝑥= 𝑘 𝑦 2
5= 𝑘 4 2
16×5=𝑘
80=𝑘
𝑥= 80 𝑦 2
Inversely proportional
(c) When 𝑥=5
𝑥= 80 𝑦 2
5= 80 𝑦 2
𝑦 2 = 80 5
𝑦 2 =16
𝑦= 16
𝑦=4
General equation
substitution
constant
Final equation
Key Words
Directly/ inversely proportional
square
cube
root
equation
substitute
variable
constant

14. Worksheet on proportion

17. Revision 2

18. Revision Remembering work on speed time graphs
Annotate these diagrams with the best words
Speed-time graphs
Distance—time graphs
A train changes speed as shown in the
speed—time graph.
acceleration
total distance
Going back to the start
speed
Constant Speed
decelerating
Resting

19. Revision of Tree Diagrams – Probability
Flash back

20. Tree Diagrams Remember this
A vending machine offers tea or coffee; with or without sugar; and with or without milk.
Use a tree diagram to show the variety of drinks on offer
Decision 1 Decision 2 Decision 3

21. Independent red red blue red blue blue
Peter has ten coloured cubes in a bag.
Three of the cubes are red and 7 are blue.
He removes a cube at random from the bag and notes the colour before replacing it.
He then chooses a second cube at random. Record the information in a tree diagram.
First Choice
Second Choice
red
red
blue
red
Independent
blue
blue

22. Characteristics red blue Going along the branches you multiply
down
Going along the branches you multiply
red
blue
First Choice
Second Choice
The probabilities for each event are shown along the arm of each branch and they sum to 1.
Ends of first and second level branches show the different outcomes.
Probabilities are multiplied along each arm.
Characteristics

23. Probability (Tree Diagrams)
Q3 Sports
Probability (Tree Diagrams)
Question 3 Peter and Becky run a race and play a tennis match. The probability that Peter wins the race is 0.4. The probability that Becky wins the tennis is 0.7. (a) Complete the tree diagram below. (b) Use your tree diagram to calculate (i) the probability that Peter wins both events. (ii) The probability that Becky loses the race but wins at tennis.
Race
Tennis
0.6
0.3
0.7
Peter Win
P(Win and Win) for Peter = 0.12
0.4 x 0.3 = 0.12
0.4 x 0.7 = 0.28
0.6 x 0.3 = 0.18
0.6 x 0.7 = 0.42
Peter Win
0.4
Becky Win
P(Lose and Win) for Becky = 0.28
0.7
Peter Win
Becky Win
Becky Win

24. Thinking about the concept of dependents events

25. Dependent What is the probability of a) RR b) RB c) BR d) BB
Peter has ten coloured cubes in a bag.
Three of the cubes are red and seven are blue.
He removes a cube at random from the bag and notes the colour but does not replace it.
He then chooses a second cube at random. Record the information in a tree diagram.
What is the probability of a) RR b) RB c) BR d) BB
Dependent Events
r r
b b b b b b b
First Choice
Second Choice
red
r r r
b b b b b b b
red
blue
r r r
b b b b b b
r r r
b b b b b b
red
Dependent
blue
blue