1. 𝐴

2. B

3. 𝐴′

4. 𝐵′

5. (A ∪𝐵)

6. (A ∩𝐵)

7. (A ∩𝐵)′

(A 𝑈𝐵′) This is quite complex Watch

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

Complete this table

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= 216 24 𝑛=9 substitution constant Final equation Key Words Directly/ inversely proportional square cube root equation substitute variable constant

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= 80 2 2 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

Worksheet on proportion

Revision 2

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

Revision of Tree Diagrams – Probability Flash back

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

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

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

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

Thinking about the concept of dependents events

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