1. Revision 2

3. 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

4. Answer the questions for each graph
Speed-time graphs
Distance—time graphs
A train changes speed as shown in the
speed—time graph.
a What is the speed of the car from London to Crawley?
b The car breaks down at Crawley. For how long does the car break down?
c What is the speed of the car from Crawley to Brighton?
d The car is towed on a trailer back to London from Brighton. At what speed is the car towed?
a Find the total distance travelled by the train, and thus find the mean speed for the whole journey.
b Find the train's acceleration between A and B, B and C, and C and D.

6. Revision of Tree Diagrams – Probability
Flash back

7. 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

8. 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

9. 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

10. 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

11. Thinking about the concept of dependents events

12. 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

13. New questions to work on – they are difficult – you need to read the questions carefully !

15. Draw a tree diagram – it is hard to keep track of the answers

17. Draw a tree diagram – it is hard to keep track of the answers

21. Page 185 Exercise 2 1
a) (i) x = 8 (ii) 32
b) (i) x = 5 (ii) 12 (iii) 19
c) (i) x = 3 (ii) 36 (iii) 44
d) (i) x = 36, y = 14 (ii) 58 (iii) 54