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

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.

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

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

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

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

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