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Revision Topics.

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1 Revision Topics

2 James has a fair six sided die numbered 1 to 6. which he rolls twice.
a) Complete the tree diagram to show the possible outcomes. 1 6 Roll a 2 1 6 × 1 6 Roll a 2 1 6 Not a 2 1 6 × 5 6 5 6 Roll a 2 5 6 × 1 6 1 6 5 6 Not a 2 Not a 2 5 6 1 36 b) (i) b) Calculate the probability that James rolls Two 2s Only one 2. 5 36 × 5 36 = 10 36 = 5 18 (ii)

3 A bag contains 3 red and 7 blue balls.
A ball is take from the bag at random and then replaced. Another ball is then selected from the bag. (a) Complete the tree diagram . 0.3×0.3 =0.09 Red 0.3 Red 0.3 Blue 0.7 Red 0.3 0.7 blue Blue 0.7×0.7 =0.49 0.7 b) What is the probability of both balls being of the same colour? = =0.58

4 Example A ladder, 2.8 m long, leans against a wall. The bottom of the ladder is 1.25m from the foot of the wall. Calculate the height up the wall the ladder reaches. ℎ 2 = − 2.8m ℎ 2 =6.2775 h ℎ= ℎ=2.51 m 1.25m

5 𝑃𝑁 2 = 25 2 − 11 2 𝑃𝑁 2 =504 𝑃𝑁= 504 𝑃𝑁=22.4499… Example
The diagram represents a radio mast held up by a series of wire cables. 𝑃𝑄=𝑃𝑅=25 m, 𝑄𝑁=𝑁𝑅=11m and angle 𝑆 𝑄 𝑁=35° Calculate the length PS Calculate the angle 𝑃 𝑄 𝑆 P (a) 𝑃𝑁 2 = 25 2 − 11 2 25m 𝑃𝑁 2 =504 S 𝑃𝑁= 504 25m 𝑃𝑁= … 35° tan 35 = 11 𝑆𝑁 Q R N Hyp 11m opp 35° 𝑆𝑁= 11 tan 35 11m adj 𝑆𝑁= … 𝑃𝑆= −15.709… 𝑃𝑆=6.74 m

6 cos 𝑄 = 11 25 (a) =0.44 Hyp 25m opp 𝑄=63.89… 𝑃 𝑄 𝑆=63.89−35 𝑃 𝑄 𝑆=28.90° 35° 11m adj


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