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