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Functions
Sin = cos (90o − )
Cos = sin (90o − )
Tan = cot (90o − )
Tan =
Pn = n!
Arrangement of r objects from n objects
n
Secant = sec =
2 tan A
1 tan 2 A
CHAPTER 6: PERMUTATION AND
COMBINATION
1
...
2
...
Find
(a) the number of ways to arrange all the letters
in the word
...
(c) The number of ways of arranging 4 letters
out of the 6 letters such that the last letter is
‘S’
...
sin
cos
Total arrangement = 2 P1 × 5 P5 = 240
...
OR:
5
4
3
1
Number of ways = 5 × 4 × 3 × 1 = 60
zefry@sas
...
my
6
2
...
The members are elected
from 7 parents, 6 teachers and the principal of
the school
...
(b) the committee consists of the principal, 3
teachers and 4 parents
...
(a)
+ (0
...
03760
(b)
2
...
14
CHAPTER 8: PROBABILITY
DISTRIBUTION
1
...
Example: The volume of packet drink produced
by a factory is normal distributed with a mean of
500 ml and standard deviation of 8 ml
...
(a)
P(X > 510) = P(Z >
510 500
)
8
(b) P(490 < X < 510)
npq
Example:
In a survey of a district, it is found that one in
every four families possesses computer
...
(b) If there are 2800 families in the district,
calculate the mean and standard deviation
for the number of families which possess
computer
...
edu
...
25) = 0
...
X
Z = standard normal score
X = normal score
= mean
= standard deviation
7
number of committees = total number of
committees – number of committees with
no teacher – number of committees with 1
teacher
...
3760 0
...
63
(b) number of committees =
6
Mean, = np = 2800 × 0
...
3
Standard deviation =
number of committees = 1C1 13C7 = 1716
(elect 1 principal, and 7 committee
members from 13 = 7 parents and 6
teachers)
1
P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6)
= 6C4 (0
...
75)2 6C5 (0
...
75)
490 500
510 500
8
8
= P(1
...
25)
= 1 – P(Z > 1
...
25)
= 1 – 2(0
...
7888
CHAPTER 9: MOTION ALONG A
STRAIGHT LINE
1
...
Return to O again s = 0
Maximum/minimum displacement
(a)
b
Distance =
ds
=0
dt
(a)
s = 2t – t2
t = 5,
s = 10 – 25 = 15 m
(b) Return to O again s = 0
2t – t2 = 0
t(2 – t) = 0
t = 0 or
constraints
...
Form the optimum equation
ax + by = k
4
...
5
...
Example:
School uniform
Shirt
Shorts
zefry@sas
...
my
the inequalities are:
(i) x + y ≥ 10
(ii) 10x + 20y 800
x + 2y 80
y 1
x 2
1
y≥ x
2
To draw x + y = 10, x = 0, y = 10 and y = 0,
x = 10
To draw x + 2y = 80
x = 0, 2y = 80, y = 40
y = 0, x = 80
To draw y =
1
x
2
x = 0, y = 0
x = 40, y = 20
...
maximum profit = 5 × 40 + 3 × 20 = RM 260
...
zefry@sas
...
my
10