1 TO EXCELL in You need to… set TARGET familiar with FORMAT of PAPER do EXERCISES Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise Exercise M M y y T T A A R R G G E E T T
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FORMAT&COMPONENT
1
TO EXCELL in
You need to…
set TARGET
familiar with FORMAT of PAPER
do EXERCISESExercise Exercise Exercise Exercise Exercise
sin2 x + 3cos x = 32 sec2 x + tan2 x = 5 ………have different functions ……….
Proofing: Use Identity
Remember :
cot
.1tan,
Acos
AsinAtan , sec 2x =
x2cos
1, cosec A =
Use of Trigo Ratios: Examples:
From the question given, If sin A = , A is not acute,
1. Determine the quadrant involved. ……second……………….
2. Determine the values of the other trig. fxn cos and tan = negative
in the quadrant. cos A =53 , tan A = –
find sin 2A
3. Do you need to use identity? sin 2A = 2 sin A cos A
4. Substitute values = 2 ( ) (53 )
=25
24
Sketch Graphs
y = a sin b x + ca =a cos b x + ca tan b x + c b =
c =
Basic Graphs
2
1-
–1-
Asin
1
y = sin x
max / minimum point
number of basic shape between 0 and 2
14
increase / decrease translation of the
2
1-
–1-
y = cos x y = tan
2
x
FORM 5 TOPICS
15
TOPIC 6: PERMUTATIONS & COMBINATIONS
Permutations = …order of arrangement is important Combinations =…order not important….
Three committee members of a society are to bechosen from 6 students for the position ofpresident, vice president and secretary. Findthe number of ways the committee can be
chosen.
Permutations: 6P3
Three committee members of a society are to bechosen from 6 students. Find the number ofways the committee can be chosen.
Combination: 6C3
with condition:Find the number of different ways the lettersH O N E S T can be arranged if it mustbegin with a vowel.
2 5 4 3 2 1
conditionvowels = 2 choices
Find the number of ways 11 main players of afootball team can be chosen from 15 localplayers and 3 imported players on the
condition that not more than 2 importedplayers are allowed.
condition 2 Import.
Case : (2 Import, 9 local) or 3C2.15C9
(1 import 10 locals) or + 3C1.15C10
( 0 import 11 locals) + 3C0.15C11
TOPIC 7: PROBABILITY
P(A) =)S(n
)A(n
- Probability event A or B occurs = P(A) + P(B)
- Probability event C and D occurs = P(A) . P(B)
Considering several cases:
Probability getting the same colors = Example: (Red and Red) or (Blue and blue)
Probability of at least one win in two matches = (win and lose) or (lose and win) or (win and win)
Or using compliment event = 1 – (lose and lose)
TOPIC 8: PROBABILITY DISTRIBUTION
BINOMIAL DISTRIBUTION
- The table shows the binomial probability distribution ofan event with n = 4 .
-
-
NO
- Fo
- T
- T
TO
M
re
st
m
______
0.30.25
0.2
0.15
0.1
0.05
P(X)
X = r r = 0 r = 1 r = 2 r = 3 r = 4
16
total = 1
formula: P(X = r) = n C r p r q n – r
mean, = np standard deviation = npq
RMAL DISTRIBUTION
rmula :
XZ
ype 1 : Given value of X find the value of Z find th[use formula] [use
ype 2 : Given the probability Find the value of Z Find i[use log book] [use
PIC 9: MOTION IN STRAIGHT LINES
Displacement, s Velocit
s = dtvd
dv
aximum velocity -dt
dv
turn to O s = 0 -
ops momentarily v = 0
ax. acceleration
P(X) 0.2 0.15 0.3 0.25 0.1
0 1 2 3 4 X=r
Graph of Binomial Prob Distribution
variance = npq
e probabilitycalculator]
ts value of X .formula]
y, v Acceleration, a
t
s
dt
dva =
2
2
dt
sd
0 a = 0
-
0dt
da
FORM 5 TOPICS
17
TOPIC 10: LINEAR PROGRAMMING
Given:
(i) y > x – 2 (ii) x + y 5 (iii) 4x y
(a) Draw and shade the region, R, that satisfy the three inequalities on the graph paper providedusing 2 cm to 2 units on both axes.
(b) Hence, find, in the region R, the maximum value of 2x + y where x and y are integers.
–3 –2 –1 0 1 2 3 4 5 6
1
2
3
4
5
6
–1
–2
–3
–4
2 possible maximum points (x, y intergers)
(1, 4) and ( 3, 2) . Point (3, 1) cannot be
taken because it is not in R (it’s on dotted line)