Page 6 - Spotlight A+ Form 4 & 5 Mathematics KSSM

Formulae

• Speed = change of distance • An ungrouped data set is changed uniformly by
change of time multiplying a constant, c.
= the gradient of the distance-time graph (a) The range for the new data set
= c × the range for the original data set
• Distance travelled = area under speed-time graph (b) The interquartile range for the new data set
= c × the interquartile range for the original
• Area of trapezium data set
1
= × sum of the length of parallel sides × height (c) The standard deviation for the new data set
2
• Acceleration = change of speed = c × the standard deviation for the original
change of time data set
= the gradient of the speed-time graph (d) The variance for the new data set
= c × the variance for the original data set
2
• Average speed = total distance travelled
total time taken • P(A) = n(A)
n(S)
sum of data
• Mean, x = number of data • P(Aʹ) = 1 – P(A)

• Mean, x = sum of (midpoint × frequency) • A and B are two independent events

sum of frequencies
P(A ∩ B) = P(A) × P(B)
• Range = largest value of data – smallest value of data
• A and B are two non-mutually exclusive events
n
• If is an integer, s, then the first quartile, P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
4
x + x
• A and B are two mutually exclusive events
.
s
Q = ©PAN ASIA PUBLICATIONS
s + 1
1 2 P(A ∪ B) = P(A) + P(B)
n
• If is not an integer but lies between s and s + 1, • Monthly net income
4
then the first quartile, Q = x . = total monthly incomes – total monthly
1 s + 1
expenditures – monthly fixed saving
• Second quartile, Q = median
2
• If 3n is an integer, s, then the third quartile, • Premium
4 x + x = face value of policy × (premium rate per RMx)
RMx
Q = s 2 s + 1 . • Amount of required insurance
3
• If 3n is not an integer but lies between s and s + 1, = (percentage of co-insurance) × (insurable value of
4
then the third quartile, Q = x . property)
3 s + 1
d –b

1
• Interquartile range = Q – Q 1 • A = ad – bc –c a 
–1

3
x
x
• Variance, σ = ∑(x – ) 2 or σ = ∑x 2 –  2 PAʹ
2
2
N N • Scale factor, k = PA


x
• Standard deviation, σ = ∑(x – ) 2 or σ = ∑x 2 –  • Area of image = k × area of object
x
2
2
N
N
• For ungrouped data in frequency table, variance,
x
σ = ∑f(x – x) 2 2 ∑fx 2 –  , standard
 or σ =
2
2
N N



x
deviation, σ = ∑f(x – x) 2 or σ = ∑fx 2 –  .
2
N
N
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Formula Spotlight A+ Mate Tg4.indd 8 15/03/2021 3:52 PM