1.AMathsE Z
+
+
USING FORMULAE and calculator

2. The formulae are arranged in order of
MATHEMATICS COMPONENTS
ALGEBRA
GEOMETRY
CALCULUS
TRIGONOMETRY
STATISTICS
3. ALGEBRA
Quadratic Equationsax2 + bx + c = 0
1
When to use
Unable to factorise
x2 + 5x 3 = 0
Example
Solve the simultaneous equation. Give your answer to three decimal places.
Example
4. ALGEBRA
Press
-1
Press
Mode
Screen Display
Press
5
=
Unknowns?
23
Press
1
EQNMATVCT
1 2 3
Press
-3
=
Press
a?
0
Press
2
COMP
To leave EQN Press Mode (1X)Press
1
x2 + 5x 3 = 0
calculator
c= 3
a= 1
b= 5
3x
=
Degree ?
2 3
x1=
0.697224362
=
x2=
4.302775638
5. Indices
ALGEBRA
amxan= a m + n
aman= a m n
( am )n=a m n
When to use
2
3
4
i. index number with the same base / can be made the same.
ii.Does not involve addition/substraction
a)2x+ 1 . 4x = 16
b)2x=5
c)3x+ 3x 1=12
Example



6. Logarithms
ALGEBRA
WHEN TO USE
5
6
7
8
-Simplify

Evaluate

7. Find the value 8. Solve the equation.. loga m n=n loga m
Change the base
9. Logarithms
Given find
in terms ofm.
4
Change the base
log2
7
m
4
4
=
2
log2
= log2 22 = 2log22= 2
10. Arithmetic Progression
ALGEBRA
9Tn = a + (n 1)d
10
n
[
]
-
+
=
d
n
a
S
)
1
(
2
n
2
a =first term,d = common difference,
n = number of term
when to use
T term
S sum
d = T2-T1
11. Geometric Progression
ALGEBRA
11 Tn = ar n 1
12
13
when to use
T term
S sum
common ratio
Sn
sum to infinity
12. GEOMETRY
COORDINATE GEOMETRY
Distance between 2points: A(x1,y1), B(x2, y2)
Equation of locus
WHEN TO USE
Example
Point P moves such that its distance from the originis equals to its distance to a point A(1, 2). Find equation of the locus of P.
=
PO
PA
P(x, y)
P(x, y)
A(1, 2)
O(0, 0)
=
13. GEOMETRY
COORDINATE GEOMETRY

Mid point

14. Perpendicular bisector
midpoint
15. COORDINATE GEOMETRY
GEOMETRY
Q
m
R

n
P
WHEN TO USE
3
A point dividing a segment of a line
given:
The ratio of the distance between two points.
Example
(x1, y1)
PR : RQ = n : m
(x2, y2)
16. COORDINATE GEOMETRY
GEOMETRY
A
C
B
Area of triangle
How To Use
given: three vertices
ABCA
Area =
17. COORDINATE GEOMETRY
GEOMETRY
P
(0,4)
Q
(8,0)
(4,-2)
R
Calculate the area of triangle PQR.
= [ 0 + 0 + 32 16 - (-16) - 0]
= 16
18. Vectors
GEOMETRY
5
Example
If u = 2i3j
then, u =
6
=
when to use
Magnitude = distance
2i3j
r=xi+yj
unit vectors
19. DIFFERENTIATION
CALCULUS
b)
WHEN TO USE
a)y = x2 ( 1 + x )3
20. Integration
CALCULUS
4Area under curves
y
atx- axis
aty-axis
x
x = (y 2)2
y = x2 + 3x
2
1
area =
1 3
Area of shaded
=area
area
when to use
21. Integration
CALCULUS
atx- axis
aty-axis
5volumes of revolutions
22. STATISTICS
On screen
Scl Mode All
1 23
CLR
SHIFT
On screen
Mem clear
-------------
Press
Press
3
=
ChooseMODESD
23. STATISTICS
STATISTICS
5,7, 14,20
Mean
5+7+14+20
4
= 11.5
24. STATISTICS
5
7
14
20
M+
M+
M+
M+
USING CALCULATOR
Key-in the data:
Mean
5,7,14,20
Screen Display
Press
n=
1
n=
2
n=
3
n=
4
AC
25. 1 2 3
5.937
SHIFT
mean
S-Var
=
1
2
SHIFT
=
2
2
standard deviation
26. STATISTICS
STATISTICS
WHEN TO USE
Mean
x
f
0(2)+1(5)+2(4)+3(1)
2 + 5 + 4 + 1
27. STATISTICS
STATISTICS
WHEN TO USE
Standard Deviation
Variance
= get rid of square root
28. STATISTICS
STATISTICS
WHEN TO USE
median
29. 40 = 20 .2
6
(5)
9
19.5 24.5
19.5 + 3.333 = 22.83
30. When frequencies are involved,
CALCULATOR
31. INDEX NUMBERS
STATISTICS
WHEN TO USE
Price Index
Q1=price of item at specific time
Q0= price of item at base time
Ratio
Pie Chart
Angles
Percentage
Pictograph
Bar Graph
Composite Index
W= Weightage
32. Permutation & Combination
STATISTICS
Use calculator
n = number of objects,
r = number of chosen objects
when to use
Permutation
Combination
33. Probability
STATISTICS
46
8 10
35
7
2
2
A
B
= { 1 to 10},A = { even numbers }andB = { prime numbers }
Find the probability to select an even or prime numbers.
when to use
two events
+

P(A or B)=
=
34. Probability Distribution
STATISTICS
12 mean, =np
when to use
BINOMIAL DISTRIBUTION
Given the probability success (p) of an event that has only two outcomes..
symbol
Standard deviation
NORMAL DISTRIBUTION
Z= standard score,
To find X , change to Z score .
35. CIRCULAR MEASURE
TRIGONOMETRY
in radians
WHEN TO USE
Length of arc, s = r
2 Area of sector , A =r2
36. On screen
DRG
D R G123
Ans
1.25
SHIFT
2
press
=
press

press
CONVERT RADIAN TO DEGREE
1.25 radian degrees
Example
1.25r
71.61972439o
713711.01
37. CHANGE TO RADIAN
CHANGE TO DEGREE
38. TRIGONOMETRY
A
B
0.54
= 329 6
Find ,
a) in radians,
b) in degrees & minutes.
360 = 2
(a)major angle, =
2 0.54
=5.744radians
(b)In degrees
5.744
= 329.107
39. Solution of Triangles
TRIGONOMETRY
A
c
b
B
C
a
Area of triangle=ab sin
C
WHEN TO USE
Sine Rule
,
Cosine Rule
C = included angle
40. Trigonometric Functions
TRIGONOMETRY
WHEN TO USE
3 sin 2A + cos 2A = 1
4 sec2A = 1 + tan2A
cosec2A = 1 + cot2A
6 sin2A = 2 sinA cosA
7 cos 2A= cos2A sin2A
= 2 cos2A1
= 1 2 sin2A
8 tan 2A =
Basic Identities
Double angles
proving
9 sin (A B) = sinAcosB cosAsinB
10 cos (A B) = cos AcosB sinAsinB
11 tan (A B) =
Addition angles
41. 9 sin (A B) =sinAcosB cosAsinB
sin(A+B)= sinAcosB+ cosAsinB
sin (AB) = sinAcos B cos AsinB
10 cos (A B) = cos AcosB sinAsinB
cos (A +B) = cos AcosB sinAsinB
cos (A B) = cos AcosB+ sinAsinB
42. Thank you
Be Smart
Have a nice day!