Coordinate Geometry
Suggested Readings: New Trent Mathematics S3B Chapter 9
Distance formula :AB=x1-x22+y1-y22
Slope of a line: mAB=y1-y2x1-x2
Coordinates of mid-point x1+x22,y1+y22
Index Law and Factorization
Suggested Readings: New Trent Mathematics S3A Chapter 1, 2
Law of indices
· am×an=am+n
· aman=am-n
· a0=1
· a-n=1an
· amn=amn
· abn=anbn
· abn=anbn
Methods of factorization
· Cross Method
· Identities
o a2-b2=a+ba-b
o a+b2=a2+2ab+b2
o a-b2=a2-2ab+b2
Statistics Report
Suggested Readings: New Trent Mathematics S3B Chapter 11
Mean=Sum of all dataNo of data
Median = (n/2)th data
Mode = the data with the highest frequency
Weight Mean=Sum of each datum multipied by the correspondening weightSum of the weight
Probability
Suggested Readings: New Trent Mathematics S3A Chapter 6
PE=Number of favoutable out omes Numbner of possible outcome
Experimental probability of the event E =Number of Successful trials Numbner of trial
The expected Value =sum of (probability of each event×value)
Mensuration
Suggested Readings: New Trent Mathematics S3A Chapter 4
Area of a square / Length2Perimeter of a square / length ×4
Area of a rectangle / length ×width
Perimeter of a rectangle / length+width×2
Area of a Parallelogram / base×height
Area of a triangle / base ×height2
Area of a Trapezium / a+bheight2
Area of a circle / πr2
Circumference of a circle / 2πr
πd
Area of a sector / πr2×θ360°
Arc length / 2πr×θ360°
πd×θ360°
Volume of a cuboid / length ×width×height
Volume of a prism / Base area ×height
Volume of a cylinder / πr2h
Total area of lateral faces of a prism / perimeter of the base ×height
Total surface area of a prism / perimeter of the base ×height+2×base area
Curved surface area of a cylinder / 2πrh
Total surface area of a cylinder / 2πrh+2πr2
Volume of the pyramid / 13×base area ×Height
Volume of a circular cone / 13×πr2×Height
Curved surface area of a right circular cone / πrl
Total Surface area of a right circular cone. / πrl+πr2
Volume of a sphere / 43πr3
Surface area of a sphere / 4πr2
Ratio of the area of 2 similar figures. / A1A2=l1l22
Ratio of the Volume of 2 similar figures. / V1V2=l1l23
Detuctive Geometry and Trignometry
Suggested Readings: New Trent Mathematics S3A Chapter 5,
New Trent Mathematics S3B Chapter 10
Important Lines
Angle bisector à the line divided an interior angle into halves
Perpendicular bisector à the line that perpendicularly divides a side of triangle evenly.
Altitude à the line that passes through a vertex of a triangle and is perpendicular to the side opposite to the vertex.
Median à the line that passes through the vertex of a triangle and the mid-point of the side opposite to the vertex.
Trigo Ratio of special angle
30o / 45o / 60oSin / 12 / 12 or 22 / 32
Cos / 32 / 12 or 22 / 12
tan / 13 or 33 / 1 / 3
Trigo Identities
· tanθ=sinθcosθ
· sin2θ+cos2θ=1
· cos90o-θ=sinθ
· sin90o-θ=cosθ
· tan90o-θ=1tanθ
Equations of Straight Line
Two point form à y-y2y-x2=y1-y2x1-x2
Point slope formà m=y-y2x-x2
Slope intercept formà y=mx+c
General form
Given Ax+By+C=0
Where x-intercept = -CA
y-intercept= -CB
slope = -AB