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21 Feb 2008, 01:53
Kudos
Bookmarks
Triangle:
1) Area of triangle with vertcies (x1,y1), (x2,y2), (x3,y3) = \(1/2[x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]\)
2) Area of circumcircle in equilateral ∆ with side a = \(Pi*a^2/3\)
3) Area of incircle in equilateral ∆ with side a = \(Pi*a^2/12\)
4) Altitude of equilateral ∆ with side a = \(a*sqrt3/2\)
5) An equilateral triangle has the maximum area
Circle:
1) Equation of circle with center at (h,k) and radius (r) = \((x-h)^2 + (y-k)^2 = r^2\)
2) Two circles will touch or intersect each other if the distance between their centers ‘d’ is such that \(R-r <= d <= R+r\)
3) The equation of tangent to the circle \(x^2 + y^2 = r^2\) at the point (x1,y1) is \(x*x1 + y*y1 + r^2=0\)
Line/Linearity:
1) Distance of point (x1,y1) from line ax+by+c = \(|ax1+by1+c|/sqrt(a^2+b^2)\)
2) Reflection of a point (x,y) across a line y=x is (y,x)
3) Reflection of point (x,y) across a line y=-x is (-y,-x)
4) Coordinates of point dividing a segment (x1,y1) and x2,y2 in proportion r:s is \((rx2+sx1/r+s), (ry2+sy1/r+s)\)
5) If the slope of line is negative, line slants downward from left to right (\)
6) If the slope of line is positive, line slants upward from left to right (/)
Misc1:
1) Number of diagonals = N(N-3)/2 ; N= number of sides
2) Area of square = \(1/2 * d^2\) ; d = diagonal
Number Theory:
1) Any perfect square can be expressed in the form \(4n or 4n+1\)
2) If A:B=C:D, then \(A+B/A-B = C+D/C-D\)
3) If a/b=c/d=e/f….. then \(a/b=c/d=e/f=a+c+e/b+d+f\)
4) LCM * HCF = product of two numbers
5) Sum of first n natural numbers = \(n(n+1)/2\)
6) Sum of first n even numbers= \(n(n+1)\)
7) Sum of first n odd numbers= \(n^2\)
8) Sum of cubes of 1st n natural numbers = \([n(n+1)/2]^2\)
9) Sum of squares of 1st n natural numbers = \(n(n+1)(2n+1)/6\)
Misc2:
1) Clock Angle = \(mod [(60H-11M)/2]\); where H = value of hour hand, M = value of minute hand. ex. 2:30, H=2, M=30
--
Let me know if they are helpful. Will add more..
1) Area of triangle with vertcies (x1,y1), (x2,y2), (x3,y3) = \(1/2[x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]\)
2) Area of circumcircle in equilateral ∆ with side a = \(Pi*a^2/3\)
3) Area of incircle in equilateral ∆ with side a = \(Pi*a^2/12\)
4) Altitude of equilateral ∆ with side a = \(a*sqrt3/2\)
5) An equilateral triangle has the maximum area
Circle:
1) Equation of circle with center at (h,k) and radius (r) = \((x-h)^2 + (y-k)^2 = r^2\)
2) Two circles will touch or intersect each other if the distance between their centers ‘d’ is such that \(R-r <= d <= R+r\)
3) The equation of tangent to the circle \(x^2 + y^2 = r^2\) at the point (x1,y1) is \(x*x1 + y*y1 + r^2=0\)
Line/Linearity:
1) Distance of point (x1,y1) from line ax+by+c = \(|ax1+by1+c|/sqrt(a^2+b^2)\)
2) Reflection of a point (x,y) across a line y=x is (y,x)
3) Reflection of point (x,y) across a line y=-x is (-y,-x)
4) Coordinates of point dividing a segment (x1,y1) and x2,y2 in proportion r:s is \((rx2+sx1/r+s), (ry2+sy1/r+s)\)
5) If the slope of line is negative, line slants downward from left to right (\)
6) If the slope of line is positive, line slants upward from left to right (/)
Misc1:
1) Number of diagonals = N(N-3)/2 ; N= number of sides
2) Area of square = \(1/2 * d^2\) ; d = diagonal
Number Theory:
1) Any perfect square can be expressed in the form \(4n or 4n+1\)
2) If A:B=C:D, then \(A+B/A-B = C+D/C-D\)
3) If a/b=c/d=e/f….. then \(a/b=c/d=e/f=a+c+e/b+d+f\)
4) LCM * HCF = product of two numbers
5) Sum of first n natural numbers = \(n(n+1)/2\)
6) Sum of first n even numbers= \(n(n+1)\)
7) Sum of first n odd numbers= \(n^2\)
8) Sum of cubes of 1st n natural numbers = \([n(n+1)/2]^2\)
9) Sum of squares of 1st n natural numbers = \(n(n+1)(2n+1)/6\)
Misc2:
1) Clock Angle = \(mod [(60H-11M)/2]\); where H = value of hour hand, M = value of minute hand. ex. 2:30, H=2, M=30
--
Let me know if they are helpful. Will add more..
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
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21 Feb 2008, 02:14
Kudos
Bookmarks
Srp,
they are pretty useful
thanks,
Pras
they are pretty useful
thanks,
Pras
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
