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College Math 2 Final Study Guide

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1. Sum of n terms in a Geometric Sequence
Sn= a1 (1-rn )1-r to find r divide a2a1 2. Summation Notation i through n example: i=1nai = a1 + a2 + a3……. an 3. Example: 10i5i= 10*9*8*7*6*5i5i= 30240 4. Finding n terms in arithmetic sequence an=a1+ (n-1)d 5. Finding n terms in geometric sequence an=a1*rn-1 6. Sum of first n terms of an arithmetic sequence
Sn=(a1+an)*n2
7. Absolute value of a Complex number
Z=a2+b2 a + bi 8. Finding polar form (z= r*(cos theta + i* sin theta) of complex number (z= a + bi)
A = r*cos theta B= r* sin theta R=a2+b2 Theta = tan-1 (ba ) 9. Converting from rectangular (x,y) to polar (r,theta)
R= x2+ y2 theta = tan-1 (yx) 10. Dick’s theorem for finding roots (a+bi)^
R=a2+ b2 theta = tan-1 (ba ) r^*( cos (theta * ^) + i* sin (theta * ^)) 11. Finding rectangular from polar
X= r*cos theta Y=r*sin theta 12. Law of Sines
Sin Aa=Sin Bb= Sin CC 13. Angle of oblique triangle
Area = b*c*Sin A2 a*b*Sin C2 a*c*Sin B2 14. Law of Cosines a= b2+c2- 2*b*c*Cos A b= a2+c2- 2*a*c*Cos B c= a2+b2- 2*a*b* Cos C 15. Heroin angle
Area = S*S-a*S-b*(S-c) S = a+b+c2 16. Permutations nPr= n!n-r! 17. Combinations nCr= n!n*r!*r! 18. Magnitude of v v= a2+b2 19. Position vector
Initial point (x1,y1) Terminal point (x2,y2)
V = x2-x1*i+y2- y1*j 20. Word problem
V= v*Cos ∅i+ v*Sin ∅j 21. Logarithms logbMN= logbM+ logbN Product Rule logb(MN)= logbM- logbN Quotient Rule logbMp=p*logbM Power Rule 22. A = P*(1+ rn)nt
T = logAP(n*(log1+ rn 23. Example:
23x=10
log210=3x ln10ln23 = x 24. Example
8x=32768
log832768=x ln32768ln8=x 25. Empirical probability
P (E) = observed number of times E occurstotal number of observed occurrences 26. Theoretical probability
P (E) = number of outcomes in event Enumber of outcomes in sample space S= n*(E)n*(S) 27.…...

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