EIT FE Exam - Algebra

1. Logarithms
2. Complex Number
3. Polar Coordinates
4. Polynomials
5. Polynomial Functions
6. Roots
7. Progression and Series

1.Logarithms

Practice Questions and Answers

http://www.mhhe.com/math/precalc/barnettca2/student/olc/chap04practice.html
http://examtimequiz.com/maths-mcq-on-logarithms/
http://www.indiabix.com/aptitude/logarithm/053002

http://moodle.tbaisd.org/pluginfile.php/68285/mod_resource/content/0/Assessments/ExponentialsLogsMCPreTest.pdf

http://www.mdc.edu/main/images/Exponential%20%26%20Logarithmic%20Functions_tcm6-61374.PDF


2.Complex Number
http://www.mhhe.com/math/precalc/barnettca2/student/olc/graphics/barnett01caaga_s/ch02/downloads/pc/ch02section4.pdf

Practice Questions and Answers
http://www.mdc.edu/main/images/Complex%20Numbers_tcm6-61106.PDF

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0ahUKEwiN8-OnzKXSAhVC7WMKHebXA18QFgggMAE&url=http%3A%2F%2Fwww.newpaltz.k12.ny.us%2Fcms%2Flib%2FNY01000611%2FCentricity%2FDomain%2F132%2FComplex%2520Numbers%2520Multiple%2520Choice%2520Practice%25201.doc&usg=AFQjCNHuLfRGfgoXDj2YR7MUyBFe5vyivQ&sig2=NdSlAal0r1BHNeWf435ItA&bvm=bv.147448319,d.cGc

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0ahUKEwiN8-OnzKXSAhVC7WMKHebXA18QFggmMAI&url=http%3A%2F%2Fwww.murrieta.k12.ca.us%2Fcms%2Flib5%2FCA01000508%2FCentricity%2FDomain%2F1456%2FComplex_Numbers_Quiz_2.doc&usg=AFQjCNFnYmhcAFnGh3yGx_jjlpzqKWZSyw&sig2=o5P1mG5X1lbeZE2wXO2AfQ&bvm=bv.147448319,d.cGc

http://us.mcqslearn.com/math/complex-numbers.php

3.Polar Coordinates
Polar Coordinates
 http://baldwinfochtman.weebly.com/uploads/1/4/5/4/14541278/polar_graphing_pre-test_for_slo.pdf

http://www.nptel.ac.in/courses/122101002/downloads/Problems%20&%20Solutions/Lecture%202.pdf

http://shawtlr.net/test_pdf/tm12_a.pdf

http://www.cabrillo.edu/~lshipley/math%203/math3finalrev.PDF

http://sites.csn.edu/ehutchinson/notes/6_3notes128.pdf

4.Polynomials

http://www.mhhe.com/math/precalc/barnettca2/student/olc/chap03practice.html

https://valenciacollege.edu/learning-support/math/documents/3.8.28MultiplyingPolynomials2.pdf

https://valenciacollege.edu/learning-support/math/documents/3.3.28Addingandsubtractingpolynomials3.pdf

http://mastmedical.org/ourpages/auto/2013/12/13/55478588/Review%20Polynomials.PDF


7.Progression and Series
http://www.mhhe.com/math/precalc/barnettca2/student/olc/chap06practice.html


 Problem: Arithmetic Progression
The 6^th term of an arithmetic progression is 12 and the 30^th term is 180.

 Bring your calculator to Linear Regression in STAT mode:
MODE → 3:STAT → 2:A+BX and input the coordinates.
 

X (for n)	Y (for an)
6	12
30	180

1. What is the common difference of the sequence?
 an=am+(n−m)d
a30=a6+(30−6)d
180=12+24d
d=7 b   →   common difference


2. Determine the first term?
an=a1+(n−1)d
a30=a1+(30−1)d
180=a1+29(7)
a1=−23     →   first term


To find the first term:
AC → 1 SHIFT → 1[STAT] → 5:Reg → 5:y-caret and calculate 1y-caret, be sure to place 1 in front of y-caret.
1y-caret = -23   →   answer for the first term
3. Find the 52^nd term.
an=am+(n−m)d
a52=a6+(52−6)d
a52=12+46(7)
a52=334     →   52^nd term

To find the 52^nd term, and again AC → 52 SHIFT → 1[STAT] → 7:Reg → 5:y-caret and make sure you place 52 in front of y-caret.
52y-caret = 334   →   answer for the 52^nd term
4. If the n^th term is 250, find n.
an=am+(n−m)d
250=12+(n−6)(7)
n=40     →   40^th term, a₄₀ = 250


To find n for a_n = 250,
AC → 250 SHIFT → 1[STAT] → 7:Reg → 4:x-caret
250x-caret = 40   →   answer for n

5. Calculate the sum of the first 60 terms.
Sum of AP is given by the formula
S=12n[2a1+(n−1)d]

Sum of the first 60 terms
S=12(60)[2(−23)+(60−1)(7)]
S=11,010
  →   answer

Sum of the first 60 terms:
AC → SHIFT → log[Σ] → ALPHA → )[X] → SHIFT → 1[STAT] → 7:Reg → 5:y-caret → SHIFT → )[,] → 1 → SHIFT → )[,] → 60 → )






6. Compute for the sum between 12th and 37th terms, inclusive.
Sum between 12th and 37th terms, inclusive.
S=S37−S11
S=12(37)[2(−23)+(37−1)(7)]−12(11)[2(−23)+(11−1)(7)]
S=3679
  →   answer