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MATH 101 College Algebra: Practice Final Exam Solutions, Exams of Algebra

Harford Community CollegeAlgebra

Solutions to the practice final exam for harford community college's math 101 college algebra course. Topics covered include dividing complex numbers, completing the square, using the quadratic formula, substitution, graphing, finding the center and radius of a circle, equations of lines, finding the vertex of a quadratic function, rational roots, vertical and horizontal asymptotes, domain of a function, finding the inverse of a function, logarithmic and exponential equations, solving equations, finding the vertex, focus, directrix of a parabola, and gaussian elimination.

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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Harford Community College Name____________________
STEM Division Date________________
Spring 2009 Instructor: S. Rook
MATH 101 – College Algebra: Practice Final Exam Detailed Key
1) Divide and leave in a + bi format:
i
i
3
2
54
−
+
2) Solve by
completing the square
:
025
2
=−+ xx
3) Solve by
using the quadratic formula
: xx 733
2
=+
pf3
pf4
pf5
pf8

Partial preview of the text

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Harford Community College Name____________________

STEM Division Date________________

Spring 2009 Instructor: S. Rook

MATH 101 – College Algebra: Practice Final Exam Detailed Key

  1. Divide and leave in a + b i format : i

i

  1. Solve by completing the square : 5 2 0

2 x + x − =

  1. Solve by using the quadratic formula : 3 x 3 7 x

2

  • =
  1. Solve by utilizing a substitution : 3 x − 14 x + 8 = 0

5) Graph by using a table of values with at least FOUR points : ( )

2 f x = 5 − x

x f( x )

-2 1

-1 4

0 5

1 4

2 1

9) Use f ( x ) = 2 x + 5 and ( ) 1

3 g x = x − for 9) and 10) to find the following:

a) ( f − g )( x ) b) ( f ⋅ g )( x ) c) ( f o g )( x )

10) Use synthetic division to determine whether ( x + 4 )is a factor of

3 2 P x = x + x − x − - make a conclusion based on the result :

  1. Use the Rational Zeros Theorem to list the POSSIBLE zeros of

3 2 P x = x − x + x + :

Use ( )

2

2

x x

x R x for 12) – 14) to find:

  1. The equation of any vertical asymptotes:

  2. The equation of any horizontal asymptote AND explain why by referencing the

degrees of the numerator and denominator :

14) The domain of R ( x ):

( − ∞, − 5 ) U(− 5 , 8 ) U( 8 ,+∞)

19) Find the vertex , focus , directrix , AND sketch the parabola: ( 3 ) 2 ( 1 )

2 x − =− y +

  1. Use Gaussian Elimination to solve BY HAND :

x y

x y

  1. Find the inverse of A BY HAND : (^) 

A

22) Find the first four terms of the sequence: a 1 = 1 , an =( n + 3 ) ⋅ an − 1 + 1

  1. Determine whether the sequence is arithmetic, geometric, or neither – EXPLAIN

WHY :

a) 4 , 11 , 18 , 25 ,K b) 1 , 4 , 9 , 16 ,K c) ,K 81

a) Arithmetic – the difference between any two successive terms is 7

b) Neither – the difference between any two successive terms is NOT the same

AND the ratio between any two successive terms is NOT the same

c) Geometric – the ratio between any two successive terms is

1 ⁄ 3

  1. Find the sum of the first 68 terms of the arithmetic sequence whose n

th term is

an = 5 n + 6