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final_exam_part_ii.pdf

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Intermediate Algebra

Final Exam Part II

Prof. Hanson

Date ________________________

Class________________________

Name___________________________________

There are 13 questions on this part of your final exam. You are required to complete only 10 for grading. Each question

is worth 6 points. You must clearly write “OMIT” on the 3 questions you do not want graded.

Answer the following questions. Show all work necessary to receive partial credit.

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so

state.

1)

y=x-3

y = -2x + 6

Find the solution to the system of equations by the substitution or addition method.

2)

x + 6y = 6

2x – 7y = -7

1

Solve and check your solution(s).

3)

5x – 4 = 4

Find the equation of a line with the properties given. Write the equation in slope intercept form and then graph the

NEW LINE only on the axes below.

4)

Through (2, 1) and perpendicular to the line whose equation is y =

1

x + 4;

2

Hint: Start by using the point slope form of an equation, given by y – y1 = m(x – x 1 )

2

Factor both parts of this question completely. Hint: factor the first one by grouping.

5) a)

b)

ax + x – am – m

x3 + 27

Add or subtract. Be sure to simplify if possible.

6)

3x

4

6

+

x + 1 x – 1 x2 – 1

Divide and simplify if possible.

x 2 + 11x + 30

x 2 + 6x

7)

÷

x 2 + 12x + 35 x 2 + 15x + 56

3

Solve the equation and check your solution.

8)

-2x

x

2x – 3

=

+

2x + 2 4x + 4

x+1

Solve the equation by the quadratic formula. x =

-b ± b2 – 4ac

2a

9) x 2 + 7x + 7 = 0

Divide using long division.

8m 3 + 12m 2 – 4m + 8

10)

m+2

4

Simplify the complex fraction.

4+

11)

2

x

x 1

+

4 8

Solve the quadratic equation by factoring the left hand side completely.

12)

2x 2 – 16x + 30 = 0

Subtract the following expressions. Hint: first convert each of the radicals to its simplest form.

13)

3 20 – 2 45

5

…

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