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Enter expression, e.g. (x^2-y^2)/(x-y)

Enter expression, e.g. x^2+5x+6

Enter expression, e.g. (x+1)^3

Enter a set of expressions, e.g. ab^2,a^2b

Enter equation to solve, e.g. 2x+3=4

Enter equation to graph, e.g. y=3x^2-1

Depdendent Variable

Number of equations to solve:

Equ. #1:

Equ. #2:

Equ. #3:

Equ. #4:

Equ. #5:

Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

Solve for:

Enter inequality to solve, e.g. 2x+3>4

Enter inequality to graph, e.g. y<3x^2-1

Dependent Variable

Number of inequalities to solve:

Ineq. #1:

Ineq. #2:

Ineq. #3:

Ineq. #4:

Ineq. #5:

Ineq. #6:

Ineq. #7:

Ineq. #8:

Ineq. #9:

Solve for:

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BEGINNING ALGEBRA

Total is out of 100 pts. EQUIPMENT: pencil, eraser, color pencils, ruler, calculator. Show all work on the
paper here. Step DOWN between steps. (Keep exact answers.) Circle the final answer on multi-step (non-graph)
problems. IF more space is needed to finish a problem, say “see back” and put just the finish on the back of
another page. Little credit will be given for unsupported answers. (Projected time needed is ≈ 50 minutes.)
Good Luck, remember good test-taking strategies, and to breathe.

(5 pts) Graph the equation.

To do this, complete a t-table (here) with any
intercepts identified at least three points total.
Put the graph on the graph paper provided.
Label appropriately (axes, intercepts as their
ordered pairs, scale).

(5 pts) Simplify. Write using positive exponents
only.

(4 pts) Evaluate when y = –4.

(4 pts) Simplify (by reducing).

(3 pts) Find the domain of the rational expression.
Write it in set-builder notation.

(5 pts) Perform the indicated operation(s).

(6 pts ea, 12 pts total) Solve completely. Show all flowchart steps: i) read, ii) let x =, iii) verbal model, iv)
equation, v) solve, vi) interpret (makes sense?, complete sentence). Leave number answers exact (as whole
numbers, fractions, or mixed numbers, no decimals or rounding).

13) Two boats leave a marina. One travels north, and the second travels west. After 30 min, the second boat has
traveled 2 miles farther than the first boat and the distance between the boats is 10 miles. Find the distance
each boat traveled. (Hint- Draw a picture)

14) The width of a rectangular painting is 2 in. less than the length. The area is 48 in.² Find the length and
width.

(5 pts each) True or False. Show reasoning in either case. (No reason, no credit.)

16) The following is a quadratic equation.

17) (2 pts total) Matching. Complete the following statements using the words/phrases in the list. Write just the
letter for the appropriate phrase in each blank. Some words may not be used, and some may be used more
than once. Some sentences require more than one response.

a) binomial
b) difference of cubes
c) difference of squares
d) factor
e) Greatest Common Factor
f) grouping
g) linear
h) prime
i) quadratic
j) rational
k) solution
l) sum of cubes
m) trinomial
n) Zero Product Property

I. A equation contains a second degree polynomial (a variable to the 2^nd power).
II. The first step you try when factoring is to try to take out the___.
III. A ___ equation contains at most a first degree polynomial (a variable to the 1^st power).
IV. The ___ says IF ab = 0 THEN a = 0 or b = 0.
V. To ___ a polynomial means to write it as a product.
VI. ___ A expression or equation contains ratios (fractions) of polynomials, P/Q , where Q ≠ 0.

VII. A^3 – B^3 = (A – B)(A^2 + AB + B^2) is the factoring pattern for a ___.
VIII. A ___ of a linear or a quadratic equation is any value that makes the statement true upon replacement.
IX. To factor four terms, try to factor by ___.
X. When factored, a trinomial usually will break down as a product of two ___s.

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