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Beginning Algebra Departmental Review Sheet
Unless otherwise stated, all work should be done
algebraically, all work should be shown, and answers should be simplified.
No formula sheets or note cards are allowed for use during the final exam.
Outcomes are from the course outline. Problems here are in the order as presented there .
You may want to work some core 1-5 outcome problems last, so they are freshest going into the final exam.
[Core Outcome 1, Sec 2.1, 2.2, 2.3]
Solve each equation. Check your solution(s).
[Core Outcome 2, Sec 2.4, 2.5, 2.6]
Solve. Show all the steps: i) Read the problem, ii) Assign (Label the unknown: x represents what words, develop a verbal
model), iii) Write an equation , iv) Solve , v) State the answer (as a compete sentence), vi) Check (makes sense?).
5. Find two consecutive odd integers such that twice the greater is 17 more than the lesser.
6. The total number of Democrats and Republicans in the
U.S. House of Representatives during the 109th Congress was 434.
There were 30 more Republicans than Democrats. How many members of each party were there? (Source: World
Almanac and Book of Facts 2006.)
7. In one day, a store sold
as many DVDs as CDs. The total number of DVDs and CDs sold that day was 273. How
many DVDs were sold?
8. In triangle ABC, angles A and B have the same measure,
while the measure of angle C is 60° greater than each of A and
B. What are the measures of the three angles?
9. The perimeter of a rectangle is 36 yd. The width is 18
yd less than twice the length. Find the length and the width of the
10. The perimeter of a triangle is 28 ft. The medium side
is 4 ft longer than the shortest side, while the longest side is twice as
long as the shortest side. What are the lengths of the three sides?
11. The euro is the common currency used by most European
countries, including Italy. On January 29, 2006, the exchange
rate between euros and U.S. dollars was 1 euro to $1.2128. Ashley went to Rome and exchanged her U.S. currency for
euros, receiving 300 euros. How much in U.S. dollars did she exchange?
12. If an investment of $8000 earns $1280 in simple interest in 4 yr, what rate of interest is being earned?
[Core Outcome 3, Sec 3.1, 3.2, 3.4]
Graph each linear equation. Label appropriately (axes, scale, intercepts).
[Core Outcome 4, Sec 4.1, 4.2]
Simplify. Write each using positive exponents only.
22. True or false (show a reason):
[Core Outcome 5, Sec 5.1, 5.2, 5.3, 5.4, Summary
Exercises on Factoring]
[Core Outcome 6-1, Sec 1.2, 1.4, 1.5, 1.6, 1.7, 1.8]
True or False (show reasoning).
Perform the indicated operations and simplify (no calculator).
[Core Outcome 6-2, Sec 1.2, 1.3, 1.4, 1.7, 1.8]
37. Evaluate xy – x2 , if x = –4, and y = –7. (Show the substitution step.)
38. Simplify. –5(y + 1) + 2(3 – 5y)
[Core Outcome 6-3,
Chapter 1 and Appendix B word problems, Sec 2.4, 2.5, 2.6]
See problems in Core Outcome 2 for examples
[Core Outcome 6-4, Sec 1.1, Appendix B, 1.4, 1.5, 1.6]
Perform the indicated operations. No calculator allowed.
[Core Outcome 6-5, Sec Appendix B, 2.6]
43. 45 is 30% of what number?
Solve. Show all work. Write the final answer as a complete
44. A retailer has $23,000 invested in her business. She finds that she is earning 12% per year on this investment. How much
money is she earning per year?
45. Four tires cost $398.00. How much do 7 tires cost?
True or False (show reasoning)
46. 6 is a solution of the equation 4x = 25.
47. –15 is a solution of the inequality x + 5 ≤ – 7
is in simplest form.
52. Find the any values of the variable for which the rational expression is undefined. Write answers with ≠.
53. A ladder is leaning
against a building. The distance from the bottom of the ladder to the building
is 4 ft less than the
length of the ladder. How high up the side of the building is the top of the ladder if that distance is 2 ft less than the
length of the ladder? (See figure)
[Additional Content Outcome 7 (a), Sec 2.5, 3.3 obj2, 3.4
Solve for the indicated variable
54. , for h
55. P = 2L + 2W, for W
56. Solve , for y
[Additional Content Outcome 7 (b), (1.1, 1.2, 1.3, 1.4,
1.5, 1.6), Roots & Radicals Packet ]
Evaluate, if possible.
Use the Product and Quotient Properties of Radicals to
simplify the following expressions. Assume that all variables
represent non-negative real numbers.