The questions below will review the areas of mathematics that are covered in Test B. These areas are:
* rules for exponents (integral and negative) * absolute value
* square roots * manipulating literal fractions having letters
* factoring * solving simultaneous equations
* word problems * lines and points graphed on a plane
* inequalities * solving quadratic equations
You should try to review these questions (and take Test B) if you have taken two years of high school algebra or have taken one or two semesters of College Algebra. Successful completion of Test B will place you into Statistics (Math 125) and PreCalculus (Math 129 or 130). After submitting the review questions you will receive an analysis of what courses you would be eligible to take if this review had been Placement Test B instead of Practice for Placement Test B. Answers will be given after clicking the submit button below. In addition, a link will be provided to an interactive PreCalculus review which might be helpful for any additional review.
Click the Submit button at the bottom of the test when you are finished.
Please forward any comments, criticisms, suggestions to: Michael Greeley
Part One In problems 1 - 3, find the numerical value when a = -3 and b = 2:
2. (-b)^{4} + 3a + 5a^{2} - 2a^{3}
3. a - |a + b| + |a - b| -3 1 3 7 15
In Problems 4 and 5, simplify the expression as much as possible:
In Problems 6 and 7, solve for x:
In Problems 8 - 13, perform the indicated operations and simplify:
1 + 13b2 + b 1 - 2b13 + b 1 + 13bb - 2 1 - 13b4 + b 1 - 3b2 + b
16. Find all real values of x such that 48x^{2} - 33 = 0.
17. Given that q^{3} = 11 and x^{15} = 121, express x in terms of q.
20. If a is a real number such that a^{3} = a^{2 }, which of the following must be true about a?
In Problems 21 and 22, Solve for x.
22. |4 - x| < 4
23. Which of the following is a solution of 6x^{2} = 5x + 50?
26. Find the solution (x,y) to these simultaneous equations:
3x + 4y = 17
2x - y = 4
27. Find all solutions (x,y) satisfying these simultaneous equations:
x + y = 8
xy = 0
28. Find the equation of the straight line passing through the points (7,19) and (9,23).
29. Which statement is true about the slope m of any straight line perpendicular to the graph
of 3x + y = 129?
30. Find the value of y when x = -1 for the following graph: -3 -2 -1 1 2
31. What is true of lines L and M, graphed here?
32. Which diagram contains the graphs of y = -x^{2} + 2x and x = 2?
Part Two
33. Given that it is not true that all the students in a math class of seventeen students are Irish, which of the following statements follow logically from the given?
34. Suppose that at most seventeen people in the world really understand Steven Hawking's theories of the origin of the universe. Further, suppose that at least six of them live in England, at most two of them live in Wales, at least three of them live in France and at least four of them live outside of France.
Although the exact number of them who live outside of Great Britain is actually indeterminate without further information, there is a smallest range in which that number must certainly lie. Find that range, assuming that all ranges listed are inclusive of the endpoints.
(Great Britain consists of England, Scotland and Wales.)
35. You have 20 identical black socks and 20 identical white socks in a dresser drawer. Assuming that it is too dark to see and all socks feel the same, how many socks must you pick to make sure that you get a pair?
37. Photocopies of a document cost 5 cents each. There is a discount of 20% for copies eleven through thirty and a discount of 40% for copies in excess of thirty. Find the cost of photocopying 100 copies of a document.
39. Take a number x. Triple it; then subtract 1 from the result; next square this result; and finally add the original number to the last result.
Express in terms of x the result of the above four-step process.
40. Ball-point pens cost 39 cents each. Pencils cost 7 cents each. Assuming that you have at most $4.92 to spend and you must buy exactly 20 items, find the smallest number of pencils you can buy.
42. A side of square B is 3 less than a side of square A. If you double the area of square B and add 2, your result equals the area of square A.
Find the length of a side of square A.
43. A rectangular rock garden 19 yards long and 10 yards wide is surrounded by a stone path of uniform width. The outer boundaries of the path form a rectangle concentric with the garden.
If the path were made 1 yard wider, its area would increase by 118 square yards. Find the width of the path.