The questions belowwill review the areas of mathematics that are covered in Test C. These areasare:
* slopes and intercepts of straightlines
* parabolas and quadratic equations
* exponential, logarithmic and trigonometric functions: their graphs and inversefunctions
Youshould try to review these questions (and take Test C) if you have successfullycompleted an Intermediate Algebra course with Trigonometry. Successful completion of TestC will place you into Calculus (Math 140) and Introduction to ComputerProgramming (CS 110). After submitting the review questions youwill receive an analysis of what courses you are eligible to take if this reviewhad been TestC instead of Practice Test C. In addition, a link will be providedto an interactive PreCalculus review which might be helpful for any additionalreview.
Click the Submitbutton at the bottom of the test when you are finished.
Please forward any comments, criticisms, suggestions to: Michael Greeley
Part OneIn problems 1 - 4, perform any indicated operations, then simplify:
5. Which of these inequalities is equivalent to |x - 2| < 1?
6. If a is a real number such that a^{3 } = a, which of the following mustbe true about a?
a is positive a is negative a = -1 a = -1, a = 0, or a = 1 a is between -1 and 0
7. Line L passes through the point (-1, 10) and has slope equal to -7.Find an equation of the line that passes through thepoint (-1, 10) and isperpendicular to line L.
The slope of the segment AB is:
12. How is the graph of y = x^{2} - 4x + 3 located relative to the line y = -2?It is always above the line It is always below the line It intersects the line at two points The line is tangent to it at one point The line intersects it at one point but is not tangent to it.
13. How far is the point (1, -1) from the center of the circle (x - 2)^{2} + (y + 3)^{2} = 2?Ö2 Ö5 __Ö13 5 13
14. find all real values of x such that 16x^{4} - 81 = 0.
18. Given that ab^{2} = 12 and that ab^{5} = -96, find a: -2 -3 84 none of those 19. Fahrenheit temperature F is obtained from Celsius temperature C by the formula F = 95C + 32. When is the Fahrenheit reading exactly twice the Celsius reading?Never Part Two20. Let f(x) = x^{2} + 2x. Find: f(3 + h) - f(3)h, assuming h ¹ 0
2h - 9 h - 8 h + 1 8 + h h^{2} + h - 9h
21. Let f(x) = 10 - 3x. Select the result of subracting f(x) + 1 from f(x+ 1).
0 10 2f(x + 1) -4 none of those
22. If g(x) = mx + b, g(4) = -11, and g(-3) = 24, then
g(x) = -11 g(x) = 24 g(x) = -5x + 9 g(x) = -3x + 24 none of those
±12 ±2 2.9 12 and 2 -12 and -2 25. Let f(x) = x2x - 1. Find a formula for f^{-1}(x), the inverse of f. 2x - 1x -x2x - 1 x2x - 1 1 - 2xx x When used without subscript as in problems 26, 27, and 28, log means log_{10} and ln means log_{e}with e approximately 2.718.
0.389 0.072
27. Solve for x: 10^{4logx} = 9.36
28. Find all x which are solutions to: log x=2 - log(x -15).
12(A + B ) AB e^{AB}
30. Find x if ln(lnx)=0.1 0 e 1/e 10
31. Solve for x: 49^{x} = 64.6449 ln8ln7 ln64 - ln49 3ln2 - ln7 ln æçè 6449ö÷ø
32. Which of the following is equal to 10?ln(10^{e}) 10^{lne10} e^{ln10} e^{10} 10^{e}
33. Identify the graph of h(x) = 2^{x+2} - 8.
34. Identify the graph of g(x) = ln(x + 1) + 1.
Part Three
-0.940 -0.5 -0.342 0.342 0.940 No solutions in that interval.
38. Find arccos(-.5) in radians. (Note that arccos means the same as cos^{-1}.)p3 2p3 -p6 p6 -2p3
39. The graph of y = 4sinæçèx + p3ö÷ø crosses the x-axis at x = ?2p3 2 p6 0
40. Given that cosA = 4/5, find side s.
36 48 75 80 100
41. Which of the following equals cos(x + h)?
cosxcosh + sinxsinh cosxcosh - sinxsinh 2sinxcosh cosxsinh + sinxcosh none of those
43. Find x, the length of the indicated side.