1.   Solve the absolute value equation shown below. Show all work!
     

2.   Solve (3x + 1)² = 7 Show all work!
     

3.   Solve 2x² + 3x - 8 = 0 by completing the square. You MUST complete the square and show all work!
     

4.   Solve the equation given below. Show all work!
     

5.   Solve the equation given below. Show the Algebraic Solution!
     

6.   The weight of a body W varies inversely as the square of its distance d from the center of the earth. A man weighs W=200 pounds on the face of the earth, which is d=4000 miles from the center. How much will the man weigh 1000 miles up from the surface, which is 5000 miles from the center of the earth? Show All Work!
     

7.   If f(x) is as defined below, find and simplify f(t + 1).
     

8.   State fhe domain of the function f(x) given below.
     

9.   A door has a length that is 4 feet more than its width. The area of the door is 14 square feet. Find the length and width of this door. Round to nearest hundredth of a foot. Note that area equals length times width. Show all work!
     

10.   Find the equation of the line passing through the points shown below. Show All Work!
     

11.   A ball is thrown up into the air and its height y is given by the function y = -16t² + 56t + 8 where t is time in seconds. At what value of t does the ball obtain a maximum height? Show All Work!
     

12.   Sketch the graph of f(x) = -2(x + 4)². Show the vertex and at least two other points.
     

13.   The graph of the absolute value function is given below along with a shifted graph. Identify the equation of the shifted graph.
     

14.   Given f(x) = 3x² + 2, evaluate and simplify the expression shown below. Show Work!
     

15.   Given f(x) = 2x + 3, find the inverse function f^-1(x). Then show that (f o g)(x) = x and (g o f)(x) = x.
     

16.   Use polynomial division to show that (x - 2) is a factor of f(x) = 3x³ - 2x² - 5x - 6. Then use this result to write f(x) as the product of (x - 2) times a quadratic. Show All Work!
     

17.   Graph the rational function shown below. Indicate ALL asymptotes of the graph and show at least 4 points on the graph.
     

18.   Rewrite LOG₁₆64 = 1.5 in exponential form and rewrite x² = 3 in logarithmic form.
     

19.   Write the expression below as a sum or difference of logs or multiples of logs.
     

20.   Write ½ LN x + 2LN (x + 4) as a single logarithm by applying properties of logarithms.
     

21.   Solve the equation LOG₁₀(x + 3) + LOG₁₀(x + 1) = 1. Round to 3 decimal places. Show All Work!
     

22.   A population of bacteria is growing exponentially according to the function N(t) = 200e^kt where N(t) is the number of bacteria at time t hours. If N(t)= 500 when t = 4 hours, what will the population be when t = 12 hours? Round final answer to nearest whole number. Show All Work!
     

23.   Solve 2e^4x + 3 = 4. Round final answer to 3 decimal places. Show All Work!
     

24.   A person selling widgets sells 100 widgets/day and makes $40 net profit for the day. If they increase their number of widgets sold per day to 120 widgets/day they make $65 in net profit per day. Assuming there is a linear relationship between number of widgets sold per day (x) and net profit per day (y), find the following: A) A linear model that relates net daily profit (y) to widgets sold per day (x). Write as a linear equation. Hint: This amounts to finding the equation of a line. B) The amount of net profit made daily (or lost) if there ZERO widgets are sold each day. Hint: Plug into the formula you found in Part A. Show All Work!
     

25.   X units are sold per day at a profit of $2 per day, not including daily overhead costs. Daily overhead costs are $80. Find a function f(x) that gives the net profit per day that takes into account the overhead costs. Also, what is the minimum number of units that must be sold each day to make a net profit of $100 per day? Show ALL work!
     

Free Practice Test Courtesy of YourPracticeTest.com