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Math 154 Practice Midterm I

Please work out each of the given problems.  Credit will be based on the steps that you show towards the final answer.  Show your work.

  Printable Key

Problem 1  (15 Points)  Solve the inequality.  Write the solution on a number line.

        2x² - 5x > 3

Solution

Problem 2

A. (13 Points)  Solve  x^1/2 + 2x^1/4 - 8  =  0  

Solution

B. (13 Points)  Solve

  Solution

Problem 3  (12 Points)  Find the domain of

            x² - 5x - 1
                                                    
          x³ - 3x² + 2x

Solution

Problem 4

Answer the following True or False.  If True, explain your reasoning, if False, explain your reasoning or show a counter-example.

A.     (7 Points)  All parabolas y = ax² + bx + c are graphs of functions.

Solution

B.     (7 Points)  If the vertex of the parabola y = ax² + bx + c   has positive y-coordinate and the parabola is concave up, then the parabola has two x-intercepts.

Solution

C.     (7 Points)  If a graph has two y-intercepts then the graph is not the graph of a function.

  Solution

Problem 5  Let f(x) = 3x + 2, g(x) = x + 3, and c(x) = -1.  Find

A) (5 Points)     f _° g (x)  

Solution

B) (5 Points)        f(x + h) - f(x)
                                                                  
                                    h

Solution

C) (5 Points)      g(f(1))     

Solution

D) (5 Points)    c _° f (2)     

Solution

E) (5 Points)           c(x)g(x)
                                                                
                             f(x) - 7c(x)

Solution

Problem 6  (15 Points)   You are constructing a rectangular room such that one side of the room is 14 feet longer than the other side, and the distance from opposite corners is 26 feet.  What are the dimensions of the room?  Give your answer accurate to two decimal places.

  Solution

Problem 7  (16 Points)  Graph the quadratic function.  Label any intercepts, the vertex, and the axis of symmetry.

        y  =  -2x² + 4x + 6

  Solution

Problem 8  The graphs of y = f(x) and y = g(x) are given below.  Find

A.     (5 Points)  f(0)

B.     (5 Points)  g(-1)

C.     (5 Points)    g _° f (1)  

D.     (5 Points)      f(1)
                                              
                     g(-1)

  Solutions

Extra Credit:  Write down one thing that your instructor can do to make the class better and one thing that you feel that the instructor should continue doing.

(Any constructive remarks will be worth full credit.)