14 questions on algebra

  

MATH QUIZ 2017

 
 

Perform each of the following calculations involving complex numbers, and write the answer, simplified as much as possible, in the form a + bi, where a and b are real numbers. 

1. (3 pts) (4+2i) – (6 – 8i) (work not required)

2. (3 pts) i18 (work not required)

3. (3 pts) Show work.

4. (5 pts) Find the solutions of the equation 2x2 + 6x = 1.  Simplify your answer as far as possible. Do not express your answer as a decimal  Show work.  

5. (2 pts each) Look at the graph and state the intercept(s), vertex, and range, and indicate which of equations A, B, C, or D, represents the graph.  [No explanations required.]

  

Graph

Fill in the blanks 

Equation

 

State the y-intercept:   

a.___________

State the x-intercept(s):

b._______ c._______

State the vertex:

d.____________

State the range:

e._____________

The graph represents which   of the following equations? 

f. Choice:____

A. y = –x2 + 4x – 3

B. y = –2x2 – x + 3

C. y =  x2   – 2x + 3

D. y = x2 + 2x – 3

6. (3 pts each) Consider the equation 9x2 + 12x – 5 = 0.

(a) Find and state the value of the discriminant, b2 – 4ac. Then state whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exists. Show work.

(b) Find the exact solutions of the equation. Simplify as much as possible. Show work. You are welcome to use any of the techniques which apply and that you prefer (i.e., factoring, applying the principle of square roots, completing the square, or the quadratic formula.) 

7. At A water tank is being filled by water being pumped into the tank at a volume given by the formula, P(t) = 60t +1060, where t is in minutes. At the same time the water tank has a leak and the volume of water draining out of the tank is given by the formula L(t) = 3t2, where t is in minutes. 

a.(2 pts) The volume, V, of water in the tank at any minute, t, is the difference of the volume of the water being pumped into the tank and the volume of water linking out of the tank. Find the volume function, V(t).

b. (2 pts) What is the volume of water in the tank after 17 minutes? Show work.

c. (2 pts) The volume function is a quadratic function and so its graph is a parabola. 

Does the parabola open up or down?  How do your know? _______________________

d. (5 pts) Find the vertex of the volume function V(x). Show work.

e. (2 pts) State the number of minutes which yield the maximum volume.

The maximum volume is _______________  at  ____________  minutes

8. (6 pts) State he domain and then solve the equation. Show work.

9. (5 pts) Solve and write interval notation for the solution set. 

Show careful algebraic work/explanation.

10. (4 pts) For f (x) = x4 – 3x2  − 8, use the Intermediate Value Theorem to determine which interval must contain a zero of f. Work/Explanation required  4. _______

A. Between 0 and 1

B. Between 1 and 2

C. Between 2 and 3

D. Between 3 and 4

11. (2 pts each) Each graph below represents a polynomial function. Complete the following table. 

(no explanation required)

  

Graph

 

Is the degree of   the polynomial odd or even? (choose one)

 

Is the leading   coefficient of the polynomial positive   or negative? (choose one)

 

How many   real number zeros are   there?

12. (2 pts each) Let .

(a) Write f(x) with the numerator and denominator completely factored.

(b) State the domain.

(c) State the vertical asymptote(s).

(d) State the horizontal asymptote. 

(e) State the y-intercept.

(f) State the x-intercept(s).

13. (5 pts,) Solve the absolute value inequality and write your answer in interval notation for the solution set.

| 5 - 6x | ³ 7. Show all work. 

 

14. (5 pts.) Solve the absolute value inequality and write your answer in interval notation for the solution set.  

| 6x – 5 | < 9. Show all work.