Sample Second Hourly Exam

1. A salesman finds if the price of tickets is x dollars, he can sell 5000 - 20x per concert. Express the revenue R as a function of x. Use this to calculate the revenue when the price is 50 dollars.

R = sell x price

Revenue____R = (5000 - 20x) x _________________

R = (5000 - 20x50) 50 = (5000 - 1000) 50 =

At 50 dollars___200,000_______________
 

2. Find the product of the polynomials: (x² - 4x + 3) (x - 2)

x²  (x - 2) - 4 x (x - 2) + 3 ( x - 2) = x³  - 2x² - 4x² +8x + 3x - 6

Answer__x³  - 6x²  +11x  - 6___________________
 
 

3. Evaluate the expression: (2y - 3x²) ²

(2y - 3x²)(2y - 3x²) = 4y² - 12yx² + 9x⁴
 

Answer___4y² - 12yx² + 9x⁴__________________
 

4. Factor completely: 49xyz - 63x²y + 70xy²

7xy(7z-9x+10y)

Answer____7xy(7z-9x+10y)_________________

5. Use the AC method to factor completely: 6 x² - 7 x - 20

AC=-120 factors -15 and 8 = -7 so 6x² - 7x -20 becomes 6x² - 15x +8x -20

factor by grouping 3x(2x-5) +4(2x-5)
 

Answer___(3x-4)(2x-5)__________________
 

6. Solve the equation: 0 = x² - 5x + 6

0 = (x -3) ( x - 2) so

Answer____x=3,2_________________
 

7. Use long division to find 3x² + 5x - 7 divided by x - 4

                   3x + 9 +29/(x-4)
x-4  |  3x² + 5x - 7
          3x2 - 4x
                   9x  -7
                  9x  -36
                          29
Answer_____________________

8. Perform and simplify: 

(x-3)(x-2)  (x+3)
(x-3)(x+3) (x-3)
 

Answer_(x-2)/(x-3)____________________

9. Perform and simplify: 

Multiply top and bottom by LCD

Answer_____(2x-3)/x________________

10. Perform the operation and simplify: 

5(x+1) +  4(x-2) = 9x - 3

Answer_(9x-3)/[(x-2)(x+1)]____________________

11. Solve for x: 

Multiply by 2x to get 4 + 3x = 10 or 3x = 6 so x = 2

Answer__2___________________

12. Solve for x: 

Multiply by xyz to get yz +xz = xy. take xz to right side to get yz = xy -xz

Factor out x to get yz = x ( y - z) Now x = yz/(y-z)

Answer________x = yz/(y-z)_____________

13.

13. If Jane can finish a report in 3 hours, and Mike can finish the job in 5 hours. How long will it take them to finish a report if they work together?

Answer___15/8__________________
 

14. (r⁷s³)⁴(s²r⁶) ⁵

r²⁸s¹²s¹⁰r³⁰ = r⁵⁸s²²
 

Answer_____r⁵⁸s²²________________
 
 

15. 
 

(16^-1a⁸b^-4)^-1/4  = 16^1/4a^-2b¹

Answer_2b/a²___________________

16. 

2a²bc³cubed root ( bc²)

17. 2 root(3x) - 5 root(27x)

= 2 root(3x) - 5(3)root(3x) = -13root(3x)

Answer_____________________
 

Rationalize the denominators:

18. 

Multiply top and bottom by cubed root of 2
 

Answer_2 cubed root of 2____________________
 
 

19. 

Multiply top and bottom by conjugate of denominator 3 + i

Gives 6 - i - 3(-1) over 9 + 1 or (9 - i ) / 10

Try to do the same problem but (2-3root2)/(3-root2)

Answer_____________________
 

Solve for x:

20. 3root(x+3) - 7 = 5

3 root(x+3) = 12
root(x+3) = 4
(x+3) = 16
x = 13