﻿ FINAL EXAM INTRODUCTORY ALGEBRA

This forward slash /  means a fraction and hence also division.

1. Translate the following English sentences into a mathematical sentence:

a)    eight y plus seven p

b)    nine r minus fifteen m

c)    3t multiplies by 4f

2. What is the difference between 7x and 9t if x = 4 and t = 2 ?

3. What is the additive inverse of:

a)   7

b)   4/5

c)   3t

d)   - |-7|

4. What are the values of the following expression:

a)  (-4)2

b)  -42

c)  -(-3)2

d)  40 ÷ 23  + 7 - 4(3)

5. Convert Fahrenheit temperature of 48 degrees to Celsius

6. Solve (Find the value of m)   m/6    +   m/14    =  80/42

7. Change the following into an equation and solve:

What percent of 80 of 72?

What is 38% of 53?

43 is 23% of what number?

8.  Find the value of t:    9t - 3 = 2t + 18

9.  Solve for p.       4p + 3r3  = 2r2 - 5p + 2t

10. How many liters of a 30 % mixture must be combined with 4 liters of a 55% mixture to obtain a 37% mixture?

11.   7p degrees plus (5p - 25) degrees = 90 degrees. How many degrees does p equal?

12.   Is ordered pair (m, r) = (2, 9) a solution 4m + 3r = 36 ?

13.  Graph

a)  y = 4x + 3

b)  - 4x + 2y = 6

c)  3y = -6x - 9

14.  Find the slope of the line connecting the following sets of coordinates.

a)  (-2, 4), (3, -2)

b)   (3, 5), (-4, 5)

c)  (7, -2), (7, 3)

15. Are the graphs of the following functions parallel, perpendicular or neither?

y - 6 = 3x + 2y               3y + 2 = -x - 3

16.  Simplify

a)  x3 y4 (x2 y-2 )

b)  -3t/6t4 =

c)  (x4t3 p-5)-7 (Write the answer without negative exponents.)

17.  Write the following in scientific notation.

a)   5,650,000,000

b)   0.00000342

18. Perform the indicated operations and change the answers to decimal notation.

a)   (3 x 10-4) (5 x 107)

b)   (4.67 x 10-8) x (5.6 x 103)

c)   (7.3 x 105 ) ÷ ( 4 x 10-8)

19. Give the degree of the following polynomial and write it in ascending order.

t2 - t5  + 7t + 9t7 - 8

20. Perform the indicated operation.

a)  (7u3 - 3u2 + 4u -3) - ( 3u2 - 2u + 7)  =

b)  (8t6 + 7t4 - 2t2 + 6) + (7t5 - 6t4 + 2t - 4) =

c)  7y (-3y4 + 2) =

d)  (t3 - 4t2 + t - 6) ÷ (t -3) =

21. Factor  3t3 - 6t2 + 9t =

22. Solve by graphing and state what approximately x and y equal

3y + 4x = 2

4y + x   = 7

23. Solve by the substitution method.

y = 4x + 3

-2x + 3y = 4

24. Solve by the elimination method.

3t - 4y = 10

5t - 4y = 12

25. What is the domain of x and what makes the expression undefined?

4t/(t - 8)

26. Reduce to lowest terms.

a) (45 t3y4) / (9t2 y6)

b)  p/(4p +5tp)

27. Multiply and simplify the answer

(-3t3/4y) x (8y4x/9t6