Download Math 31 – Exam 3

Math 31 – Exam 3 – Be sure to have completed all text homework also to be
completely ready for the exam.
1. Is the ordered pair (-2, 4) a solution to the system: 3x + y = -2
x–y=2
2. Solve each of the following by graphing.
2x  3y  6
2x  y  3
a.
b.
2 x  y  2
4x  2 y  6
3. Solve each of the following by substitution.
y  x 1
5x  4 y  9
a.
b.
x  2 y  3
4 x  3 y  24
4. Solve each of the following by the addition method.
3 x  2 y  48
2 x  7 y  17
a.
b.
9 x  8 y  24
5 y  17  3 x
d.
c.
c.
c.
x  3
y 1
y  5  2x
4x  2 y  6
3 x  2 y  3
2 x  5 y  17
4 x  6 y  12
6 x  9 y  12
Set up and solve appropriate equations for all word problems.
5. A company budgets $100,000 for new computers. Deluxe computers cost $800
each and basic computers cost $450 each. If the company wishes to purchase 139
computers, how many of each type should they purchase?
6. The sum of two numbers is 130. the second number is 20 less than 4 times the
first number. Find the two numbers.
7. The weekly demand model for a new video game is given by N= -p + 520. The
weekly supply model for the same game is N = 3p + 400. For these equations p is
the price of the game and N is the number sold or supplied each week. Find the
price at which the supply and demand are equal. How many would be sold at this
price?
8. Graph the systems.
a.
2x  y  4
b.
y  x 1
x  y  1
x2
9. For each system in problem 8, name one specific solution.
10. Identify each of the following as a monomial, binomial or trinomial. Give the
degree of each.
a. 2 x 5  4 x 3
b. 9 x 4 y 3  5 x 2 y 2  7 x 2 y
11. Add/subtract each of the following:
a. (2 x 4  9 x3  4 x  5)  (15x 4  8x 2  5x  4)
b. (8x 4 y 3  7 x3 y  6 y 2 )  (3x 4 y 3  8 y 2 )
12. Simplify each expression.
a. x10 x 4
b. (3x3 )2
 8 x3 
e.  6 
 2x 
2
4x y 
i.
 2 x 
2
 2 x 
f.
2 3
(6 x5 )
12 x3
c. 3x0
d. (-5y3)2(3y4)3
g. 42  33
h.
( z 4 ) 3
z 
 5 2
4 2
3 5
j. (4 x5 y 2 )2 (2 x 5 y 7 )
13. Find each product.
a. 2u 2v 4 (4u 2  5v  2u 3v 2 )
d. (2x + 3)2 e. (x2 – 5)2
14. Divide:
15 x 4  20 x 2  10 x
a.
5x
b. (4x – 6)(2x + 1) c. (2x – 5y)(2x + 5y)
f. (3z + 2)(3z3 + 2z2 – 5z – 3)
b.
6 x3  x 2  3x  2
2x  3
8 x3  1
c.
2x 1
15. Write 1.67 x 105 in decimal notation.
16. Write 0.0000032 in scientific notation.
17. Multiply: (2.4 x 106)(1.2 x 10-8)
Answers: 1. no 2. a. (-3, 4) b. infinite solutions c. (-3, 1) 3. a. (3, -4) b. (5, 4)
 34 85 
c. no solution. 4. a. (8, 12) b.  ,  c. (1, -3) d. no solution. 5. 32 basic,107 deluxe
 31 31 
6. 30 and 100. 7. p = $30, 490 sold. 8. see below. 9 various ans. Possible. 10.a.
binomial, degree 5. b. trinomial, degree 7. 11. a. 17x4-9x3-8x2+x+9
16
43
b. 11x4y3 – 7x3y - 2y2 12. a. x14
b. 9x6 c.3
d. 675y18 e. 6
f. -4x8 g.
x
432
11 8
1
x y
h. 22 i.
j. -32x5y3
13. a. 8u 4 v 4  10u 2v5  4u 5v 6 b. 8x2-8x – 6
z
512
c.4x2 – 25y2 d. 4x2 +12x + 9 e. x4 – 10x2 + 25 f. 9z4 + 12z3 – 11z2 – 19z – 6
20
14. a. 3x3 – 4x + 2
b. 3x 2  5 x  6 
c. 4x2 +2x +1 15. 167,000 16. 3.2 x 10-6
2x  3
17. 2.88 x 10-2