Download MAT1033 Exam 2 - S14 - Jahn.tst

MAT1033 Intermediate Algebra
Professor George Jahn
Practice Exam 2
Name______________________________________________
Solve the system by graphing.
1) 2x + y = -4
6x + 5y = 0
y
20
-20
20
x
-20
Decide whether the ordered pair is a solution of the given system.
2) (-5, 3)
2x + y = -7
4x + 2y = -14
Solve the system by substitution.
3) 3x - 13 = -y
2x + 9y = -8
1
Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.
4) 5x - 4y = -3
15x - 12y = 9
Solve the problem.
5) The perimeter of a rectangle is 40 m. If the width were doubled and the length were increased by 14 m, the
perimeter would be 82 m. What are the length and width of the rectangle?
6) A sum of money amounting to $5.00 consists of dimes and quarters. If there are 26 coins in all, how many are
quarters?
7) Ellen wishes to mix candy worth $2.16 per pound with candy worth $3.72 per pound to form 26 pounds of a
mixture worth $2.76 per pound. How many pounds of the more expensive candy should she use?
8) Mardi received an inheritance of $60,000. She invested part at 10% and deposited the remainder in tax-free
bonds at 7%. Her total annual income from the investments was $5100. Find the amount invested at 10%.
2
Apply the product rule for exponents, if possible.
9) (-3x5 y)(-4x9 y2 )
Evaluate the expression. Assume all variables represent nonzero numbers.
10) (-3)0 + (-2)0
Evaluate the expression.
7 -2
11)
5 -4
Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if
necessary.
12) 5x -3
3
Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all
variables represent nonzero numbers.
x-14
13)
x-8
Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero
real numbers.
14) (x5 )-3
Express the number in scientific notation.
15) 0.000657
Write in standard notation.
10 × 105
16)
2 × 107
4
Add or subtract as indicated.
17) (-2 - 5x4 + 8x6 - 7x5 ) + (-2x5 - 7x4 - 6 + 3x6 )
18) (-6x3 + 9x2 + 4) - (-5x3 + 2x - 5)
For the given polynomial function, find the requested value.
19) f(x) = -8x2 + 6x + 10; find f(2)
For the given pair of functions, find the requested item.
20) Given f(x) = 5x - 4 and g(x) = -9x + 9, find (f - g)(x).
Find the product.
21) (x + 4)(x2 - x + 8)
5
22) (a - 7)(a + 7)
23) (10a - 1)2
Divide.
24)
27x4 + 24x2 + 21x
3x
25)
x2 + 10x + 21
x+3
6
Answer Key
Testname: MAT1033 EXAM 2 - S14 - JAHN
1)
y
20
-20
20
x
-20
{(-5, 6)}
2)
3)
4)
5)
6)
7)
8)
Yes
{(5, -2)}
Inconsistent: no solutions
width 7 m, length 13 m
16 quarters
10 pounds
$30,000
9) 12x14y3
10) 2
625
11)
49
12)
5
x3
13)
1
x6
14)
1
x15
15) 6.57 × 10-4
16) 0.05
17) 11x6 - 9x5 - 12x4 - 8
18) -x3 + 9x2 - 2x + 9
19) -10
20) 14x - 13
21) x3 + 3x2 + 4x + 32
22) a 2 - 49
23) 100a 2 - 20a + 1
24) 9x3 + 8x + 7
25) x + 7
7