Download MAT 092 Beginning Algebra

MAT 090 Beginning Algebra
Spring 2014 Midterm
NAME:_________________
1. State whether the following statements are TRUE or FALSE. No explanation is needed.
A) 3 
2 6

5 15
B)  3 2  9
C) 2  4x  6x
2. A list of numbers is shown below, graph these numbers on a number line.
 9,
5,

2
, 
10
, 4
3
3. Translate the following mathematical symbols into verbal statements:
A) 2 x  3
B) C  2 R
2
4. Use the commutative law of multiplication to write an equivalent expression for x  3x  5
5. Use the associative law of addition to write an equivalent expression for 2x  3 y   5
6. Use PRIME FACTORIZATION to help you simplify the following fractions:
30
45
7. Perform the indicated operations below. Answers should be in lowest terms (you do not need
to use prime factorization). SHOW YOUR WORK.
A) 2
1
2
1
4
3
D) 60  3 4
B)
9 2

4 3
E)  2   2 23  3 2
2
C)  12   6  4   2
5
3
x 
8
4
8. Simplify the following expression: 16 
9. Solve the following equations. To receive full credit, you must show your work.
A) 3x  9  5x  7
B)
3
9
x
4
8
C) 5x  3  x  4  2x  2x  5
D)
3
1
x
4
2

2
3
11. Solve the following formulas for the indicated variable. Please show your work.
A) A 
x y
solve for x.
3
B) 2 x  3 y  6 solve for y.
12. Solve the following inequality. Extra Credit - Put your answers in interval notation.
A) 4  5 x  2 x  8
B) x 
2 1

3 2
13. SET UP and SOLVE the following word problems. Define and label your
unknowns, set up the equation(s) you would use to solve the word problem, and then solve
your equations to get a final answer…watch your units!
A) Rob and Rachel are laying new tile in their home. They rent a cutting saw from Algebra
Construction Company. They need to pay a $50 fee for the saw and then there is a charge of
$10 for every hour that they have the saw. If their budget for this rental is $300, how many
hours can they keep the saw?
B) The perimeter of a rectangular lot is 210 feet. The length of this lot is 25 feet longer than
its width. Find the length and width of this rectangular lot.
14. SET UP ONLY the following word problems. Define and label your unknowns, and
set up the equation(s) you would use to solve the word problem. You do not need to solve
your equations.
SET UP ONLY.
A) Double the difference of a number and three is the quotient of that number and five increased
by six.
B) In a recent survey, seven students said that they loved the Dodgers. This represented 35%
of the students in the survey. How many students participated in the survey?
C) Joe’s monthly commission rate at Nambe Motors is 2.5%. What sales amount will Joe
need to generate in order for him to earn $3,000 in commission?
D) Find the base of a triangle whose area is 44 ft 2 and whose height is three more than
double the base.