SampleProblems - Stony Brook University Mathematics...

Stony Brook University MAP 103
Mathematics Department Proficiency Algebra
Julia Viro Fall 2014
Sample Problems
The list below shows which types of problems are expected to be discussed in class and what is
the appropriate level of difficulty.
Week 1 (August 25-29) Integers. Operations of addition and multiplication and their
properties (commutativity, associativity and distributivity). Parentheses and order of
operations. Rational numbers. Addition, subtraction, multiplication and division of frac-
tions. Complex fractions.
1. Calculate without pen and paper:
a) 69 + 37 - 19 + 63, b) 2 · 38 · 5, c) 25 · 2014 · 4, d) (35 + 47) - (31 + 17)
2. Calculate without calculator: a) 71 - 21 · 4, b)
5
/
7
-
4
/
3
7
/
1
÷
2
/
7
, c) - 3 -
3
4
· 2 -
5
8
+3 ÷ 2
3. Bring the fraction
128
280
to simplest terms.
Week 2 (September 1-5. No classes September 1 and 2) Powers with integer
exponents. Exponential rules. Real numbers and operations on them.
1. Calculate without calculator:
a) ( - 3)
2
+ 2
- 3
b) (( - 1)
3
)
5
c) 2
4
· 3
- 2
· 2
2
· 3
3
d)
( - 5) 2 · 3 8
( - 3)
5
· 5
3
e) 3 π 2 - 3 -
π
2
2
(leave the answer in terms of π )
Week 3 (September 8-12) Notion of variable. Algebraic expressions. Composing
algebraic expression after word description.
1. The length of a side of a square is x . What is the perimeter of the square? What is
the area of the square?
2. Bob earns x dollars per hour, Ann earns twice as much. How much more will Ann
earn than Bob, if she will work 3 hours and he will work 2 hours?
3. A pair of jeans costs x dollars. What will be the price of it on a 35% sale?
4. On Monday, Jim spent x min playing his favorite video game. Next Tuesday, he played
10 min less than on Monday. On Wednesday, he payed three times more than Monday
and Tuesday together. How much time did spend Jim playing these three days?
5. Two identical boxes contain x chocolate bars. How many chocolate bars will be in five
such boxes?
6. Cam has to cover the distance of x miles. He went 3 hours with a constant speed of y
miles per hour. How many miles does he have left to go?

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