Download 2009 IM 1 Sem2 Review

Int. Mathematics 1
Semester 2 Final Exam Practice Problems I
Name_____________________
Part I: Basic Skills and Word Problems
1. A cube has side length 12. Use the equation Volume = (side length)3 to find the volume of the cube.
Show reasoning.
12
12
[A] 36 units3 [B] 144 units3
[C] 1728 units3
[D] 864 units3
12
[E] None of these
2. Simplify and evaluate the expression using order of operations given that x = -3 and y = 2
2 x2  y( y  1)  8
3. Give an example of a composite number and explain clearly why it is composite.
4. Factor the monomial
20x 2 y3
[A] 2(2)(2)(5)(x)(x)(y)(y)(y)
[B] 2(2)(5)(x)(x)(y)(y)(y)
[C] 2(2)(5)
[D] 2(5)(x)(x)(x)(y)(y)
[E] None of these
5. Find the Greatest Common Factor of 12 and 32, showing reasoning.
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6. Write a variable expression for the difference of 5x and 47
7. On a number line, what is the distance between 5 and -8? Explain your reasoning.
8. During one week of unusual weather, the daily temperatures at noon were measured as follows:
12  C, -14  C, -8  C, 32  C, -2  C. What has the average daily temperature at noon over these
five days? Show reasoning.
9. Plot and connect the points A(2, 5), B(1, -4) and C(-5, 8)
In which quadrant is point C located?
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10.
Solve for x showing all necessary steps
5(x - 2) + 7 = 47
11.
Write down the factor tree of 120, and then write its prime factorization.
12.
Explain clearly why the numbers 14 and 45 are relatively prime.
13.
Write the fraction in simplest form.
48 x 4 y 2
[A] 44xy
[B] 12xy
4 x3 y 3
[C]
12 y
12x
[D]
[E] None of these
x
y
14.
Two farmers are planting seeds in a row right next to each other. Both start at the same point,
but the first plants a seed every 8 inches. The second plants a seed every 14 inches. After how
many inches will they plant their seeds right next to each other? Show reasoning.
15.
Find the value of x for the figure, showing reasoning.
Perimeter = 252
5x
2x
3x + 12
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16.
In a typical school year, school is in session for 6 hours a day for 180 days of the year. For how many
minutes is the school in session? Show reasoning.
17.
Write the decimal as a fraction or mixed number in simplest form. Show reasoning.
3.2
[A] 32/100
[B] 16/5
[C] 8/25
[D] 16/50 [E] None of these
(Bonus Type Question+1) Write the decimal 0.43 as a fraction or mixed number, showing reasoning.
18.
3
4
Find the sum of 5  6 , showing reasoning. Leave your answer as a mixed number.
5
5
19.
Solve for x, showing reasoning.
20.
One weekend, two friends decide to see who can catch more air off of a ski jump. Oompie takes the
2
1
jump and travels 26 feet while Loompie travels 32 feet off the jump. Who won the contest and by
3
2
how much? Leave your answer as a mixed number and show reasoning.
8
10
 x
3
3
21. Find the product. Leave as a simplified improper fraction or simplified mixed number
 5  1
5  3 
 6  2
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22. Ann is shopping for the best cell phone package. The total cost and number of minutes are given below.
Which plan gives the best cost per minute rate? Show reasoning.
[A] $45 for 1000 minutes
[C] $60 for 1200 minutes
[B] $35 for 800 minutes
23. At a certain time of the day, the length of one’s shadow is proportional to his or her height. A tree that is
16 feet tall casts a shadow of 7 feet. How long would the shadow of a 6 foot man be at the same time of day?
Show all reasoning.
24. If LMN
L
OPQ , as shown, then which side of the second triangle corresponds to side LN ?
P
O
Q
N
M
25. In the previous problem, LM = 40, OP = 30 and PQ = 21, then what is the length of side NM ? Show
reasoning.
26. A sculptor is planning to create a large statue of a bear from a small figurine, using the same proportions.
The front leg of the bear on the figurine measures 5 inches, whereas it will be 3 feet in length on the larger
statue. Calculate the scale of the small figurine to the large statue.
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Part II: Vocabulary
Master vocabulary list:
Domain, range, inputs, outputs, numerical expression, variable, variable expression, evaluate,
verbal model, power, exponent, base, order of operations, integer, negative integer, positive
integer, absolute value, opposites, additive inverse, coordinate plane, ordered pair, mean,
commutative property, associative property, like terms, inverse operations, rational number,
repeating decimal, terminating decimal, unlike fractions, least common denominator, reciprocals,
ratio, equivalent ratios, proportions, using a cross product, similar figures, corresponding parts,
congruent
Note – vocabulary words will be used at most once, and not all words will be used
Fill in the blank:
A whole number greater than zero is called a(n)_________________________
Two numbers that add to zero are called _______________________________
The amount that a retailer adds onto the wholesale price of an item before selling it is referred to as the
________________________
Two fractions that do not have the same denominators are called ______________
The distance of a number from zero is called its____________________________
A fraction whose numerator and denominator are both whole numbers is referred to as a
__________________________
The agreed upon procedures for simplifying, solving and evaluating expressions and equations are
known as ____________________________
Two operations that undo or cancel each other out are called ___________________
Consider the power 57. The 5 is called the __________________ and the 7 is called the
___________________
The inputs, or x – coordinates of a relation are referred to as the ___________________
A verb that means “to find the value of” is _________________________
Terms that can be combined into a single term are called _______________________
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