fall 2013 – MTH 138 – midterm
instructor: M.Schmidtová
90 minutes, no notes, no books, only calculators are allowed
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NAME: KREPOP score: 70 /

All calculations must be included,
if only results are written they will not be graded.

FORMULAS

ar.as=ar+s ar:as=ar-s
a-n=1/an (an)m=an.m
(ab)n=an.bn (a/b)n=an/bn

(a+b)(a-b)=a2-b2
(a+b)2=a2+2ab+b2 (a+b)3=a3+3a2b+3ab2 +b3
(a-b)2=a2 -2ab+b2 (a-b)3=a3 -3a2b+3ab2 +b3
x3+y3=(x+y)(x2-xy+y2)
x3 -y3=(x-y)(x2+xy+y2)

a(x-x1)(x-x2)=ax2+bx+c
Vx= -b/(2a)

Pythagorean Theorem a2+b2=c2

1. True or False? State your answer clearly. [4pts]

a) (a+b)3=a3+b3

b) 5(a-b)-c(a-b) = (a-b).(5-c)

c) a.(b.c)=ab+ac

d) (a:b):c= a: (b:c)

2. Convert the repeating decimal c=8.666666… into a fraction. Complete calculation must be shown. [4pts]

3. Using a calculator evaluate the problem. [3pts]

4. Simplify the problem and write the answer in form of one fraction and using positive exponents only. [4pts]

5. Write in simplified form. [4pts]

6. Rationalize the numerator. [4pts]

7. Perform the indicated operations. [3pts]

8. The area of large square is equal to the sum of the area of the small square and the areas of the four congruent (zhodn é ) triangles. Translate this verbal statement into a mathematical equation and simplify as much as possible. [4pts]

9. Factor out, relative to the integers, all factors common to all terms. [3pts]

10. Factor out, relative to the integers, all factors common to all terms….