Download MAC 1105 Self- Assessment Exam 1 Sanchez

Self-assessment B
One-dimensional mathematics
Name: ___________________________________
Complete:
1. Give an example of an irrational number: ______________
2. Give the only whole number which is not a natural number: _______________
3. Write the number i 95 in the form a + bi : _____________
4. Write the product (3 – 7i)(5 + 2i) in the form a + bi: ___________
5, Write the formula for the discriminant of the quadratic equation ax 2  bx  c  0 : ___________
6. If the solutions of a quadratic equation are not real numbers, then the discriminant is ________
a) zero
b) positive
c) negative
7. If the two solutions of a quadratic equation are equal, then the dsicriminant is _________
a) zero
b) positive
c) negative
8. The fraction equivalent to the decimal 1.333333….. is _____________
9. The fraction equivalent to the decimal 1.33 is _____________
10. The fraction equivalent to the decimal 0.21515151515… is _____________
11. Write the quadratic equation with the two solutions -7 and 12. _________________
x 2  ( x1  x 2 )x  x1x 2  0
12 Write the quadratic equation with the two solutions 2 + 3i and 2 – 3i _________________
x 2  ( x1  x 2 )x  x1x 2  0
13. If one solution of a quadratic equation with real coefficients is 5 – 3i, then the other solutions is
___________
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Multiple choice questions:
_________14) Which of the following is equivalent to the expression
a) 10
b) -4
c) 4
_________15) Which of the following is equivalent to the expression
a) 20
b) 6
c) -6
| -3
+7| ?
| 13 | - | -7 |
?
_________16) If x has a value greater than 5, which of the following is equivalent to the
expression | 5 – x| ?
a) 5 + x
b) 5 - x
c) x - 5
_________17) Which of the following intervals indicates all the real number less than -3 ?
a) ( ,  3]
b) [3,  )
c) ( ,  3)
d) ( 3,  )
_________18) Which of the following intervals indicates all the real numbers which are
greater than 5, but at most 10.6
a) (5, 10. 6]
b ) [5, 10.6)
c) (5, 10.6)
d ) [5, 10.6]
_________19) Which of the following intervals indicates all the real numbers which are
non-positive
a) ( , 0]
b) [0,  )
c) ( , 0)
d) (0,  )
_________20) Which of the following intervals indicates all the real numbers which are
less than 5 or at least 7
a) (5, 7]
b) [5, 7)
21. Find the solution of the equation
c) ( ,  )
|21 – 3x|
= 12
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d) ( . 5)  [7,  )
21 _________________
Perform the operations required to simplify and write the answers in the forma a + bi
22) 15 - 4i - (-3 - 12i) + 5(-1
23)
Answer:
22)
+ 4i)
 20  10i
3 i
23)
24. Find the solution of the equation 2x 2  2x  2  3 Answer: __________________
Use the quadratic formula. a = _____
b = ______ c = ______ Careful!
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25. Find the solution of the inequality  3  7  2x  15 . Give answer in interval notation.
26. Find the solution of the inequality
| 8 - 4x |
> 12 . Give answer in interval notation.
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27. Solve the inequality: x 2  5x  14  0
Step 1 - Solve the equation.
Step 2 – Place the solutions of the equation on the number line.
Step 3 – Investigate which intervals on the number line are solutions of the inequality.
Step 4 - Write the answer below in interval notation.
Answer: _______________________
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