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Mathematics 098 fourth test review problems
√
ab + b2 = a + b for all positive numbers a and b.
√
2. True or False: x2 = x for all positive and negative real numbers x.
3. Simplify: (in part (c) you may need to use the imaginary unit i)
1. True or False:
(a)
√
y8
(b)
√
32
(c)
√
s
−64
(d)
3
x
5
(e)
x24
8y 6
2
4. Use radical notation to rewrite each expression. Simplify if possible.
(a) 5x1/3
(b) − 82/3
6. Simplify:
5. Use a fractional exponent to rewrite
the expression
√
4
x3
q
− 20x8 y 7
8. Simplify:
2
1
1
−
x
y
7. Multiply & simplify
√
√ 2
x+ y
9. Use long division or synthetic division to simplify:
3x2 − 4x + 7
x−2
10. Find a line equation for the line which has slope equal to 3/4 and which passes through
the point (x, y) = (3, −6).
11. Reduce:
5−x
x2 − 25
12. Simplify:
4x2
2
3x − 1
−
+ 4x + 1 2x + 1
13. Solve the absolute value inequality |x − 40| < 3
14. Find all the solutions of
(a)
√
2x − 5 = 3
(d) m12 = 1.5
(b)
√
x = −6
(e) x17/12 = 2
(c)
(f)
x−3
=4
2x + 1
√
3
2x − 5 = −2
page two
15. The pressure P of a gas varies inversely with the volume V of the container holding the
gas. If the pressure P = 8 atmospheres when the volume V = 3 cubic centimeters, calculate
the pressure P when the volume is V = 4 cubic centimeters.
16. Find all the solutions of
(a) ex = 12
(b) 10 log(x/10) = 55
17. What is the domain of f (x) =
x3
5−x
?
− 10x2 + 25x