Test 3 Mat 1101 Worksheet With Answers - 2011
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1
2Test 3
MAT 1101
Spring 2011
Name ________________________
Simplify all answers and show your work!
1) Exponents are a shortcut for repeated ____multiplication__.
6
2
2) Why can we not simplify 5x
+ 2x
any further? The terms aren’t like terms.____________________
____________________________________________________________________________________
3) When we have a variable with an exponent raised to another exponent, what do we do with those
5
3
exponents? [Ex: (x
)
] ___Multiply them________________________________________________
3
3
3
3
4) Combine like terms: –7x
+ 3x
– 2x – 4x
+ 3x __–8x
+ x_____________________
x 5 −
2
-1
5) If f(x) =
, find the inverse (f
(x)).
6) Solve the inequality: 5 – 2(3x + 1) ≥ 6(x – 4)
8
x 8 +
2
9
-1
f
(x) =
x ≤
5
4
2
2
7) Solve the inequality: –2 < 6x + 7 < 5
8) Add: (–2x
– 6x – 11) + (4x
+ 15x – 8)
3
1
2
< x <
2x
+ 9x – 19
−
−
2
3
2
2
9) Subtract: (24x
– 13x + 7) – (8x
+ 2x – 4)
2
16x
– 15x + 11
10) Determine if “factoring by grouping” can be used on the following expressions. Justify your
answer.
3
2
4
8
4
8
6
5
2
a) 6x
+ 18x
– 3x – 9
b) 4x
y
– 14xy
+ 6x
y
+ 21x
y
3
9
10
Outers: –54x
Outers: 84x
y
3
9
10
Inners: –54x
Inners: –84 x
y
Yes
No
Factor the following completely:
4
3
2
8
3
7
3
2
11) 18x
y
– 45x
y
– 27x
y
12) 8x
– 24x
– 3x + 9
2
3
2
5
4
2
9x
y
(2x
– 5y
– 3xy
)
(x – 3)(8x
– 3)
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