Download Practice Problems for Challenge to Precalculus

Practice Problems for Challenge to Precalculus Accelerated:
Powers and Radicals, Answers
1
125
2) 4
9
3)
4
4) 32
5) 4 2
1)
6)
5
25
7) 2 3 2
8) 9 2
Write each of the following in their most simplified form. The final answer should have no
negative exponents.
z2
x8 y18
11)
b19
4a 2 c8
16 y 24
10)
x
12)
81p 9
q
9)
Simplify the following radicals. If there are radicals in the denominator, rationalize them.
Radicals must be expressed with the smallest number under the radical possible (for
example,
32 should be written as 4 2 ).
13) 7 2  5 3
17)
6 5  2 15  25 3
15
15) 47  16 2
18)
2 5  15
5
14  7 5
2
19)
3 6 3 2  2 3
3
14) 13 3  26 2
16)
Solve the following equations. Be sure to check for extraneous solutions.
20) x  15
21) x  2
22) No solution
23) No solution
24) x  4
25) x  2 (5 is an extraneous solution)
26) No solution
27) x 
13  129
2
Write each of the following expressions as a single fraction.
28)
5 x  24 x  21
 2 x  3 x  2 
2 x  27
x 2  16
8 x  5
30) 2
x  2 x  15
29)
a 2  2ab  b 2
a 2  b2
3c  4
32) 2
2c  c  10
31)
Solve the following equations. Make sure to indicate any extraneous solutions.
33) No solution (x = –2 is extraneous)
34) x  5  2 22
35) No solution
Factor each of the following expressions as completely as possible.
36) x 2  x  5 x  2 
40)  3x  4 y 
37)  3x  2 y 2  9 x 2  6 xy 2  4 y 4 
2
41)  x  21 x  2 
38)  4 x 2  1  2 x  1 2 x  1
42)  5x  3 x  1
39) x  2 x  3 x  5
43)  x  29  x  4 
Solve the following equations.
44) x  5, 2
46) x  3 ,1
5
47) x  29, 4
45) x  0,  3 ,5
2
Find the vertex, x-intercepts, and ranges for each of the following parabolas.
48) Vertex:  6, 4  , x – intercepts:  4,0  ;  8,0  , Range: y  4
49) Vertex:  2, 15 , x – intercepts: none, Range: y  15
50) Vertex:  5,9  , x – intercepts: none, Range: y  9




51) Vertex: 5 ,  9 , x – intercepts: 1 , 0 ;  2, 0  none, Range: y   9
8
2
4
8
Precalculus Honors topics
Find the Vertical Asymptotes and Zeroes for the following Rational functions:
1) Zeroes:  2,0  ;  3,0 
Vertical Asymptotes: x  1
2) Zeroes: none
Vertical Asymptotes:
x  2; x   1
2

Vertical Asymptotes:
x  0; x  4; x  4
Write the following expressions as logarithms with a single argument.
5) log 50
6) ln
x  x  5
 x  3
7) log 48
8) ln
135
2
Solve the following equations for x.
9) x  3
10) x  15

3) Zeroes:  3 , 0
5
Vertical Asymptotes: none
4) Zeroes:  2, 0 
11) No solution
12) No solution