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ALG2/TRIG Regents Review #4
Directions:
Choose the best answer. Answer ALL questions. Show ALL work in column 2. If
there is no mathematical work to be shown, write an explanation or definition to support your answer!
This counts as a quiz grade!!!
1. Solve x  8  15  17 , if possible.
a. There are no solutions.
b. The solutions are -10 and -6.
c. The solutions are 10 and -6.
d. The solutions are 10 and 6.
2. Solve
a.
b.
c.
d.
2 p 2  12 p  28  4 p  4 .
p=8
p=4
p = -8
p = -4
1
3. Evaluate  
7
1
a. 
49
1
b.
49
c. 49
d. -49
2
4. Factor completely: x 3  5 x 2  8 x  40
5. Simplify the expression: 343 p 3 q 9 3
1
a. 7 4 pq 3
b. 7 p 3 q
c. 7 pq 9
d. 7 pq 3
6. Let f ( x)  3 x  3 and g ( x)  4 x 2 . Find g(f(2)).
a. 34
b. 36
c. 39
d. 37
7. Find an equation for the inverse of the relation
y = 18x + 11
1
11
a. y   x 
18
18
1
11
b. y  x 
18
18
1
11
c. y  x 
18
18
1
11
d.  y   x 
18
18
8. Solve the following radical equation
4 x  11  12  20
9. A theater company plans to hire people to build a
stage set. The work time t (in hours per person)
varies inversely with the number p of people
hired. The company estimates that 20 people
working for 400 hours each can complete the job.
Find the work time per person if the company
hires 50 people.
10. Solve and check.
x
1
6
 
x6 9 x6
a. x = -6
b. x = 60
c. x = 6
d. There is no solution.
11. Find the product
3x 2  3x
x 2  3x  2

5 x 2  20 x  20
x2  x
12. Find the quotient
4 x 2  24 x  32
 x  2
13x 2
9
13. Simplify: x  3
5
6

x3 x
14. Solve by completing the
square
15.Write
a.
b.
c.
d.
12x
5
3
5
using radical notation.
12x3
125 x3
3
12x5
123 x5
16.A company had total sales of $4,800,000 in 1988.
Each year between 1988 and 1993 the sales
increased by 12%. What were the total company
sales in 1993? Round your answer to the nearest
dollar.
a. $8,459,240
b. $7,552,893
c. $9,474,349
d. 32,256,000
17. A company had a total debt of $500,000 in 1990.
Between 1990 and 1999 it reduced its debt 13%
each year. Write an exponential equation for this
situation.
a. D( x)  500,000(0.87) x
b.
c.
d.
18. What are the domain and range of this function?
a.
b.
c.
d.
Domain: all real numbers; Range: y ≥ –4
Domain: –2 ≤ x ≤ 2; Range: y ≥ –4
Domain: x ≥ –4; Range: all real numbers
Domain: x ≥ 0; Range y ≥ 0
19. The distance d traveled at a constant speed r is
directly proportional to the time t spent traveling.
A car moving at a constant speed travels 150
miles in 2.5 hours. Which proportion represents
how to find the number of miles the car travels
after 6 hours, if its speed remains constant?
a.
150 d

2 .5 6
b.
d
2.5

150
6
c.
150 6

2 .5 d
d.
150
6

d
2.5
20. What is the equation of y = |x| translated 1 unit up
and 6 units to the left?
a. y = |x – 6| + 1
b. y = |x – 1| + 6
c. y = |x + 1| + 6
d. y = |x + 6| + 1