Algebra 2 and Trigonometry Honors
Midterm Review Supplement
1.
2.
If logb x  y , then x equals
(1) y  b
(3) y b
y
(2)
(4) b y
b
Solve for x (round to tenth): 2e 5 x  2  8
3.
Find the center, radius, domain and range of the following circle:
x 2 + y2 –2x –8y – 8 = 0
4.
The expression log 3 (8  x ) is defined for all values of x such that
(1) x  8
(3) x  8
(2) x  8
(4) x  8
5.
A certain bacteria grows at a rate of 3.5% each month modeled by the equation B = B0*er*t where
B0 is the initial amount, r it the rate of growth, and t is the time in months. If there were 500
bacteria present in the beginning, how many bacteria will be present in 4 months? How many in 2
years?
6.
Find the center, vertices, domain and range of the following ellipse:
64x2 + 768x + 16y2 - 96y = -1424
7.
Which expression is not equivalent to log b 36 ?
(1) 6 logb 2
(3) 2 logb 6
(2) logb 9  logb 4
(4) logb 72  logb 2
8.
Solve for x to the nearest hundredth: 4e 0.5 x  1  11
9.
Find the center, radius, domain and range of the following circle:
x2 + y2 – 18x + 6y + 9= 0
10.
If log a = 2 and log b = 3, what is the numerical value of log
(1) 8
(2) –8
(3) 25
(4) –25
a
b3
?
11.
In the beginning there were 100 tons of radioactive waste. It decayed exponentially at a rate of
4.6% modeled by the equation A = A0*ek*t where A0 is the initial amount, k it the rate of decay,
and t is the time in years. In how many years will there be 50 tons of radioactive waste left?
12.
Find the center, vertices, domain and range of the following hyperbola:
25x2 – 9y2 – 250x – 36y + 364=0
13.
The speed of sound, v, at temperature T, in degrees Kelvin, is represented by the equation
T
v  1087
. Which expression is equivalent to log v?
273
1
(1) 1087  log T  log 273
2
1
1
(2) 1087( log T  log 273)
2
2
1
1
(3) log 1087  log T  log 273
2
2
(4) log 1087  2 log( T  273)
14.
Solve for x to the nearest thousandth: 3  5e x 1  12
15.
Find the center, radius, domain and range of the following circle:
5x2 + 5y2 - 20x + 25y - 5 = 0