Pre - calculus Semester 1 Final Review
(Latest Update ) Questions &
Answers 100% Correct - (Grade A)
What is e to the tenth place? - correct answer 2.7
Simplify: log(a + b) - correct answer Can't be done!
log(a + b)
Simplify: log(a - b) - correct answer Can't be done!
log(a - b)
What is log(ab) expanded? - correct answer log(a) + log(b)
What is log(a) + log(b) simplified? - correct answer log(ab)
What is log(a/b) expanded? - correct answer log(a) - log(b)
Simplify: log(a/(bc)) - correct answer log(a) - log(b) - log(c)
OR.... log(a) -(log(b) + log(c))
What is log(a) - log(b) simplified? - correct answer log(a/b)
What is log(a)^p expanded? - correct answer p * log(a)
What is log(subscript b)(b)?
,"Log base b of b" - correct answer 1
What is p * log(a) simplified? - correct answer log(a)^p
What is log(subscript b)(1)?
"Log base b of 1" - correct answer 0
What is the change of base formula? - correct answer
Parent function: exponential equation - correct answer y = a * b∧x
Exponential growth - correct answer y = p(1 + r) ^t
y = y-value on graph (how much is remaining at that time)
p = principle: starting point
r = rate: percent written as a decimal (ex: 5% is 5/100 ---> 0.05)
t = time (usually in years, but can be in other units of time)
Exponential decay - correct answer y = p(1 - r)^t
y = y-value on graph (how much is remaining at that time)
p = principle: starting point
r = rate: percent written as a decimal (ex: 5% is 5/100 ---> 0.05)
t = time (usually in years, but can be in other units of time)
What is the compound interest formula? - correct answer y = P (1 + (r/n)) ^(nt)
, y = money resulting at the end of being compouned
p = principle: starting point
r = rate: percent written as a decimal (ex: 5% is 5/100 ---> 0.05)
n = number of times the interest is compounded for that unit of time (t) (ex:
compounded quarterly ---> n = 4)
t = time (usually in years, but can be in other units of time)
Infinitely compounded:
(Optional: 99% GUARANTEE IT WILL NOT BE ON TEST) - correct answer y = a*(e^kt)
y = total money earned
a = principle: starting point
e = A NUMBER (about 2.7)
k = rate: percent written as a decimal (ex: 5% is 5/100 ---> 0.05)
t = time (usually in years, but can be in other units of time)
Half-life - correct answer y = P(1/2)^(x/n)
y = life remaining
P = starting point
1/2 = half-life (note: let's say it triples in size, instead of losing 1/2, then it would be 3
instead of 1/2 ..... now let's say it has quarter life, than it would be 1/4 instead of 1/2)
x = number of years you are measuring for (ex: I am trying to find the 1/2 life of a
bottle of shampoo after 12 weeks ---> x = 12)
(Latest Update ) Questions &
Answers 100% Correct - (Grade A)
What is e to the tenth place? - correct answer 2.7
Simplify: log(a + b) - correct answer Can't be done!
log(a + b)
Simplify: log(a - b) - correct answer Can't be done!
log(a - b)
What is log(ab) expanded? - correct answer log(a) + log(b)
What is log(a) + log(b) simplified? - correct answer log(ab)
What is log(a/b) expanded? - correct answer log(a) - log(b)
Simplify: log(a/(bc)) - correct answer log(a) - log(b) - log(c)
OR.... log(a) -(log(b) + log(c))
What is log(a) - log(b) simplified? - correct answer log(a/b)
What is log(a)^p expanded? - correct answer p * log(a)
What is log(subscript b)(b)?
,"Log base b of b" - correct answer 1
What is p * log(a) simplified? - correct answer log(a)^p
What is log(subscript b)(1)?
"Log base b of 1" - correct answer 0
What is the change of base formula? - correct answer
Parent function: exponential equation - correct answer y = a * b∧x
Exponential growth - correct answer y = p(1 + r) ^t
y = y-value on graph (how much is remaining at that time)
p = principle: starting point
r = rate: percent written as a decimal (ex: 5% is 5/100 ---> 0.05)
t = time (usually in years, but can be in other units of time)
Exponential decay - correct answer y = p(1 - r)^t
y = y-value on graph (how much is remaining at that time)
p = principle: starting point
r = rate: percent written as a decimal (ex: 5% is 5/100 ---> 0.05)
t = time (usually in years, but can be in other units of time)
What is the compound interest formula? - correct answer y = P (1 + (r/n)) ^(nt)
, y = money resulting at the end of being compouned
p = principle: starting point
r = rate: percent written as a decimal (ex: 5% is 5/100 ---> 0.05)
n = number of times the interest is compounded for that unit of time (t) (ex:
compounded quarterly ---> n = 4)
t = time (usually in years, but can be in other units of time)
Infinitely compounded:
(Optional: 99% GUARANTEE IT WILL NOT BE ON TEST) - correct answer y = a*(e^kt)
y = total money earned
a = principle: starting point
e = A NUMBER (about 2.7)
k = rate: percent written as a decimal (ex: 5% is 5/100 ---> 0.05)
t = time (usually in years, but can be in other units of time)
Half-life - correct answer y = P(1/2)^(x/n)
y = life remaining
P = starting point
1/2 = half-life (note: let's say it triples in size, instead of losing 1/2, then it would be 3
instead of 1/2 ..... now let's say it has quarter life, than it would be 1/4 instead of 1/2)
x = number of years you are measuring for (ex: I am trying to find the 1/2 life of a
bottle of shampoo after 12 weeks ---> x = 12)
