Algebra 2 Regents Review Topics (Introduction.)
TEST TAKING TIPS
Most Common Challenging Concepts Students
TIP 1: Examine the question.
TIP 2: Examine the answers.
TIP 3: Use a calculator whenever possible to check and solve.
In these algebra 2 review sessions we will be exploring strategies, important techniques and approaches to solving algebra 2 regents questions more efficiently.
- Exponential Questions/ Interest Rate Problems
The equation in question has an exponent which is negative (-0.10x) and is an exponential equation.
START: Question is asking which is not equivalent, which mean we need to examine if the answers are same as the question. The obvious choice is (1) but that can be checked with a calculator.
Simplest solution: Using graphing calculator enter each of the choices and the given question into the options so check which are the same.
MODE is set to funct.
Wrong way to enter this exponential function:
Notice if you enter this choice as it is written in the question it is not correct:
Right way to enter this exponential function choice:
Choice (1) and the question yield the same graph. But the question is asking which of the following is not equivalent.
Negative exponent rules say that one over a base to a positive power can be turned into a negative power.
Adding exponents because the base is the same. Ex 2^3 * 2^4 = 2^7.
Ans choice 4 is not equivalent.
Interest rate problems involve interest rate formula. On the last pages of the regents exam you can find the formula sheet.
“The exponential e is used when modeling continuous growth that occurs naturally such as populations, bacteria, radioactive decay, etc. You can think of e like a universal constant representing how fast you could possibly grow using a continuous process.”
Converting the percent to decimal.
A0 – initial amount = 5000
A – final amount = 9110
K= rate of change
t – time 30 years
Formal solution :
divide both sides by 5000
take the natural log of both sides
bring forward the exponent (rules of logs)
lne = 1
0.599 =30r divide by 30 both sides
r= 0.5999/30 =0.019997 ~0.02 = 2%
Now suppose you did not know how to use natural logs and solve this problem.
Shortest solution Substituting Answers
If you have no idea what this equation represents and missed or intentionally slept through classes with rate, growth and exponential problems. Look at the choices and try to use any math that you already know.
Choice 1. Every hour, the amount of pain reliever remaining is cut in half.
Hour = t time.
One hour = t =1 substitute t into the formula.
If every hour the amount would be half the answer would be half of 220= 110 this equation is not going to produce that. The reason is that it is already halved by the fraction but there is an extra fraction in the exponent.
Lets check with the calculator entering and using proper parenthesis.
207 is not half of 220.
Choice 2. In 12 hours, t=12 substitute into the function to find how many milligrams will be remaining.
Reducing 12/12=1 there will be 110 mg remaining. This is choice 4.
In 24 hours= t, there will be 55 mg remaining not zero.
Ans choice 4.
If the test day is the first time you have seen exponential problems do not panic. Using a calculator you can solve these problems with ease.
START: Graph this function. Pick a number for a, b, since the first choice says that a >0 and b>1 lets pick a=1 b=2. Graph this function.
We can see from the graph that the function is going up which means it is increasing on the domain of the function( -inf, +inf).
The y intercept is (0,a) we choose a to be 1 in our example.
Y intercept is where the graph hits (intercepts) the y axis.
The y intercept is (0,1) is this true? Lets find it on the graph.
To find the exact value hit 2ndCalc and type x=0 hit enter, this finds the exact value of the function at (0=x, 1).
If you wanted to check algebraically substitute x =0 into the function
1 * 2^0 = 1 =y.
The asymptote is y=0. Asymptote is the value a function comes close to but never reaches. Where is y=0, in this case it is not just a point, it is a line.
Where is this line located? It is a line where all the y values are zeros which is the x axis. This is the line exponential function never reaches.
You can check this by hitting the TRACE FUNCTION and using the left arrow scroll as left as possible. You will notice that the values of the function approach zero but never get to it. Y= 0.0089 . Y = 0.0045…
This statement is true.
The x intercept is (b,0) we choose b =2. The x intercept (2,0) is this true?
X intercept is where the graph hits (intercepts) the X axis.
Does this graph hit the x axis at (2,0)? No. So this statement is false.
Ans choice 4.