SPRING STUDY GUIDE – Algebra 2 Pre-AP
Well, this is it guys! We have made it to the end of our Spring semester together. As we prepare for our final exams, I
want to make it known that I believe that you all have the capacity to ace the Algebra 2 Pre-AP exam. Make sure that
you are taking the final steps necessary to stay fresh on the concepts that we’ve learned in the past few months. I hope
you all had a great school year, and let me know if you need any assistance. ~ Mr. Lacy
(FULL ANSWER SHEET WILL BE POSTED ON CLASS WEBSITE ON SUNDAY AFTERNOON – www.dallasisd.org/lacy)
Steps to Getting an Inverse
* Switch the x and y variables.
* Solve for y.
Projectile Motion
s(t) = – 16t2 + v0t + h0
v0 = Initial Velocity
h0 = Initial Height
Domain and Range
* Domain is the set of all x values that are included in a function.
* Range is the set of all y values that are included in a function.
* x values where there are vertical asymptotes and holes CAN’T be included in the domain.
* y values that are on a horizontal asymptote can’t be included in the range (normally).
* y values that are in a hole can’t be included in the range.
Logarithmic and Exponential Equations/Functions
* The inverse of y = logb(x) is y = bx
* The function ln(x) is a logarithm with base e.
* In word problems, the exponential equation used for growth and decay is y = a * bx
a = initial amount/value
b = rate of growth/decay
x = time
y = final amount
Direct and Inverse Variation
* Direct Variation
𝑦 = 𝑘𝑥
* Inverse Variation
𝑦=𝑥
𝑘
As x increases, y increases. As x decreases, y decreases.
As x increases, y decreases. As x decreases, y increases.
1. How does the asymptote change when y = 2x is changed to y = 2x + 4?
2. Write a rational function that does not include y = 4 in the range, and doesn’t include x = 5 in the domain.
3. Write a possible denominator for the following function if the horizontal asymptote is y = 2
4. Find the standard form of each circle given in general form. Also, give the center and radius.
A)
B)
5. Identify each conic section from the given equations.
A)
D)
B)
E)
C)
6. What are the solutions to the system of equations? What quadrant is each solution in?
𝑦 = 3𝑥
2 +2𝑥−3
𝑦=1
7. The volume V of gas varies inversely to the square of the pressure P. The volume of a gas is 360 cm 3 under pressure of
30 kg/cm2. What will be its volume under a pressure of 55 kg/cm2?
8. The volume V of gas varies inversely to the square of the pressure P. The volume of a gas is 450 cm3 under pressure of
60 kg/cm2. What will be its pressure if the volume of gas is 330 cm3?
9. What conic section is formed when a plane slices a cone…
A) …perpendicular to its height
B) …parallel to its slant height
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10. What is the inverse of 𝑦 = log⁡(𝑥) ?
11. A gerbil population is 5000 and grows at a rate of 30 percent each day. What is the population after 5 days?
12. What is the inverse of y = ex ? Draw the graph.
13. Solve each rational equation/inequality.
14. The decay of the element Algebranium is modeled by the equation y = a ( 1 – r )t. If Algebranium decays at a rate of
28 percent each year, write an exponential equation to model this situation.
15. A rocket is launched from a platform that is 20 feet in the air at a velocity of 80 feet per second. At the same time, a
flare is shot from the ground at a velocity of 90 feet per second. Write a pair of equations that can be used to display this
situation.
A) Do the rocket and the flare ever meet? If so, how many seconds does it take for them to meet?
16. Write 3 points that make this system of inequalities true.
f(x) < – x2 + 5x + 7
g(x) > x2 – 4x – 5
17. A population is given by the function p(t) = 15000 (1.03)t .
Write an interval of t where the population is less than 20000.
Write an interval of t where the population is greater than 20000.
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18. The rational function 𝑓(𝑥) = 𝑥+3 is shifted 4 units to the right. What is the new equation?