Equations
Expressions/Inequalities
Functions
Polynomials
Word problems
Potpourri
100
Solve:
14x^-2+x^-1–3=0
What is
{7/3, -2}
100
Simplify the expression:
(sqrt2)/(sqrt(x-3)+sqrt(x))
What is
(sqrt(2x)-sqrt(2x-6))/3
100
Find f o g. Find the domain of the composite.
f(x)=(7x)/(x+4)
g(x)=x-3
What is
(7x-21)/(x+1); D={x|x≠-1}
100
Sketch the polynomial using the real roots:
f(x)=-4x^2(x^2+7)(x-5)
What is:
x=0, bounce
x=5, through
(imaginary roots would not cross real x-axis!)
100
How many ways can Ms. Kelly make a smoothie out of the following options?
1 milk; 3 options
3 fruits; 6 options
2 add-ins; 4 options
What is 360 smoothies?
3 x 20 x 6
100
Write the equation of a circle with diameter endpoints of (–15, 3) and (–7, –5).
What is
(x+11)^2+(y+1)^2=32
200
Solve the system of equations:
What is (–1, 8) and (4, 3)?
200
Solve:
8x^2+2x-3≥0
What is 
200
Suppose (7, –5) is on the graph of f(x), what point would be on –6f(x–7)+2?
What is (14, 32)?
200
Write a degree 4 polynomial with the roots of 4, –3i and 0.
What is
x^4+9x^2-4x^3-36x
200
A chemist needs to create 30 liters of a 40% acid solution for an experiment. In her laboratory, she only has access to two bottles of stock solutions: a 25% acid solution and a 50% acid solution.
How many liters of the 25% solution and how many liters of the 50% solution must she mix together to achieve her goal?
What is 12 L of 25% and 18 L of 50%?
200
Identify the vertex, focus, and directrix of the parabola with the equation:
(x-4)^2=-32(y+11)
What is (4, –11), (4, –19), and y=–3?
300
Solve the equation:
What is x=4?
300
Solve:
(x-7)/(x+2)≥4
What is [–5, 2)?
300
State any holes or asymptotes:
f(x)=(x+7)/(x^3+9x^2+14x)
What is: holes at x=–7, VA at x=0, x=–2, HA at y=0
300
Find the remaining roots of the polynomial given that 8-i is a root:
x^3-13x^2+17x+195
What is 8+i and –3?
300
You have $6,000 to invest in either account. Which would you choose if you are going to leave your investment for 20 years?
Account A: 4.12%, compounding monthly
Account B: 4.45%, compounding quarterly
What is Account B?
($13,658.31 vs $14,539.15)
300
Expand the logarithmic expression using properties of logarithms: 
What is 
400
Solve the system: 
What is (5, 4, –5)?
400
Factor the expression fully:
64x^2-48x+9-25y^2
What is (8x-5y-3)(8x+5y-3)
400
Find the inverse. State the domain and range of f(x).
f(x)=(9x-2)/(x+4)
What is
f^-1(x)=(4x+2)(9-x); D={x|x≠-4} R={y|y≠9}
400
Find the value for k such that (2x–3) is a factor:
2x^3+5x^2+k+15
What is k=–33?
400
An eco-conscious architectural firm is designing a rectangular "green roof" community garden on top of a downtown skyscraper. The garden will be bordered on one side by a massive, floor-to-ceiling solar panel accent wall, which requires no extra partitioning.
To protect the fragile alpine plants from high-altitude winds on the other three sides, the firm plans to install structural glass fencing. They have a budget that allows for exactly 160 linear feet of glass fencing.
What is the maximum area for the garden they can create?
What is 3200 square feet?
(40ft x 80ft)
400
Find the finite sum. 
Then find the infinite sum.
Finite sum:
1456/81
Infinite sum:
18