Probability and Counting
Logs and Inverses
Mystery??
Systems of Equations and Linear Programming
Polynomials and Complex Numbers
100
There are 35 people in this class. How many possible different arrangements are there of students for group 2?
1256640
100
What is the inverse of f(x)=3x+4?
The inverse is g(x)=(x-4)/3
100
Sketch y=(x-1)(x+4)2
...
100
Solve the system y=3x+2; y=-2x+7.
(1, 5)
100
Where on the a graph can you find the real roots of a polynomial?
The x-intercepts.
200
3 fair coins are flipped, what's the probability of getting at least one heads?
7/8
200
How can you tell by looking at a graph if two functions are inverses?
They are inverses if they are symmetrical about the line y=x.
200
What is g-1(g(3))?
3
200
Find the equation of the quadratic that passes through the points (-4,5), (-1, -16), and (3,12).
y=2x2+3x-15
200
What are the roots of the polynomial y=5x(x+1)2(x-3)3?
The roots are 0, -1, and 3.
300
You win a spinner game if you spin the same color twice. There are 3 colors-- red that takes up 1/2 of the circle, blue that takes up 1/4 of the circle, and green that takes up 1/4 of the circle. What's the probability that you win?
.375 or 3/8
300
What is log9x=3/2?
27
300
Complete the square to put into graphing form: y=2x2-12x+23.
y=2(x-3)2+5
300
If you are trying to figure out the equation of an nth degree polynomial by solving a system of equations, how many points that lie on the polynomial do you need?
n+1
300
Simplify 5/(3+4i)
(3-4i)/5
400
You are spinning a spinner twice. The spinner is 25% red, 35% blue, and the rest green. What is the probability that you spun green given that you got the same color twice?
About 46.4%
400
Solve log3(x+1)+log3(x-2)=5
x=(+-sqrt(29)+1)/2
400
Solve for x: 5x + 1 – 7 = 28
1.21 or log7/log5
400
Find the equation of the cubic that passes through the points (-1,-2), (2, 37), (1, 4), and (-3, -128).
y=5x3-2x+1
400
(3x3+5x2+1)/(x-1) has a remainder of what?
The remainder is 9.
500
At Luigi’s Pizza, they have 7 different toppings choices. How many different 3-toppings pizzas can you make if you are allowed to repeat toppings?
84
500
Find the inverse of y=sqrt(x+4)-1. If there is a restricted domain for the inverse, include it.
y=(x+1)2-4 for x>=-1
500
Find all roots of f(x)=x3+8
x=-2, x=1+sqrt(3)i, x=1-sqrt(3)i
500
A company makes a product in two different factories. At factory X it takes 30 hours to produce the product and at factory Y it takes 20 hours. The costs of producing these items are $50 at factory X and $60 at factory Y. The company’s labor force can provide 6000 hours of labor each week and resources are $12,000 each week. How should the company allocate its labor and resources to maximize the number of products produced?
The company should make 150 of the products at factory X and 75 of the products at factory Y.
500
You are using a polynomial to model the curves of a rollercoaster. You know the roots/x-intercepts occur at x=-2,x=1(double root), with a triple root at x=-4. The coaster goes through the point (5, -34992). What is the exact equation of a polynomial function with these characteristics?
y=-3/7(x+2)(x-1)2(x+4)3