Exponents and Radicals
Inverse Variation
Solving quadratic equations
Rational Expressions and Equations
Grab Bag
100
Simplify.
(2x^3)^3
8x^9
100
If it takes one person working alone 100 hours to complete a jigsaw puzzle, how much time would five people each need to devote to the same project?
20 hours
100
Factor.
8x^2-4x
4x(2x-1)
100
State the excluded values for this expression.
(x^2+3x+1)/((x+3)(x-1))
x=-3 and x=1
100
True or false. Squirrels are unable to vomit.
True.
200
Simplify.
sqrt[(81x^12)/(16y^8)]
(9x^6)/(4y^4)
200
g(x)=x/2
Does this equation represent an inverse relationship? Why or why not?
No because the x is in the numerator, not the denominator. That is a linear relationship.
200
Find the roots.
x^2=-14x-48
The roots are x=-6 and x=-8 .
200
Simplify. State all excluded values.
(x-2)/(x^2-6x+8)
x cannot be 2 or 4
1/(x-4)
200
Spider silk is very strong. How many times stronger is it than steel of the same width?
Five times
300
Simplify.
(sqrtx)^8(sqrtx)^-6
x
300
Is this an example of direct or inverse variation? How do you know?
“As the number of players gets larger, the number of shots made by each gets smaller.”
Yes because as one variable increases the other decreases.
300
The equation for a rocket’s height in the time since launch (t) is
h(t)=-16t^2+32t
. How long was the rocket in the air?
2 seconds
300
Multiply and state all excluded values.
(4x+12)/(12x+9)∙3/(x+3)
x cannot be -3 or -3/4
4/(4x+3)
300
How many hearts does an octopus have?
Three
400
Simplify.
∛(81x^12 )
3x^4∛3
400
The graph shows the relationship between the number of friends who attend a camping trip and the cost per participant. The friends are splitting the cost of the van but each person needs to pay their own entrance fee. What is the most likely cost of the entrance fee?
$15
400
Factor.
3x^2+7x-20
(3x-5)(x+4)
400
How many solutions does this equation have? What are they?
x/(x-2)=(x+4)/x
One solution, x=4
400
On average, humans kill about 100 million sharks per year. How many humans do sharks kill in the same amount of time?
10
500
Simplify.
3sqrt(20x^7 )
6x^3sqrt(5x)
500
Write an equation to model this relationship.
y=32/x
500
Based on the discriminant, describe the solutions to this equation. You must state the number and the type.
x^2-5x+3
The equation has two irrational solutions.
500
How many solutions does this equation have? What are they?
1/(y-4)-y/(y^2-16)=0
No solutions
500
How do vultures cool down their legs in hot weather?
They urinate on them. It also kills any bacteria they may have picked up by walking on dead animal carcasses.