POLYNOMIALS & RATIONAL EXPRESSIONS
CREATING EQUATIONS
EQUATIONS & INEQUALITIES
FUNCTIONS
Number & Quantity Standards
Seeing Structure in Expressions
Interpret categorical and quantitative data
Graphing
100
Simplify
(3x^2-7x+4)+(5x^2+2x+9)
8x^2-5x-5
100
A phone company charges $30 monthly fee plus $0.20 per text. Write and solve an equation to find how many texts you can send if you want your bill to be $50.
30+0.20x=50
100 texts
100
Solve
3/(x-2)=5
x=13/5
100
Given
f(x)=2x^2-5x+1
find f(4)
f(4)=13
100
rewrite
using rational exponents
x^(5/3)
100
Rewrite by completing the square
x^2+4x+4
(x+2)^2
100
The ages of 7 students in a club are:
12, 14, 13, 15, 14, 12, 16
Question: Find the mean age.
13.71
100
What is the line of symmetry?
A line of symmetry is a line that divides a figure into two mirror-image halves.
200
Factor
x^2-5x+6
(x-2)(x+3)
200
A babysitter charges $10 flat fee plus $6 per hour. Write an equation for total cost C as a function of hours h.
C=10+6h
200
Solve
sqrt(2x+7)=x−1
x=2+sqrt10
200
What is the definition of a function?
A function is a relation for which each value from the set of the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.
200
A wooden board is measured to be 8.264 feet long using a tool that is only accurate to the nearest 0.05 ft.
8.25 ft
200
The expression
P(t)=100(2.08)^t
models a population after t years.
Rewrite the expression to show the percent growth rate and interpret the meaning of the number 2.08.
This shows a 108% growth rate per year.
The base 2.08 means the population is multiplied by 2.08 each year.
200
The scores on a quiz are:
88, 76, 92, 85, 91, 89, 77
Question: Find the median score.
88
200
What is the slope?
The slope of a line measures how steep the line is.
300
Find the remainder when
f(x) =
2x^3 - 3x^2 + 4x - 5
is divided by
x-2
7
300
A coach is buying snacks for a tournament: chips cost $5 each and drinks cost $3 each and has a budget of $35.
Write a system of inequalities representing the situation.
300
Solve
∣4x−9∣=7
x=4,x=21
300
Rewrite in
2y-4=x
slope-intercept form
y=1/2x+2
300
A large water tank is being filled at a constant rate. After 10 minutes the tank contains 200 gallons of water.
20 gallons per minute
300
A company’s profit can be modeled by the expression
P(x)=50x-(13x+240)
where x is the number of units sold. Identify the meaning of each term in the expression in the context of profit.
(50x): revenue — $50 received per unit sold.
(13x): variable costs — $13 cost per unit.
(240): fixed costs.
300
The number of pets owned by 10 students is:
2, 1, 3, 2, 4, 2, 1, 3, 2, 3
Question: Find the mode of the data.
2
300
What is slope-intercept form?
y=mx+b
400
Simplify
(x+4)/(x-2) * (x-6)/(x+4)
(x-6)/(x-2)
400
Solve the formula for h
B = 1/4 gh
h = (4B)/g
400
Solve by substitution
y=2x+3
3x+y=12
(x,y)=(5/9, 5/33)
400
Given
f(x)=2x^2
write
g(x) = f(x) +6
g(x)=2x^2+6
400
Simplify
(x^(2/3))^2
x^(4/3)
400
A rectangular garden has an area given by
A=x^2-9x
Factor the expression to reveal information about the garden’s dimensions.
A=x(x-3)
400
The daily temperatures (°C) for 5 days are:
20, 22, 19, 21, 24
Question: Find the standard deviation.
~1.72°C
400
What does it mean to have a slope of zero?
The line is horizontal.
500
Rewrite
(3x^2+3x-4)/(x+2)
in the form q(x)+r(x)b(x) using long division
q(x)=3x−3
Remainder r(x)=2.
500
A student is buying snacks for a club meeting: chips cost $4 each and drinks cost $2 each and has a budget of $25.
4x+2y≤25
500
Solve:
x^2+9=0
Write answers in a ± bi form.
x=3i
500
For the function g(x)=4x-2, find the average rate of change from x=0 to x=4.
4
500
A student is tracking the cost of driving their car each week by recording miles driven and gallons of gas used.
Identify three meaningful quantities that should be defined for building a model to describe the weekly driving cost and explain why each quantity is important.
Miles driven per week (miles/week). — needed to compute fuel cost and wear; it’s the driver of total cost.
Gallons of gas used per week (gallons/week). — directly relates to money spent on fuel and can be used with price per gallon.
Price per gallon (dollars/gallon). — converts gallons used into dollars spent; necessary to compute weekly fuel cost.
500
Rewrite
x^2−5x−14=0
by factoring.
x=7orx=−2
500
A scatter plot shows the relationship between hours studied (x) and test scores (y) for 5 students. Find a linear model
y=mx+b
that approximates the data.
y≈3.125x+63.75
500
What is the point-slope formula?
(y-y1)=m(x-x1)