Linear Equations
What is the slope of the line y = 3x - 5?
The slope is 3
What is the next term in the arithmetic sequence: 2, 5, 8, 11, ?
14
If f(x) = 2x + 3, evaluate f(4).
11
Factor out the greatest common factor (GCF) from:
6x+18
6(x+3)
Solve for x:
x + 4 > 10
x > 6
Solve for x: 2x + 5 = 13
x = 4
What is the common difference (d) of the sequence: 15, 11, 7, 3,
-4
Does the set of ordered pairs {(1, 2), (2, 4), (1, 5)} represent a function? Why or why not?
No, because the input 1 has two different outputs (2 and 5).
Factor completely: x^2 - 25.
(x-5)(x+5)
When solving an inequality, when must you flip the inequality symbol?
When multiplying or dividing both sides by a negative number.
Write the equation of a line in slope-intercept form with a slope of 2 and a y-intercept of (0, -4).
y = 2x - 4
Find the 10th term of an arithmetic sequence
where a1 = 4 and d = 3.
a10 = 31
What test can be applied to a graph to determine if it is a function?
The Vertical Line Test
Factor Completely: x^2 + 7x + 10
(x+2) (x+5)
The population of a small town is growing at a rate of 5% per year. The initial population is $1,200. Write a equation for the growth rate.
y = 1200(1.05)^x
What are the x-intercept and y-intercept of 3x + 4y = 12?
x-intercept: (4, 0); y-intercept: (0, 3)
Write the explicit formula for the arithmetic sequence: 5, 9, 13, 17
What is the domain of the function represented by
{(1, 3), (2, 6), (5, 9)}?
{1, 2, 5}
Factor Completely: x^2 - 8x + 12
(x - 2)(x - 6)
A brand-new car was purchased for $20,000$. Its value decays by 10% each year, modeled by:
y = 20000(0.90)^x. What will the value of the car be after 2 years?
y = 20000(0.90)^2 = 16,200
Write the equation in slope-intercept form of the line passing through (2, 5) and (4, 11).
y = 3x - 1
Maya puts $15 in her piggy bank during the first week of the year and increases her savings by $4 each subsequent week. Write an explicit formula for how much she deposits in week n, then calculate how much she will deposit in week 26.
an = 15 + (n-1)
an = 4n + 11
Week 26: 4(26) + 11 = 104 + 11 = 115.
If g(x) = x^2 - 3x, evaluate g(-2).
10
The area of a rectangular garden is given by:
x^2 + 7x + 10. If x = 3, what are the actual numerical length, width, and total area of the garden?
(x + 2) and (x + 5)
3+2 = 5ft and 3+5 = 8ft
The population of a town grew exponentially at a constant rate of 4% per year. If the population was 16,224 after 2 years, what was the initial population of the town?
16224 = a(1.04)^2
(1.04)^2 = 1.0816
a = 16224/1.0816
a = 15000