Calculus Path
Statistics Path
MTH070
Elementary Algebra
Pre-PreCalculus, part 1
vs.
MTH062
Quantitative Literacy 1
Math for "Real" Life
Which class is right for you?
Is calculus in your future or NOT?
Systems Equations
Solve for x and y:
-x+3y=-4
-3x-4y=27
Choose a variable to eliminate. Eliminate x first. Multiply equation 1 by -3:
-3⋅(-x+3y=-4)
-3x-4y=27
Distribute:
3x-9y=12
-3x-4y=27
Add the equations together:
-13y=39
Solve for y:
y=39-13=-3
Substitute into one of the equations and solve for x:
-x+3(-3)=-4
-x-9=-4
-x-9+9=-4+9
-x=5
x=-5
We think the solution is (-5,-3).
CHECK:
Plug both values into the other equation to check:
-3(-5)-4(-3)=15+12=27
It checks!!!
§ 1-2 Eighteen Trillion and Counting
Problem situation: How Big Is a Billion or a Trillion?
So, where on the number line is 1 billion? Make a mark for 1 billion on the number line.
In news about politics and government, BIG numbers are talked about often. Below is a chart showing the national deficit over time.
On a scale from 0 to 1 trillion, 1 billion is very close to zero, since 1 trillion is 1000 billion!
Imagine a stack of 1,000 one‐dollar bills, which is about 4.3 inches tall.
Complete the table below:
| $ Amount | Height (inches) | Height (feet) | Height (miles) |
|---|---|---|---|
| $1,000 | 4.3 | ||
| $1 million | 4,300 | 358 | |
| $1 billion | 4,300,000 | 358,333 | 68 |
| $1 trillion | 4,300,000,000 | 358,333,333 | 68,866 |
This means that a stack of $1 bills, 3.5 trillion high, would reach the moon.
Polynomial Division
x3-3x2+4x-5x-2
Use long division to find the quotient and remainder:
x-2
What do you multiply by x to get x^3?
Guess: x^2 and multiply:
| x^2 | ||||
| x-2 | )x^3 | -3x^2 | +4x | -5 |
| x^3 | -2x^2 |
Now subtract:
| x^2 | |||||
| x-2 | ) | x^3 | -3x^2 | +4x | -5 |
| -(x^3 | -2x^2) | ||||
| -1x^2 | +4x |
What would you multiply by x to get -1x^2?
Guess: -1x and multiply.
| x^2 | -1x | ||||
| x-2 | ) | x^3 | -3x^2 | +4x | -5 |
| -(x^3 | -2x^2) | ||||
| -1x^2 | +4x | ||||
| -1x^2 | +2x |
Now subtract:
| x^2 | -1x | ||||
| x-2 | ) | x^3 | -3x^2 | +4x | -5 |
| -(x^3 | -2x^2) | ||||
| -1x^2 | +4x | ||||
| -( | -1x^2 | +2x) | |||
| 2x | -5 |
What would you multiply by x to get 2x?
Guess: 2 and multiply.
| x^2 | -1x | +2 | |||
| x-2 | ) | x^3 | -3x^2 | +4x | -5 |
| -(x^3 | -2x^2) | ||||
| -1x^2 | +4x | ||||
| -( | -1x^2 | +2x) | |||
| 2x | -5 | ||||
| 2x | -4 |
Now subtract.
| x^2 | -1x | +2 | |||
| x-2 | ) | x^3 | -3x^2 | +4x | -5 |
| -(x^3 | -2x^2) | ||||
| -1x^2 | +4x | ||||
| -( | -1x^2 | +2x) | |||
| 2x | -5 | ||||
| -( | 2x | -4) | |||
| -1 |
Solution: (x^3-3x^2+4x-5)/(x-2)=x^2-x+2+(-1)/(x-2)
CHECK:
(x-2)(x^2-x+2)-1=x^3-3x^2+4x-5 check.
§ 2-1 A Taxing Set of Problems
Problem Situation: Calculate income tax for tax bracket
| If Taxable Income Is: | The Tax Is: |
|---|---|
| Not over $18,150 | 10% of the taxable income |
| Over $18,150 but not over $73,800 | $1,815 plus 15% of the excess over $18,150 |
| Over $73,800 but not over 148,850 | $10,162.50 plus 25% of the excess over $73,800 |
Suppose a couple, married with no kids, filing jointly, earned $93,000 with no other interest or income.
Based on the standard standard married filing jointly deduction, their taxable income is $93,000-$20,300=$72,700
According to the tax table above their income tax is
$1,815+0.15*($72,700-$18,150)=$9,997.50
Compare this to line 15 of the table below:
Disclaimer:
You should check with your advisor before taking a math class leading to calculus. Algebra classes are known to cause stress, anger, depression, and occasionally rashes, as well as lead to calculus. Please consult a physician if negative symptoms persist.