## 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

`(x^3-3x^2+4x-5)/(x-2)`

Use long division to find the quotient and remainder:

`x-2 \ bar(")"\ x^3-3x^2+4x-5)`

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.