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Math 111 Chapter 1 Sections 1 & 2 Reviews

MTH ·111·First ·day · Review Name 

Solve · and · check





A · student · multiplies · each · side · of · the · equation · · · by · 2 · and · produces · the
equation · · Has · the · student · produced · an · equivalent · equation ? · · Explain .

 
3. Suppose we attempt to solve the equation 4x = 7x by first dividing each
side of the equation by x. The result is 4 = 7, which is not true. Explain what
happened.


A · student · solves · the · literal · equation · · for · the · variable · P. ·The · student's
· answer  ·  is · · is · this · a · correct · response? · Explain.
A · tutor · states · that · the · formula · · can · also · be · expressed · as .· · Do ·
you · agree?
 

Mth 111 Topics

Chapter 1 Overview

Section 1.1 Solving Linear Equations
Solving Linear Equations involving distributive property
and foil
Solving literal equations
Applications average,
mixture, uniform motion, work

Section 1.2
Solving quadratics:
o by factoring and zero product principle;
o square root;
o completing the square;
o quadratic formula;
Discriminant
Applications: square box, tossing an object
 
Forming Equivalent Equations
An equation can be rewritten into an equivalent form
by:

1. Simplify either side

2. Using the Golden Rule of Algebra

Do unto one side as thou hath done unto the other

3x = 7y equivalent to 3x + 5 = 7y + 5

3. Interchanging sides
 
Linear Equations :

A linear equation in a single variable x is an equation that can be
written in the form

ax + b = 0

where a and b are real numbers, with a not 0.

Solve


 
Solve


 

Literals Equations : formulas with several unknowns

1. 10 = a - 4x, solve for x

2. 8 = ax + 3x , solve for x

3. P = S - dt, solve for t
 

Word Problems

1. What do you need to know to solve the problem?
Write this down in English.

2. Assign numbers to the known parts. Assign a
letter to the unknown parts

3. Translate this into an algebraic equation or
inequality.

4. Solve.

5. Make sure that your solution answers the original
question
 
Useful Formulas

Business:

Revenue = Profit - Cost
Simple Interest : I = Prt

Mixtures:

(1st % × Amt) + (2nd % × Amt) = Final % × Amt

Rate problems:

Distance = rate × time

Work Problems:

(part done by A ) + (part done by B) = 1 whole job

Averages:


 
Applications:

Averages:

The average on your four tests is 91.25. Your test scores are 92, 86,
and 98 with one test score gone missing. Find it!
 
Simple Interest : I = Prt

You invest part of a $10,000 bonus in a 2% simple
interest account and the remainder of the money at
5% simple interest. Together the investments earn
$400 per year. find the amount at each rate.

let x be amount in 2%
let 10000 - x be amount in 5%
t = 1


 
Rate problems : Distance = rate × time

Example : Two boats traveling the same direction leave a harbor at
noon. After 3 hours they are 60 miles apart. If one boat travels
twice as fast as the other, find the average rate of
each boat.

First we need to picture the situation. Let A be the slower boat and B be the faster one.

Let x mph be the average rate of boat A. The average rate of boat B is 2x
mph. Since they are 60 miles apart after 3 hours, the difference in the
distance traveled by the faster boat B and the slower boat A is 60 miles.

distance traveled by B – distance traveled by A = 60

(average rate of B)(time) – (average rate of A)(time) = 60



The average rates are 20 mph and 40 mph