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 · theequation  · · 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.
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| Mth 111 Topics Chapter 1 Overview Section 1.1 Solving Linear Equations  Solving Linear Equations involving
distributive propertyand 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 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
(average rate of B)(time) – (average rate of A)(time)
= 60 |
 The average rates are 20 mph and 40 mph |
A · student · solves · the · literal ·
equation · 
· for · the · variable ·
P. ·The · student's
A · tutor · states · that · the ·
formula · 
· can · also · be ·
expressed · as 
.· · Do ·