Word problems strategy guide chapter 1 translations i

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Word Problems Strategy Guide : Chapter 1: [Translations] i. Pay Attention to Units: a. Additive Relationships: Adding terms with the same units does not change units ii. Equations to Know: a. Total Cost ($) = Unit Price ($/Unit) * Quantity (Units) b. Profit ($) = Revenue ($) – Cost ($) c. Total Earnings ($) = Wage Rate ($/Hour) * Hours Worked (Hours) d. Miles = Miles Per Hour * Hours e. Miles = Miles Per Gallon * Gallons Chapter 2: [Strategy – Work Backwards] i. How to Work Backwards: a. Step 1: Start with B or D i. Build table for inputting answers and checking relations b. Step 2: Narrow Your Answers i. If answers are in ascending order, testing B or D will either eliminate other answers or provide answer by elimination c. Step 3: Pick/Find Answer ii. When to Work Backwards: a. Clean, Numerical Answer Choices b. Questions ask for a discrete Number iii. When not to work backwards: a. Large/Ugly Numbers b. When question asks for a combination of variables Chapter 3: [Rates] i. Equations to Know: a. Rate * Time = Distance b. Rate * Time = Work ii. Relative Rates: a. 2 Bodies Working/Moving at the same time i. Moving Towards Each other – Add Rates ii. Working Together – Add Rates iii. Moving Away – Add Rates iv. Same Direction – Subtract Rates (For difference/distance growth as time progresses) v. One Worker undoing work of other – Subtract Rates
Chapter 4: [Choose Smart Numbers] i. How do Smart Number Work? a. Step 1: Choose Smart numbers to replace the variables. i. If numbers are related, be certain smart numbers fit these conditions ii. Three things to keep in mind: 1. Pick numbers with different characteristics a. Even/Odd/Prime/Positive/Negative/etc. 2. Follow all constrains given in the problem 3. Choose numbers that work easily in the problem b. Step 2: Solve the problem with chosen smart numbers i. Draw Circle around answer to distinguish it c. Step 3: Find a match in the answers ii. When to use smart numbers a. Problem contains only unspecified values/variables iii. When not to use smart numbers a. Problem contains a value with impact on variables and value has a fixed value Chapter 5: [Overlapping Sets] i. Overlapping Sets: 2 or more given sets of data that partially intersect with each other ii. STRATEGY: The Double-Set Matrix (Only used on 2 sets) A Not A Total B 8 14 22 Not B 7 1 8 Total 15 15 30 a. This allows to structure problem, whether constants, variables, or percents, in such a way that relationship is clear Chapter 6: [Statistics] i. Average = of allTerms Number of Terms ii. Median: The Middle Number a. The middle value in a list of values placed in increasing order i. For sets with an odd number of values, the median is the unique middle value when data is arranged ii. For sets with an even number of values, the median is the average of the two middle values when the data is arranged b. Median of Sets containing unknown values i. Possible to determine if you know duplicate equal numbers are in set and question gives clues about things like average or range iii. Standard Deviation: Describes the spread, or variation, of the data in a set a. Standard Deviation indicates how far from the average (Mean) data points

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