by StaceyKoprince Mon Oct 27, 2008 3:59 pm
Good! So part of fixing these areas is why you're making the mistakes you're making. Eg, for absolute values with inequalities: are you forgetting to try the negative possibility (if you're trying numbers) or to solve for the negative option of an inequality (if you're solving inequalities)? Are you forgetting to flip the sign when dividing by a negative? Etc. And the same type of thing with divisibility and other number properties issues.
One thing I find my students struggling with for NP is what I call "theory" problems. The problem is testing out some theory and doesn't use real, problem-specific numbers to do so. Instead, you often have to try multiple numbers (or sets of numbers) to figure out what's going on theoretically. (Your "is n/18 an integer" problem is a classic example.) Are you specifically struggling with these?
And why exactly are you making mistakes with fractions in word problems? Are you translating incorrectly when you try to put the word problem into math? Are you messing up when manipulating (adding, multiplying, whatever)? Etc.
As for plugging in numbers - yes, this is a great technique and can be used multiple times on the test. Here's when you can use the technique: when the problem is talking about a number for something but only with variables or percentages or fractions or in some abstract way. The problem NEVER gives you a real, specific number for whatever you're talking about, either in the problem itself or in the answer choices. So, for example, if you get a problem about the cost of a TV set and it only ever refers to the cost in terms of percentages (it goes up 10% and then it goes down 15%...) and then the answer choices are all in percentages too - then you can pick your own number and just use that to do the problem. (If you're using our books, this is the smart numbers technique in the FDP book.)
Alternatively, you might have a problem that says "what must be true" or "what could be true" or asks a yes/no question on DS. Those number property theory problems I was talking about earlier often use these setups. Look again - if they never give real numbers for whatever they're talking about, but just fractions or percents, then you can try numbers. Most of the time, for "must be true" problems, you actually have to try multiple numbers and what numbers you try will have a significant impact on whether you get the problem right! Draw a number line and label these things: zero, one, negative one. Then draw an arrow from one to the right (to indicate other positive numbers greater than one), an arrow from negative one to the left, and a little line from zero to one and another line from zero to negative one. You've just divided the number line into major categories that have different properties from one another for various NP concepts. Try things from the different categories - whatever you're allowed to try for the problem. Eg, if they tell you x is non-negative, you can try zero, one, integers bigger than one, and fractions between zero and one.
The other giveaway that you can use this technique: there are variable expressions (no equals signs or inequalities signs) in the answers. Then you can pick a number for the variable(s) in the answers and just do the problem with real numbers instead. (If you're using our books, this is the VIC technique.)
Stacey Koprince
Instructor
Director, Content & Curriculum
ManhattanPrep