Term
| What are some key features of Accumulation FRQs? |
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Definition
Accumulation FRQs...
1) Are word problems with real-world context.
2) always provide you with at least one function that represent a rate of change. If you're given two rates, one would represent the rate at which something comes in, and the other would represent the rate at which something comes out.
3) Generally given a starting value. |
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Term
| What are some common tasks you might be asked to perform on an Accumulation FRQ? |
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Definition
1) Use a definite integral to calculate accumulation (how much water entered the tank from t=a to t=b).
2) SPAM (how much water is at the tank at time t=b?)
3) Use SPAM to find an abs. max/min on [a,b] (at what time is the amount of water in the tank at a maximum?)
4) Use SPAM to write an expression for the antiderivative (integral from t=a to t=t...use a dummy variable in the integrand).
5) Average Value
6) Average Rate of Change
7) Interpret the meaning of an integral.
8) Interpret a derivative (is the amount of water increasing or decreasing at time t?) |
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Term
| Tips for solving Accumulation FRQs |
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Definition
1) If none has been provided, give a name for the antiderivative function.
2) If none has been provided, give a name for the overall rate function (rate in minus rate out).
3) Identify the tasks that are obvious, like SPAM, first. |
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Term
| What are key features of Table FRQs? |
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Definition
| You're given a table of values and a word problem with context. |
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Term
| What are some common tasks you might be asked to perform on Table FRQs? |
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Definition
1) Use Riemann Sums or Trapezoidal Sums to approximate any of the tasks you might be asked to do for Accumulation FRQs (SPAM, Avg. Value, Accumulation)
2) Determine whether the approximation was an overestimate or underestimate.
3) IVT (is there a time t on (a,b) for which the function hits this value)
4) MVT (is there a time t on (a,b) for which the derivative of the given function hits some value?)
5) Approximate the derivative at a point using avg. rate of change. |
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