Now you’ll have a chance to try a few more test-like questions. Some guidance is provided, but you’ll need to fill in the missing parts of explanations or the step-by-step math to get to the correct answer. Don’t worry—after going through the examples at the beginning of this chapter, these questions should be completely doable. If you’re still struggling, review the worked examples in this chapter.
Special relativity is a branch of physics that deals with the relationship between space and time. The Lorentz term, a term that relates the change in time, length, and relativistic mass of a moving object, is given by the following formula:
In the formula, v is the relative velocity of the object and c is the speed of light in a vacuum.
Which of the following equations correctly represents the relative velocity in terms of the other variables?
Use the scaffolding that follows as your map through the question. Kaplan's strategic thinking is on the left, and bits of scratchwork are on the right. If you aren’t sure where to start, fill in the blanks in the table as you work from top to bottom.
| Strategic Thinking | Math Scratchwork |
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Step 1: Read the question, identifying and organizing important information as you go You need to identify the expression that equals relative velocity. Translation: Solve
the given equation for v. |
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Step 2: Choose the best strategy to answer the question Don’t let the multiple variables intimidate you; just treat them as you would when
manipulating a “friendlier” equation. Start by undoing the radical so you can get
to what’s underneath, and then isolate the correct variable. |
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Step 3: Check that you answered the right question Did you get (D)? If so, you’re absolutely correct! |
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Now try simplifying a fairly complicated-looking radical expression:
Given that g and h are both positive, which of the following is equivalent to the expression
?
Use the scaffolding that follows as your map through the question. Kaplan's strategic thinking is on the left, and bits of scratchwork are on the right. If you aren’t sure where to start, fill in the blanks in the table as you work from top to bottom.
| Strategic Thinking | Math Scratchwork |
|---|---|
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Step 1: Read the question, identifying and organizing important information as you go You need to simplify the given expression. |
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Step 2: Choose the best strategy to answer the question Identifying the GCF should be your first step. Once this is complete, check to see whether any part of it can be “cube rooted” and placed outside the radical. Double check to make sure no factoring was missed, and then look for a match in the
answer choices. If you can’t find one, try rewriting the expression. |
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Step 3: Check that you answered the right question If your answer is (B), congrats! You’re correct. |
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Ready to try an exponent question?
Human blood contains three primary cell types: red blood cells (RBC), white blood cells (WBC), and platelets. In an adult male, a single microliter (1 × 10−3 milliliters) of blood contains approximately 5.4 × 106 RBC, 7.5 × 103 WBC, and 3.5 × 105 platelets on average. What percentage of an adult male’s total blood cell count is comprised of red blood cells?
Use the scaffolding that follows as your map through the question. Kaplan's strategic thinking is on the left, and bits of scratchwork are on the right.
| Strategic Thinking | Math Scratchwork |
|---|---|
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Step 1: Read the question, identifying and organizing important information as you go You need to calculate the percent of an adult male’s blood that is comprised of red
blood cells. |
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Step 2: Choose the best strategy to answer the question |
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Remember that a percentage is derived from a ratio that compares a partial quantity
to a total quantity. Write an equation that compares the RBC count to the total blood
cell count and simplify. You can save time by using exponent rules instead of punching
everything into your calculator. Note that the answer choices are fairly far apart. Compare the numerator and denominator of your simplified expression; you can estimate the resulting quantity and eliminate incorrect answers accordingly. Multiply the RBC fraction you found by 100 to convert it to a percent. |
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Step 3: Check that you answered the right question Did you get (D)? If so, you’re absolutely correct! |
It's time to try a question involving rational expressions.
A botanical garden is draining its lily pad pools for the winter using three pumps. The second pump is two times faster than the first pump and the first pump is three times faster than the third. Let x be the number of hours that it takes the third pump to drain the pools by itself. If the three pumps work together, which expression represents the fraction of all the lily pad pools that the second pump can drain in 1 hour?
Use the scaffolding that follows as your map through the question. Strategic thinking is on the left, and bits of scratchwork are on the right.
| Strategic Thinking | Math Scratchwork |
|---|---|
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Step 1: Read the question, identifying and organizing important information as you go You need to identify the expression that could represent the portion of the draining done by the second pump in one hour. |
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Step 2: Choose the best strategy to answer the question |
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Don’t assume that the terms related to the pumps are ordered 1-2-3 in the equation. Start by ordering the pumps in order of increasing drain speed. |
speed: ___ < ___ < ___ |
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Write the pump speeds as a ratio based on the information in the question stem. Use the second pump component of the ratio to derive an expression that represents the portion of the draining it could complete in one hour. |
___ : ___ : ___
2nd pump completes ___ |
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Step 3: Check that you answered the right question Did you get (A)? If so, congrats! You’re right. |