Lesson Two - PhD Tutor

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Lesson Two - PhD Tutor
Chapter Eight - The Science Test
The Science section of the ACT is one of the most feared and difficult
sections for students. The real difficulty does not come from lack of a strong skill
set in the sciences but that it requires good analytical skills. Theoretically no prior
knowledge of science is needed to answer the questions. You will not be able to
use your calculator in this section but you will not need one. All of the
information needed to answer the questions is presented in each of the seven
passages in the form of experiment description and resulting data. The problem
really lies in deciphering the tables, graphs, and charts presented in each type of
passage.
The test contains forty questions that must be completed in thirty-five
minutes. There are three types of passages requiring different types of
interpolative skills.
a.) Three single experiments with associated data and five problems.
b.) Three passages with multiple experiments, associated data and six
questions.
c.) One passage of conflicting or differing theories or approaches with the
associated data. This passage contains seven questions.
At this point you should take time to revisit the test timing strategies
discussed before.
First the strategies mentioned in scanning a passage in the Reading section
should be applied to the Science Reasoning section. When reading the written
sections, you should underline topic sentences and differentiating data while
reading the passage the first time.
As mentioned previously, the challenge is related to deciphering the charts,
tables and graphs. So now we will address this issue. Some of you will have
taken an AP Statistics course and will be familiar with much of this basic
material.
Figures are visual presentations of results, including graphs, diagrams,
photos, drawings, schematics, maps, etc. Graphs are the most common type of
figure and will be discussed in detail; examples of other types of figures are
included at the end of this section. Graphs show trends or patterns of relationship.
Tables present lists of numbers or text in columns, each column having a
title or label. Tables are not used to show a trend or a pattern of relationship
between sets of values – figures are used. They are used to correlate data in
differing categories.
When you first read the passage, you should scan and characterize the table
in the following order:
1.) The Title – Mean Performance on Cognitive Tasks by Adults Aged 30 –
80.
2.) The left side labels: Naming, Vocabulary, Digit span, etc. …
3.) The horizontal labels of Age Group and subcategories.
Do not examine the table for more detail until you are asked a question
referring to the data in the appropriate table.
Charts or graphs are used to present trends such as:
Distribution of ages when retirement account balance reaches zero
Observing the chart/graph above, it is easy to see trends. Remember our
discussion of functions and the tangent point on a curve having a slope that
indicates an increase or decrease. On your first read of charts or graphs, scan the
title the curve labels and a general trend. Do not spend more time on the chart
until asked a specific question about change or trends. On first read, only scan the
chart for labels and trend.
Answering the Questions
The most important step in answering the questions, as always, is
understanding what you are being asked to determine. Then consider the
parameters of the question. The parameters are specifics such as the age span
under question or the specific category being examined.
Wait! Don’t run off yet to the tables or graphs. Now look at the answers for
that question. Look at the sign, trends, order of magnitude or change – increase
by increasing or decreasing exponent of ten as with 102 vs. 105 . Now go to the
table or charts to gather information that is appropriate to the question asked.
Now let’s talk about the art of interpolation
.
The data set here is {104,117,133,145,160,171}. Usually you are able to
estimate the answer say for a x value of 2.5 to be 128. This is usually sufficient
based on the spread of the values in the answer choices.
However if you need to be more accurate you can extrapolate. While most
of the questions in the ACT will not need quadratic or logarithmic fits, you
should be aware of the slope between several points. This will be easy to
determine by doing a quick graph on your test booklet if necessary.
For arguments sake, let’s assume that we do need to have an accurate value
not an approximation we then perform an extrapolation. Extrapolation means
creating a tangent line at the end of the known data and extending it beyond that
limit. Linear extrapolation will only provide good results when used to extend the
graph of an approximately linear function or not too far beyond the known data.
If the two data points nearest the point x0 to be extrapolated are (xk-1,yk-1)
and (xk.yk), linear extrapolation gives the function:
(
)
(
)
This is identical to linear interpolation if xk-1 < x0 < xk . It is possible to
include more than two points by averaging the slopes over the interpolated data.
So the above mentioned set is {104,117,133,145,160,171} with a x change
by one between each value of y.
y(x0)= 117 + (.5/1)*16 = 125
Finally Take a Practice Science Section

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