# The Importance of Organization for Word Problems

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Molly worked at an amusement park over the summer.Every two weeks she was paid according to the following schedule:at the end of the first two weeks she received \$160.At the end of each subsequent two week period she received \$1, plus an additional amount equal to the sum of all the payments she had received in the previous weeks.How much money was Molly paid during full 10 weeks of summer?

A. 644
B. 1288
C. 1770
D. 2575
E. 3229

To start, let’s create a table just to lay out the general information first:

After 2 weeks —> \$160

After 4 weeks —-> \$1 + (all previous)

After 6 weeks —-> \$1 + (all previous)

After 8 weeks —-> \$1 + (all previous)

After 10 weeks —-> \$1 + (all previous)

Then fill in what the “all previous” would mean:

After 2 weeks —> \$160

After 4 weeks —-> \$1 + \$160 = \$161

After 6 weeks —-> \$1 + (\$160 + \$161) = \$161 + \$161

After 8 weeks —-> \$1 + (\$160 + \$161 + \$161 + \$161) = \$161 + \$161 + \$161 + \$161

After 10 weeks —> \$1 + (all previous) = eight \$161’s

At this point we can see that “all previous” is going to equal the initial \$160 + seven \$161 and then we’re adding \$1 to it, so it’s really just \$161 x 8 = \$1288

We have an interesting sequence:

After 2 weeks —> \$160

After 4 weeks —-> one \$161

After 6 weeks —-> two \$161

After 8 weeks —-> four \$161

After 10 weeks —-> eight \$161

Basically the “number” of \$161’s just doubled from 4 weeks to 10 weeks.

Now to add them all up, again, we’re just going to count up all of the number of \$161’s.

We have our initial \$160 + 15*(\$161) = \$2575. The correct answer is (D).

You will see over and over again that it’s not the Math calculations in Word Problems that will trip you up, but the inability to be super organized on your scratch paper. 🙂

# Interpreting Evidence Correctly on the ACT and SAT

In all three types of ACT Science passages, you will need to be able to understand how evidence is presented and be asked to answer questions based on the evidence. These are a bit like Reading questions.

To interpret evidence correctly, you need to focus on the results. Draw logical conclusions based on the presented data, and actively read the information in the accompanying passage. It’s important to know the difference between direct and inverse variation.

To answer Interpreting Evidence questions correctly, ask yourself these 3 questions: – What is the evidence presented? – Whose position is supported by the evidence? – What does the evidence suggest?

Interpreting evidence for Data Representation and Research Summaries ends up requiring more Data Analysis skills, since data is a large component of those passages. For Conflicting Viewpoints, interpreting evidence is a matter of keeping the two theories (two scientists) straight. Watch this video for a strategy on how to do this!

This video describes how to answer “Inference” questions on the SAT and ACT Reading Test. You may wonder what this has to do with ACT Science, but sometimes interpreting evidence is a LOT less scientific than it sounds, and a LOT more like reading comprehension. Remember that you can only make an inference BASED on something directly stated. Incorrect answer choices are frequently “out of scope.”

# Grammar Guide: the usage of “those”

Confused about how “those” works on the SAT, ACT, GRE, or GMAT? Let’s take a look at a question from Manhattan GMAT that uses this word!

Salt deposits and moisture threaten to destroy the Mohenjo-Daro excavation in Pakistan, the site of an ancient civilization that flourished at the same time as the civilizations in the Nile delta and the river valleys of Tigris and Euphrates.

A) that flourished at the same time as the civilizations
B) that had flourished at the same time as had the civilizations
C) that flourished at the same time those had
D) flourishing at the same time as those did
E) flourishing at the same time as those were

In general, “those” is the plural of “that.” It’s in a group called “determiners” along with “this”, “that”, “these”, “those,” “here” and there that are technically pronouns but often function more like adjectives.

For C, D, and E, “those” is meant to mean something like “the ones” and could be used as a pronoun to replace a plural antecedent if there was one in the sentence, and if the construction was parallel.

# What to Expect on the ACT Science Test

The ACT Science section can cause a lot of unnecessary worry among test-takers. However you can still receive a strong score even if you aren’t a budding Albert Einstein. Careful reading and note-taking (the same skills you use for Reading Comp!) are enough to answer most questions. Remember – the answer has to be based on the information in the paragraphs and/or tables. You just have to know where to look!

The ACT Science Test will always be the fourth test you’ll take. It will have 7 passages and you’ll have 35 minutes to complete them. That’s about 5 minutes per passage so moving confidently through this test is essential! It takes practice to gain confidence in interpreting data and understanding the meaning of unfamiliar vocabulary. Luckily, you already have all of the skills necessary to do this from your high school Science classes.

Experiments of some type are described in most of the passages. A group of scientists will be studying some type of phenomenon. They will usually conduct two experiments to see how certain factors affect the phenomenon. Often a graph, table or diagram will accompany the description of the experiments to show the results. Here are some two important steps to help you analyze the experiments:

1. Identify the Purpose & Method

Make sure to underline the Purpose & Method for each Experiment as you read (don’t wait until you finish reading everything or you’ll be too confused and overwhelmed). The Purpose tells you why the scientists are conducting the experiment. What are they trying to find out? Look for verbs like “to study…” or “to examine…” in the first explanatory paragraph. That is often where the description of the Purpose can be found. The Method for each experiment will be described in the following paragraphs. Make sure to make note what is similar and what is different between the two Experiments. Sometimes the scientists will change one factor or more factors between the experiments to see if the results change.

2. Understand the Factors

Factors, also known as variables, are important elements of the experiments. These are often things like temperature, pH, pressure, time, distance, etc. Depending on a way the variable is being used in each experiment, it can be called either dependent or independent. Independent variables are those factors that are controlled by the scientists. Did the scientists increase the heat in the experiment? Did they add or remove pressure? If the scientists were the ones controlling the variable, it is independent. Dependent variables are what the scientists observed changing. Let’s say that when the scientists increased the heat in our hypothetical experiment, the time also increased.

# The ACT: All things coordinate geometry

Some of the most challenging Math questions on the ACT involve Coordinate Geometry, so it’s important you have a solid grasp on the formulas and concepts tested. The most basic concept you’ll encounter is inequalities. To graph a range of values, you’ll need to draw a number line and plot the beginning and end of the range using an open or closed circle and a solid line.

Which of the following graphs represents the solution to the set of the inequality |x| > 3 on the real number line?

For a question, like this we’d need to solve |x| > 3 before we can graph it. Remember that the ACT loves to make seemingly easy problems more difficult by combining them with other topics (like absolute value). We have to remove the absolute value symbol by splitting the inequality in two, and we have to remember to flip the sign for the inequality that becomes negative.

x > 3  and x < – 3 become our answer to |x| > 3.

Remember that when we graph this solution set, the circles must be open because the symbols don’t have the line that indicates “or equal to”.

A few more formulas to know:

Slope = Rise / Run = Change in y / Change in x

As long as you know any two points on a line, you can find the slope. Remember that parallel lines have the same slope, and perpendicular lines have negative reciprocal slopes. You’ll also need to know how to recognize the graphs for linear and non-linear equations.

y = mx + b

This is called slope-intercept form. An equation in this form will always make a straight line on a graph (notice how neither x nor y have an exponent). In this form, b is the y-intercept (the point on the y-axis where the line crosses) and m is the slope.

y = ax^2 + bx + c

This is the standard equation for a parabola. In this equation c represents the y-intercept. A standard equation in which a variable is squared will never make a straight line.

The standard equation of a circle is (x – h)^2 + (y – k)^2 = r^2 where (h, k) is the center point of the circle and r is the radius. For example, on test day you might see a circle plotted on a graph, let’s say its center is (0,4) and the diameter is 8. All we’d have to do to find the equation of that circle is plug in r = 4 and (h,k) = (0,4) into our standard equation:

(x – h)^2 + (y – k)^2 = r^2
(x – 0)^2 + (y – 4)^2 = 4^2
(x)^2 + (y – 4)^2 = 16

Check out some awesome video explanations using problems with these formulas on Learnist!

# Learnist: Point of View in ACT Science questions

The key to better scores on the ACT Science Test Conflicting Viewpoints passages is to hunt down each author’s point of view. As you read each passage, look closely for keywords that help you identify the author’s opinions.

If there are multiple paragraphs, remember that the scientist or student usually uses the first few sentences to introduce his topic and start a discussion of the main idea. The final paragraph wraps up the discussion and reinforces the Main Idea. If you are having trouble finding what the overall point of view is for the passage, go back to the very beginning and the very end.

Don’t feel like you need a big background in Science to get Point of View or other Science questions correct. These are very close to Reading Test questions! Use these three tips:

• Don’t Be Confused by the Extraneous Information
• Cut Through the Scientific Jargon
• Never Leave an Answer Blank

Try a few practice questions on this ACT Science: Point of View learnboard!

# ACT Science: How to Compare Two Experiments

One type of ACT Science passage, Research Summaries, will present descriptions of one or more related experiments and will require you to answer questions about one or both experiments. To compare them accurately, answer the following questions as you read. Make sure to underline, circle, or otherwise mark up the passages as you read!

1. How is each experiment set up? Make sure you understand the method for each experiment. What tools/processes/chemicals are used?

2. What does the data show? Pay close attention to the results of each experiment. Usually this is presented in tables or charts. How do the different variables relate to one another? Draw arrows on the tables to show the trends. Keep the following definitions in mind:

Independent variables: These are factors that are controlled by the scientists. Did the scientists increase the heat in the experiment? Did they add or remove pressure? If the scientists have control over the variable, it is independent.

Dependent variables: These are factors that the scientists observe changing. This is what the look for and how they record data — but they don’t control it.

Direct variation: This is when two things change in the same way over time. If Column A increases and Column B increases at the same time, we can say that the two vary directly.

Indirect variation: If when Column A increases, Column B decreases, there is an indirect (also called inverse) variation between the two elements.

3. How do the experiments differ? There will be certain elements common to both experiments, and one or more elements will change from Experiment 1 to Experiment 2. Circle the new information. Then focus on the results – do the variables interact similarly or differently in the 2nd experiment? Is the range of data greater or smaller?

# How to Pace Yourself on the ACT Reading Test

The ACT Reading Test is 35 minutes long and contains 40 questions (10 questions on each passage). This means you’ll have slightly less than 9 minutes to spend on each of the 4 passages, so pacing yourself is essential.

One way you can focus your timing is to briefly flip through the entire test BEFORE you begin. You will always see 4 passages and you must always answer all 40 questions, but that doesn’t mean you have to approach them in the order in which they are presented on the test. As you practice, you will start to realize which passages are easier and which are more challenging for you.

For example, if Prose Fiction is your strong point but Natural Science passages make you nervous, it may make sense for you to do the Prose Fiction passage first and save the Natural Science passage for last. Just because the Natural Science passage is first, doesn’t mean you’ve got to do it right away. If you do decide to skip around, make sure you are still bubbling in your answers into the corresponding numbers on the answer grid. You don’t want to lose points because you bubbled incorrectly!

Another way you can pace yourself appropriately is by practicing your active reading skills. Do you find yourself getting lost in the details or are you someone who tends to read too quickly and miss some of the important information? For the ACT Reading Test, you’ve got to strike a balance between reading for the author’s point of view and for the function of each paragraph and also noting the location of important details in case you need to come back later. Make sure you underline anything that seems significant to you – look for words and phrases that reveal the author’s opinion or summarize or give the main idea of each paragraph. Practice with an egg timer. If you are spending more than 3 minutes reading and marking passages, you are risking not being able to finish all of the questions on test day.

Remember there is no wrong answer penalty on the ACT test so you need to make sure to bubble in something, even if you are running out of time!

# Learnist: Basic Algebra on the ACT and SAT

Expert Katie Cantrell over at Learnist offers a great look at the fundamental algebra concepts on the ACT and SAT exams. Refresh how to isolate variables, solve basic equations, and apply the order of operations on Test Day!

This video in particular covers several ways to conceive of variables, how to solve linear equations with fractions, and how to check your work to ensure that you have found the correct answer.

# Learnist: ACT Science and Data Representation

The Data Representation format on the ACT Science Test will ask you to understand and interpret information presented to you in graphs or tables. Occasionally there will also be charts, scatterplots, and diagrams.

As the video below outlines, it’s important to REALLY analyze all the data you’re given. The point of Data Rep is to determine your ability to pinpoint and extract conclusions from a series of data. 38% of the ACT Science passages will be in this format.

Making sure you have a strong understanding of the data will save you lots of headache when you read the questions. The questions will be so much easier if you spend just a few minutes focusing on the data. Check out tutor Jim Jacobson’s strategy for just how to do that in this video!

Need to see a passage in action? Sparknotes reviews some basic strategy, then shows you a passage exactly like one you’ll see on Test Day. Start with the intro, then when you get to the chart, you should glance over it to make sure that you know what’s being measured and that, in general, you feel comfortable finding information in the chart.

Now try some ACT Science Test Data Representation questions on your own on Learnist!