ACT Geometry Practice and Tips

tutoringThe Math section on the ACT challenges you with several types of questions. About 12 to 15 percent of those questions are related to geometry. Putting a few easy tips into practice can help you to perform your best on the ACT geometry questions.

Memorize Formulas
As you prep for these questions, it’s a good idea to memorize some basic formulas of geometry. Some formulas are not provided for you on the test. A few examples include:

  • Volume = (area of base) (height)
  • Circle circumference = 2πr
  • Circle area = πr2
  • Rectangle = lwh

When you memorize basic geometry formulas, you’ll be able to work through the questions in a timely and efficient way. Of course, knowing the formulas is not enough: You must be able to put them into practice.

Take Timed Practice Tests
Working through ACT geometry practice questions is an essential part of preparing for this section of the test. However, don’t forget to time your practice tests. You have 60 minutes to complete all 60 questions on the ACT Math section. This means you have no more than a minute to dedicate to each one. Chances are good that you’ll spend just a few seconds on some questions and up to 30 seconds on others. Completing a timed practice test is an excellent way to establish a test-taking rhythm so you know when to move on to the next problem. You can always skip a problem that is especially puzzling and return to it later on. Ideally, you want to finish the Math section with a few minutes to spare so you can review your answers.

Analyze Incorrect Answers to Practice Questions
Analyzing the answers to your ACT geometry practice questions should be part of your test prep. If you got an answer wrong, it’s important to go back and look at your work. Where did you make the mistake? You may find that you’ve made the same mistake on other problems. This is helpful information because once you’re aware of it, you can avoid making the same error again. An important question to ask is, “Why did I make that mistake?” You may find that you rushed through a problem, forgetting part of the formula, or perhaps you calculated the area when the question asked for the perimeter. Being aware of why you made a mistake can help you refocus and avoid making the same errors.

Draw Diagrams and Shapes
You can use scratch paper on the ACT. Drawing shapes and diagrams can help you to organize the elements of each geometry question. Also, you can write down the formula for a problem as well as its steps so you can review what went wrong if your answer is not among the options. It’s unnecessary to mentally picture a shape labeled with all of its measurements as well as the formula that goes with the problem. Using your scratch paper saves time and can clarify each step in the process.

Eliminate Wrong Answer Choices
Another tip to remember as you practice ACT geometry problems is to get into the habit of eliminating answer options that are clearly incorrect. Dealing with fewer answer options can make a problem look a lot simpler. Also, it can help you complete all of the problems more quickly.

Practice Throughout the Day
It’s a good idea to create a detailed study schedule that includes practicing your geometry skills for the ACT. In addition to that, try reviewing geometry problems throughout the day. One idea is to make flashcards that display the different formulas you need to memorize. Keep them in your bag or pocket to review while you’re standing in line to buy lunch, waiting for the bus, or waiting for class to begin. Studying and reviewing throughout the day gives you several more opportunities to sharpen your geometry skills outside of your formal study time.

The professional instructors at Veritas Prep are experts when it comes to geometry, algebra, statistics, and every other type of math on the ACT. In fact, we can prep you for all sections of the test! You’ll study with an instructor who scored in the 99th percentile on the exam. Plus, we give you several options so you can study for the ACT in a way that is most convenient for you. We have online and in-person courses, private tutoring, and On Demand instruction. Call today and give us the opportunity to guide you toward excellence on the ACT!

3.14 Reasons to Love Pi

Pie ChartEvery March 14, numerically expressed as 3/14, math nerds and test prep instructors celebrate the time-honored tradition of “Pi Day,” deriving plenty of happiness from the fact that the date looks like the number 3.14, the approximation of π. Pi (π) is, of course, the lynchpin value in all circle calculations. The area of a circle is π(r^2), and the circumference of a circle is 2πr or πd.

As you study for a major standardized test, you know that you’ll be working with circles at some point, so here are 3.14 reasons that you should learn to love the number π:

1) Pi should make you salivate.
On any standardized test question, if you see the value π, whether in the question itself of in the answer choices, that π tells you that you’re dealing with a circle. Some test questions disguise what they want you to do – you may have to draw in a triangle to find the diagonal of a square, for example – but circle problems cannot hide from you! π is a dead giveaway that you’re dealing with a circle, so like Pavlov’s Dog, when you see that signal, π, you should respond with a biological response and conjure up all your knowledge of circles immediately.

2) Pi can be easily cut into slices.
Whether you’re dealing with a section of the area of a circle or a section of the circumference (arc length), the fact that a circle is perfectly symmetrical makes the job of cutting that circle into slices an easy one. With arc length, all you end up doing is using the central angle to determine the proportion of that section (angle/360 = proportion of what you want), making it very easy to slice up a circle using π. With the area of a section, as long as the arms of that section are equal to the radius of the circle, you can do the exact same thing. Just like an apple pie or pizza pie, if you’re cutting into slices from the center of the circle, cutting that pie into slices is a relatively simple task.

3) You can take your pi to go.
You will almost never have to calculate the value of pi on a standardized test: almost always, the symbol π will appear in the answer choices (e.g. 5π, 7π, etc.), meaning that you can just carry π through your calculations and bring it with you to the answer choices. If, for example, you need to calculate the area of a circle with radius 3, you’ll plug the radius into your formula [π(3^2)] and just end up with 9π, which you’ll find in the answer choices. With most other symbols (x, y, r, etc.) you’ll need to do some work to turn them into numbers. Pi is great because you can take it to go.

3.14) The decimals in pi are just a sliver.
If you ever are asked to “calculate” pi (which typically means that the question is asking you to approximate a value, not to directly calculate it), you can use the fact that the .14 in 3.14 is a tiny sliver of a decimal. For example, if you had to estimate a value for 5π, 5 times 3 is clearly 15, but 5 times .14 is so small that it won’t require you to go all the way to 16. So if your answer choices were 15.7, 16.1, 16.4, etc., you could rely on the fact that the decimal .14 is so small that you can eliminate all the 16s.

Other irrational numbers like the square root of 2 and square root of 3 have decimal places more in the neighborhood of .5, so you will probably need to work a little harder to estimate how they’ll react when you multiply them even by relatively small numbers. But π’s decimals come in small slivers, allowing you to manage your calculations in bite size pieces.

So remember – there are 3.14 (and counting) reasons to love pi, and learning to love pi can help turn your test day into a piece of cake.

Are you getting ready to take the SAT, ACT, GMAT or GRE? Check out our website for a variety of helpful test prep resources. And as always, be sure to follow us on Facebook, YouTubeGoogle+ and Twitter!

By Brian Galvin.

The New SAT vs. the ACT: A Simple Test Comparison

Law School Images“Are ‘SAT’ and ‘ACT’ the same thing?” If you’ve been thinking about this question, you’re not alone. Many high school students are curious about the similarities between these two tests and how different they really are.

A quick SAT-to-ACT comparison can help you to decide whether to take the new SAT, the ACT, or both.

Scoring
The scoring scales for the ACT versus new SAT are very different. The highest score you can earn on the ACT is a 36. There are four sections on the ACT, and you receive a raw score for each section, which is changed into a scaled score ranging from one to 36. Your final score is the average of your four scaled scores. On the other hand, the highest score you can achieve on the new SAT is 1600. You receive a subscore for each section of the new SAT, and your final score is the sum of your subscores.

Math Questions
When making an SAT-to-ACT comparison, you’ll find that both tests include questions on advanced math concepts such as geometry and trigonometry as well as algebra. Of course, knowledge of arithmetic is necessary on both tests. One difference between the two Math sections is that you’re given 60 minutes to complete 60 questions on the ACT and 80 minutes to complete 58 questions on the new SAT. You’re also allowed to use a calculator throughout the Math section on the ACT, but your calculator use is limited on the new SAT.

Science Questions
One major difference in the new SAT versus ACT test is that there’s no specific Science section on the new SAT. However, some of the skills you use in science class are tested in other sections on the new SAT. For instance, in the Math section you’re often asked to analyze the information given on a chart or graph, and the Reading section contains passages that cover science-related topics. The ACT does have a section of Science questions – earth science, chemistry, and biology are among the sciences found on the ACT. You must answer a total of 40 questions in 35 minutes in the Science section of the ACT.

Reading Questions
When making an SAT-vs.-ACT comparison, you’ll see that the Reading sections on both tests share a lot of similarities. The Reading sections on both exams feature several passages accompanied by questions. The SAT has five passages, while the ACT has four. In addition, the two tests share many of the same question types. For instance, they both have main idea, detail, vocabulary-in-context, and inference questions. In addition to those, the new SAT has data reasoning, technique, and evidence support questions. You’re given 35 minutes to finish 40 questions on the ACT and 65 minutes to finish 52 questions on the new SAT Reading section.

Writing and English Tests
There is a Writing & Language section on the new SAT that requires you to improve on phrases found within the given passages. There may be grammar or punctuation errors in the passage or problems with sentence structure. You’ll read the passage and select the better options for the underlined phrases.

The ACT has an English section with passages that also contain underlined phrases. Your task is to find a better alternative to the phrase or, in some cases, select the “no change” option. Once again, there may be grammar errors or problems with punctuation, sentence structure, or organization. You are given 45 minutes to finish 75 questions in the English section on the ACT and 35 minutes to complete 44 Writing & Language questions on the new SAT.

The Essay
When it comes to the essay on the ACT vs. new SAT, both tests make this section optional. For the new SAT Essay section, you’re required to analyze an argument and offer evidence as to why the author’s argument is valid or invalid. Alternatively, the ACT Essay section presents you with three different perspectives on a particular issue, and your job is to evaluate each of them. On both essays, your score depends on your ability to organize your thoughts, present evidence, and convey your ideas in a clear way.

Are “SAT” and “ACT” the same? In some ways, the answer is “yes,” but in many others, the answer is “no.” Regardless of which test you take, our professional instructors can help you practice for it. Look at our video tutorials and sign up for our in-person or online test prep courses today!

Want to learn more about how the SAT and ACT differ? Attend one of our upcoming free live online SAT vs. ACT workshops to determine which exam is right for you. And be sure to find us on Facebook, YouTube, Google+ and Twitter!

Improve Your Speed on the ACT Math Section Using Math Fluidity

stopwatch-620Speed is key on the Math Section of the ACT – you have only 60 minutes to complete 60 questions. However, this doesn’t mean you should spend one minute on each question, as not every question on in this section is created equal. Many questions (particularly Questions 1-30) are problems that you can solve in under one minute. In fact, you should aim to solve Questions 1-30 in less than 30 minutes – around 25 minutes is the goal.

That’s because some of the later questions, particularly the questions from Questions 40-60, will require more than a minute. Basically, you want to put aside extra time for the tricky questions at end of the section by completing the easier, earlier questions as quickly as possible. If you do Questions 1-30 in 25 minutes, then you have 35 minutes to do Questions 31-60.

One way to improve your speed on the Math Section is to develop what I call “math fluidity.” That means recognizing how common patterns, formulas and special rules can help you solve any particular problem. To illustrate, take a look at the following triangle problem:

Triangle ABC (below) is an equilateral triangle with side of length 4. What is the area of triangle ABC?

ACT Triangle 1

 

 

 

The first step to any geometry problem is writing down what relevant common formula you’ll need to solve the problem; i.e. whenever I’m asked the area of a triangle, at the top of my work space I’ll write:

A = (b*h)/2

Having the formula in front of you will be helpful because right away, it’s clear that although we have some information, we don’t have all the information we need to solve this problem – we have the base of the triangle (4), but not the height. Since the height of an equilateral triangle always goes from one angle to the opposite side, where it forms two 90-degree angles, drawing the height of an equilateral triangle creates two identical triangles, as shown below:

ACT Triangle 2

 

 

 

Many students would now conclude that they need the Pythagorean theorem to solve for the height (that line bisecting the equilateral triangle). This is where math fluidity comes in. Although you could use the Pythagorean theorem, it’s much faster to instead recognize what type of triangle you are dealing with.

Whenever you split an equilateral triangle in half, you create two 30-60-90 triangles. These are also called “special right triangles” because they always follow the rule that the shortest side is always “x,” the side opposite the 60-degree angle is always x√3, and the hypotenuse is always 2x. See the triangle below:

ACT Triangle 3

 

 

 

So, rather than spend any time solving for the height of the our triangle by using the Pythagorean Theorem, recognize that because the hypotenuse is 4 and the base is 2 (of either of the smaller triangles), and because the triangle is a right triangle, the height must be 2√3. Therefore, the area of the larger triangle is  (2√3)(4)(1/2), which equals 4√3.

Instantly recognizing that the two smaller triangles are 30-60-90 triangles only saves a little bit of time – if you can regularly shave off 20 seconds on question after question by recognizing special rules or how best to apply formulas, you’ll accrue saved time that can later be spent on harder math questions. Speaking of which, math fluidity also applies to tricky questions – similar to what we previously saw, recognition will break down hard questions into easier, faster steps.

So, let’s take a look at a more difficult question. Note, this next example is especially relevant for students shooting for 99th percentile or perfect scores. Although many students can solve the following question if given enough time, few students can solve it quickly enough to get it correct on the ACT. Here’s the problem:

In triangle ABC below, angle BAE measures 30 degrees. What is the value of angle AED minus angle ABE?

A) 30ACT Triangle 4
B) 60
C) 90
D) 120
E) 150

 

Although there are several ways to solve this problem, math fluidity will help with whatever approach you choose. As I mentioned earlier, it is always best to start by writing down a relevant formula, as it will include what information you have and what information you need. In this case, I’m looking for AED-ABE. Because I’ve also been given the measure of angle BAE, I’ll write down:

BAE = 30 and BAE + ABE = AED

Here’s where math fluidity comes in; the second formula is based off a theorem that you probably learned (and then forgot!) in your geometry class. I do recommend (re)memorizing it for the ACT as follows: a measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

ACT Triangle 5Are you drawing a blank? If so, take a moment to think about why that statement is true. If the smaller two angles of a right-angle triangle, as shown at left, are 40 and 50, then if we extend a line as shown to form the adjacent exterior angle x, then x + 50 = 180, so x = 130.

 

Also, 40 + 50 + 90 = 180, since the sum of interior angles of a triangle always add up to 180. So, if x + 50 = 180, and  40 + 50 + 90 = 180, then x+ 50 = 40 + 50 + 90.

Removing the 50 from both sides, we can conclude that x = 40 + 90, or x (the adjacent  exterior angle of one interior angle) is equal to the sum of the other two interior angles.

Now, returning to our original problem:

If BAE = 30 and BAE + ABE = AED, then:

30 + ABE = AED

AED – ABE = 30

Therefore, our answer is A, 30.

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By Rita Pearson