# Proportions and Probability

Proportions and probability questions are common in ACT math sections. The can be expressed in algebraic equations, fractions or as word problems.  They’re tough. These problems include ratios, proportions, rates, averages, probability, permutations and combinations.  There are basic formulas you can memorize to help you through.

For example, ratios compare two quantities by division.  So, it will be written fraction form x/y or with a colon x:y.

Proportions are two equal ratios written as fractions with one term missing:  4/12=x/36.  To solve you cross-multiply 12x times 36 then divide by 4 so your answer for the missing term is 12.

A rate is something per something.  That’s really vague, better illustrated with examples like distance/time as in miles per hour or feet per second.

Probability questions are solved using a three-part formula that looks like this:

probability = # of desired outcomes/ # of possible outcomes

So the most common types of probability questions on the ACT math section will ask you to find the probability of something happening.

Be aware that there are common traps intentionally built into proportion and probability questions to trip you up.  With rate problems, for example, the most common mistake is problems that involve average speeds when multiple speeds are involved.  Students will average two separate trips together instead of the average speed for the whole trip.  The best way to prepare for “traps” is to consult a prep course and do practice math problems like those outlined here.

# Math Formula Sheet

If you don’t already have one, you need to create your own Math formula sheet.  Try to limit it to one to two pages.  It should contain all the basic mathematical formulas that you need to know.

As you gradually learn them, you can remove the ones that you can’t remember and gradually reduce the size of the list. To start, it is fine to have a very long list that is more than a few pages because you will need to know a lot of basic formulas.

Here are some basic formulas that you should have on your list:

1 foot = 12 inches

1 yard = 3 feet

1 mile = 5,280 feet

1 inch = 2.54 centimeters

1 quart = 4 cups

1 ton = 2,000 pounds

1 pound = 16 ounces

# Percent questions on the ACT

Basic, algebraic percent questions are common on the ACT test.  They range in difficulty from simple & straightforward to confusing & challenging. One question might ask you to find out what percent is a number out of another number.   Others might include multiple percents in the same problem.  Most percent questions on the ACT can be solved using the same, three-part formula.  percent = part/whole x 100

Percent means 100th.  A percent is 1/100th of something. You can change a percent into a decimal by adding a decimal point two places to the left and drop the percent sign.   15%= .15    You can change it to a fraction by writing it over 100.  15/100

The most common types of percent questions are

• Percent Taken Off
• Percent Change
• Combined Percents

Percent Taken Off- The question will either give you a whole and ask you to find a new value when a percent is taken off.  For example, a purse at \$80 is discounted 10%.  What is the price of the discounted purse?   First, subtract the percent from 100 (equals 90).  Then, convert 90% into a decimal->( .90)  Last, multiply the decimal by the whole amount .90 x 80 =72.  Your answer  is \$72.00.

Percent Change- This question will give you a value and a new value, and ask you to find the percent increase or decrease between those values.  Using the same example above, the question might ask if a purse that cost \$80.00 was discounted to \$72.00, what percent was the discount?  The answer is 10%

Combined Percents-  This question will give you a whole value, then take a percent off of the whole value twice consecutively.  Here’s an example:  A purse retailed for \$80.00 on Monday. It was discounted 10% one day, and 20% the next day.   What is the total percent discount applied to the purse?  The answer is a \$24.00-discount because the cost of the purse was \$56.00 after the combined 30% discount.

# Introducing the ACT Math Section

As previously stated, there are 60 questions in the math section of the ACT exam.  The math questions break down into the following areas:

• 24 pre-algebra and basic algebra questions
• 14 plane geometry questions
• 10 intermediate algebra questions
• 8 coordinate geometry questions
• 4 trigonometry questions

These questions will not be ordered from easiest to hardest.  They will be mixed together.  You are allowed to use a calculator to help you solve math questions on the ACT.  If you can avoid a calculator on the easier math problems, you’ll save yourself some time since the section is timed into a 60-minute window.  All the questions in the math section are worth the same amount of points, so make sure you answer the questions you are confident that you know.

# Preparing for the exam

As a student, going to school, there are many things that we have to deal with.  We have to adjust to the environment around us as well as the people around us.  We have to study for many different subjects and exams.

College is very important because it is the starting point of our future.  So it is very important that we do well to prepare to go to college.  While in school, we learn many different subjects and topics but there is one very useful subject that is with use from kindergarten to college and that is Math.  So it is no wonder that the ACT exam focuses on Math.

The ACT exam allows colleges to compare different students from different schools based on how well they perform on the Math portion of the ACT.  The Math portion of the exam is weighed heavily for students interested in pursuing a college degree in mathematics, science, finance, technology, and related fields.  Like all standardize exams, the ACT can be studied for strategically.  This because the Math portion of the exam is well defined and fixed.  It has the same type of questions on it year after year so, this gives student a great opportunity to prepare and do better on the exam if they know which types of questions to study for.

We all have to take the exam if we want to get into college so those who take the time to prepare will have a better opportunity to do well and attend the best schools.

So how to you prepare for the Math portion of the ACT?  Here are a few tips to score better:  First, review all your Math notes, look over your books and go over all your Math concepts that you have learned through the years.  You will need to master everything.  As you go over your Math books, go through chapter by chapter and do the practice problems and see if you can solve the problems and get the right answers.  This will help you get more accurate at problem solving and comfortable with working with Math formulas.

Then go through the ACT prepare exams and see how you do.  Your ability to solve complex problems will ensure that you will do better on the real test.  Having a good understanding of the techniques that you need to apply to each type of question is very important because under the time pressures of the SAT, having good techniques will help you.

At this stage of preparing for the ACT, it will be helpful to work with a tutor who can help you learn Math concepts that you did not previously understand.  Have the tutor focus on your weakness so that you can improve on those concepts that cause you the most problems.

You should also consider working with an online site that provides online tutoring as they then to be more affordable than an in person tutor.  There are also online sites that you can pay to help you prepare for the Math portion of the ACT as well.  They also provide techniques and knowledge on how to solve and answer the questions that tend to be on the exam.

# Type of Math Questions

The Math portion of the ACT exam seeks to find out your math skills and what you learned and retained from the grades of 9 to 11.  With sixty questions and sixty minutes to answer those questions, the math section of the exam is broken down to these areas of math based on past exams:

• 10 to 15 questions focusing on Pre-Algebra;
•  10 to 12 questions focusing on basic Algebra;
•   9 questions focusing on intermediate Algebra;
•   10 questions on coordinate Geometry;
•   12 to 14 questions on plane Geometry; and

# Math Exam Portion

The Math portion of the ACT is a 60 question test.  You have sixty minutes to answer all sixty mathematical questions.  This portion of the ACT exam is design to test a test takers mathematical skills acquired by the 11th grade.

Unlike when I took the ACT, you can now use a calculator on the ACT Math portion of the exam.  However, not all calculators are permitted.  We will discuss more on the ACT’s calculator policy on what type of calculators are allowed and which are not permitted.

Typically, you will need to know some basic math formulas to answer the exam questions but knowledge of complex formulas are not necessary.  However, a good understanding and knowledge of complex math formula is helpful since it will allow you to do computation faster and hopefully correctly.

# Welcome Potential College Students!

You have arrived at the ACT Math Prep Course site.  The Math portion of the ACT examination is the most likely area of the ACT test that high school student can stand to improve their score through taking a prep course and doing practice exams.  Through years to providing prep materials to high school students, we have help you improve your Math score by teaching the math skills that are most important and that are routinely tested on the exam.

Through hard work and focusing an type of questions that are difficult to you, you can gave confidence that you can get them right and improve your overall score.  That is why taking a prep course focusing on the Math portion of the exam can be very effective.