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.
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
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.
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.