The Math Section of the ACT is unique among the "big four" sections of the exam: English, MATH, Reading and Science.
First, it is the only section with five answer choices instead of the usual four choices found in all other sections. See two examples below of a Math and English question respectively:
Second, it is the only section that is not subdivided into "passages".
The first difference is kind of a bummer because it means that if you are forced to guess on a question the odds are longer that you will guess correctly. The second difference is also kind of a bummer because it makes it slightly harder to regulate your timing---if you know your per passage timing goal, it's easy to check if you are on pace.
Don't worry though! We have tips below to help overcome these two annoying features and master the ACT Math Section!
First, recall the Math Section's basic format:
it has exactly 60 questions
you will get 60 minutes to finish
you can use use your own scientific calculator for the entire test
most the questions are based on algebra, geometry and a little trigonometry (especially SOH CAH TOA problems!)
the questions get harder as you go
Next check out these go-to tips to ramp up your math score!
BASIC MATH SECTION STRATEGIES
1) FOCUS ON PROBLEMS YOU KNOW HOW TO DO & GUESS ON THE HARD ONES!
This core strategy comes from three facts:
FACT ONE...the math test's questions get significantly harder as you go from question 1 to question 60.
FACT TWO...all questions, no matter how difficult, are worth the same point value: 1 POINT.
FACT THREE...it is a timed test.
Putting these facts together you can see why it makes zero sense to spend a lot of time on questions you don't know how to do right away. If you did so, you would be wasting time for just one point and that assumes you somehow manage to figure out how to correctly answer that tough question.
This core strategy also helps manage your timing. You should spend 90 percent or more of your time on questions you know how to do and do them well! The right answer for tough questions is always "guess and move on"! Don't let those hard questions suck up your time. And don't leave them blank! Make your best guess right away on tough ones and star them on your test booklet if you think you might want to come back to it later. Sometimes students leave tough questions blank thinking they will come back later, but then forget to come back. There is no penalty for guessing on the ACT so don't leave any questions blank.
There are not separate "passages" in the Math Section like there are in the other three sections, but you can sort of think of the test as subdivided into three equal parts:
Questions 1-20 are the "easy" first section
Questions 21-40 are the "medium" middle section
Questions 41-60 are the "hard" final section
Some general timing guidelines:
If you are okay, but not a rock star at math, chances are you should focus on the first 40 or so questions of the test and make quick guesses on the rest.
If you struggle with math, make the first 30 questions your main area of focus.
If you excel at math you can possibly afford to spend some time on the last 20 questions.
2) READ THE QUESTIONS CAREFULLY AND DON'T RUSH THE EASIER ONES!
"Read the question carefully" might seem like obvious advice, but it is worth emphasizing. At Academic Tutoring we have seen how this simple advice isn't always followed. Students who take the ACT often, understandably, try to save time by rushing this part of the process.
What happens to just about everyone when they rush through even easy math problems? We all know this answer: They make silly mistakes! And, unfortunately, you do not get partial credit for your work on the ACT math test like you might get from your high school math teacher. So on the easy questions that you know how to do, use a careful step-by-step approach and get those points!
3) USE THE FIGURES TO MAKE GOOD GUESSES!
The instructions for the ACT Math section warn students that the drawn figures they sometimes provide for problems are not necessarily "drawn to scale". That normally means you should not make guesses based on what the figure looks like. See the example below:
Suppose you were asked to figure out angle BAC in the triangle above. You might hesitate to make a visual guess after reading the ACT's warning. But the truth is that the figures they provide are almost always very accurate! So, when you can't do a problem in a simpler way, USE THE FIGURES TO MAKE GOOD GUESSES!
EXAMPLE: In the figure above you might guess that angle BAC looks like it is less than 90 degrees and more than 45 degrees. And you would be correct! Use the guide below to help make even a better guess.
If you guessed around 70 degrees for angle BAC you would be very close! The answer choices (in degrees) for this problem were:
You can see that based on a visual guess you could have easily eliminated answers A, D, and E. If you are curious, the correct answer is C. You could have used the inverse cosine of (5/13) to get the same answer, but a visual guess worked just as well!
4) WORK BACKWARD FROM THE ANSWERS
Some of the questions in the Math section are difficult to do because they are confusing word problems. In many of these harder problems you can use a technique called "working backward from the answers" or some students call it "guess and check".
In general, use this technique when there are numbers or formulas in the word problem that you can test the answer choices against to see which one works.
Check out this Math ACT problem as an example:
"A worker cut a straight wooden board into three pieces. The longest piece was twice as long as the second and the second piece was twice as long as the third. How long was the longest piece in feet if the entire uncut board measured 21 feet."
This problem confuses many students because you have to carefully sort out all the math relationships between the different board lengths. A simple approach to this is working backward from the answers to see if you can get to the measurement of 21 feet, the length of the entire board.
To use this technique, it's almost always best to start at the middle number in the answer bank, which for this problem is choice C, 10 feet. Test this number against the problem's facts about the cut board and see if you get to 21 feet. If you get an answer that is too big, try a smaller number. If you get an answer that is too small, try a bigger number.
To use the "guess and check" method assume answer C (10 feet) is the right answer. That means we are, for the moment, pretending that the longest board is 10 feet.
According to the problem then, the second piece is half as long as the longest piece so it would be 5 feet. And the third piece would be 2.5 feet because it is half as long as the second piece. When you add 10 + 5 + 2.5 you get 17.5 feet which is too small! So let's try Answer B, 12 feet.
Half of 12 is 6 and half of 6 is 3. Let's add those numbers now: 12 + 6 + 3 = 21! This is correct! So answer B is the right choice. Nice thing about this technique is that you do not have to create complicated equations to solve problems.
5) USE YOUR OWN EASY NUMBERS INSTEAD OF VARIABLES!
Some problems confuse students because they use too many variables to easily deal with.
Check out this Math ACT problem as an example:
If a > b and b > c and a is less than zero, which one of the following equations has to be true?
A) bc = 0
B) bc < 0
C) bc > 0
D) ab < 0
E) ac < 0
With all the abc's and inequality symbols in this problem it can easily be confusing to think through. Try using your own easy numbers to figure it out!
Pretend "a" is equal to -3 because the problem said "a" is less than zero and -3 is an easy number to work with.
Now "b" can be -4 because it has to less than "a".
And "c" can be -5 because it has to be less than "b".
Let's use these easy numbers to test the answers now:
A) bc = 0...(-4)(-5) is 20 not 0 so it's WRONG!
B) bc < 0...(-4)(-5) is not less than zero WRONG!
C) bc > 0...(-4)(-5) > 0 CORRECT!!!
D) ab < 0...(-3)(-4) is not less than 0 WRONG!
E) ac < 0...(-3)(-5) is not less than 0 WRONG!
Not so bad right! Try this technique on problems in your next practice test!
6) READ THE QUESTION ONE MORE TIME BEFORE YOU ANSWER IT!
So simple to do! Remember that the ACT Math Section sometimes gets a little tricky with their questions. For example, you may find yourself doing an ACT Math problem that involves the area of a circle (the ACT people love circle problems!) and you get excited because you remember that the "area of a circle is equal to pi times the radius squared"
CIRCLE PROBLEM: A circular swimming pool has an area of 64pi feet squared. How long must the pole of a cleaning net be in feet to reach across the pool at its widest point?
So suppose you use the area number they give you for the circle, 64pi, and you then use the area of a circle formula to calculate that the radius of the circle is 8 ft. Great! See the work below:
Area = pi times radius squared
64pi = pi times radius squared
64 = radius squared (the pi's cancelled)
8 = radius!
Now suppose you see 8 is answer choice C and you happily feel like you can pick C and move on to the next question. But did you notice that they actually were asking what the diameter is? To reach across the entire pool you would need to span the diameter of the circle which is twice the radius. Right above answer C is Answer B, which is 16 feet, the correct answer!
Long story short, try to minimize these kinds of errors. The makers of the ACT know students will sometimes get a little careless and so they pick answers that are true numbers (the radius is truly 8!) but they are not correct answers!
7) REVIEW AND MEMORIZE BASIC FORMULAS!
The ACT Math Section does not supply you with math formulas to use on the test, but the formulas you might need for the exam are pretty common and you can improve your score by memorizing them as well as reviewing how to use them:
Here is a good set of formulas to start with:
7) DO PRACTICE TIMED TESTS!
Math skills get rusty quickly so even simpler problems on the ACT Math Section can be hard. Be sure to do many practice timed Math Section tests to prep for your actual ACT.
Seek out tutoring if you are having any trouble recalling the basics of algebra, geometry and trig. And even if your math skills are strong think about getting some tutoring for the ACT Math Section itself because there are many strategies and tips that are unique for this particular math test.
The good news is that the ACT Math Test does not change much from year to year so you can practice older exams to get ready for the latest one!
8) WRITE OUT STEPS IF YOU NEED TO!
Yay! You do get to use your fancy graphing calculators for the entire ACT Math Section, but remember that your calculator can't think for you.
And remember that you are given all kinds of work space in your exam booklet to write out your solutions in pencil.
Easy calculator based errors to make:
Forgetting to use parentheses in squared calculations
Combining too many steps into one calculation
Having your calculator set in radian mode instead of degree mode
There are other types of errors as well. Bottom line is that there is no one best way to mix the use of your calculator with your use of hand written steps for the Math Section. In general you should write out each of your problem solving steps to minimize the silly errors that arise when you do quick mental calculations.
Even advanced math students mess up problems by adding when they should have subtracted or vice versa. You can be your own best friend in the ACT Math Section by writing out your steps and trying to catch these kinds of flubs. Use the calculator to do the calculations after you have them written out. Keep track of where you are on the problem with your pencil and paper!
We hope these tips help your ACT Math Prep!
GOOD LUCK and let us know what tips worked for you!