5 ACT Math Careless Mistakes With Negative Numbers (and How to Stop Them)
Most students who lose points on ACT Math are not missing hard questions. They are missing easy ones. A negative sign drops. A step happens in the wrong order. The answer they picked is sitting right there in the choices, because the test writers knew exactly which slip students would make.
In a recent one-on-one session, a student scored well below what they knew. When we looked at the missed questions together, the problem was not the math concepts. It was the same few small slips, over and over. By the end of the session, the student was catching their own errors and explaining every step. Here is what we worked on, so you can do the same.
Why careless mistakes cost so much on ACT Math
The ACT Math test gives you 45 questions in 50 minutes, about 67 seconds per question, and every question has four answer choices. That pace pushes students to work in their heads. Mental math is exactly where negative signs disappear and steps get done out of order.
The wrong answer choices are not random. Many of them are the exact number you get when you make one of these slips. If you make the slip, your answer will be there waiting for you.
The 5 ACT Math careless mistakes we see most
- Squaring a negative without parentheses. Plugging x = -2 into x² and writing -4 instead of 4.
- Losing a sign when multiplying. Treating 2(-3) as +6 instead of -6.
- Adding before subtracting. Working 10 - 4 + 3 as 10 - 7 = 3 instead of 9.
- Undoing an equation in the wrong order. In 3x + 6 = 30, dividing 30 by 3 before subtracting the 6.
- Stopping one step early. Finding 3x and choosing that number when the question asked for x.
The 4 rules that fix them
Rule 1: Wrap it
Every time you plug a number into an expression, put it in parentheses, even when it is positive. If a = 5 and b = -3, then 3a - 2b becomes 3(5) - 2(-3). Function notation works the same way: if f(x) = 2x + 1, then f(-4) = 2(-4) + 1.
Rule 2: Powers first, and parentheses keep the sign
(-2)² means (-2)(-2), which is 4. Without parentheses, -2² means -(2 × 2), which is -4. Rule 1 protects you here: wrap the -2 first, and the sign stays with it. Also square before you multiply by anything in front: 2(5)² is 2(25) = 50, not 10² = 100.
Rule 3: Know your sign rules
- A negative times a negative is positive: (-4)(-5) = 20
- A negative times a positive is negative: 7(-4) = -28
- Subtracting a negative is the same as adding: 15 - (-6) = 21
Rule 4: Undo it backward, then check
To solve 3x + 6 = 30, think about what happened to x. It was multiplied by 3, then 6 was added. Undo those steps in reverse: subtract 6 (3x = 24), then divide by 3 (x = 8). Then plug 8 back in to check: 3(8) + 6 = 30.
PEMDAS: the part most students get wrong
Most students learn PEMDAS as six steps in a row. It is really four steps, and two of them are pairs.
- Parentheses
- Exponents
- Multiplication and Division, together, left to right
- Addition and Subtraction, together, left to right
Addition does not come before subtraction, and multiplication does not come before division. The letters are in that order so the word is easy to say.
- 12 ÷ 3 × 2 = 4 × 2 = 8 (not 12 ÷ 6 = 2)
- 10 - 4 + 3 = 6 + 3 = 9 (not 10 - 7 = 3)
- 50 - 15 + 4 = 35 + 4 = 39 (the minus belongs only to the 15)
Two worked examples
Evaluate 2m² - 5m when m = -3.
Wrap it: 2(-3)² - 5(-3). Power first: 2(9) - 5(-3). Multiply: 18 - (-15). Subtracting a negative means adding: 18 + 15 = 33.
Solve 2x - 7 = -19.
Add 7 to both sides: 2x = -12. Divide by 2: x = -6. Check: 2(-6) - 7 = -12 - 7 = -19.
Use scratch paper, even if you are fast
The students who make these slips most often are the ones who say they do everything in their heads. Writing each step takes a few seconds and catches the error before you bubble. On a test where the wrong answer is designed to match your mistake, those seconds are worth it.
Before you pick an answer, run the slip check:
- Did I wrap every plugged-in number in parentheses?
- Did I do the power before multiplying?
- Did I check the sign?
- Did I go left to right on the pairs?
- On an equation, did I plug my answer back in?
Download the free cheat sheet
Get all four rules, the PEMDAS table, both worked examples, and the slip check on one printable page. Keep it next to your practice tests until the rules are automatic.
Get help before test day
Nova Scholars runs a live ACT Bootcamp on Outschool, built around trying real ACT-style questions first, then fixing the exact mistakes each student makes. One-on-one sessions are also available for students who want targeted help.
Frequently asked questions
How many questions are on the ACT Math test?
45 questions in 50 minutes, with four answer choices per question.
Is PEMDAS left to right?
Yes, for the paired steps. Multiplication and division are done together from left to right, and so are addition and subtraction.
What is (-2) squared?
4. A negative number times itself is positive. Only -2² without parentheses equals -4.
How do I stop making careless mistakes on ACT Math?
Wrap plugged-in numbers in parentheses, do powers before multiplying, check every sign, work the paired PEMDAS steps left to right, and write your steps on scratch paper.
