Ready to tackle some difficult ACT® Math questions? If you don’t love math but are doing what it takes to improve your ACT® Test score, these questions are for you.
The Toughest ACT® Math Questions
The toughest ACT® math questions fall into two types: advanced concepts and complex questions.
Advanced concepts questions cover what you learn in precalculus and trigonometry. If you've not yet taken precalculus, you might not (yet) have the knowledge you need to solve the questions.
Other tough math questions are basic concepts asked as complex questions. These may look overwhelming, but look closely, and you'll see these are relatively common math ideas in disguise. Even if you haven’t finished Algebra II, you can solve these questions.
Strategies for Difficult ACT® Math Questions
Here are a few strategies to help you with the toughest ACT® Math questions.
Don’t assume your initial answer is correct because it's one of the choices available. The ACT® Test is written to anticipate your mistakes. Double-check your work, and don’t just choose the first answer you see from your calculations.
Don’t get stuck. Question 24 isn’t necessarily easier than 27. If you get stuck, make your best guess, mark that question, and move on. Look for familiar concepts, and do your best to make it through all the questions. You can return to any questions you've flagged if you have time at the end.
Keep practicing. Especially for complex questions, practice helps you determine what the question is asking. And you'll build confidence as you recognize concepts you've practiced within these tough questions.
Ready to Practice?
Advanced Concepts Questions
Solution Steps for Question 60:
To find the element in the upper left of the product matrix, multiply the upper left element of the first matrix (3) by the upper left element of the second matrix (w). ADD that product to the product of the upper right element of the first matrix (5) and the lower left element of the second matrix (y). The result is 3w + 5y. Only Answer J has this correctly expressed in the upper left position.
Solution Steps for Question 54:
The domain of a function is simply the values of x that “work” for the function. In this case, the graph shows no value for the function when x = 1 or when x = -2. Or look at the equation itself: any value of x for which the denominator will equal zero is NOT part of the domain (you may remember learning about undefined fractions in math class). The equation x²+x-2 =0 is true when x = 1 or when x = -2. Both methods result in Answer J.
Complex Questions (Basic Concepts)
These math questions do look complicated. But they have basic concepts you can figure out with some organization and step-by-step thinking.
Solution Steps for Question 57:
Area of a rectangle = LW
New Length = 70%L = 0.70L
New Width = 115%W = 1.15W
Area of new rectangle = (0.70L)(1.15W)
Area of new rectangle = 0.805LW = 80.5%LW = 80.5% of Area of the original rectangle
Question asks for how much SMALLER the area is: 100% - 80.5% = 19.5% SMALLER: Answer B is correct
Solution Steps for Question 58:
Find how many cartons can be placed in a box: 172/12.6 = 13.65 cartons, but you can’t have a partial carton. Therefore, each box can hold a maximum of 13 cartons. Subtract 13 multiple times from the total of 84 cartons to find how many cartons will be in the partially-filled box:
84 - 13 = 71
71 - 13 = 58
58 - 13 = 45
45 - 13 = 32
32 - 13 = 19
19 - 13 = 6
6 cartons, each weighing 12.6 ounces, have a total weight of 75.6 ounces, which is Answer K.
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