Ready to tackle some difficult ACT Math questions? If you are looking to conquer any (math) challenge or don’t love math but are doing what it takes to improve your ACT score, these questions are for you.
The Hardest ACT Math Questions
The hardest ACT math questions (the last 10 to 15 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 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. The last ten questions are more challenging than those at the beginning, but question 54 isn’t necessarily easier than 57. If you get stuck, move on and hammer the next few questions. Look for familiar concepts and do your best to make it to the end.
Keep practicing. Especially for the 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) and 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) for a result of 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, looking at the graph shows that there is no value for the function when x = 1 or when x = -2. This can also be solved by looking at the equation itself: any value of x for which the denominator will equal zero is NOT part of the domain. 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, has a total weight of 75.6 ounces, which is Answer K.
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