![]() The radius is the key to unlocking other important circle things, such as the area, circumference, sector area, or arc length. Here’s another important tip: Whenever you are dealing with circles, and you aren’t given the radius, your first step should be to find the radius. This means that all of the details in the question give you important clues that you need to solve the problem. The ACT rarely gives you any unnecessary information in a math word problem. Since we found that x=2 y we can sub in x for2 y in the expression above and get our answer: C: Using the exponent rule x m x n= x m+n, we know that So, plugging in 8 for x, the answer choice equivalents would be: So now we have the numerical answer we are looking for in the answer choices, expressed in terms of x (which we determined equals 8. When y=3, the expression in the question 2 y+2 equals 32. So now we have a corresponding value for x. ![]() You see, this problem is a great candidate for plugging in numbers for x and y and seeing what works. ![]() Let’s talk about the test prep strategy way first. There are two ways to solve this problem: the “math” way and the “test prep strategy” way. Which of the following best describes the graph of y = p(x) in the standard (x,y) coordinate plane? The function values for p(x) vary directly as x for all real numbers. Which of the following is the value of m(m(n))?ġ2. Which of the following could be the equation of the function?ġ1. The graph below shows a function graphed in the standard (, ) plane. If sin = –, which of the following could be true about ?ġ0. If the students arrived back at Thomas Jefferson High School two hours later, approximately what was the average speed for the entire field trip?ĩ. Finally, the bus drove 40 miles straight back to the high school. The bus then stopped for lunch in a suburb before continuing on a 3 hour tour of countryside at a constant speed of 10mph. Students at Thomas Jefferson High School boarded the bus for a field trip that went 15mph through a 30 mile section of the city. If it took Suzanne 3 hours to arrive at the pet store, what was her average speed in miles per hour for the entire car ride from her home to the pet store?Ĩ. Then, she left and drove another 30 miles to the pet store, but this time only drove at 10 mph. It took her 2 hours to get to her aunt’s house. Suzanne drove 40 miles to see her aunt and was going 20 mph. What is the value of the seventh term in the sequence?ħ. In a geometric sequence in which all of the terms are positive, the second term is 2 and the fourth term is 10. What would s have to be so that is divisible by (x + 2)?Ħ. ![]() Which of the following is an equation of the largest circle that can be inscribed in the ellipse with the following equation?ĥ. What is the probability that the number on the card is an irrational number?Ĥ. is written on the first card, on the second, on the third and so on through, with no numbers repeated. The shaded region inside the circle and outside the triangle has an area of square centimeters. Point D is the midpoint of AC, which is 22 cm long. As shown in the figure below, A is the center of the circle, and right triangle ABC intersects the circle at D and E. Which of the following expresses 2 (y+2)in terms of x?Ģ. Let x and y be nonzero real numbers such that 2 (y+1)=2 x. Want to make sure you’ve mastered the trickiest concepts in all areas? For ACT challenge problems from other ACT sections, check out:ġ. Think you’re ready to put your skills to the test? Check out the twelve ACT math challenge problems we’ve put together for you below. Does it mean you can’t solve them? Absolutely not! To master these problems, you’ll need to refresh your understanding of the concepts, then put them into practice. Instead, it’s because they take some of the foundations of math topics you’ve already studied in school, like pre-algebra, algebra, and geometry, and turn them into multi-step processes that may combine concepts from different areas.ĭoes this make them challenging? Yep. If you’re wondering why hard ACT Math problems are so difficult, know that it’s not because they test crazy advanced topics like multivariable calculus or anything like that.
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