Math Tips from UWorld

2/6/2019 4:34:03 PM
Hello, UWorld math author here. With the ACT exam coming up this weekend, I thought it could be helpful to give you all some insight into some trends we've noticed based on user performance, specifically regarding concepts that students particularly struggle with in our QBank.

For each topic, I will provide some example question numbers. In the Create Test mode of our desktop app, there is a Custom mode, where you can search by specific question numbers. Enter those numbers in that box to search for them specifically. If it happens to be a question question you've already taken, it won't show up, and you'll have to use the Search feature in the menu on the left side of the screen. Sorry, mobile users, but our Android and iPhone apps don't have the Custom Test feature.

Fundamental Counting Principle

Something that tends to trip up students is how to count a number of options using the Fundamental Counting Principle.

This question in its simplest form can be something like "If a restaurant has 3 soup options, 4 sandwich options, and 5 side dish options, how many different combinations of orders are there?" And the answer would just be 3 * 4 * 5 = 60. (see questions 502996, 503446, 503359)

However, this topic can get even more complicated when some analysis is to be performed on the options. Sometimes one of the values is fixed. For example, consider he restaurant mentioned above. The ACT could give a question like "Jeremy knows he wants to order a BLT for his sandwich. How many possible orders can me make?" In this case, there is only 1 option for the sandwich, so the number of possible orders Jeremy can make is 3 * 1 * 5 = 15. (see questions 503301, 503312, 503313)


Matrices

Matrices are a fairly high-level concept that consistently appears at least once on every recent TIR exam. Moreover, they tend to be some of the lowest-performing questions in our QBank. Knowing how to add or subtract matrices (questions 502871 and 503358), multiply matrices (502917), calculate the determinant of a 2x2 matrix (502876 and 503617), or know when a matrix product is defined (504107) could help elevate your score.

The ACT also tends to combine matrices with simple algebra, requiring you to solve for a variable in a linear or possibly even quadratic equation after manipulating matrices. These can be some of the trickier questions on the test, so it may be helpful to practice such questions. (503722, 503905, and 504282)


Tomorrow, look for some helpful tips on Polynomials. Good luck with your ACT prep!


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