Tip #22 to Get a Top ACT Math Score (page 2)
Many kids think matrices are super high-level math that they could never get, but the ACT asks only the most basic matrices questions. First, let's get the stress out. Have a good scream, hug it out, and we'll move on.
Mostly, the ACT uses matrices like ordinary charts, like the charts in Skill 15. Reading these is no different than checking the sports page. In fact, if these questions just omitted the word matrix, more kids would try them and get them right. Just including the word matrix in a question can change its ranking from "easy" to "hard."
There are a few things that the ACT might actually ask you to do with matrices.
- The first is to add matrices. This is so easy that you barely do it in school. To add matrices, you just add the numbers in each location. You'll see this in the drills.
- The second thing they could ask is for you to multiply matrices. They ask this very rarely, but the key when they do is to know that when you multiply two matrices, the result will have as many rows as the first and as many columns as the second matrix. For example, a 2-row by 3-column matrix times a 3-row by 4-column matrix will have 2 rows and 4 columns. And the middle numbers (3s in this case) must match or the matrices can't be multiplied.
- That's about it for big ol' scary matrices. If the ACT asks you to do anything else, they will tell you how to do it in the question. They won't expect you to have anything else memorized.
Let's look at this question:
Solution: This question definitely scares most kids away. But if we just drop the words matrix and matrices, it's a normal chart question. The first chart shows how many kids are in each club, and the second chart shows how the student body is divided by grades, i.e., the freshmen are 0.3 or "three-tenths" of the school. So 0.3 of the total of 20 kids in the Yoga Club must be frosh: (0.3)(20) = 6 freshmen in the Yoga Club.
Easy, right. Some kids think matrices belong in college-level Calc III, but on the ACT they are no problem!
Correct answer: K
- By definition the determinant equals ad – bc. What is the value of when m=–2 and n=3 ?
- In a recent high school election, the number of votes for three candidates is shown in the following matrix.
- The matrix below shows the lights at a stadium (sections A through H) that are on and off, with 1 representing on and 0 representing off. Based on this information and the information in the matrix, which of the following is true?
- All lights in sections A to H are on.
- All lights in sections A to H are off.
- The lights in sections A, C, and H are off.
- The lights in sections A, C, and H are on.
- There are five lampposts at the stadium.
The school paper reported that the winner received votes in the ratios shown below. Given these matrices, what is the number of juniors who voted for the winner?
- A Notice that this question asks for the determinant, which I didn't teach you. That's because the ACT defines it in the question, and you just have to follow the directions that are given. You could get this one even if you never heard of a matrix, as long as you didn't make the connection and freak out. Sometimes ignorance is bliss. On the ACT, always follow the directions that are given in a question; they give you lots of good info. So plug m =–2 and n = 3 into the matrix and follow the directions for the determinant to get (3(–2))(3(3)) – (2(–2))(4(3)) = –54 – (– 48) = – 6
- K These matrices are just charts showing data. Take a moment to understand the charts, and then the question is easy. In fact, if we dropped the word "matrix" from this question, fewer people would be intimidated, and it'd be ranked easier. So don't ever get intimidated by the word "matrix". It's just a chart of data. Angino won the election with 50 votes. The part of his votes that came from juniors was 0.2, so multiply 50 × 0.2 = 10 votes from juniors.
- C Again, just a chart of data, like Skill 15. Take a moment to understand the chart and then it's easy. A 1 tells us that the lights in that section are on, and a 0 tells us that they are off. So choice C is correct, the lights in sections A, C, and H are on.
- H To add matrices, just add the terms that are in the same spot in each matrix. So
Go to: Tip #23
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