Hi there.
It has been a while since I've done a math post. In this one, I cover some ACT math preparation questions.
The ACT is a standardized test that is for college admissions for the United States. It assesses skills in English, Mathematics, Reading and Science (optional).
Since I am based in Canada, the ACT is not mandatory for applying to Canadian universities. There are a few high school students in Canada that do aim for universities in the United States.
For the mathematics portion of the ACT, test takers have 50 minutes for 45 questions. This is just over 1 minute per question. I have heard the math section is not that difficult for Canadians but I wanted to take a look at some of the ACT math questions.
Math text and images rendered in LaTeX (lay-tech) with QuickLaTeX.com.
This first question involves the average/mean formula. Add up all 5 scores then divide by five. Then equate this to the mean score of 72, then solve for x.
The answer is D or x = 90.
Question 4
For question 4, note that the 3 angles in a triangle add up to 180 degrees. We know that angle B is 143.6 degrees and the last 2 angles are the same.
The angle measure of A is 18.2 degrees or letter F.
Question 5
This question is simple for a grade 12 math student. Use grade 10 math to factor the quadratic to get (x-6)(x+5). Answer C.
Question 6
This question may be unfair. I know that matrices are not in the Ontario math curriculum. The answer to this is actually simple given that the student is taught matrices.
Multiply the 5 in front of the square matrix to each entry to get the answer J.
Question 7
This question can be confusing. The test taker has to realize that you have to get the greatest common factor (GCF) of 30 and 75. The answer is B, 15.
Fifteen members can have 2 tickets each which equals 30. The same 15 members have 5 snack vouchers each to which equals to the total of 75.
Question 8
With this question, you have to interpret the scenario and put it as a formula. Do 35 multiplied by the length of the skid (l). Then take the square root of the result.
From here, you have to simplify square roots to obtain of the answer options.
The answer is H.
Question 18
Not all high school math courses teach complex numbers. This question may be weird and unanswerable for some.
The square root of negative 1 is the complex number i. For this one, the answer is J or 3 + 4i.
Answer is J.
Question 19
For this question, it is obvious that the arithmetic sequence formula needs to be used. One problem could be trying to remember the formula for the n-th term in an arithmetic sequence.
Let d be the common difference in the arithmetic sequence, t_{n} be the n-th term of the sequence, and n be the number position of the n-th number in the sequence.
Answer B.
Question 24: Note that 180 degrees is pi radians. Convert the 40 degrees to radians.
The answer to Q24 is G.
Question 25: This question is simple. When you do minus 4, it means you move the f(x) function down by 4 units. Answer is A.
This one is a simple probability question provided that the student has learned probability. Two mutually exclusive events mean that the 2 events cannot happen at the same time. That is P(A and B) = 0. Answer J
This question is from probability and statistics. To be more specific, the topic is on the average/mean. This is a little different as you have a frequency table for the data.
Do number of cities times the number of tourists for each of the 3 cities and then add them. After that, divide that by 100.
Answer is C.
This question involves probability with expected values. There is a lot of text in the question.
You have two outcomes, coin C being faceup or coin being face down. The faceup coin probability is triple of the coin being face down. It is okay to assume that the probability of the coin being faceup is 3 out of 4. Coin facedown probability is 1 out of 4.
| Outcome | Probability | Payout |
|---|---|---|
| Coin Faceup | 3/4 | $1 |
| Coin Face Down | 1/4 | $2 |
To compute the expect value, you have to multiply the probability with its respective payout. Then add the products together.
Answer is A or $1.25.
This ACT math section covers a lot of different math topics from algebra, advanced functions, basic number theory, probability and statistics.
In practice, I got two questions wrong out of 45. However, I did not time myself. Fifty minutes for 45 questions could be tough. You have to take some time to recognize type of math the question is from. Then you have to think of the right approach/strategy to get the answers. To do this fast is not easy for students and even for (older) math tutors.
There are a few geometry, probabilty and statistics questions on here. They are not hard but if a student has not taken the Grade 12 Data Management course in Toronto (or Province of Ontario) then the test taker would not be able to answer probability & statistics questions well.
Thank you for reading.
