Can you pass the mathematics GRAD test for high-school students?

Minnesota Graduation-Required Assessments for Diploma (GRAD) sample test provided by MN Assessment portal. 2012 MN GRAD results from the Minnesota Department of Education. Calculator designed by Scott Lewis from The Noun Project.

Note: An earlier version of this test showed an incorrect answer for question 19. The answer has been corrected.

Comments (27)

  1. Submitted by Tim Milner on 12/06/2012 - 09:58 am.

    22 of 22

    in a little less than 20 minutes. Not bragging at all – as middle aged man with a BA in chemistry and MBA who has worked his entire life in a manufacturing/quality assurance environment, I would expect not to miss too many high school math questions. (If you start in with calculus, I will run for the hills!!)

    Much more important, from my perspective, is the relationship of the questions to the job functions that most of my employees perform each day. I would say that 12 or so of the 22 questions were similar to the math skills my employees need to use every day in figuring out percentages, fractions, etc. The other 10 or so questions were at a higher level of math complexity than what they would normally have to do during a normal work day.

    Does anyone know what the score (or the percentage of correct answers) is required to pass?

    • Submitted by Rachel Kahler on 12/06/2012 - 10:31 am.


      At least that’s what it said when I finished.

      • Submitted by Tim Milner on 12/06/2012 - 12:05 pm.

        80% is far too high

        a score to pass the test if the goal of the test is functional math skills. Some of the questions are simply too hard focus on math terms that are not commonly used. (We use mean all the time – we never use median. I would expect not one employee to know the difference in application)

        My guess is most of my supervisors/managers would not score 80% or above – and yet – they are extremely competent in the math skills needed to do their jobs very well.

        I am going to ask them (there are 6) to take the test later today and will post scores later.

        • Submitted by Alan Palazzolo on 12/06/2012 - 02:22 pm.

          The test is weighted differently each year.

          As noted when you complete the test, the passing grade is based on a weighted scale as determined each year.  We used 2012 results as our base line, which was 80%.  Keep in mind, though, this test is not the one from 2012, it is only a sample test, so things don’t match up perfectly.  So we are guessing a bit on whether a 80% would pass this specific test.  See the links in the footnote right below the test for more details.

          • Submitted by Rachel Kahler on 12/06/2012 - 02:36 pm.


            Modern calculators have a lot of the functions in this test built in. Pretty much plug and play. I used the basic calculator on my computer–a graphing calculator would have made things much easier.

        • Submitted by Tim Milner on 12/06/2012 - 06:12 pm.

          They scored

          between a low of 10 and a high of 15. Almost no one got the graphing questions. But everyone got the fraction and percentage questions – things they do each day.

          If the purpose is to test competency for really world jobs, these questions are too hard.

        • Submitted by Donald Larsson on 12/11/2012 - 05:46 pm.

          Where the children are all above average

          I’m no math whiz, but the difference between mean and median averages is an important distinction in a society driven by statistics. Take, say, 99 random individuals plus Bill Gates and calculate the “average” income of all 100. The mean will look pretty good. The median, I suspect, will not be as impressive.

  2. Submitted by Paul Udstrand on 12/06/2012 - 10:06 am.

    This test is far too difficult

    NO ONE fills bird feeders using algebra, nor would it even be rational to do so. This is a test of math geekiness, not likely required math skills.

  3. Submitted by Dan Fehler on 12/06/2012 - 10:27 am.

    Question 16

    Someone explain number 16. I don’t understand how I got it wrong.

    • Submitted by Rachel Kahler on 12/06/2012 - 10:34 am.

      Need to know the terminology

      The mean, or average was 53. The median is the number midway between the highest and lowest numbers–the difference between the highest number and lowest number is 16, so half is 8. Add that to the lowest number (or subtract from the highest number) and you get 53. None of the others were equivalent in meaning or results.

      • Submitted by Dana Bacon on 12/06/2012 - 01:28 pm.

        Correction re. the median calculation

        That question could be used as a vocab example for pedantry. Here’s what the test makers really hoped students would know: “If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values.” Since 52 and 54 were the 5th and 6th numbers in the list, their mean is 53 – just like the list as a whole.

  4. Submitted by Rachel Kahler on 12/06/2012 - 10:30 am.

    I passed

    It wasn’t easy, and I didn’t cheat. At least, not really. I passed, getting 2 wrong (my own fault for not thinking the problems through). Is this doable for all high school students…I don’t know. I’m inclined to say, it depends. If a student looked at this test and did the problems without critically thinking about them, it might be quite hard. The top of that scoreboard was a doozy. However, you CAN cheat without cheating. The angle of view from an observer 5 feet off the ground was 50 degrees. That indicates that the triangle is not “square” because the angle is greater than 45 degrees. That means the height of the vertical “leg” of the triangle is greater than the horizontal one, which is 16 feet, and you have to keep in mind that the observer is 5 feet from the ground. Adding 5 feet to a “leg” that must be greater than 16 feet results in an answer that must be more than 21 feet. There was only one answer that fit that bill.

    I do take exception with question 15, though. I believe the correct answer is not available. I believe it should be 69, not 71. But, one can also cheat without cheating on that one. Every odd game (e.g., 1, 3, and 5) added 11 sales to the previous odd game after game 1. That means that game 7 should have 66 sales and game 8 must have more. However, the even games (2 and 4) each showed sales ending in 9–game 2 had 49, game 4 had 59. There is not a clear pattern that links the even games and odd games, so I was inclined to think that they must show separate patterns. Since 69 was not available, the next closest answer that might fit a pattern would have been 71. 71 would have been correct if game 2 showed 48 sales instead of 49 (of course, the graph was not marked finely enough, so it’s possible that it was simply hard to distinguish 48 from 49).

    As far as language barriers being an issue, I can see where literacy would be a problem. However, the key words in each of these problems appeared to be mathematical terms. A student that had learned the mathematical terms should be able to pick out the keys in MOST of these problems, but there were a few that appeared to be an issue for those with limited English language skills and/or literacy skills. However, if you are unable to read at the level of these math problems, and don’t have a learning limitation that could provide an allowance on this test (as provided by MN law), then you’ve got other problems keeping you from graduating. Of course, there’s the matter of identifying all students with learning limitations that affect reading skills…

    So, is the GRAD math test an appropriate gate for ALL students? Probably not, especially if they’re not taught how to think outside the box (or rectangular prism). I can also imagine that in districts with limited funds and/or areas where the students come from families with limited resources, students that have learning limitations that affect their ability to take the test for reasons other than math skill would definitely get the short end of the stick due to lack of identification.

    • Submitted by Rachel Kahler on 12/06/2012 - 02:42 pm.

      Question 19

      I note that the answer to question 19 has been changed. I had it correct the first time ’round, but the new answer would have resulted in me getting 3 wrong. However, I don’t think the new answer is correct. Does anyone have a calculation that results in the new answer? My calculation would be 1/4 x 1/4 x 3/4.

      • Submitted by Duncan Davidson on 12/06/2012 - 06:10 pm.

        Your math includes just blue/blue/not-blue. You can also get blue/not-blue/blue or not-blue/blue/blue. That leads to 9 favorable outcomes out of the 64 possible outcomes.

    • Submitted by Daniel Olson on 12/07/2012 - 02:12 pm.

      That fuzzy graph question was frustrating…

      “I do take exception with question 15, though. I believe the correct answer is not available. I believe it should be 69, not 71.”

      I got 69 also. I guessed 71, though since it wasn’t an option.

  5. Submitted by Bill Gleason on 12/06/2012 - 11:50 am.

    I’d strongly suggest

    that anyone who has not done so please read the accompanying article in today’s

    Few would likely mourn an end to Minnesota’s high-school exit tests

    What is particularly striking is:

    “A final irony: Mustering an impressive math score on the ACT turns out to be significantly easier than passing the GRAD. Indeed a number of Minnesota colleges and universities accept lower scores for admission.

    Passing the state test is equivalent to an ACT math score of 22, four points higher than a score many schools consider four-year college eligible. A fourth of students accepted to Minnesota four-year colleges had an ACT score of 18 or lower.”

    This test is definitely overkill.

    • Submitted by Rachel Kahler on 12/06/2012 - 12:56 pm.

      ACT score of 18 or lower

      While it’s possible it’s overkill (I’m not sure who did the calculations to determine that passing is the equivalent of an ACT score of 22), looking at it the other way, is an ACT score of 18 being acceptable at universities really a good thing? And if it is, is the portion of students getting less than a score of 18 your average student or are they given some leeway due to learning difficulties? Really, for your average student, a score of 18 is not something to write home about. A score lower than 18 is not good. Keep in mind, because colleges have had to rely more and more on tuition, it is in their interests to accept more students, even if it means having lower standards. In fact, about a third of college students drop out after their first year and half never graduate. And, in fact, if you have to take “catch up” courses or can’t handle the “academic rigors” of college, you’re already on the road to college failure. (;

      That being said, as has been mentioned elsewhere by posters on MinnPost, not every high school graduate is or should be college-bound. There is little reason to expect them to all be ready and able to go to college. That doesn’t mean, though, that the standard should necessarily be lowered. The average ACT math score is about 21. It should not be unreasonable to hope to hit an average ability that reflects this. IF the equivalent of passing this test is an ACT math score of 22 (really, I want to know how this was calculated), then we can expect at least half of all students to fail it. But it’s somewhat less than that; not a lot, but somewhat. Kids take it in the 11th grade and have 3 chances to pass it. If students retake the ACT, they tend to get a higher score–sometimes much higher. So–are kids retaking the GRAD? If so, how do their scores change? In the end, how many fail all 3 times? Those are the kids we need to evaluate and identify why and how things might be adjusted to provide them with a more realistic goal or an alternative goal. I don’t think that we should lower the standards so that the more advanced students are not challenged.

  6. Submitted by Pat Thompson on 12/06/2012 - 02:27 pm.


    Which was a failing grade. Embarrassing, I know, but I believe in honestly reporting how adults do on these tests we require of students.

    I have completely forgotten everything about graphing and slopes, and so pretty much got all of those wrong. I’m pretty sure I would have passed this in high school, however, possibly with 90% or better, based on my grades in algebra and geometry (yeah, yeah, easy to say, I know). I bailed out of math after the combined trig/algebra 2 class (11th grade) class.

    The parts of the test that were no problem for me required the kinds of skills and knowledge I’ve used as an employed adult for the past 34 years, minus a couple of errors where I didn’t read the question closely enough.

  7. Submitted by Chelle Blakely on 12/06/2012 - 06:00 pm.

    I flunked

    Yes, I could have passed this when I left high school or in college when I was struggling through calculus. But all those teachers lied. Since I ended up not working in my science major, I have NEVER used this stuff. I have been well employed, a productive member of society, and paid my taxes without ever calculating a slope.

    I am curious whether this test has ever been validated? Who designed it and for what purpose? Do the results accurately measure its intention?

    I support strong math standards. The skills I would like to see required are those that support critical thinking and cause and effect. We need skills like reading charts and graphs, basic statistics, and drawing valid conclusions – especially when the conclusion is that no conclusion can be drawn. Politicians and journalists are horrible at this. The number of murders went up by 20. Sensationalism sells newspapers, but do we need to panic until we have looked at the long term trend, compared this to other similar sized cities, factored in mass shootings, etc? (Yes, I’ll grant there is a possibility to look at the slope line of the trend there.)

    I suggest our legislators, obviously a group of people who have done well for themselves in our society, take the entire test themselves before they require it for high school gradation.

  8. Submitted by Paul Udstrand on 12/06/2012 - 07:51 pm.

    This is not the ACT or a substituion for it

    Even if you go to college, few students will need this level of math literacy and people seem to be forgetting that many colleges don’t require the ACT for admission. The function of K-12 education isn’t simply to teach math. There’s no way to you bring every student up this proficiency level without devoting a disproportionate level of instruction to math at the expense of other subjects and skills. If you want a good score on the ACT, take the ACT. There’s no reason to structure a basic skills requiremtnt test on different test that students study for separately. Look, the fact is our existing adult population will score just a poorly on this test as the high school students on pretty much the exact curve if not worse. That fact proves this level of literacy is not necessary.

  9. Submitted by Joe Musich on 12/06/2012 - 08:33 pm.

    teachers ?

    Interesting this was not posted by teachers! One could speculate that teachers have given up trying to be heard.

  10. Submitted by Dan Landherr on 12/07/2012 - 10:10 am.

    20 of 22 in 15 minutes

    And my big errors were with terminology (what is the definition of “price” versus “cost”). This test seems like something I could have passed in the 10th grade rather easily. Multiple choice makes it that much easier. I have used nearly all of those calculations in daily life since leaving high school in my personal life. Calculations I need to be able to perform for my job are understandably much more difficult.

    I’ll take issue with the poster who claimed we’re spending too much time on math to the detriment of other subjects. I think it speaks more to a personal dislike of math than it’s importance in becoming a successful citizen. In the most recent election we had candidates who both claimed that their economic plan was mathematically correct while claiming the opponent was incorrect. They both had authoritative think-tanks backing their calculations. If you can do the math yourself the decisions become clear. If not you are left with voting for the guy with the best smile.

  11. Submitted by Paul Udstrand on 12/08/2012 - 09:36 am.


    I didn’t say we ARE spending too much time on math, I said we would have to spend a disproportionate amount of time on math if we wanted 100% our students to pass this test. Currently 40% are failing this test and that’s out of the 77% make it that far. Ya know it’s kind of funny, a bunch of math folks are claiming that math instruction produces superior intellects yet they are failing to grasp the basic problem here. If we were to actually implement this requirement we would deny high school diplomas to 50% our student after 12 years of education. Do you really think 12 years of education are a complete wast of time if a student can’t pass THIS test? Look, MN public schools have produced more than their fair share of very successful individuals over the last 50 years without ever requiring this level of math proficiency.

    This is exactly how requirements like this produce circular tunnel vision. You create a requirement and a test to meet it and then pretend that test is the only meaningful outcome of 12 years of education. Once it’s required everyone has to pass it and they all have to pass it because it’s required.

    Ironically it’s something of a math problem. We’re not dealing with a population of math experts, we’re dealing with a population that will distribute along a normal bell curve of math ability and interests (ranging from expertise to minimal ability rather than complete illiteracy), THAT’s why 40% of the students are failing this test, not simply because the system is failing to teach the math.

    The proposition that math expertise produces better citizens is simply math fetishism. People like Alan Greenspan led this country into the Great Recession, and they did it using very complex math formulas. A population of math experts would not solve all of our problems. For the record, no one is promoting math illiteracy so it’s a false dichotomy to claim that we either have to require this test or abandon all math instruction entirely.

    • Submitted by Dennis Wagner on 03/24/2016 - 09:00 pm.


      Flunked the test! Why wouldn’t you use a compass to do the driveway? Seems the questions were 8 mile circular routes to get to a 20 step solution. Meaning, not practical analytical thinking, in appropriate use of tools. No wonder our kids can’t solve real world problems, they don’t get real world tools. Hats, you have a set up charge of $40, and a series of volume discounts, if you assume what a future price would be, bad guess, “Get a quote from the supplier”

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