Can you answer these five 8th grade math questions correctly?

state math test question composite

On Wednesday the state Education Department released half of the questions from this year's ELA and mathematics state tests for grades 3-8. From the NYSED EngageNY site:

These questions have been annotated to display the kinds of thinking students are required to do in the new Common Core Tests. These documents will be helpful for better understanding the requirements and expectations of the Common Core state tests.

The Common Core and standardized testing have gotten a lot of attention (much of it criticism) over the last year. And as a result, we were curious about what sorts of questions are on these tests -- so we browsed through a few of them today. And we couldn't help but quiz ourselves a bit along the way.

We figured you might be interested in doing that, too. So we pulled five questions from the 8th grade mathematics test -- they're after the jump with the (hidden) answers.

Before we jump in: Looking at these five questions is like squinting through your fingers through a keyhole -- it's not going to provide a complete look at what's on the tests, nor is it going to provide any good perspective on the Common Core.

Here are all the sample math questions for the 8th grade test. We didn't include any of the English language arts questions from the 8th grade test because they involved reading longer passages -- here's the test if you'd like to have a look.

Explanations are direct from the sample questions.

Question 1

8th grade math test 1

(click to reveal answer)

Question 2

8th grade math test 2

(click to reveal answer)

Question 3

8th grade math test 3

(click to reveal answer)

Question 4

8th grade math test 4

(click to reveal answer)

Question 5

8th grade math test 5

(click to reveal answer)


Earlier on AOA: Are you smarter than an Albany 8th grader (circa 1882)?


3 out of 5 and I'm stunned beyond belief.

Good news! My daughter, who possesses a freshly-minted math education degree, did all these questions correctly. There's hope!

4 out of 5. (And I used a calculator to do the basic arithmetic.) Still have no idea what #3 is about. I don't know what a function is. I must have been home sick that day (in 1965) .

However, the explanations seem really abstruse to me, even for the ones I got right.

The math MA in the household got 5/5 but he disputes some of the explanations. Are these typical or are these harder than most?

This is pretty solid, appropriate stuff for 8th grade. Very impressive. I dont know why Common Core gets flak. If the US has to compete in education with the rest of the world, this is pretty much par for the course.

The key to understanding #3 is understanding that there can't be two different outputs for the same input. So the fact that 3 yields two different outputs tells us that inconsistent rules are being applied, therefore this cannot be the result of a single "function".

I have no opinion on the common core, but it is also worth remembering that any student taking this test would have studied all the math tested in this sample, and therefore would have been taught the meaning if "function" in this context.

5 of 5 and I did them in my head. These were fun. Thanks for posting.

@chrisck #3 is tricky, I had gotten it wrong until I read the explanation, and I think its about the definition of function. For any x there is one y value. Thus in the table, as there are 2 different y's for the same X, its not a function of x.


Wait, fun? Daniel your concept of fun is VASTLY different than mine. :)

5 for 5... and I agree this is where I'd want my kids to be by 8th grade.

These seem about right for 8th grade. I did all these topics back in middle school in the early 2000s, and they were in the NYS standards far before Common Core. Students should definitely be able to answer these.

Much higher-order and more conceptual than the way math was taught/tested back in the day. Perhaps future generations will be more mathematically literate.

@KM -- I think you may be right. I think the fact that I didn't know how to answer #3 is that they didn't cover this function/input/output stuff in 8th grade in 1965. And apparently there was no subsequent time in school where I would have picked it up (since as a typical girl of that era I ultimately got tracked away from STEM oriented classes).

I have okay math skills (enough to get by in life), but they aren't great. And I went to good Westchester County schools. Seems the roll out on Common Core was pretty bad, but I can't fault the goal of higher standards.

I make video games and all of these are pretty useful in my field. Anyone that says they are not doesn't want to make video games.


The third one is more of a trick question to me than a math question, so I could see how it would be missed.

4 for 4! I am not counting #3 because I take issue with the 4 options. The last table is just a quadratic function that would have a sideways U-shape. Definitions aside, x will still determine the y value(s), so still a function. Maybe they learn in 9th grade that their 8th grade lessons were not entirely true.

Got 4/5, didnt pay close attention to options in #3 - reading the answer made it obvious, non-random functions cannot have different outputs for same inputs..

On side note, i went to school till 9th grade in Russia (Soviet Union to be more precise, ages ago..) and these are about 5th-6th grade questions there..

These are fantastic questions. Numbers 1 and 2 can be done with a calculator, but they don't NEED to be. A student who understands the properties of exponents will be able to solve them quickly and easily. The test doesn't shut out students who need to rely on a calculator -- the question just becomes a different kind of exercise to them.

Number 5 isn't about reading a graph -- anyone should be able to do that. Instead the question is asking how one should interpret data and trendlines. This is a great test of true numerical literacy, without requiring any actual numerical manipulation.

Like the other commenters, I'm not as much a fan of #3 -- basically, the question seems to be trying to determine if the student knows the definition of a function. Still, at least the question is not asking "What is the definition of a function?" -- the question forces the student to apply their knowledge to a problem, rather than just regurgitating facts.

I taught high school physics for four years. My biggest complaints about students' math abilities were that they were used to only seeing math in the context of math class -- standalone problems with no application. Teaching recipes to students borders on useless. People who are "good at math" aren't necessarily born that way -- they're just taught to see the natural connections between numbers rather than how to manipulate them towards an end result. Numeracy can be taught.

The answer to "When will I ever use this?" is very plainly that "you won't" for many topics in algebra and beyond. However, English teachers never have to justify assigning Moby Dick to students, even though the likelihood of them becoming seafaring whalers is zero. Learning about literature is not about the specific content, it's about learning an appreciation for plot, metaphor, motivation, etc. Mathematics can and should be similar.

@James Cronen -- it may be that English teachers do have to justify teaching "Moby Dick." My understanding is that there is now a greater emphasis on non fiction in English classes to prepare students for work in the information age.

When I hit 'back,' it covers the answers back up! Maths are fun.

While I did get the correct answer for question #4 it was more from the process of elimination method I used when I was taking Regensts and similar tests (20-someodd years ago) than the formula in the answer. I knew it couldn't be 47 or 60 because those numbers were both used in the description of the problem (that's the oldest trick in the multiple choice book) and just looking at HNK it's clearly not the same size as either. Similarly 107 couldn't possibly be right given HNK's visible size and that of the two already given. That left 73 as the answer by default.

But shouldn't the formula be 180 - (60 + 47+FNM+GHN)?

I got 2/5 - the way i figure it is you nerds ruined the curve. Im shoving Daniel B into a locker so hard after class.

Man... I got 5 out of 5. You'd think I'd be happy except that in 8th grade when it mattered, I probably would have got 2 or 3 at the most. I was a horrible math student!

@Just A Guy... no, the formula for #4 is correct. Angle GNL (or the line GL) is 180 degrees. Given that it is split up into 3 angles on one side and 2 out of the 3 angles are given, you can deduct those from 180 to obtain the 3rd angle (FNM). This angle is exactly the same as HNK, which is evident from the picture and it is a rule when you learn geometry of intersecting lines. Hence, the answer is 180-60-47 = 73

I had 4/5 and i starts in 7th grade this year

5/5 pretty easy questions I worked them all in my head as long as you know what a function is an have basic understanding of math should have no problem. Although I I'm an engineering student. Math is a wonderful thing.

I got 5/5 and I'm in 7th grade! I think the quiz was easy but, #3 was tricky.

Both I and my 7th grader got 5/5 :). Would have been very embarrassing if he had beaten me..

..and I confess that I agree with Daniel that math is fun. On the other hand, I teach neuroscience and play boardgames competitively, my geek quotient was already stratospheric..

My parents won't let me take the AOA sample test this year because it might stress me out so I don't know if I improved since last year!

i'm in eight grade and these questions are so easy the real test is way harder.

that was too easy(im 8 grade)

I believe that question 3 is wrong because the same number could have that kind of output, for example, 3+13 then square root it, it in fact equals 4 and -4... I wonder who made that question.

4/5 not bad....even though I just started 9th grade....I didn't use the calculator and i got #2 wrong.......But I thought #3 was the so easy.

5/5 and 8th grade. The answer to the third question is in fact correct. A function never has two y-values for 1 x-value. Even if it is a square root function, you just take the positive square root of whatever is under the radical.

i swear i got 5/5 and i am in grade 8

I got 5/5 very easy questions #3 one was a simple question.

5/5 in 7th grade in my head but nice problems

#3 Was simple an input value cant have 2 different out put values. Im in the sixth grade and got 5/5

i dont know the #2
but i answer all correctly except for #2

These are all really really easy 5/5. Given I am in College Algebra, but if parent's aren't able to help there kids with these problems than Common Core isn't the problem that's for sure..

This is so easy. I am in grade 5. Why does everyone say 3 is hard. It is Sinch

3/5 and i am very happy that iam of class 6 and scored atleast 3 marks

5/5 :D

as easy as a cake

Im in seventh grade, in grade 5 we did none of that, i dunno what americans do in math, but i can tell you canadians dont do this...

so tough for 2nd grade:D

I got 5/5 and I'm in 8th grade, yet I would have known how to solve these problems in 7th grade.

I graduated HS in the 60s. Did not have algebra till 9th grade and Geometry in 10th grade. I retook some of this in a college when my daughter needed help and received As. This is all Greek to me now. do 7th and 8th graders really understand this. My son was a math genius with an IQ of 170. He may have liked this, but I think it is unfair and just plain confusing to push concepts that seem so advanced, without understanding the basics.
I am saying this as my 8th grade grand daughter is struggling with her math, and I know her father is smart, but never was taught these concepts till a later age. Yet, as he is trying to help her, as she is crying, he said that her younger daughter had this a few years ago...I don't think so.

Men usually remember stuff they had at that age, but it was really when they were older. I think it is a bunch of nonsense to push this stuff down kids throats at a young age, and when they really do not understand it. It is painful to watch this. She is a very smart girl. I am glad I am not in 8th grade now! And I went through University and Graduate with mostly As.

What is a function? That's the only one I got wrong.

Hi,I'm 8th grade and I'm from Iran I did 5 of 5 and BTW these are the easiest questions I have ever seen.
This is one of our normal questions:
(...) means it continues to
The answer is not so long.

good q i got 3/5 this is about what i am learning in 8th right now

i m solve the 5out of 5 then i am 8 grade

Im a6th grader and easily answered 4/5 of your questions. They were easy breezy.

Quite easy questions. I scored 4/5 .

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