These free diagnostic tests help you discover your child or student's level in math, and to find out EXACTLY where they have gaps (if any). They are endofyear (EOY) tests — in other words, meant to be taken AFTER studying the particular grade.
While the tests ARE placement tests for Math Mammoth complete curriculum, they work equally well as GENERIC math assessment tests.
Using the tests will allow you to tailor the instruction to help the child/student right where they need help the most. You can EASILY find out if your student has not learned specific topics, because the tests group the questions by topic. Just look at the test results per "sections" of similar problems (addition, multiplication, measuring, geometry, place value, problem solving).
You can always send me your child's test results if in doubt. (Just send me the point counts for each test item.)
To start, look over the tests and try to find the highest level one that you THINK your student or child will pass. Then you would naturally administer that test.
The video below explains the basics of HOW to use these tests:
This table shows the possible score ranges and how to interpret the result:
Score  Meaning 

90% or more  Administer the next higher level test. 
80% to 89%  The student can go on to the next grade level in Math Mammoth. 
70% to 79%  The student can probably go on to the next grade level in Math Mammoth, but may need help in filling in gaps. Use your judgment. 
50% to 69%  The student can possibly be placed to the grade level of the test. Or, you might administer the next lower level test in order to get a fuller picture of what the student knows and doesn't know. 
less than 50%  Administer the next lower level test. 
However, it's quite possible that just that one test will not give you a good overview of what the student has mastered. So don't be afraid of administering two or even three tests — or parts of tests. For example, let's say a student gets 70% on a test, and in particular, they get a low score in the geometry section of the test. In that case, it is beneficial to administer the GEOMETRY sections of the next lower level tests also, in order to find out how "large" a gap they have in geometry.
Sometimes, a student who is seriously behind can get a low score on even THREE subsequent tests. Basically, their skills and knowledge are "all over the place" so to speak. Such students can benefit from a tailored approach where the materials they will study will be exactly matched to the gaps they have.
One more important thing. To reduce the testtaking stress, don't put any strict time limit for the completion of the test. We don't want students to build any anxiety over this placement test or tests. Now, some children have already developed anxiety towards testtaking and/or towards math in general. In such cases, it might be best to avoid even these tests, or at least postpone the testtaking until the anxiety has subsided somewhat.
These are allmetric and formatted to Letter size paper. For grades 12, the tests use Canadian coins and bills.
The international versions are formatted to A4 paper size, use a space for thousands separator (35 230), and only use metric units. The tests for grades 1 and 2 include a section on counting coins, which is with Australian currency. The rest of the tests don't have questions about coins or bills, and use the "$" symbol for currency.
The versions below are formatted to A4 paper size and only use metric units. They use British coins and bills.
The versions below are formatted to A4 paper size, use a space for thousands separator (35 230), and only use metric units. They use euro coins and bills, and a decimal comma for money amounts.
Tip: If you notice your child has problems with one or two concept areas in a particular test, but otherwise does fine, you can use Math Mammoth Blue Series books to "fill in those gaps". You can also email me with your test results if you have trouble deciding which Blue Series book you should use for such remedial work.
Math Mammoth gradelevel review workbooks can also be used to pinpoint areas of weakness or to review a whole grade level of topics.
Here is an example of one student's test results and the placement advice I gave to the parent of this student.
Background: the student began homeschooling the same year as the tests were taken and is technically in 7th grade. She had started doing Teaching Textbooks Algebra 1. However, the parent noticed that she didn't know some basic fraction information, decided to look for a supplement, and came across Math Mammoth.
The student took three endofyear tests: for grade 6, grade 5, and grade 4. She did not do very well in the grade 6 test, but you can see her work for grade 4 and grade 5 tests in the links below. If you decide to send me your child's test results, it is not necessary to send me the complete test like this person did, but it makes a good example. Most people send me only the point counts for the various test items.
And here is my assessment and recommendations:
Student attempted the 2nd grade EOY test:
Add & Subtract 2A, Add & Subtract 2B, and half of Add & Subtract 3.
Student attempted the 3rd grade EOY test:
(possibly Add & Subtract 2A) Add & Subtract 2B, Add & Subtract 3, Multiplication 1, and Division 1.
Student attempted the 4th grade EOY test:
Add & Subtract 3, Multiplication 1, Division 1, Multiplication 2, and Division 2.
Area of lack  Remedial book 

Addition and subtraction facts within 010  Subtraction 1 
Addition and subtraction facts within 018  Add & Subtract 2A 
Place value of tens and ones  Place Value 1 
Place value of 3digit numbers  Place Value 2 
Place value of 4digit numbers  Place Value 3 
Mental math  addition and subtraction strategies for 2digit numbers  Add & Subtract 2B 
Mental math  addition and subtraction strategies for 3digit numbers  Add & Subtract 3 
Multiplication concept, multiplication tables, or simple multiplication word problems (grade 3)  Multiplication 1 
Multidigit multiplication and related word problems (grades 45)  Multiplication 2 
Basic word problems  Foundational Word Problems 
Prime factorization, LCM, GCF (grades 46)  Multiplication & Division 3 
Basic division concept (singledigit divisors) and related word problems (grade 3)  Division 1 
Long division and related word problems (grades 45)  Division 2 
Reading the clock, telling time, or elapsed time  Clock 
Any measuringrelated difficulty within grades 13, including not knowing metric units  Measuring 1 
Geometric concepts within grades 13  Early Geometry 
Geometry (grades 47)  Geometry 1 and Geometry 2 
Fraction concepts within grades 24  Introduction to Fractions 
Fraction topics within grades 56  Fractions 1 and Fractions 2 
Basic concept of decimals (grades 34)  Decimals 1 
Decimal arithmetic (grades 56)  Decimals 2 
Ratios and proportions (grades 67)  Ratios, Proportions & Problem Solving 
Percent (grades 67)  Percent 
Integers (grades 67)  Integers 
Statistics (grades 57)  Statistics & Probability 
By Maria Miller
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