ISEE math practice test: timed Quantitative Reasoning and Math Achievement by level
ISEE math is two sections, Quantitative Reasoning and Mathematics Achievement: 68 questions in 65 minutes at the Lower Level and 84 questions in 75 minutes at the Middle and Upper Levels, with no calculator. This free practice test has 24 original questions per level across both sections, timed at the real pace, with worked answers.
Test Ninjas wrote all 72 questions. The format, timing and content areas on this page come from E3n's ISEE Quick Facts Guide 2026–2027 and ERB's What to Expect on the ISEE guides, checked November 12, 2026.
ISEE math practice test by level
Each level has two parts that match the two ISEE math sections: 12 Quantitative Reasoning questions, then 12 Mathematics Achievement questions. At the Middle and Upper Levels, the last 5 Quantitative Reasoning questions are quantitative comparisons, as on the real test. Take one part or both. With the timer on, the clock gives you the same time per question as the real ISEE: 23:03 for both Lower Level parts and 21:34 at the Middle or Upper Level.
ISEE math practice test: 24 questions per level
Pick your level and which part to take. Answer on screen (you can change answers until you check them), then choose Check answers for your score by part and content area. No calculator: use scratch paper, as on the real test.
ISEE Lower Level math practice test (applying to grades 5–6)
Quantitative Reasoning: 12 questions
Word problems. Most need reasoning more than long calculation. Real section: 38 questions in 35 minutes, about 55 seconds each. Clock for this part: 11:03.
Mathematics Achievement: 12 questions
Grade-level skills: work each one out by hand. Real section: 30 questions in 30 minutes, about 1 min each. Clock for this part: 12:00.
Answer key: ISEE Lower Level math practice test
Quantitative Reasoning: 1. C · 2. A · 3. B · 4. D · 5. B · 6. C · 7. A · 8. D · 9. C · 10. A · 11. B · 12. D
Mathematics Achievement: 1. A · 2. C · 3. C · 4. B · 5. D · 6. B · 7. A · 8. C · 9. D · 10. B · 11. D · 12. A
Each question's worked explanation is on the page at test-ninjas.com/isee-math-practice-test. A percent correct is not an ISEE stanine.
ISEE Middle Level math practice test (applying to grades 7–8)
Quantitative Reasoning: 12 questions
Word problems and quantitative comparisons. Most need reasoning more than long calculation. Real section: 37 questions in 35 minutes, about 57 seconds each. Clock for this part: 11:21.
Quantitative comparisons (questions 8 to 12)
Compare the quantity in Column A with the quantity in Column B. Information about one or both quantities may appear above them. Every comparison has the same four choices:
A The quantity in Column A is greater.
B The quantity in Column B is greater.
C The two quantities are equal.
D The relationship cannot be determined from the information given.
Mathematics Achievement: 12 questions
Grade-level skills: work each one out by hand. Real section: 47 questions in 40 minutes, about 51 seconds each. Clock for this part: 10:13.
Answer key: ISEE Middle Level math practice test
Quantitative Reasoning: 1. A · 2. B · 3. D · 4. A · 5. C · 6. B · 7. D · 8. C · 9. B · 10. A · 11. D · 12. C
Mathematics Achievement: 1. C · 2. B · 3. A · 4. D · 5. A · 6. B · 7. D · 8. C · 9. B · 10. D · 11. C · 12. A
Each question's worked explanation is on the page at test-ninjas.com/isee-math-practice-test. A percent correct is not an ISEE stanine.
ISEE Upper Level math practice test (applying to grades 9–12)
Quantitative Reasoning: 12 questions
Word problems and quantitative comparisons. Most need reasoning more than long calculation. Real section: 37 questions in 35 minutes, about 57 seconds each. Clock for this part: 11:21.
Quantitative comparisons (questions 8 to 12)
Compare the quantity in Column A with the quantity in Column B. Information about one or both quantities may appear above them. Every comparison has the same four choices:
A The quantity in Column A is greater.
B The quantity in Column B is greater.
C The two quantities are equal.
D The relationship cannot be determined from the information given.
Mathematics Achievement: 12 questions
Grade-level skills: work each one out by hand. Real section: 47 questions in 40 minutes, about 51 seconds each. Clock for this part: 10:13.
Answer key: ISEE Upper Level math practice test
Quantitative Reasoning: 1. B · 2. C · 3. D · 4. B · 5. A · 6. C · 7. D · 8. A · 9. D · 10. C · 11. A · 12. B
Mathematics Achievement: 1. B · 2. D · 3. A · 4. C · 5. B · 6. D · 7. D · 8. B · 9. A · 10. A · 11. C · 12. C
Each question's worked explanation is on the page at test-ninjas.com/isee-math-practice-test. A percent correct is not an ISEE stanine.
0 of 24 answered
Last verified against E3n's ISEE Quick Facts Guide 2026–2027, the ISEE About and Preparation pages on admission.org, and the What to Expect on the ISEE guides for each level: November 12, 2026. All 72 questions are original and written by Test Ninjas.
Keep practicing ISEE math A free Test Ninjas account gives you full-length ISEE practice tests and an explanation for every question.
The Lower, Middle and Upper Levels each have two scored math sections: Quantitative Reasoning (section 2) and Mathematics Achievement (section 4). Reading Comprehension sits between them, and there's a 10-minute break after Quantitative Reasoning (ISEE About).
Math is the biggest part of the test at every level: 68 of the Lower Level's 127 multiple-choice questions and 84 of the 160 at the Middle and Upper Levels. Your level depends on the grade you're applying to, not the grade you're in now. The online and paper tests have the same question counts and timing, and in both you can go back to skipped questions within the section you're working on.
Two rules shape how you take both sections. There's no penalty for wrong answers, because scores are based only on the number you answer correctly, so answer every question. And calculators are not allowed unless a student has an ISEE-approved accommodation (Quick Facts Guide).
How much time you get per ISEE math question
You get roughly a minute per question in every ISEE math section. Mathematics Achievement at the Middle and Upper Levels is the tightest, at about 51 seconds a question; Lower Level Mathematics Achievement is the most generous, at exactly 60 seconds.
Time per question = official minutes ÷ official questions. The practice clock is 12 × that pace, rounded to the second.
Section
Real time per question
Clock for this page's 12 questions
Lower Level: Quantitative Reasoning
55 seconds
11:03
Lower Level: Mathematics Achievement
1 min
12:00
Middle Level: Quantitative Reasoning
57 seconds
11:21
Middle Level: Mathematics Achievement
51 seconds
10:13
Upper Level: Quantitative Reasoning
57 seconds
11:21
Upper Level: Mathematics Achievement
51 seconds
10:13
That surprises many Middle and Upper Level students: Mathematics Achievement feels like school math, but it has 47 questions in 40 minutes, so there's no time for long, careful work on every problem. Quantitative Reasoning gives slightly more time per question, and its questions are built so that a good approach is faster than brute-force calculation. If the timer shows you running short, read ISEE time management strategies, and remember that a blank answer can't be right, while a guess might be. See why to guess on the ISEE.
Quantitative Reasoning vs Mathematics Achievement
Quantitative Reasoning measures how you think with math, often with little or no calculation. Mathematics Achievement measures the math you've been taught, and more of its questions need you to carry out a calculation. Both sections draw on the same content areas: numbers and operations, algebra, geometry, measurement, and data analysis and probability, plus problem solving (What to Expect on the ISEE).
Quantitative Reasoning asks you to estimate, find the rule in a pattern, compare quantities, interpret data and reason about probability. A typical question can be solved in a few lines if you see the structure. In question 4 at the Middle Level, you don't need any real rectangle: doubling one side and tripling the other multiplies the area by 6.
Mathematics Achievement looks like a school math test: compute, solve, simplify, convert. Some questions use math vocabulary (median, obtuse, factor), and wrong answers are built from common procedural mistakes, such as doing operations in the wrong order.
Measurement has one rule worth knowing. ERB's guides say that when a question needs a U.S. customary conversion (feet in a mile, ounces in a pound), the conversion is given in the question. Metric conversions within the same unit family, such as centimeters to meters or liters to milliliters, are not given, so you need to know them. Questions 8 and 11 at the Lower Level test exactly that.
Quantitative comparisons appear only in Middle and Upper Level Quantitative Reasoning. Each one shows a quantity in Column A and one in Column B, and the answer is always one of four fixed choices: A is greater, B is greater, they're equal, or the relationship can't be determined. A short method handles most of them:
Read the information above the columns first. "x is a negative number" or "0 < x < 1" usually decides the question (Middle question 9, Upper question 12).
If both columns are only numbers, D is impossible. Two fixed numbers can always be compared, so the answer is A, B or C. ERB's guides tell you to check first whether you have enough information to compare.
Simplify or estimate instead of calculating fully. To compare √50 with 7, compare 50 with 49. Leave π in both columns.
When a column has a variable, test several allowed values: a positive whole number, 0 or 1 if allowed, a negative number and a fraction. If two allowed values give different results, the answer is D (Upper question 9: x could be 4 or −4).
Do the same thing to both columns. Adding, subtracting, or multiplying by a positive number keeps the comparison the same. Don't multiply or divide both columns by a quantity that might be negative.
ERB lists the same five content areas for both math sections at every level; what changes is the grade level of the skills. The lists below are our summary of the topics you should be ready for in each area, based on the What to Expect guide for each level. They're not an official checklist, and a real test won't cover every item.
Lower Level (applying to grades 5–6)
Numbers and operations: place value, rounding and estimating, all four operations with whole numbers, factors and multiples, comparing and adding fractions, decimals, simple percents.
Algebraic concepts: number patterns and input-output rules, one-step equations with an unknown, order of operations.
Geometry: angles (acute, right, obtuse), perimeter and area of rectangles and squares, symmetry, faces, edges and vertices of solids.
Measurement: elapsed time, money, metric units, U.S. units (with conversions given).
Data analysis and probability: tables and bar graphs, mean, median, mode and range, the probability of a simple event.
Numbers and operations: negative numbers, operations with fractions, mixed numbers and decimals, ratios and rates, percents including percent change, exponents, primes and factors.
Algebraic concepts: writing and solving one- and two-step equations, simplifying expressions with the distributive property, patterns and simple inequalities.
Geometry: angle sums in triangles and polygons, circles (circumference and area), the coordinate plane.
Measurement: perimeter and area of composite figures, volume of rectangular prisms, unit rates and speed, conversions.
Data analysis and probability: mean, median, mode and range, averages from totals, the probability of single and combined events.
Use your results to decide what to study, not to predict a score. A percent correct on 24 questions is not an ISEE stanine. On the real ISEE, the number of questions you answer correctly in a full section becomes a scaled score, which is compared with students applying to the same grade to give a percentile and a stanine from 1 to 9 (ISEE score reports). The ISEE score calculator shows how those scores relate, and ISEE stanines explained covers what schools see.
Read the content-area table first. The official score report also breaks each section into subsection categories, so a weak area on this page is worth fixing before test day. The study-next list links our pages for your weakest areas.
Compare the two parts. Low Quantitative Reasoning with solid Mathematics Achievement usually means the skills are there but the reasoning shortcuts aren't. Practice estimating, testing values and reading what the question really asks. The reverse usually means a skill gap: relearn the procedure, then drill it.
Sort every miss by its cause. Didn't know the skill, made a slip, or ran out of time. Each explanation names the trap the wrong choices are built on, which tells you which one it was.
Check your pace. If you scored well untimed but ran short timed, the fix is speed and question order, not more content.
Don't retake the same set right away. You'll remember the answers. Re-solve your misses from scratch a few days later, then check your progress with fresh questions: another level's set, our daily practice pages or a full-length test from the free ISEE practice test page.
A 3-week ISEE math plan
Spend week 1 finding and fixing gaps, week 2 building Quantitative Reasoning speed, and week 3 practicing under real time. About 30 minutes a day is enough for this plan; add time if your test date is close.
Week 1: find and fix the gaps
Day 1: take both parts of this test at your level, untimed. Note your two weakest content areas.
Days 2–5: one weak area a day. Re-solve your misses in it without looking, then do 10 to 15 questions on that area from the pages in your study-next list.
Day 6: make a one-page sheet of the rules and formulas you forgot. Use the formula sheet as a checklist.
Day 7: rest, or a short mixed review.
Week 2: Quantitative Reasoning
Days 8–10: word problems: before calculating, write what the question asks for. Estimate first and eliminate choices that can't be right. See ISEE word problem strategies.
Days 11–12 (Middle and Upper): quantitative comparisons with the five-step method above, 10 a day. Lower Level: more patterns, estimation and data questions.
Days 13–14: a timed set of 12 from our Quantitative Reasoning practice at the real pace (about 57 seconds a question, 55 at the Lower Level).
Week 3: work at the real pace
Day 15: take this test again with the timer on. Your misses from week 1 should be fixed; any new ones are your last targets.
Days 16–17: timed Mathematics Achievement drills from our daily practice. Middle and Upper: aim for about 50 seconds a question.
Day 18 or 19: a full-length practice test with all sections, from our free ISEE practice test page, so you feel where the math sections fall in the day.
Final days: light review of your one-page sheet. No new topics the night before.
Frequently asked questions
No. The ISEE Quick Facts Guide lists calculators among the prohibited materials, unless a student has an ISEE-approved accommodation for calculator use. Scratch paper and pencils are provided at test centers for the online test, at-home testers keep four sheets of scratch paper, and on the paper test you can work in the unprinted space of the test booklet. Practice the questions on this page by hand.
The Lower Level has 68 math questions: 38 in Quantitative Reasoning (35 minutes) and 30 in Mathematics Achievement (30 minutes). The Middle and Upper Levels have 84: 37 in Quantitative Reasoning (35 minutes) and 47 in Mathematics Achievement (40 minutes). Math is more than half of the multiple-choice questions at every one of these levels.
You can print this page as one. Choose a level and part, then use the print button: the print layout drops the site header and controls, keeps each answer and explanation in a collapsed box under its question, and adds an answer key on the last page. For a full-length printable ISEE with all five sections, see our free ISEE practice test page. ERB's free What to Expect on the ISEE guides also include a paper practice test for each level.
Quantitative Reasoning tests how you reason with math: estimating, spotting patterns, comparing quantities and interpreting data, usually with little or no calculation. Mathematics Achievement tests the grade-level skills you have learned in school, so more of its questions need real calculation and some use math vocabulary. Both draw on the same content areas: numbers and operations, algebra, geometry, measurement, and data analysis and probability.
No. At the Lower Level, Quantitative Reasoning is all word problems. Quantitative comparisons, where you compare Column A with Column B and choose from four fixed answers, appear only at the Middle and Upper Levels, alongside word problems.
No. A percent correct on a 24-question practice set is not a stanine. The real ISEE turns the number of questions you answer correctly on a full section into a scaled score, then compares it with the scores of students applying to the same grade to give a percentile and a stanine from 1 to 9. Use your results here to decide what to study. Our ISEE score calculator shows how raw scores, percentiles and stanines relate.
The format is the same: 37 Quantitative Reasoning questions in 35 minutes and 47 Mathematics Achievement questions in 40 minutes at both levels. The content is more advanced at the Upper Level, with more algebra, functions and multi-step geometry. Each student is compared only with students applying to the same grade, so a harder test does not mean a lower percentile.
No. Test Ninjas wrote all 72 questions on this page to match the format and content areas of the ISEE math sections at each level. None is copied or adapted from an official ISEE test. ERB publishes its own sample questions in the What to Expect on the ISEE guides, and E3n offers a free online sample test for each level on admission.org.