ISEE Mathematics Achievement: 47 questions in 40 minutes
Mathematics Achievement is the fourth ISEE section: 47 questions in 40 minutes at Middle and Upper Level, 30 questions in 30 minutes at Lower Level, with no calculator. It is traditional math in one or more steps, from simple addition and subtraction at Lower Level up to second-year algebra at Upper Level.
Updated October 31, 2026 · by AdmitTest
The counts are from E3n's guides for Upper, Middle and Lower Levels (2021). The section sizes and clocks match the 2026-27 Quick Facts. The guides use NCTM standards for grades 6-8 at Middle Level and grades 8-11 at Upper Level. The samples below are Upper Level questions written by us; tap a choice to check.
Topics by level
| Skill area | Lower (30) | Middle (47) | Upper (47) |
|---|---|---|---|
| Whole numbers | 4-7 | 7-10 | with number sense: 5-11 |
| Decimals, percents, fractions | 4-7 | 7-10 | with number sense |
| Algebraic concepts | 4-7 | 9-13 | 13-17 |
| Geometry | 2-5 | 4-6 | 5-8 |
| Measurement | 2-5 | 4-6 | 5-8 |
| Data analysis and probability | 4-7 | 5-9 | 8-13 |
The Upper Level is mainly algebra and data. Numbers and fractions matter more at Middle and Lower.
Numbers, fractions and percents
Work these by hand until they are quick: fractions to decimals to percents, percent of a number, ratios, order of operations.
Sample · Numbers, decimals, percents, fractions · written by AdmitTest
6 is 60% of what number?
- 10
- 66
- 100
- 360
Answer: A. 6 is 60/100 of the whole, so the whole is 6 × 100/60 = 10. Answering 100 comes from misplacing the decimal point.
Algebra
Write each step on its own line. Most lost points here are small slips, such as a dropped negative sign or a term not multiplied, and the wrong choices are often built from those slips. If you have time, put your answer back into the equation.
Sample · Algebra · written by AdmitTest
y varies directly with x. When x = 8, y = 16. What is y when x = 2?
- 32
- 10
- 4
- 2
Answer: C. Since y varies directly with x, y = 2x (because 16 ÷ 8 = 2). When x = 2, y = 2 × 2 = 4. Answering 2 comes from dividing by the constant twice.
Geometry and measurement
Draw and label a figure if none is given. Know the area and perimeter of common shapes, angle facts and how units convert. Check that your answer is in the unit the question asks for.
Sample · Geometry · written by AdmitTest
A circle has a radius of 9 feet. What is its area, in terms of π?
- 81π square feet
- 36π square feet
- 18π square feet
- 9π square feet
Answer: A. Area = πr² = π × 9² = 81π square feet. Answering 9π square feet comes from forgetting to square the radius.
Sample · Measurement · written by AdmitTest
At 6 AM the temperature at a ski hill was −1°F. By noon it rose 15 degrees, and by midnight it fell 7 degrees from the noon temperature. What was the temperature at midnight?
- 7°F
- 8°F
- 9°F
- 21°F
Answer: A. Start at -1, add the rise: 14. Then subtract the fall: 14 − 7 = 7°F. Answering 21°F comes from adding the fall instead of subtracting.
Data and probability
Read the title and axes before the numbers. Know mean, median, mode and range, and write a probability as the number of wanted outcomes over all outcomes.
Sample · Data and probability · written by AdmitTest
Here are the numbers of points a player scored in 5 games: 15, 17, 19, 24, 20. What is the mean of the numbers?
- 9
- 18
- 19
- 95
Answer: C. Add the numbers: 15 + 17 + 19 + 24 + 20 = 95. Divide by 5: 95 ÷ 5 = 19. Answering 9 comes from finding the range instead.
Pacing: about 51 seconds a question
40 minutes for 47 questions is about 51 seconds each; at Lower Level it is 60 seconds (our arithmetic). Questions get harder as the section goes on, so a question that needs long working can wait until your second pass. There is no penalty for a wrong answer, so answer everything before the clock ends.
On our tests the section has all 47 or 30 questions on the real clock, and every question counts. The result shows each skill area, so you can see which to practice first.
Free ISEE practice tests, no sign-up. Every test is timed section by section and ends with the score of each section and skill.
Choose your level and startCommon questions
What math is on the ISEE Upper Level?
Number sense, algebraic concepts (the largest share, 13-17 questions), geometry, measurement, and data analysis and probability. E3n's range reaches second-year algebra.
Is a calculator allowed on ISEE math?
No, unless a student has an accommodation for one. Practice by hand from the start.
How many math questions are scored?
42 of 47 at Middle and Upper, 25 of 30 at Lower, by the 2021 guides. Students are not told which are unscored. On our tests all of them count.
What is the difference from Quantitative Reasoning?
Mathematics Achievement asks for the procedure, and its wrong answers come from process errors such as the wrong operation or formula. Quantitative Reasoning asks for reasoning, and its wrong answers come from logical errors.