The ISEE Mathematics Achievement section is the final math section of this admissions test. Those who excel on the ISEE are set up for success on their private school applications, so taking the time to prepare for each section in advance is worth the effort!
The ISEE (Independent School Entrance Exam, generally pronounced “isee”) is a peernormed, standardized test most commonly taken by students applying to middle and high school. To evaluate students’ reading and math skills, it consists of two ELA sections and two math sections:
ISEE Section  Time  Number of Questions 

Verbal Reasoning  20 Minutes  40 Questions (34 LL) 
Quantitative Reasoning  35 Minutes  37 Questions (38 LL) 
Break  510 Minutes  
Reading Comprehension  35 Minutes (25 LL)  36 Questions (25 LL) 
Mathematics Achievement  40 Minutes (30 LL)  47 Questions (30 LL) 
Break  510 Minutes  
Essay  30 Minutes  
Total  ~2 Hours 40 Minutes (2:20 LL)  160 + Essay (127 + Essay LL) 
Mathematics Achievement is the fourth section of the ISEE exam at all levels (lower, middle, and upper), preceding the second 510 minute break. Testtakers are given 40 minutes to answer 47 questions (so, just under a minute allotted per question).
In this deepdive into the ISEE Mathematics Achievement test, we explain the types of questions you’ll encounter on the test, strategies for working through those math problems, and the best ways to study for this section of this exam.
ISEE Math Topics
Both the Quantitative Reasoning and Mathematics Achievement sections of the ISEE test students’ math skills. The ERB (which develops the ISEE) follows standards set forth by the NCTM (National Council of Teachers of Mathematics) to determine how the ISEE tests students’ math abilities.
Each level of the ISEE tests students on a corresponding level of math knowledge; naturally, Upper Level math problems on the ISEE include more advanced mathematics concepts than on the Middle Level test. Across both math sections for all levels, the ISEE will test students on the following general concepts:
 Numbers and Operations. Understanding numbers, fractions and decimals, operations, comparing values, and relationships between numbers.
 Algebra. Understanding patterns, variables, functions, symbolic equations, and graphs.
 Geometry. Identifying, classifying, and analyzing 2d and 3d geometric objects, as well as using a coordinate plane and understanding congruency and symmetry.
 Measurement. Using formulas to make measurements of objects, converting between units, and identifying tools associated with length, weight, capacity, temperature, or time.
 Data Analysis & Probability. Analyzing and making inferences about sets of data, calculating mean, mode, range, and median, and finding probability about a scenario.
Learn more about the specific topics tested on each ISEE level on our review pages:
ISEE Mathematics Achievement Questions
The Mathematics Achievement section of the ISEE is quite similar to the Quantitative Reasoning section. The primary difference is that Mathematics Achievement has only one type of question: word problems.
Approaching ISEE Math Questions
Having a systematic approach to answer each Quantitative Reasoning word problem will help you confront and work through each question efficiently.
ISEE Math Problems: 5Step Approach  

Step 1  Do I UNDERSTAND the question?  Circle or underline important information, and write it out next to the problem.  If you get stuck, SKIP IT! Circle the question in the test booklet and answer it later.  
Step 2  Do I know which FORMULAS I should use?  Quickly write out the necessary formulas to the side of the problem.  
Step 3  Will the question take a LONG TIME to complete?  Skip it, and come back when you have time.  
Step 4  Can I INPUT VALUES to solve the question?  Use simple values such as 1, 0, and 1 to help you evaluate expressions and equations. Keep in mind all properties of algebraic and geometric concepts.  
Step 5  Can I make an EDUCATED GUESS with what I know?  Eliminate incorrect answer choices, then input the remaining answers to check your work.  
If you’re still unsure, DO NOT leave it blank. Choose the answer that makes the most sense. 
Word Problems
Each ISEE word problem is followed by four answer choices. Several of these problems may be solved without actually doing any math on paper—these questions test your ability to decipher math problems from realworld scenarios and solve them.
There is no penalty for wrong answers on the ISEE, so be sure you answer every question by making educated guesses and prioritizing problems you know.
Some word problems can take a significant amount of time to read through and solve. ISEEtakers are allotted only 57 seconds per question on this section, so conserve your time by prioritizing questions that are short, easy, or you’re most confident in answering. Once you work through the section once, go back and attempt the harder, longer questions.
Here’s an example of how to work through an upper level word problem on the ISEE Mathematics Achievement section.
1. Where does the function f(x)= x² + 7x + 10 cross the xaxis?
A. x = –5, –2
B. x = 5, 2
C. x = –5, 2
D. x = –2, –5
UNDERSTAND 
First and foremost, decide if you understand the question. If you do: write out all important information to the side of the question. If you don’t: SKIP IT and return later. 
“I know this one! I need to figure out what my values for x are when f(x), or the output, is equal to zero. 
CONTEXT 
Determine if there are any properties, rules, or formulas you know that can help. 
"I know that my output needs to be zero— I’ll replace f(x) with 0. To solve quadratics, I need to factor out the equation… so I’ll start with two parentheses."
0 = x² + 7x + 10 0 = ( ) ( ) 
LONG TIME 
Quickly determine if this question will take you a very long time to complete.
If it will: SKIP IT and return later. 
(LONG TIME) “I’ve done problems like these before, but I’m really rusty on them. I’ll come back to it later."
(SHORT TIME) “We went over this recently in class, I know exactly what I need to do!”

ESTIMATION 
Before you start solving the problem, see if estimation can help.
1. Where does the function f(x)= x² + 7x + 10 cross the xaxis?
A. x = –5, –2
B. x = 5, 2
C. x = –5, 2
D. x = –2, –5 
“I don’t think estimation will help me too much here, but I know +10 is the yintercept. My teacher also said that factors of the yintercept help determine xintercepts… my guess is that it’s the factors 5 and 2, and it has to be their negatives that are the answers…"
0 = x² + 7x + 10
0 = ( )( )
0 = (x + 5)(x + 2)
x + 5 = 0
x + 2 = 0 
How to Prepare for Mathematics Achievement Questions
The most effective way to study for the ISEE Mathematics Achievement portion is by practicing the math topics that are tested, especially by completing practice questions. The ISEE test prep process is a cycle of working through practice questions and relearning topics between benchmark ISEE exams. Based on your ISEE practice test results, you can determine which topics you have a good understanding of, versus concepts you should review more.
Make sure to use practice questions and tests designed for the ISEE exam. By practicing with questions that resemble what you’ll encounter on the ISEE Mathematics Achievement section, you’ll become comfortable with solving those types of problems. Use the strategies we’ve described above as you practice, and you’ll be familiar with what to do come test day.
In addition to regularly practicing with testspecific questions, make sure to take at least one benchmark for your ISEE ahead of test day. Not only will this help you gauge your current skills and see how much you need to improve, but taking multiple practice exams is proven to improve testtaking performance.
Personalized Online ISEE Prep
Use these ISEE Quantitative Reasoning strategies as you prepare for this section of the test! Remember that taking practice tests before your ISEE test day (and retaking it once you learn from your first attempt) will grant you the most opportunities to learn from your mistakes and give a strong performance. If you’re looking for an ISEE math practice test to help you utilize the strategies we talked about above, consider Piqosity’s ISEE courses!
Along with our fulllength ELA and Math online courses for grades 611, we offer the best ISEE test prep courses on the market, for all levels of the exam. Each course includes detailed topic lessons, hundreds of questions, and 12 fulllength practice tests, together with personalized practice software that identifies your weaknesses and helps you study effectively.
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