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SHSAT Math: Your Ultimate Guide to Acing the Test


The Specialized High Schools Admissions Test (SHSAT) is a critical exam for students seeking admission to one of New York City's specialized high schools. A significant component of the SHSAT is the math section, which tests a range of mathematical skills and concepts. In this comprehensive guide, we will delve into every aspect of SHSAT math, including topics covered, practice questions, and strategies to ace the test. Whether you're looking for SHSAT practice tests, math formulas, or tips on tackling the hardest questions, this article has you covered.

Understanding the SHSAT Math Section

Importance of SHSAT Math

The SHSAT math section plays a crucial role in determining a student's overall score and, consequently, their chances of admission to a specialized high school. Mastery of the math section can significantly boost a student's total score.

Structure of SHSAT Math

The SHSAT math section consists of 57 multiple-choice questions. The section also includes ‘grid in questions’ which require students to provide numerical answers on a bubble sheet. These questions are designed to test a variety of mathematical skills, from basic arithmetic to more complex algebra and geometry problems.

Scoring in SHSAT Math

Each question on the SHSAT math section is worth one point. The total raw score is then converted to a scaled score, which contributes to the overall SHSAT score.

Key SHSAT Math Topics


Basic arithmetic forms the foundation of the SHSAT math section. Topics include:

  • Basic operations (addition, subtraction, multiplication, division)

  • Fractions, decimals, and percentages

  • Ratios and proportions

Having strong math skills, including arithmetic, is crucial for success on the SHSAT.


Algebra questions require understanding and solving equations, as well as manipulating algebraic expressions and equations. For example, consider a problem where you need to determine Carmen’s age using the following equation: n + 5 = 20. Topics include:

  • Solving linear equations and inequalities

  • Understanding and using functions

  • Simplifying expressions


Geometry questions test a student’s ability to understand geometric shapes, sizes, and properties of figures. Topics include:

  • Properties of triangles, circles, and polygons

  • Perimeter, area, and volume calculations

  • Coordinate geometry

Data Analysis

Interpreting data and analyzing data presented in various forms are key components of data analysis questions. Topics include:

  • Reading and creating graphs and charts

  • Statistical measures (mean, median, mode)

  • Probability

Developing a SHSAT Math Study Plan

Creating an effective study plan is crucial for mastering SHSAT math. Start by assessing your current strengths and weaknesses. Take a diagnostic SHSAT practice test to identify the areas where you need the most improvement. Focus your initial efforts on these weaker areas to build a solid foundation.

Next, break down your study schedule into manageable chunks. Allocate specific time slots for different math topics on the SHSAT, such as arithmetic, algebra, geometry, and data analysis. Consistency is key, so aim to study a little each day rather than cramming all at once. Use a variety of study materials, including textbooks, online resources, and SHSAT math practice tests, to keep your study sessions engaging and effective.

Incorporate regular review sessions into your study plan. Revisiting previously covered material helps reinforce your learning and ensures you retain important concepts. Utilize SHSAT math questions and problems from past exams to test your knowledge and gauge your progress.

SHSAT Math Formulas You Need to Know

Essential Formulas

Memorizing key math formulas is vital for success in SHSAT math. Important formulas include:

  • Area and perimeter of basic shapes (triangles, rectangles, circles)

  • Volume of solids (cylinders, spheres, prisms)

  • The Pythagorean theorem: 𝑎2+𝑏2=𝑐2a2+b2=c2

Application Examples

Applying these formulas correctly is crucial. For example, to find the area of a rectangle, use the formula Area=length×widthArea=length×width.

Tips for Tackling SHSAT Math Problems

Understanding the Question Types

Different question types on the SHSAT require different approaches. Familiarize yourself with:

  • Multiple-choice strategies

  • Gridded response techniques

Practice Mental Math

Improving your mental math skills can save valuable time during the test. Practice calculations in your head to become faster and more accurate.

Importance of Practicing with SHSAT Math Problems

Practicing with SHSAT math practice problems is one of the most effective ways to prepare for the test. Start with easier problems to build your confidence and gradually move on to more challenging questions. This progressive approach helps you develop a deeper understanding of the material and improves your problem-solving skills.

Use SHSAT math practice tests to simulate real test conditions. This not only helps you get used to the format and timing of the exam but also allows you to practice managing test-day stress. Analyze your performance on these practice tests to identify patterns in your mistakes and adjust your study plan accordingly.

Additionally, consider joining study groups or finding a study partner. Collaborating with peers can provide new insights and different approaches to solving SHSAT math questions. Explaining concepts to others is also a great way to reinforce your own understanding.

How to Approach SHSAT Math Questions

Strategies for Success

  • Read Carefully: Ensure you understand what the question is asking.

  • Test Strategies: Develop and apply effective test strategies to tackle different types of questions efficiently.

  • Break Down Problems: Simplify complex problems into manageable steps.

  • Double-Check Work: Verify your calculations to avoid careless errors. Ensuring you arrive at the correct answer is crucial for success. Additionally, understanding why a wrong answer was chosen and how to correct it can significantly improve your performance.

Common Pitfalls to Avoid

  • Rushing: Take your time to avoid simple mistakes.

  • Overlooking Details: Pay attention to all parts of the question.

  • Misinterpreting Questions: Ensure you fully understand the problem before solving.

Common SHSAT Math Questions and How to Solve Them

Understanding common SHSAT math questions and how to solve them can give you a significant advantage. Here are some examples of frequently asked question types and strategies for tackling them:

Word Problems

Word problems require careful reading and translation of text into mathematical equations. Start by identifying key information and determining what the question is asking. Set up an equation based on the given data and solve it step-by-step. Practice with a variety of word problems to become proficient in this skill.

Geometry Problems

Geometry problems on the SHSAT often involve calculating areas, perimeters, and volumes. Memorize essential geometry formulas and practice applying them to different shapes and figures. Pay attention to diagrams and labels, and make sure to double-check your calculations.

Algebraic Equations

Solving algebraic equations involves isolating the variable on one side of the equation. Practice solving linear equations, quadratic equations, and systems of equations. Use techniques such as substitution and elimination for systems of equations, and practice factoring and using the quadratic formula for quadratic equations.

SHSAT Math Practice Test: Why It's Essential

Benefits of Practice Tests

Taking practice tests helps students familiarize themselves with the test format, identify strengths and weaknesses, and build test-taking stamina.

Additionally, taking practice tests can help students prepare for the actual test day by familiarizing them with the test format and timing.

Where to Find Practice Tests

Reliable practice tests can be found in SHSAT prep books, online resources, and through tutoring centers specializing in SHSAT preparation.

Reviewing and Analyzing SHSAT Math Practice Tests

Analyzing performance on SHSAT math practice tests is critical for improvement. After completing a practice test, take the time to thoroughly review each question, especially the ones you got wrong. Understand the rationale behind the correct answers and identify any gaps in your knowledge.


Keep a detailed log of your mistakes, noting the type of question and the specific error made. This will help you identify patterns and focus your study efforts on areas that need the most attention. Regularly reviewing this log can prevent you from repeating the same mistakes on future tests.


Use the insights gained from your practice tests to adjust your study plan. If you notice consistent weaknesses in certain topics, allocate more study time to those areas. Consider seeking additional resources or tutoring for topics that are particularly challenging.

Effective Study Strategies for SHSAT Math Skills

Creating a Study Schedule

Developing a structured study schedule ensures consistent preparation. Allocate specific times for each math topic and practice regularly.

Utilizing Resources

Use a variety of study resources, including textbooks, online tutorials, and practice tests, to cover all aspects of SHSAT math.

Study Tips

  • Practice Regularly: Consistent practice is key to improvement.

  • Seek Help: Don’t hesitate to ask teachers or tutors for assistance.

  • Review Mistakes: Learn from errors by reviewing and understanding them. Developing strong problem-solving skills is crucial for success on the SHSAT math section and for managing time effectively during the exam.

SHSAT Math Practice Resources

Books and Guides

Utilize comprehensive SHSAT study materials, including prep books that provide detailed explanations and practice questions. Recommended titles include:

  • Barron’s SHSAT

  • Kaplan’s SHSAT Prep

Online Platforms

Leverage online resources and practice tests. Websites such as Khan Academy and official NYC DOE resources offer valuable practice materials.

Tutoring and Classes

Consider enrolling in SHSAT prep classes or hiring a tutor for personalized guidance and structured learning.

Hardest SHSAT Math Questions: How to Conquer Them

Examples of Difficult Questions

Tackling difficult questions requires a deep understanding of math concepts and the ability to apply them in complex scenarios. Examples might include multi-step algebra problems or intricate geometry questions.

The hardest questions often appear in the math portion of the SHSAT, requiring both mathematical abilities and reading comprehension to excel.

Solutions and Strategies

  • Break Down Problems: Simplify complex questions into smaller, more manageable parts.

  • Check Work: Always review your answers to ensure accuracy.

  • Practice: Regularly challenge yourself with difficult problems to improve your skills.

Maximizing Your Score on SHSAT Math

To maximize your score on the SHSAT math section, it is essential to develop effective test-taking strategies. Start by familiarizing yourself with the test format and question types. During the exam, read each question carefully and avoid rushing. Prioritize answering the questions you find easiest first to secure those points and build confidence.


Use the process of elimination to narrow down answer choices. Even if you are unsure of the correct answer, eliminating one or two incorrect options increases your chances of guessing correctly. Manage your time wisely, ensuring you have enough time to review your answers and tackle any skipped questions.


Stay calm and focused throughout the test. If you encounter a particularly difficult question, take a deep breath and move on to the next one. You can always return to it later if time permits. Maintaining a positive mindset and staying resilient can make a significant difference in your performance.

SHSAT Math Practice Test: Sample Questions and Answers

Practice Problems

Arithmetic Example: Practice problems like this one: If a shirt costs $30 and is marked down by 25%, what is the sale price? Some questions may be ‘grid in’ questions, requiring students to fill in the correct numerical answer on a bubble sheet.


Solution: $30 - ($30 * 0.25) = $22.50

Algebra Example: Solve for x: 2𝑥+3=112x+3=11


Solution: 2𝑥=82x=8 𝑥=4x=4

Geometry Example: What is the area of a triangle with a base of 5 units and a height of 8 units?


Solution: Area=12×5×8=20Area=21​×5×8=20 square units

Detailed Solutions

Each practice problem should be followed by a step-by-step solution to help students understand the process of solving each type of question.

SHSAT Math and Time Management

Importance of Time Management

Efficient time management is crucial during the SHSAT math section. Students must balance speed and accuracy to complete all questions within the time limit.

Effective time management is crucial for test takers to complete all questions within the time limit.

Time-Saving Strategies

  • Skip and Return: If a question seems too time-consuming, move on and return to it later.

  • Use Shortcuts: Familiarize yourself with mathematical shortcuts and tricks to solve problems faster.

  • Practice Timed Tests: Regularly practice with timed tests to build your time management skills.

Math Topics on SHSAT: Detailed Breakdown

Advanced Arithmetic

In addition to basic arithmetic, the SHSAT math section may include more advanced arithmetic topics such as:

  • Exponents and Roots: Understanding powers and square roots.

  • Scientific Notation: Working with very large or very small numbers.

Advanced Algebra

Beyond basic algebra, students might encounter:

  • Quadratic Equations: Solving quadratic equations by factoring, completing the square, or using the quadratic formula.

  • Systems of Equations: Solving systems of linear equations through substitution or elimination.

Advanced Geometry

Advanced geometry topics can include:

  • Theorems: Applying theorems such as those of Pythagoras, Thales, and others.

  • Transformations: Understanding translations, rotations, reflections, and dilations of shapes.

Building Confidence with SHSAT Math Practice

Regular Practice

Consistency is key. Regular practice builds familiarity and confidence with the types of questions asked on the SHSAT.

Simulated Test Conditions

Practice under test-like conditions to improve your ability to perform under pressure. This includes timing yourself and minimizing distractions.

Analyzing Performance

Review your practice test results to identify strengths and weaknesses. Focus on areas that need improvement to ensure comprehensive preparation.

Students should also review their performance in the English Language Arts section to ensure comprehensive preparation.

Additional Practice Questions

Challenging Arithmetic Problems

Problem: A car travels 60 miles in 1.5 hours. What is its average speed in miles per hour? This is one of the challenging arithmetic problems that tests your understanding of speed and distance.

Solution: 60 miles / 1.5 hours = 40 mph

Problem: If 3/5 of a number is 24, what is the number?

Solution: Number=24×53=40Number=24×35​=40

Complex Algebra Questions

Problem: Solve for y: 3𝑦−4=2𝑦+63y−4=2y+6

Solution: 𝑦=10y=10

Problem: Simplify: (2𝑥−3)(𝑥+4)(2x−3)(x+4)

Solution: 2𝑥2+8𝑥−3𝑥−12=2𝑥2+5𝑥−122x2+8x−3x−12=2x2+5x−12

Advanced Geometry Challenges

Problem: Find the circumference of a circle with a radius of 7 units.

Solution: Circumference=2𝜋×7=14𝜋Circumference=2π×7=14π

Problem: Calculate the volume of a rectangular prism with length 4 units, width 3 units, and height 2 units.

Solution: Volume=4×3×2=24Volume=4×3×2=24 cubic units

Mock Test Strategies

Simulating Real Test Conditions

Take full-length mock tests under timed test conditions to build endurance and familiarity with the test format.

Review and Reflect

After each mock test, review your answers, especially the incorrect ones, to understand your mistakes and learn from them.

Track Progress

Keep a log of your scores and progress over time. This helps identify patterns and areas needing more focus.


What is the SHSAT math section?

The SHSAT math section is a part of the Specialized High Schools Admissions Test that assesses a student's mathematical abilities through multiple-choice questions on various topics.

How many questions are in the SHSAT math section?

The SHSAT math section includes 57 multiple-choice questions.

What are the main topics covered in SHSAT math?

Key topics include arithmetic, algebra, geometry, and data analysis.

How can I prepare for the hardest SHSAT math questions?

Regular practice, understanding key concepts, and breaking down complex problems into simpler steps can help in tackling the hardest questions.

Where can I find reliable SHSAT math practice tests?

Practice tests can be found in SHSAT prep books, online resources, and tutoring centers specializing in SHSAT preparation.

What are the essential formulas for SHSAT math?

Important formulas include those for area and perimeter of shapes, volume of solids, and the Pythagorean theorem.


Mastering SHSAT math requires dedication, practice, and a solid understanding of the key topics and formulas. By following the strategies outlined in this guide and making use of available resources, students can significantly improve their chances of success on the SHSAT math section. Remember, consistent practice and a positive mindset are essential components of effective preparation. Navigating the SHSAT math section can feel like traversing the lone and level sands, but with perseverance, success is within reach.

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