ACT Math: Must-Know Strategies for a 36 Score 

Scoring a perfect 36 on the ACT Math section may seem like an ambitious goal, but with the right strategies and dedication, it is absolutely achievable. At The Princeton Review Singapore, we believe that any student, whether currently scoring in the mid-20s or already in the 30s, can unlock their full potential with focused preparation and smart test-taking techniques. 

The ACT Math section covers essential algebra, geometry, trigonometry, and probability concepts you’ve learned in high school. However, the challenge lies in how these topics are tested, often requiring quick thinking, problem-solving efficiency, and the ability to apply multiple concepts at once. The key to mastering this section isn’t just memorization but strategic preparation and targeted practice to improve accuracy and speed. 

In this guide, we will break down: 
✔️ Why a perfect 36 matters for your college goals. 
✔️ What does it take to achieve a top score? 
✔️ Proven strategies to strengthen your ACT Math skills. 

Whether you’re aiming for a top-tier university or looking to maximize your overall ACT score, this guide will equip you with the insights, techniques, and confidence to succeed. Let’s get started!  

The Significance of a 36 in ACT Math 

A perfect 36 on the ACT Math section is more than just a high score; it is a strong indicator of mathematical proficiency and problem-solving skills. While many top colleges consider a 34 or higher competitive, achieving a 36 provides a distinct advantage in the admissions process. 

1. Competitive Advantage 

Highly selective universities, including MIT, Caltech, and Ivy League institutions, receive applications from thousands of academically strong students. A 36 in ACT Math demonstrates a superior level of quantitative reasoning, which is particularly valuable for students pursuing STEM-related fields. 

2. Strengthening the Overall ACT Score 

Even if other ACT sections are not as strong, a perfect Math score can help balance the composite score. For example, if a student scores 32 in English or Reading, a 36 in Math can improve their overall performance and maintain a competitive standing in the admissions process. 

3. Essential for STEM Admissions 

For applicants targeting programs in mathematics, science, engineering, or business, a high ACT Math score is a key factor in demonstrating readiness for rigorous coursework. Many top technical institutions prioritize strong quantitative skills, and a 36 ensures alignment with the top 25% of admitted students. 

Aiming for a 36 in ACT Math not only enhances college applications but also increases eligibility for merit-based scholarships and strengthens an applicant’s profile in competitive admissions pools. 

Why Strive for a 36 in ACT Math? 

• Competitive Advantage at Top Universities: A 36 in ACT Math places you among the highest-achieving applicants, particularly at institutions such as Harvard, Princeton, and MIT, where the 75th percentile SAT Math score is 800 the equivalent of an ACT 36. 

• Essential for STEM Majors: If you intend to pursue a mathematics, physics, engineering, or computer science major, a perfect Math score signals your ability to handle advanced quantitative coursework and strengthens your application for competitive programs. 

• Eligibility for Scholarships: Many merit-based scholarships consider ACT scores in their selection criteria. A 36 in Math can significantly enhance scholarship opportunities and financial aid eligibility. 

Path to a 36: Effective Strategies for ACT Math Success 

Achieving a perfect ACT Math score is a realistic goal with strategic preparation and consistent effort. At The Princeton Review Singapore, we emphasize a structured approach that focuses on mastering fundamental concepts, understanding the exam format, and refining test-taking strategies. 

Why a 36 is Attainable 

The ACT Math section assesses high school-level mathematical concepts, including algebra, geometry, trigonometry, and probability. However, the test is designed to evaluate not only mathematical knowledge but also critical thinking and problem-solving skills. Success requires more than familiarity with formulas it demands the ability to apply mathematical concepts in complex and unfamiliar scenarios. 

By adopting a targeted study plan, practicing with high-quality materials, and developing effective problem-solving techniques, students can significantly improve their performance and achieve a perfect 36 in ACT Math. 

Consider the following problem: 

In the equation

x2+ mx + n = 0

, where m and n are integers, the only possible value for x is −3. What is the value of m? 

A. 3 
B. -3 
C. 6 
D. -6 
E. 9 

At first glance, this problem appears straightforward, but it requires a deeper understanding of quadratic equations. Since -3 is the only solution, the equation must be a perfect square, written as: 

(x+3)2= 0x+32= 0

Expanding this equation results in: 

x2+ 6x + 9 = 0x2+ 6x + 9 = 0

Comparing with the given quadratic equation

x2+ mx + n = 0x2+ mx + n = 0

, it is evident that m = 6. This problem highlights the importance of not just memorizing formulas but also understanding how to apply them strategically. 

Why the ACT Math Section Stands Out 

The ACT Math section is designed to assess students’ ability to apply fundamental mathematical concepts in unconventional problem formats. Unlike other standardized tests that may include advanced topics like calculus, the ACT focuses solely on high school-level mathematics, including algebra, geometry, trigonometry, and probability. However, the test differentiates students by presenting these topics in ways that require analytical thinking rather than rote memorization. 

For example, if the test simply asked, “What is the value of x if  

x2+ 6x + 9 = 0x2+ 6x + 9 = 0

?” most students would easily recognize it as a perfect square and solve for x. However, by rephrasing the question to ask for the value of m in a quadratic equation with a single root, the test challenges students to think critically and apply mathematical reasoning. 

Effective Strategies for ACT Math Success 

1. Master Fundamental Concepts: A strong understanding of core mathematical principles is essential. Ensure proficiency in algebra, geometry, trigonometry, and probability to tackle a wide range of problems effectively. 

2. Develop Strategic Practice Habits: Work through a variety of official ACT practice problems to familiarize yourself with the test’s structure and question formats. Focus on understanding how questions are framed and what they truly assess. 

3. Analyze and Learn from Mistakes: Reviewing incorrect answers is crucial for improvement. Identify patterns in mistakes and develop strategies to avoid similar errors in the future. 

4. Enhance Problem-Solving Skills: The ACT rewards students who can think creatively and apply known concepts in unfamiliar contexts. Practice solving problems in multiple ways to strengthen problem-solving flexibility. 

The Path to a Perfect Score 

Achieving a 36 on the ACT Math section requires near-perfect accuracy on practice tests. While the ACT scoring system may allow for one incorrect response while still maintaining a 36, aiming for a flawless raw score provides the best assurance of success. 

At The Princeton Review Singapore, we are dedicated to equipping students with the skills and strategies necessary to excel on the ACT. By focusing on concept mastery, strategic practice, and continuous improvement, students can significantly enhance their scores and strengthen their college applications. With the right approach, a perfect ACT Math score is within reach. 

What It Takes to Achieve a 36 in ACT Math 

Achieving a perfect score of 36 on the ACT Math section requires a clear understanding of the scoring system and a strategic approach to preparation. By knowing how your raw score translates into the scaled score, you can set precise goals and track your progress effectively. 

Understanding the Scoring Scale 

The ACT Math section is scored on a scale of 1 to 36. Your raw score, the total number of correct answers, is converted into a scaled score. The table below illustrates how raw scores typically translate into scaled scores: 

To secure a 36, you generally need to answer at least 59 out of 60 questions correctly. In some cases, the scoring curve allows for one incorrect answer while still achieving a perfect score, but this varies by test. The most effective strategy is to aim for accuracy in every practice session to maximize your chances of reaching the top score. 

Why Aiming for Perfection Matters 

While missing one question might still earn you a 36, the ACT scoring curve varies, and a single mistake could lower your score. To maximize your chances, strive for perfection in practice by mastering every concept and eliminating careless errors. 

Closing the Gap 

If you’re scoring below 36, determine how many more correct answers you need. For instance, improving from a 30 to a 36 requires about 10 additional correct answers. Targeted practice, focusing on weak areas, and mastering frequently tested question types can bridge this gap. 

The Key to Success: Strategic Practice 

Full-length, timed practice tests help simulate test conditions and pinpoint areas for improvement. Analyzing mistakes and refining problem-solving strategies will enhance accuracy and confidence, bringing you closer to a perfect score. 

A 36 in ACT Math is achievable with the right approach. By aiming for perfection, practicing strategically, and addressing weaknesses, you can significantly boost your performance. At The Princeton Review Singapore, we are committed to helping you reach your full potential and achieve top scores. 

Strategies to Achieve a 36 on ACT Math 

Step 1: Identify Your Challenges – Concept Mastery or Time Management? 

Achieving a perfect 36 on the ACT Math section requires pinpointing your main obstacles. Most students struggle with either understanding the tested concepts or managing time effectively. Identifying your specific challenge allows you to focus on the right areas for improvement. 

Assessing Your Weaknesses 

1. Simulate a Real Test 

• Take an official ACT Math practice test under timed conditions (60 minutes). 

• If you run out of time, continue answering but mark responses made after the time limit. 

2. Evaluate Your Performance 

• Timed Score: Your score within the 60-minute limit. 

• Untimed Score: Your score if all answers, including post-time responses, were counted. 

3. Analyze Your Results 

• Untimed Score below 32: Focus on content mastery review core topics such as algebra, geometry, and trigonometry. 

• Untimed Score 32 or above, but lower Timed Score: Work on time management by practicing under timed conditions and improving problem-solving speed. 

• Both scores 32 or above: Focus on eliminating careless mistakes and increasing efficiency. 

Targeted Improvement Strategies 

• Strengthen Conceptual Understanding 
  If your Untimed Score is below 32, prioritize reviewing fundamental math topics. Identify weak areas and reinforce them through focused practice. 

• Enhance Time Management 
  If you understand the content but struggle with timing, develop strategies to solve problems more efficiently. Practice pacing, recognize time-consuming question types, and refine shortcut techniques. 

• Fine-tune performance 
  If both scores are high, focus on maintaining accuracy while improving speed. Identify common errors and refine your approach to complex questions. 

A strategic approach is essential for achieving a 36 on ACT Math. By understanding your weaknesses and addressing them systematically, you can optimize your preparation. At The Princeton Review Singapore, we emphasize targeted strategies to help students maximize their potential. With consistent effort and the right study plan, a perfect score is within reach. 

Strategy 2: Master Practice and Learn from Every Mistake 

Achieving a perfect 36 on the ACT Math section requires more than just repeated practice; it demands strategic preparation and continuous learning from every mistake. Even a single error can prevent a perfect score, making it essential to approach practice with precision and discipline. The key to improvement lies not only in solving numerous problems but in thoroughly analyzing and understanding every mistake. 

Step 1: Engage in Consistent and Purposeful Practice 

The foundation of effective preparation is regular and comprehensive practice. Utilize official ACT practice tests, reputable prep books, and reliable online resources to familiarize yourself with a broad range of question types. However, solving a large volume of problems alone is not sufficient. The most significant progress comes from a structured approach to learning from errors. 

Step 2: Conduct a Detailed Analysis of Every Mistake 

Mistakes provide crucial insights into areas requiring improvement. Many students take multiple practice tests without significant score improvement because they do not thoroughly analyze their errors. A systematic review process ensures that each mistake leads to measurable progress. 

To maximize learning from mistakes, follow these steps: 

1. Identify Uncertain Questions 

• As you work through practice problems, mark any questions where you felt uncertain, even if you answered them correctly. 

• This helps identify areas where your understanding may not be fully secure, reducing the likelihood of errors on test day. 

2. Review All Mistakes Systematically 

• After grading your test, revisit every incorrect answer and all questions you marked as uncertain. 

• Include questions where you made an educated guess, even if the answer was correct. Understanding why you were unsure is just as important as reviewing incorrect responses. 

3. Maintain a Record of Mistakes 

• Use a dedicated notebook or digital document to track your mistakes. 

• For each error, document the following:  

• A summary of the question. 

• The reason for the mistake (e.g., misinterpreted the question, applied the wrong formula, miscalculated). 

• The correct solution and an alternative approach, if applicable. 

• Steps to prevent the same mistake in future attempts. 

• Organize these notes by topic (e.g., algebra, geometry, trigonometry) to identify patterns in recurring errors. 

The Value of Reflection in Learning 

Merely reviewing the correct answer is not enough. To truly understand and internalize concepts, engage in deeper reflection: 

• Why was my answer incorrect? Determine the specific misunderstanding or miscalculation that led to the mistake. 

• What concept or strategy did I overlook? Identify whether the mistake was due to a lack of knowledge or a misapplication of a known concept. 

• How should I approach similar problems in the future? Develop a strategy to avoid repeating the mistake, whether through conceptual review, practice, or refining problem-solving techniques. 

This method ensures that learning is not superficial but leads to long-term improvement. 

Transforming Weaknesses into Strengths 

Each mistake serves as an opportunity for growth. By systematically addressing weaknesses, you will develop a more solid foundation in ACT Math. Over time, repeated error analysis will refine your approach, improve accuracy, and increase efficiency, ultimately leading to a higher score. 

At The Princeton Review Singapore, we emphasize a structured and analytical approach to ACT preparation. By combining extensive practice with a rigorous review of mistakes, students develop the skills and confidence necessary for peak performance. Every error presents an opportunity to refine your understanding and approach. With consistent effort and a commitment to learning from mistakes, a perfect ACT Math score is within reach. 

Strategy 3: Identify the Root Cause of Mistakes 

Achieving a perfect 36 on the ACT Math section requires more than recognizing errors it demands a thorough understanding of why those errors occurred. Many students acknowledge mistakes but fail to analyze them in depth. A structured approach to reviewing errors ensures continuous improvement and prevents repeated mistakes. 

Why Identifying the Cause Matters 

A simple acknowledgment of an incorrect answer is not enough. Understanding the specific reason behind each mistake helps target weaknesses effectively. Common causes include: 

1. Gaps in Content Knowledge 

Issue: Lacking the necessary understanding of a concept or formula. 
Solution: 

• Identify the exact topic that caused confusion. 

• Review explanations and examples in study materials. 

• Practice similar problems to reinforce understanding. 

2. Incorrect Problem-Solving Approach 

Issue: Using an ineffective or incorrect method despite knowing the concept. 
Solution: 

• Compare your approach with the correct solution. 

• Identify problem patterns that indicate which method to use. 

• Practice applying the correct strategy to similar questions. 

3. Careless Errors 

Issue: Misreading questions, miscalculating, or solving for the wrong variable. 
Solution: 

• Read each question carefully and underline key details. 

• Double-check calculations before selecting an answer. 

• Develop a habit of verifying solutions when time permits. 

4. Time Management Issues 

Issue: Running out of time, leading to rushed answers or guessing. 
Solution: 

• Track time spent on each question during practice. 

• Skip time-consuming problems and return later. 

• Improve efficiency through timed drills. 

5. Overcomplicating the Problem 

Issue: Choosing a complex method instead of a straightforward approach. 
Solution: 

• Identify the simplest solution method before solving. 

• Build confidence in fundamental techniques. 

• Practice recognizing when to simplify calculations. 

Implementing an Effective Review Process 

1. Maintain a Mistake Log 

• Record each mistake, the reason behind it, and the correct approach. 

• Organize mistakes by topic to identify recurring weaknesses. 

2. Review Mistakes Regularly 

• Revisit the mistake log weekly to track progress. 

• Focus additional practice on frequently missed concepts. 

3. Practice Under Test Conditions 

• Take full-length timed practice tests to simulate exam pressure. 

• Analyze errors after each test to refine strategies. 

The Impact of Targeted Error Analysis 

By consistently identifying and addressing the root cause of mistakes, students improve accuracy and efficiency. This method ensures a strategic approach to preparation, leading to better performance and a higher ACT Math score. 

Strategy 4: Address Content Gaps with Precision 

Achieving a perfect 36 on the ACT Math section requires a thorough understanding of all tested concepts. If you are not consistently scoring in the 34-36 range, you likely have content gaps that need attention. These gaps may include forgotten formulas, difficulty with certain problem types, or misunderstanding foundational concepts. Identifying and addressing these weaknesses is essential for improvement. 

Identifying Content Gaps 

Content gaps can be identified through mistake analysis and test performance. Common signs include: 

• Unfamiliarity with key formulas or rules. 

• Struggling with specific question types (e.g., word problems, trigonometry). 

• Misapplying concepts in problem-solving. 

Ignoring these gaps leads to repeated mistakes. A systematic approach is required to strengthen weak areas. 

Steps to Address Content Gaps 

1. Pinpoint Specific Weaknesses 

• Use a mistake journal to track missed questions and identify recurring topics. 

• Categorize weaknesses by subject and subskill for targeted improvement. 

2. Review and Relearn Concepts 

• Study the relevant material from reliable sources such as textbooks, ACT prep books, or online tutorials. 

• Focus on understanding concepts, not just memorizing formulas. 

3. Practice Targeted Problems 

• Work on problems that focus on identified weak areas. 

• Use ACT practice tests and question banks to reinforce learning. 

4. Seek Additional Help if Needed 

• If a topic remains unclear, consult a teacher, tutor, or online resource for a different explanation. 

5. Test Mastery 

• Solve practice problems and quizzes to ensure a solid understanding before moving to new topics. 

Why This Approach Works 

Content gaps weaken overall performance. Addressing them builds a stronger foundation, improves accuracy, and enhances confidence. Consistently reviewing weak areas ensures steady progress. 

Practical Strategies for Success 

• Structured Study Plan: Dedicate time each week to specific weak areas. 

• Multiple Learning Resources: Use books, videos, and interactive tools to reinforce concepts. 

• Active Learning: Teach the concept to someone else to confirm understanding. 

• Progress Tracking: Maintain a log of reviewed topics and improvements. 

At The Princeton Review Singapore, we emphasize precision in identifying and closing content gaps. A strategic, focused approach ensures steady progress toward a perfect ACT Math score. 

Strategy 5: Reattempt Questions Before Reviewing Explanations 

To improve accuracy on the ACT Math section, it is essential to engage actively with missed questions. Simply reading explanations is a passive approach that does not reinforce learning. Reattempting questions before reviewing solutions helps strengthen understanding and prevents repeated mistakes. 

Why Reattempting Questions is Effective 

Reading an explanation immediately after missing a question does not ensure long-term retention. Actively solving the problem again forces critical thinking, improves problem-solving skills, and enhances conceptual understanding. 

Steps to Implement This Strategy 

1. Identify the Correct Answer 

• Mark the correct choice but avoid reading the explanation immediately. 

2. Reattempt the Question 

• Solve the problem again without time pressure. Focus on identifying errors and applying alternative methods. 

3. Analyze Your Thought Process 

• Reflect on mistakes and recognize gaps in understanding. Consider different strategies for approaching the problem. 

4. Compare Your Solution 

• If your reattempt is correct, analyze what changed in your approach. If incorrect, assess where you went wrong again. 

5. Review the Explanation (If Necessary) 

• Read the explanation only if the answer remains unclear. By this stage, understanding will be deeper, making the solution more meaningful. 

Benefits of This Approach 

• Active Learning: Engages critical thinking for better retention. 

• Deeper Understanding: Reinforces concepts and problem-solving techniques. 

• Long-Term Retention: Strengthens recall and prevents repeated mistakes. 

Maximizing Effectiveness 

1. Set a Time Limit – Spend up to 10 minutes reattempting each problem. 

2. Document Insights – Record mistakes, correct strategies, and key takeaways. 

3. Identify Patterns – Group similar errors to address recurring weaknesses. 

4. Use consistently – Incorporate this method into regular practice for steady improvement. 

Passively reading explanations does not lead to mastery. Reattempting questions encourages active learning, deepens understanding, and builds problem-solving skills. By integrating this strategy into study sessions, students can significantly improve their ACT Math performance. 

Strategy 6: Improve Speed and Accuracy to Finish with Time to Spare 

A perfect ACT Math score requires both accuracy and efficiency. With 60 questions in 60 minutes, you have about one minute per question. However, some problems take longer, making time management essential. Finishing early allows you to review answers and minimize mistakes. 

Why Time Management Matters 

The ACT tests your ability to solve problems under time pressure. Many students struggle to complete all questions, leading to rushed or unanswered problems. Developing speed and accuracy ensures you maximize your score. 

Steps to Improve Speed and Accuracy 

1. Practice Under Timed Conditions 

• Take full-length, timed practice tests to build endurance and familiarity with the test pace. 

• Track your time per question and work on reducing it while maintaining accuracy. 

2. Master Common Question Types 

• Recognize and quickly solve frequently tested problems. 

• Develop strategies for handling geometry, algebra, and word problems efficiently. 

3. Skip and Return to Tough Questions 

• If a question takes more than 30 seconds without progress, move on and return later. 

• This prevents wasting time on a single problem while missing easier points elsewhere. 

4. Double-check your Work 

• Use extra time to verify answers, especially those requiring detailed calculations. 

• Solve using an alternative method to confirm accuracy. 

5. Ensure Correct Answer Bubbling 

• Mistakes in bubbling can cost points. Quickly scan your answer sheet before time runs out. 

• Check in groups of five to avoid skipping or misaligning answers. 

Why This Strategy Works 

• Efficiency: Timed practice builds the ability to work quickly without sacrificing accuracy. 

• Confidence: Completing the section early allows time for review, reducing test-day stress. 

• Error Reduction: Reviewing answers helps catch and correct careless mistakes. 

Additional Tips 

1. Prioritize Easier Questions First 

• Quickly answer familiar questions to secure points before tackling harder problems. 

2. Use Shortcuts and Strategies 

• Apply techniques like plugging in answer choices, estimation, and elimination to save time. 

3. Stay Focused Under Pressure 

• If time is running out, remain calm and answer as many questions as possible. Guessing is better than leaving blanks. 

4. Simulate Real Test Conditions 

• Practice in a quiet environment with a timer to build focus and endurance. 

Final Review for a Perfect Score 

Even strong test-takers make mistakes under pressure. Completing the section early gives you time to check answers and catch errors, ensuring every point counts toward your goal. 

Strategy 7: Minimize Careless Mistakes Through Focus and Precision 

Careless mistakes can cost valuable points on the ACT Math section, even when you understand the material. Errors often result from misreading questions, rushing through calculations, or incorrectly entering values into a calculator. These small oversights can significantly impact your score, especially when aiming for a 36. 

Strategies to Avoid Careless Mistakes 

1. Read the Questions Carefully 

• Pay attention to key details such as units, variables, and what is being asked. 

• Underline or note specific instructions to avoid solving for the wrong value. 

2. Write Down Key Information 

• Keep track of units, formulas, and conversions in your scratch work. 

• Clearly label each step to ensure accuracy. 

3. Check Calculator Entries 

• Double-check numbers, parentheses, and operations before confirming results. 

• A small input error can lead to incorrect answers. 

4. Use Extra Time to Review 

• If time allows, revisit difficult questions and rework them using a different method. 

• Focus on complex calculations or questions you were unsure about. 

5. Verify Answer Bubbling 

• Ensure each answer is bubbled in the correct row. 

• Check in small groups (e.g., five at a time) to prevent misalignment errors. 

Why This Strategy Works 

• Prevents Misreading: Careful reading and underlining key details help clarify what is being asked. 

• Reduces Errors: Writing out steps and verifying calculations minimizes mistakes. 

• Boosts Confidence: Reviewing answers ensures accuracy and strengthens test performance. 

Additional Tips 

1. Practice Active Reading 

• Train yourself to slow down and fully process each question. 

2. Follow a Consistent Problem-Solving Process 

• Read → Identify key information → Solve → Verify. 

3. Stay Calm Under Pressure 

• Rushing increases mistakes. Practice time management to maintain focus. 

4. Analyze Past Mistakes 

• Review errors in practice tests to identify recurring patterns. 

By implementing these strategies, you can improve accuracy, reduce unnecessary errors, and maximize your ACT Math score. 

Strategy 8: Master Key Formulas and Math Facts for Quick Recall 

Success in the ACT Math section requires a strong grasp of fundamental mathematical concepts and formulas. While understanding the principles behind these formulas is important, committing them to memory can significantly improve efficiency and accuracy during the test. If recalling formulas or deriving them during practice takes considerable time, targeted memorization and practice will be beneficial. 

Importance of Memorizing Formulas 

The ACT Math section includes a broad range of topics, such as algebra, geometry, trigonometry, and probability. Many problems rely on specific formulas, and knowing them in advance allows for quicker problem-solving. For instance, calculating the area of a circle, determining the slope of a line, or finding the volume of a rectangular prism all require memorized formulas. Deriving these formulas during the test can consume valuable time and increase the likelihood of mistakes. 

Essential Formulas and Math Facts to Memorize 

Algebra 

• Slope of a line: m =  y2​−y1​x2​−x1​y2​−y1​x2​−x1​ 

• Quadratic formula: x =(−b ± b2− 4ac−−−−−−−√)2ax =−b ± b2− 4ac2a 

• Distance formula: d = (x2– x1)2+ (y2– y1)2−−−−−−−−−−−−−−−−−−√d = x2– x12+ y2– y12 

Geometry 

• Area of a circle: A = πr2A = 𝜋r2 

• Circumference of a circle: C = 2πrC = 2𝜋r 

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

• Special right triangles:  

• 45°−45°−90°: 1:1:2–√45°−45°−90°: 1:1:2 

• 30°−60°−90°: 1:3–√:230°−60°−90°: 1:3:2 

• Common Pythagorean triples: 3−4−5, 5−12−13, 7−24−253−4−5, 5−12−13, 7−24−25 

Trigonometry 

• Trigonometric ratios:  

• sin(θ)= oppositehypotenusesin⁡𝜃= oppositehypotenuse 

• cos(θ)= adjacenthypotenusecos⁡𝜃= adjacenthypotenuse 

• tan(θ)= oppositeadjacenttan⁡𝜃= oppositeadjacent 

Coordinate Geometry 

• Midpoint formula: ( x₁ + x₂2x₁ + x₂2 + y₁ + y₂2y₁ + y₂2) 

• Equation of a circle: (x − h)2+ (y – k)2= r2x − h2+ y – k2= r2 

Probability and Statistics 

• Probability of an event: P(E) = Number of favorable outcomesTotal number of outcomesNumber of favorable outcomesTotal number of outcomes 

• Mean (average): Mean =Sum of valuesNumber of valuesSum of valuesNumber of values 

Effective Strategies for Memorization 

1. Use Flashcards 

Writing each formula on a flashcard with a brief explanation or example can reinforce memory through repetition. Reviewing flashcards regularly is an efficient way to retain key concepts. 

2. Apply Formulas in Practice Problems 

Consistently using formulas in various problems strengthens understanding and recall. Solving diverse problems ensures familiarity with different applications. 

3. Organize Formulas by Topic 

Grouping formulas based on subject areas, such as algebra or geometry, makes it easier to retrieve them when needed. Recognizing patterns within formulas can aid retention. 

4. Utilize Mnemonics 

Creating mnemonic devices or memory aids can make recalling formulas more manageable. For example, the quadratic formula can be remembered using rhythmic phrases or patterns. 

5. Conduct Regular Self-Testing 

Periodically writing formulas from memory or attempting practice problems without reference materials helps assess retention and identify areas needing improvement. 

Advantages of Memorizing Key Formulas 

• Time Efficiency: Immediate recall of formulas allows for quicker problem-solving, providing additional time to focus on more challenging questions. 

• Error Reduction: Memorization minimizes the chances of miscalculating or incorrectly deriving formulas. 

• Increased Confidence: Knowing formulas thoroughly enhances confidence and reduces test anxiety, allowing for a more focused and efficient test-taking experience. 

Additional Techniques for Mastering Formulas 

1. Understand the Principles Behind Formulas 

Rather than relying solely on memorization, understanding the reasoning behind formulas aids in their application. Recognizing the derivation of formulas fosters deeper comprehension. 

2. Relate Formulas to Real-World Applications 

Applying mathematical formulas to everyday situations reinforces their practical significance. For instance, calculating the slope of a road or the area of a circular object strengthens familiarity. 

3. Schedule Routine Review Sessions 

Regularly revisiting formulas ensures long-term retention. Allocating dedicated study sessions for formula review prevents forgetting crucial mathematical concepts. 

Example: Applying the Pythagorean Theorem 

Problem 

A right triangle has legs measuring 6 inches and 8 inches. Determine the length of the hypotenuse. 

Solution 

Using the Pythagorean theorem: 

a2+ b2= c2a2+ b2= c2

62+ 82= c262+ 82= c2

36 + 64 = c236 + 64 = c2

100 = c2100 = c2

c = 10𝒄 = 𝟏𝟎

Thus, the hypotenuse measures 10 inches. 

By memorizing and understanding the Pythagorean theorem, this problem can be solved quickly and accurately without needing to derive the formula. 

Mastering key formulas and mathematical facts is a crucial step in achieving a strong performance on the ACT Math section. A combination of memorization, practice, and conceptual 

Strategy 9: Maintain Composure and Confidence During the Test 

Scoring well on the ACT Math section requires both strong mathematical skills and the ability to stay composed under pressure. The time constraint—60 questions in 60 minutes—can lead to stress, increasing the risk of errors. A calm and focused approach is essential for maximizing performance. 

Why Mental Resilience Matters 

Test anxiety can lead to rushed decisions, second-guessing, and careless mistakes. Maintaining confidence helps improve focus, logical reasoning, and time management. 

Strategies to Stay Focused 

1. Adopt a Positive Mindset – Trust your preparation and stay confident. If a question seems difficult, approach it systematically rather than panicking. 

2. Practice Deep Breathing – Controlled breathing techniques help manage stress and maintain concentration. 

3. Skip and Return – Avoid spending too much time on a single problem. Mark challenging questions and revisit them later. 

4. Stay Present – Focus on one question at a time instead of worrying about previous mistakes or upcoming questions. 

5. Visualize Success – Before the test, mentally rehearse solving problems efficiently and completing the section with confidence. 

Handling Setbacks 

• Avoid Dwelling on Mistakes – If an error occurs, move forward without letting it impact your performance. 

• Be Flexible – Adjust your approach if needed, ensuring you attempt as many questions as possible within the time limit. 

• Keep Perspective – A high score, even if not a perfect 36, remains a strong achievement. 

Additional Preparation Tips 

• Simulate Test Conditions – Take timed practice tests to build familiarity with the test environment. 

• Establish a Pre-Test Routine – Develop strategies that help you stay calm, such as light stretching or deep breathing exercises. 

• Prioritize Rest and Nutrition – A well-rested mind and a balanced meal contribute to better focus and performance. 

Confidence and mental resilience are just as important as content knowledge. A calm, strategic approach minimizes errors and optimizes performance. Effective preparation and a composed mindset will position you for success on test day. 

Strategy 10: Stay Consistent and Believe in Yourself 

Success on the ACT Math section requires both consistent practice and confidence. Mastering concepts and strategies is essential, but your mindset and commitment to preparation play an equally crucial role. Challenging questions and moments of doubt are inevitable, but your response to these challenges will determine your success. 

Why Consistency and Self-Belief Matter 

• Consistency Builds Mastery – Regular practice strengthens problem-solving skills, reinforces concepts, and improves speed. A steady study routine leads to long-term retention and confidence. 

• Self-Belief Drives Performance – Confidence allows you to approach problems logically without second-guessing yourself. Even when faced with difficult questions, a strong mindset helps you stay focused and persistent. 

How to Stay Consistent and Confident 

1. Follow a Structured Study Plan 

• Set a realistic schedule with dedicated ACT Math practice sessions. Track progress to stay motivated and accountable. 

2. Acknowledge Progress 

• Celebrate small improvements, whether it’s mastering a new concept or solving problems more efficiently. Recognizing growth keeps motivation high. 

3. Manage Self-Doubt 

• Struggling with a problem does not mean failure. If stuck, skip the question, move on, and revisit it later with a clear mind. 

4. Maintain a Positive Mindset 

• Replace negative thoughts with constructive ones. Instead of “I can’t do this,” remind yourself, “I have prepared, and I will find a solution.” 

5. Learn from Mistakes 

• Analyze errors to understand where you went wrong. Adjust strategies accordingly and use mistakes as learning opportunities. 

Final Thoughts 

At The Princeton Review Singapore, we emphasize that consistency and confidence are as important as content mastery. A strong study plan, positive mindset, and adaptability will help you overcome challenges on test day. Stay committed, trust your preparation, and approach the ACT Math section with confidence. Your persistence will lead to success.