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ACT Math Prep

Master counting, Probability and Geometry

Jackson Kailath

4.6

Based on 26 ratings

Jackson Kailath

The topics covered are the following:

Permutation and Combination

1.P&C Basics

2. Relationship between P&C

3. Fundamental Principle of counting

4. Permutation in Depth

5. Combination in Depth

6. Grouping Trick ( See videos)

7. Dearrangement n items

Probability

30. Probability Basics

31. Complement of an Event

32. Exhaustive Events

33. Mutually Exclusive Events

34. Independent Events

35. Conditional Probability

36. R successes in N Trials

37. Odds in favour / Odds against

The topics covered are the following:

Permutation and Combination

1.P&C Basics

2. Relationship between P&C

3. Fundamental Principle of counting

4. Permutation in Depth

5. Combination in Depth

6. Grouping Trick ( See videos)

7. Dearrangement n items

Probability

30. Probability Basics

31. Complement of an Event

32. Exhaustive Events

33. Mutually Exclusive Events

34. Independent Events

35. Conditional Probability

36. R successes in N Trials

37. Odds in favour / Odds against

38. Practise probability Qs

Geometry

39. Geometry basics: Points, lines, planes, angles, polygons

40. Triangles

41. Polygons / Quadrilaterals

42. Graphical Division

43. Shape in a Shape

44. Circles

45. Solids

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What's inside

Learning objectives

Master counting and probability for the act
Solve even difficult questions in counting and probability with amazing conceptual clarity

Counting and probability basics to advanced concepts

Master counting and probability for the act
Solve even difficult questions in counting and probability with amazing conceptual clarity
Counting and probability basics to advanced concepts

Syllabus

Counting: Permutation and Combination

What is Permutation and Combination

Factorial

Permutation Illustration

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Career center

Learners who complete ACT Math Prep | Master counting, Probability and Geometry will develop knowledge and skills that may be useful to these careers:

Educator in Mathematics

An Educator in Mathematics teaches mathematical concepts to students, requiring deep conceptual understanding and clear communication skills. This role often benefits from an advanced degree in education or mathematics. The "ACT Math Prep | Master counting, Probability and Geometry" course is perfectly aligned with the core content an Educator in Mathematics would teach, particularly at the high school or introductory college level. The detailed coverage of "Permutation and Combination," "Probability Basics to Advanced concepts" like "Conditional Probability," and comprehensive "Geometry basics: Points, lines, planes, angles, polygons, Triangles, Polygons / Quadrilaterals, Circles, Solids" provides a solid mastery of these fundamental subjects. The structured learning approach within the course, dividing topics into subcomponents and diving deep, exemplifies effective teaching methodologies and helps build a strong foundation for explaining complex ideas clearly to others.

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Actuarial Scientist

Actuarial Scientists are experts in risk management, applying advanced mathematical and statistical methods to assess financial risks in insurance and finance. This role typically requires an advanced degree. The "ACT Math Prep | Master counting, Probability and Geometry" course provides a foundational understanding of core mathematical principles directly relevant to this field. The extensive coverage of probability, including "Probability Basics," "Conditional Probability," "R successes in N Trials," and "Odds in favour / Odds against," is absolutely critical for an Actuarial Scientist, as these concepts form the backbone of risk modeling, premium calculation, and loss projection. Furthermore, the detailed exploration of permutation and combination, focusing on "Permutation in Depth" and "Combination in Depth," helps develop the exact kind of combinatorial reasoning needed for complex actuarial problems involving selections and arrangements of events and outcomes.

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Biostatistician

Biostatisticians apply statistical methods to biological and health-related research, designing studies, analyzing data, and interpreting results. This role typically requires an advanced degree, often a Master's or PhD. The "ACT Math Prep | Master counting, Probability and Geometry" course provides core mathematical skills that are indispensable for a Biostatistician. The extensive coverage of probability, from "Probability Basics" to "Conditional Probability" and "R successes in N Trials," forms the bedrock for understanding statistical inference, hypothesis testing, and epidemiological modeling. The structured approach to permutation and combination helps in understanding sampling techniques, experimental design, and analyzing genetic or biological sequences. While geometry is less directly utilized, the overall quantitative rigor and systematic problem-solving approach fostered by the course are highly beneficial for the analytical demands of this specialized and impactful scientific field.

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Quantitative Researcher

A Quantitative Researcher applies sophisticated mathematical and statistical techniques to solve complex problems, often in finance, technology, or scientific domains. This role typically requires an advanced degree, often a PhD. The "ACT Math Prep | Master counting, Probability and Geometry" course provides a fundamental mathematical toolkit that may be helpful for aspiring Quantitative Researchers. The rigorous treatment of probability concepts, such as "Conditional Probability" and "R successes in N Trials," is indispensable for developing and testing statistical models and hypotheses. The comprehensive exploration of permutation and combination, including "Permutation in Depth" and "Combination in Depth," equips learners with the combinatorial reasoning essential for designing experiments, sampling, and understanding the structure of complex data. The emphasis on mastering geometry also builds a strong foundation in spatial thinking and logical deduction, which underpins advanced quantitative methods.

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Machine Learning Engineer

Machine Learning Engineers design, build, and deploy AI models, a field that typically requires an advanced degree. The "ACT Math Prep | Master counting, Probability and Geometry" course provides fundamental mathematical concepts that are essential for a Machine Learning Engineer. A deep understanding of probability, including "Probability Basics," "Conditional Probability," and "Independent Events," is absolutely critical, as machine learning algorithms are often built upon probabilistic frameworks, statistical inference, and Bayesian methods. While combinatorics (permutation and combination) may not be as visibly central, the logical and systematic approach to counting possibilities is foundational for understanding model complexity, analyzing feature spaces, and certain aspects of algorithm efficiency. The geometric understanding, though not always direct for high-dimensional data, aids in conceptualizing data spaces and algorithmic relationships for optimization.

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Operations Research Analyst

Operations Research Analysts use advanced analytical methods to improve decision-making and efficiency within organizations, often involving complex optimization and planning problems. This field often benefits from an advanced degree. The "ACT Math Prep | Master counting, Probability and Geometry" course helps establish strong quantitative reasoning and structured problem-solving skills crucial for an Operations Research Analyst. The in-depth study of permutation and combination, including the "Fundamental Principle of counting" and "Grouping Trick," is directly applicable to optimizing resource allocation, scheduling, and logistics. The probability section, covering "Independent Events" and "Conditional Probability," is also vital for modeling uncertain scenarios and assessing risk in operational processes. The structured approach to geometry fosters spatial and logical thinking useful in various modeling contexts.

See salaries and explore the career path for Operations Research Analyst

Data Analyst

A Data Analyst frequently works with quantitative data, requiring a strong grasp of numerical reasoning and problem-solving. This course, "ACT Math Prep | Master counting, Probability and Geometry," provides foundational mathematical skills essential for success in this role. Understanding probability, as covered in topics like "Conditional Probability" and "R successes in N Trials," is crucial for interpreting data, understanding distributions, and making informed decisions based on evidence. The logical thinking fostered by mastering permutation and combination concepts, specifically the "Fundamental Principle of counting" and "Relationship between Permutation and Combination," directly translates to structuring data problems and evaluating various analytical scenarios, which are core tasks for a data analyst. Even the geometry component helps develop spatial reasoning useful in areas like data visualization or geographical data analysis within an advanced career setting.

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Financial Analyst

A Financial Analyst assesses investment opportunities and market trends, often relying on quantitative models and risk assessment. The "ACT Math Prep | Master counting, Probability and Geometry" course helps build a robust foundation in essential mathematical concepts directly applicable to this field. Probability topics like "Odds in favour / Odds against" and "Conditional Probability" are particularly relevant for understanding market volatility, evaluating asset performance, and calculating the likelihood of various financial outcomes. The structured problem-solving approach emphasized in mastering permutation and combination, particularly with "Permutation in Depth" and "Combination in Depth," enhances the logical reasoning vital for dissecting complex financial data and making informed forecasts. While geometry is less direct, the overall quantitative rigor and systematic thinking are highly beneficial for the analytical demands of a Financial Analyst role.

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Civil Engineer

Civil Engineers design, construct, and maintain infrastructure projects like roads, buildings, and bridges. This profession rigorously requires a strong understanding of physical structures and spatial relationships. The "ACT Math Prep | Master counting, Probability and Geometry" course provides foundational mathematical skills that are crucial for a Civil Engineer. The in-depth study of geometry, covering "Points, lines, planes, angles, polygons, Triangles, Polygons / Quadrilaterals, Circles, Solids," is directly applicable to structural design, drafting, surveying, and understanding the mechanics of materials. While probability may be less frequently applied in daily design tasks, understanding concepts like "Independent Events" or "Conditional Probability" may be useful for risk assessment in construction projects, material failure analysis, or even traffic flow modeling. The overall rigorous quantitative training is highly beneficial for problem-solving in this field.

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Architectural Designer

An Architectural Designer creates conceptual and visual designs and plans for buildings and structures, blending aesthetic principles with practical functionality. This role benefits immensely from a strong grasp of spatial reasoning and geometric principles. The "ACT Math Prep | Master counting, Probability and Geometry" course is particularly helpful for an Architectural Designer due to its comprehensive focus on geometry. Topics such as "Points, lines, planes, angles, polygons," "Triangles," "Polygons / Quadrilaterals," "Circles," and "Solids" are directly applicable to drafting, blueprint reading, understanding spatial relationships, and conceptualizing three-dimensional structures. The systematic approach to learning these geometric components provides a solid foundation for precise design work and visualizing complex architectural forms. While permutation, combination, and probability are less direct, the overall quantitative rigor and logical problem-solving abilities developed are valuable for structural considerations and planning.

See salaries and explore the career path for Architectural Designer

Scientific Researcher

Scientific Researchers conduct experiments, analyze data, and develop theories in various scientific disciplines. This role typically requires an advanced degree, often a PhD. The "ACT Math Prep | Master counting, Probability and Geometry" course provides a fundamental quantitative framework that may be helpful for a Scientific Researcher. The robust understanding of probability, covering "Probability Basics," "Complement of an Event," and "Independent Events," is essential for experimental design, statistical analysis of results, and drawing valid conclusions in various scientific studies. The logical and combinatorial reasoning developed through mastering "Permutation and Combination" concepts can assist in structuring experimental setups, understanding sampling, and analyzing the variability within data. Even the principles of geometry may be relevant in fields like physics, chemistry (molecular geometry), or engineering for spatial analysis and modeling of physical phenomena.

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Game Developer

Game Developers create interactive digital experiences, which often involve complex logic, physics, and visual design. The "ACT Math Prep | Master counting, Probability and Geometry" course may be useful for a Game Developer in several key areas. The robust understanding of geometry, encompassing "Triangles," "Polygons / Quadrilaterals," "Circles," and "Solids," is fundamental for 2D and 3D graphics rendering, collision detection, and level design within game engines. Moreover, probability concepts such as "Odds in favour / Odds against" and "R successes in N Trials" are directly applicable to designing game mechanics for random events, loot drops, critical hits, or statistical balancing of game difficulty. The combinatorial reasoning from permutation and combination helps in designing complex game states and ensuring efficient algorithm design for game logic and unique interactions.

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Logistics Analyst

A Logistics Analyst optimizes supply chain operations, manages inventory, and plans transportation routes to ensure efficiency and cost-effectiveness. The "ACT Math Prep | Master counting, Probability and Geometry" course provides foundational quantitative skills that may be useful for a Logistics Analyst. The concepts of permutation and combination, especially the "Fundamental Principle of counting" and "Grouping Trick," are directly applicable to optimizing routing problems, scheduling deliveries, and managing various inventory configurations. Probability topics, such as "Independent Events" and "Conditional Probability," can help in demand forecasting, assessing supply chain risks, and modeling various operational scenarios to make data-driven decisions. The logical and structured problem-solving approach emphasized across all topics is crucial for dissecting complex logistical challenges and developing efficient, data-driven solutions in a dynamic environment.

See salaries and explore the career path for Logistics Analyst

Software Engineer

Software Engineers design, develop, and maintain software systems, requiring strong logical and problem-solving capabilities. The quantitative and logical reasoning skills developed through the "ACT Math Prep | Master counting, Probability and Geometry" course may be useful for a Software Engineer. Understanding permutation and combination, with topics like "Fundamental Principle of counting" and "Relationship between P&C," is crucial for designing efficient algorithms, especially when dealing with data structures, sorting, or graph theory where counting possibilities and arrangements are key considerations. Probability concepts, such as "Independent Events" and "Conditional Probability," are also relevant for areas like randomized algorithms, simulations, or even game development. The systematic problem-solving approach cultivated by mastering geometry aids in designing logical and robust software architectures and understanding computational geometry problems.

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Urban Planner

Urban Planners develop strategies for land use and community development, often involving complex spatial analysis and resource allocation. The "ACT Math Prep | Master counting, Probability and Geometry" course may be useful for an Urban Planner by significantly enhancing spatial reasoning and quantitative problem-solving abilities. The extensive focus on geometry, including "Points, lines, planes, angles, polygons," "Triangles," and understanding "Polygons / Quadrilaterals" and "Circles," is directly applicable to site planning, zoning regulations, visualizing urban layouts, and assessing infrastructure needs. While probability and combinatorics are less central to daily tasks, the fundamental logical thinking developed through these sections contributes to optimizing resource distribution and analyzing various development scenarios. The ability to form a holistic picture of dealt topics, as emphasized by the course, aligns with the comprehensive nature of urban planning challenges.

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