A-level Mathematics for Year 12 - Course 2: Calculus, Newton’s Laws and Hypothesis Testing from edX

This course by Imperial College London is designed to help you develop the skills you need to succeed in your A-level mathematics exams.You’ll also be encouraged to consider how what you know fits into the wider mathematical world.

Over seven modules, covering an introduction to calculus, Newton’s laws and statistical hypothesis testing your initial skillset will be extended to give a clear understanding of how background knowledge underpins the A -level course.

You will investigate key topic areas to gain a deeper understanding of the skills and techniques that you can apply throughout your A-level study. These skills include:

Fluency – selecting and applying correct methods to answer with speed and efficiency
Confidence – critically assessing mathematical methods and investigating ways to apply them
Problem solving – analysing the ‘unfamiliar’ and identifying which skills and techniques you require to answer questions
Constructing mathematical argument – using mathematical tools such as diagrams, graphs, logical deduction, mathematical symbols, mathematical language, data handling, construct mathematical argument and present precisely to others
Deep reasoning – analysing and critiquing mathematical techniques, arguments, formulae and proofs to comprehend how they can be applied

What you'll learn

How to differentiate a number exponential functions
How to apply differentiation to find stationary points
How to find the equations of tangents and normals to curves
How to model growth and decay using the exponential function
How to manipulate expressions involving indices by using logarithms
How to integrate an exponential function
How to use integration to find the equation of a curve from its gradient function
How to use integration to find the area enclosed by a curve
How to use Newton’s laws to solve problems involving forces
How to use the Binomial probability distribution to find the probability of a number of successes in a series of statistical trials
How to define a statistical hypothesis test using the binomial distribution.

What's inside

Learning objectives

How to differentiate a number exponential functions
How to apply differentiation to find stationary points
How to find the equations of tangents and normals to curves
How to model growth and decay using the exponential function
How to manipulate expressions involving indices by using logarithms
How to integrate an exponential function

How to use integration to find the equation of a curve from its gradient function
How to use integration to find the area enclosed by a curve
How to use newton’s laws to solve problems involving forces
How to use the binomial probability distribution to find the probability of a number of successes in a series of statistical trials
How to define a statistical hypothesis test using the binomial distribution.

How to differentiate a number exponential functions
How to apply differentiation to find stationary points
How to find the equations of tangents and normals to curves
How to model growth and decay using the exponential function
How to manipulate expressions involving indices by using logarithms
How to integrate an exponential function
How to use integration to find the equation of a curve from its gradient function
How to use integration to find the area enclosed by a curve
How to use newton’s laws to solve problems involving forces
How to use the binomial probability distribution to find the probability of a number of successes in a series of statistical trials
How to define a statistical hypothesis test using the binomial distribution.

Syllabus

Please see course syllabus via the

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Develops fluency, confidence, and problem-solving abilities, which are core skills for A-level mathematics

Guides learners through key topic areas to gain a comprehensive understanding of A-level mathematics, building a solid foundation

Teaches skills and techniques that are directly applicable to A-level mathematics study and exams

Provides opportunities to analyze and critique mathematical methods and arguments, fostering deep reasoning

Emphasizes constructing mathematical arguments using precise language and symbols, supporting learners' mathematical communication skills

Covers essential topics such as calculus, Newton's laws, and statistical hypothesis testing, aligning with A-level mathematics curriculum

Reviews summary

High regard calculus 12

According to one review, this course is highly regarded by at least one student who feels it is good at clearing up doubts.

Helpful for clarifying concepts.

"Best course to clear many doubts."

"I would like to do it next time also for remaining portion of +2 level."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in A-level Mathematics for Year 12 - Course 2: Calculus, Newton’s Laws and Hypothesis Testing with these activities:

Review key concepts from pre-calculus

Show steps

Refreshes foundational knowledge necessary for success in A-level mathematics.

Browse courses on Algebra

Show steps

Review notes, textbooks, or online resources to recap the main concepts.
Practice solving problems related to these concepts to regain familiarity.
Seek clarification from the instructor or classmates if needed.

Review Calculus concepts

Show steps

Refresh your understanding of calculus concepts, such as limits, derivatives, and integrals.

Browse courses on Calculus

Show steps

Review your notes and textbooks on calculus.
Solve practice problems to reinforce your understanding.

Connect with a mathematics tutor or mentor

Show steps

Provides personalized guidance and support, tailored to individual learning needs and goals.

Show steps

Inquire with the instructor, department, or online platforms for recommended tutors or mentors.
Interview potential tutors or mentors to find a good fit in terms of expertise, availability, and communication style.
Schedule regular sessions to discuss course concepts, clarify doubts, and receive feedback on practice problems.

Nine other activities

Expand to see all activities and additional details

Show all 12 activities

Join a study group or online forum

Show steps

Collaborate with peers and engage in discussions to enhance your understanding.

Show steps

Join a study group or online forum related to the course.
Participate in discussions and ask questions.
Share your knowledge and help others.

Explore additional online resources

Show steps

Supplements the course materials by introducing new perspectives, deepening understanding, and expanding knowledge.

Browse courses on Mathematical Modeling

Show steps

Search for reputable websites, YouTube channels, or online courses that cover topics related to the course content.
Select tutorials that align with your learning style and specific areas of interest.
Take notes and engage with the material actively, asking questions and seeking clarification when needed.
Consider discussing your findings and insights with classmates or the instructor.

Engage in peer-to-peer learning

Show steps

Promotes collaborative learning, knowledge sharing, and diverse perspectives.

Show steps

Form study groups or connect with classmates outside of class.
Discuss course concepts, work through problems together, and share different approaches.
Provide feedback and support to peers, fostering a positive and inclusive learning environment.
Consider presenting your findings or insights to the entire class.

Follow tutorials on exponential functions

Show steps

Explore tutorials that provide step-by-step guidance on working with exponential functions.

Browse courses on Exponential Functions

Show steps

Search for tutorials on exponential functions.
Follow the tutorials and practice the examples.

Complete online problem sets

Show steps

Provides repeated practice of key concepts and techniques, leading to improved fluency and confidence in applying mathematical methods.

Browse courses on Differentiation

Show steps

Identify reputable online platforms or textbooks that offer problem sets aligned with the course topics.
Set aside dedicated time for practicing these problems.
Work through the problems methodically, striving for accuracy and understanding.
Review and analyze your solutions to identify areas for improvement.

Solve practice problems on Newton's laws

Show steps

Engage in repetitive practice by solving a variety of problems related to Newton's laws.

Browse courses on Newton's Laws of Motion

Show steps

Gather practice problems from textbooks or online resources.
Solve the problems and check your answers.
Identify areas where you need additional practice.

Compile a glossary of mathematical terms

Show steps

Provides a concise and accessible reference for key mathematical terminology used in the course.

Show steps

Create a document or spreadsheet to record the terms.
Define each term clearly and concisely, using examples and diagrams when appropriate.
Organize the terms alphabetically or by topic for ease of reference.
Share the glossary with classmates or the instructor for feedback and additions.

Create a practice problem worksheet

Show steps

Focus on the key topic areas, including fluency, confidence, problem solving, constructing mathematical argument, and deep reasoning. Use these areas to generate problems that can help reinforce concepts.

Browse courses on Calculus

Show steps

Identify the key concepts and skills covered in the course syllabus.
Brainstorm different types of practice problems that can assess these concepts and skills.
Create a worksheet with a variety of problems, ensuring a range of difficulty levels.
Consider using online platforms or collaborative tools to share the worksheet with classmates for feedback and discussion.

Develop a mathematical model or simulation

Show steps

Encourages deep reasoning and problem-solving skills by applying mathematical concepts to real-world scenarios.

Browse courses on Exponential Functions

Show steps

Identify a problem or phenomenon that can be modeled mathematically.
Research and gather relevant data to inform the model.
Develop a mathematical model or simulation using appropriate mathematical principles and techniques.
Test, validate, and refine the model based on the available data.
Communicate the findings and insights gained from the model, including any limitations or assumptions.

Career center

Learners who complete A-level Mathematics for Year 12 - Course 2: Calculus, Newton’s Laws and Hypothesis Testing will develop knowledge and skills that may be useful to these careers:

Economist

Economists conduct research in economics and teach economics at the university level. They work in a variety of fields, including microeconomics, macroeconomics, and econometrics. This course may be helpful because it will help you build a foundation in mathematical and statistical concepts, which are essential for understanding economics.

See salaries and explore the career path for Economist

Physicist

Physicists conduct research in physics and teach physics at the university level. They work in a variety of fields, including astrophysics, condensed matter physics, and particle physics. This course may be helpful because it will help you build a foundation in mathematical and statistical concepts, which are essential for understanding physics.

See salaries and explore the career path for Physicist

Mathematician

Mathematicians conduct research in mathematics and teach mathematics at the university level. They work in a variety of fields, including algebra, geometry, and statistics. This course may be helpful because it will help you build a foundation in mathematical and statistical concepts, which are essential for understanding mathematics.

See salaries and explore the career path for Mathematician

Data Scientist

Data Scientists use mathematical and statistical techniques to extract insights from data. They work in a variety of industries, helping organizations make informed decisions about their products, services, and marketing strategies. This course may be helpful because it will help you build a foundation in statistical hypothesis testing and exponential functions, which are essential for understanding data.

See salaries and explore the career path for Data Scientist

Machine Learning Engineer

Machine Learning Engineers design and build machine learning models. They use these models to solve real-world problems, such as predicting customer churn or identifying fraudulent transactions. This course may be helpful because it will help you build a foundation in statistical hypothesis testing and exponential functions, which are essential for understanding machine learning algorithms.

See salaries and explore the career path for Machine Learning Engineer

Statistician

Statisticians collect, analyze, and interpret data to help organizations make informed decisions. They use statistical techniques to understand trends and patterns in data. This course may be helpful because it will help you build a foundation in statistical hypothesis testing and exponential functions, which are essential for understanding data.

See salaries and explore the career path for Statistician

Computer Scientist

Computer Scientists research, design, and develop computer systems and applications. They work in a variety of industries, including academia, government, and industry. This course may be helpful because it will help you build a foundation in mathematical and statistical concepts, which are essential for understanding computer science.

See salaries and explore the career path for Computer Scientist

Software Engineer

Software Engineers design, develop, and maintain software systems. They work in a variety of industries, including finance, healthcare, and technology. This course may be helpful because it will help you build a foundation in mathematical and statistical concepts, which are essential for understanding software design and development.

See salaries and explore the career path for Software Engineer

Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to assess risk and make investment decisions. They work in the financial industry, helping firms make informed decisions about their investments. This course may be helpful because it will help you build a foundation in statistical hypothesis testing and exponential functions, which are essential for understanding financial data.

See salaries and explore the career path for Quantitative Analyst

Risk Manager

Risk Managers assess and manage risks for organizations. They help organizations identify potential risks and develop strategies to mitigate those risks. This course may be helpful because it will help you build a foundation in statistical hypothesis testing and exponential functions, which are used by Risk Managers to assess and mitigate risk.

See salaries and explore the career path for Risk Manager

Operations Research Analyst

Operations Research Analysts use mathematical and statistical techniques to improve the efficiency of business operations. They help organizations optimize their processes and make better decisions. This course may be helpful because it will help you build a foundation in statistical hypothesis testing and exponential functions, which are essential for understanding operations data.

See salaries and explore the career path for Operations Research Analyst

Market Researcher

Market Researchers gather and analyze data to understand consumer behavior and market trends. They use this information to help businesses make informed decisions about their products and marketing strategies. This course may be helpful because it will help you build a foundation in statistical hypothesis testing and exponential functions, which are essential for understanding market data.

See salaries and explore the career path for Market Researcher

Data Analyst

Data Analysts use statistical tools to organize information, identify trends, and support decision-making. They sometimes specialize in a particular domain, such as in finance or healthcare. This course may be helpful because it will help you build a foundation in statistical hypothesis testing and exponential functions, which are essential for understanding data.

See salaries and explore the career path for Data Analyst

Business Analyst

Business Analysts use data to solve business problems. They help organizations improve their performance by identifying opportunities and recommending solutions. This course may be helpful because it will help you build a foundation in statistical hypothesis testing and exponential functions, which are used by Business Analysts to make data-driven decisions.

See salaries and explore the career path for Business Analyst

Financial Analyst

Financial Analysts use mathematical and statistical techniques to evaluate investments. They help individuals and organizations make informed decisions about their financial portfolios. This course may be helpful because it will help you build a foundation in statistical hypothesis testing and exponential functions, which are essential for understanding financial data.

See salaries and explore the career path for Financial Analyst