A-level Mathematics for Year 12 - Course 1: Algebraic Methods, Graphs and Applied Mathematics Methods from edX

This course by Imperial College London is designed to help you develop the skills you need to succeed in your A-level maths exams.

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, 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

Over seven modules, your initial skillset will be extended to give a clear understanding of how background knowledge underpins the A
-level course. You’ll also be encouraged to consider how what you know fits into the wider mathematical world.

What you'll learn

Improve fluency and accuracy when using laws of indices and surds in a variety of calculations
Learn how to solve the types of inequalities you'll encounter at A-level and various ways to represent these
Discover how to divide any polynomial by either a linear or quadratic polynomial
Learn about the information found in different forms of the Cartesian equation of a circle and use these to solve coordinate geometry problems
Investigate the main transformations of graphs; translation, enlargement and reflection, and use these transformations to sketch new graphs
Understand the constant acceleration formulae through travel graphs illustration, speed, velocity, distance and displacement against time
Explore statistical sampling methods and weigh up the advantages and disadvantages of each one
Learn how to interpret data presented in a variety of forms including box plots, cumulative frequency curves, histograms and bar charts

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Learning objectives

fluency and accuracy when using laws of indices and surds in a variety of calculations
how to solve the types of inequalities you'll encounter at a-level and various ways to represent these
how to divide any polynomial by either a linear or quadratic polynomial
about the information found in different forms of the cartesian equation of a circle and use these to solve coordinate geometry problems

the main transformations of graphs; translation, enlargement and reflection, and use these transformations to sketch new graphs
the constant acceleration formulae through travel graphs illustration, speed, velocity, distance and displacement against time
statistical sampling methods and weigh up the advantages and disadvantages of each one
how to interpret data presented in a variety of forms including box plots, cumulative frequency curves, histograms and bar charts

fluency and accuracy when using laws of indices and surds in a variety of calculations
how to solve the types of inequalities you'll encounter at a-level and various ways to represent these
how to divide any polynomial by either a linear or quadratic polynomial
about the information found in different forms of the cartesian equation of a circle and use these to solve coordinate geometry problems
the main transformations of graphs; translation, enlargement and reflection, and use these transformations to sketch new graphs
the constant acceleration formulae through travel graphs illustration, speed, velocity, distance and displacement against time
statistical sampling methods and weigh up the advantages and disadvantages of each one
how to interpret data presented in a variety of forms including box plots, cumulative frequency curves, histograms and bar charts

Syllabus

Module 1Indices and Surds

Recognise and use the laws of indices for all rational exponents

Use and manipulate surds, including rationalising the denominator

Solve a variety of problems that include surds and indices

Module 2 Inequalities

Solve linear and quadratic inequalities in a single variable and interpret these solutions graphically

Express the solutions to linear and quadratic inequalities usingnumber lines and inequality notation, and using the terms ‘and’and ‘or’and set notation

Represent linear and quadratic inequalities in two variables graphically, using standard A-level conventions

Module 3 The Factor Theorem & Algebraic Division

Manipulate polynomials algebraically, using the factor theorem to write a polynomial as the product of linear factors or a combination of linear and quadratic factors

Divide one polynomial by another of a lower order by equating coefficients

Module 4Coordinate Geometry

Solve problems using the coordinate geometry of the circle

Complete the square to find the centre and radius of a circle from its equation

Solve problems using the properties of the angle in a semicircle, the perpendicular from the centre to a chord, and a tangent from a poin

Module 5 Graphical Transformation and Curve Sketching

Use curve sketching techniques based on the the shapes and symmetries of standard curves

Identify key features of a curve from its equation and transform the equations of linear, quadratic, rational and trigonometrical curves using translations, rotations and stretches

Use knowledge of the symmetry and asymptotes of standard curves to create sketches

Module 6 An Introduction to Mechanics

Interpret and accurately use the term distance, speed, displacement, velocity, and acceleration

Interpret graphs to do with speed against time, distance against time, velocity against time and acceleration against time, and solve problems involving motion in a straight line with constant acceleration

Apply the formulae for constant acceleration to solve problems involving motion in a straight line

Module 7 An Introduction to Statistics

Identify the ideas of a population and a sample and use simple sampling techniques to draw informal inferences about populations

Apply critical thinking to issues of representative sampling

Interpret histograms to draw informal inferences about univariate data

Interpret scatter diagrams, regression lines and the ideas of correlation to draw informal inferences about bivariate data

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Provides foundation for learning A-level maths

Taught by instructors from Imperial College London, which is recognized for its work in math

Strengthens foundation in math in preparation for A-level exams

Covers key concepts for A-level math exams, such as fluency, confidence, problem solving, mathematical argument, and deep reasoning

Includes a variety of resources, such as videos, readings, and discussions

Reviews summary

Thorough math course for a level students

Learners say that this thorough Algebraic Methods, Graphs, and Applied Mathematics Methods course is ideal for Year 12 students. The engaging assignments include many examples and exercises to help learners relearn math or prepare for higher level courses. Students appreciate the instructor's clear explanations and highly recommend this course.

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 1: Algebraic Methods, Graphs and Applied Mathematics Methods with these activities:

Review number systems

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This course requires a firm grasp of number systems. Take time to review different number systems and their underlying principles to ensure a stronger foundation.

Browse courses on Number Systems

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Review decimal, binary, octal, and hexadecimal systems
Learn to convert numbers between systems
Practice solving problems using different number systems

Organize Your Course Materials

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Stay organized and improve your learning efficiency by compiling and reviewing your course materials regularly.

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Gather all of your notes, assignments, quizzes, and exams.
Organize the materials into a logical structure.
Review the materials regularly to reinforce your understanding.

Read 'Essential Mathematics for A-Level' by Dan Green

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Supplement your course materials by reading a comprehensive book that covers the key concepts of A-level mathematics.

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Read through the relevant chapters of the book.
Work through the practice exercises provided in the book.

Seven other activities

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Master algebraic techniques

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Algebraic techniques are foundational to this course's concepts. Dedicate time to practice and master these techniques through problem-solving drills.

Browse courses on Algebraic Expressions

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Refresh basic algebraic operations
Practice solving equations and inequalities
Master factoring polynomials
Apply algebraic techniques to solve word problems

Review the Laws of Indices and Surds

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Prepare for the course by reviewing the laws of indices and working with surds.

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Revise the basic definitions and properties of indices.
Practice using the laws of indices to simplify expressions.
Work on problems involving the manipulation of surds.

Learn the Factor Theorem and Algebraic Division

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Gain a better understanding of polynomial manipulation techniques through guided tutorials.

Browse courses on Polynomials

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Follow tutorials on the factor theorem.
Learn about the process of algebraic division of polynomials.
Practice applying these techniques to solve problems.

Solve Inequalities Practice

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Sharpen your problem-solving abilities by practicing solving various types of inequalities.

Browse courses on Inequalities

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Review the different types of inequalities.
Practice solving linear inequalities.
Work on solving quadratic inequalities.
Learn how to represent inequalities graphically.

Join a study group

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Forming a study group allows you to connect with peers, discuss concepts, and gain diverse perspectives, enhancing your comprehension of the course material.

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Find like-minded peers or form a group
Establish regular meeting times and a study schedule
Collaborate on problem-solving and review course concepts

Coordinate Geometry Problem Set

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Demonstrate your comprehension of coordinate geometry by solving a comprehensive set of problems.

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Review the key concepts of coordinate geometry.
Practice solving problems involving circles.
Create a problem set that covers various aspects of coordinate geometry.

Develop a Mechanics Simulation

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Apply your knowledge of mechanics by creating a simulation that demonstrates the principles of motion.

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Design the simulation, including the objects, forces, and environment.
Implement the simulation using a programming language.
Test and refine the simulation to ensure accurate results.
Present the simulation and explain its educational value.

Career center

Learners who complete A-level Mathematics for Year 12 - Course 1: Algebraic Methods, Graphs and Applied Mathematics Methods will develop knowledge and skills that may be useful to these careers:

Data Scientist

A Data Scientist is responsible for using data to solve business problems. Data Scientists use their knowledge of mathematics, statistics, and computer science to develop and implement data-driven solutions. This course can help you build a strong foundation in mathematics and problem-solving, which are essential skills for success as a Data Scientist.

See salaries and explore the career path for Data Scientist

Operations Research Analyst

An Operations Research Analyst is responsible for using mathematical and analytical techniques to solve problems related to business operations. Operations Research Analysts use their knowledge of mathematics, statistics, and computer science to develop and implement solutions to improve efficiency and productivity. This course can help you build a strong foundation in mathematics and problem-solving, which are essential skills for success as an Operations Research Analyst.

See salaries and explore the career path for Operations Research Analyst

Statistician

A Statistician is responsible for collecting, analyzing, and interpreting data. Statisticians use their knowledge of mathematics and statistics to provide insights into data and make predictions about future events. This course can help you develop your analytical and problem-solving skills to succeed as a Statistician. The modules on statistics, graphical transformations, and curve sketching will be particularly relevant to this role.

See salaries and explore the career path for Statistician

Data Analyst

A Data Analyst is responsible for uncovering patterns and insights from data. Data Analysts use their knowledge of mathematics and statistics to interpret data and present their findings to stakeholders. This course can help you develop your analytical and problem-solving skills to succeed as a Data Analyst. The modules on statistics, graphical transformations, and curve sketching will be particularly relevant to this role.

See salaries and explore the career path for Data Analyst

Financial Analyst

A Financial Analyst is responsible for providing financial advice and guidance to individuals and organizations. Financial Analysts use their knowledge of mathematics and economics to analyze financial data and make recommendations on investments and other financial decisions. This course can help you build a solid foundation in mathematics and problem-solving, which are essential skills for success as a Financial Analyst.

See salaries and explore the career path for Financial Analyst

Actuary

An Actuary is responsible for assessing and managing financial risks. Actuaries use their knowledge of mathematics, statistics, and economics to develop and implement strategies to mitigate risks. This course can help you build a strong foundation in mathematics and problem-solving, which are essential skills for success as an Actuary.

See salaries and explore the career path for Actuary

Quantitative Analyst

A Quantitative Analyst is responsible for using mathematical and statistical models to analyze financial data and make investment decisions. Quantitative Analysts use their knowledge of mathematics, statistics, and computer science to develop and implement trading strategies. This course can help you build a strong foundation in mathematics and problem-solving, which are essential skills for success as a Quantitative Analyst.

See salaries and explore the career path for Quantitative Analyst

Investment Analyst

An Investment Analyst is responsible for researching and analyzing investments. Investment Analysts use their knowledge of mathematics, economics, and finance to make recommendations on investments and other financial decisions. This course can help you build a solid foundation in mathematics and problem-solving, which are essential skills for success as an Investment Analyst.

See salaries and explore the career path for Investment Analyst

Software Engineer

A Software Engineer is responsible for designing, developing, and maintaining software applications. Software Engineers use their knowledge of mathematics, computer science, and engineering to create software solutions that meet the needs of users. This course can help you develop your analytical and problem-solving skills, which are essential for success as a Software Engineer. The modules on graphical transformations and curve sketching will be particularly relevant to this role.

See salaries and explore the career path for Software Engineer

Mathematician

A Mathematician is responsible for developing new mathematical theories and solving mathematical problems. Mathematicians use their knowledge of mathematics to make advances in various fields, such as science, engineering, and medicine. This course can help you develop your analytical and problem-solving skills, which are essential for success as a Mathematician.

See salaries and explore the career path for Mathematician

Economist

An Economist is responsible for studying and analyzing economic data to make predictions about the future. Economists use their knowledge of mathematics, statistics, and economics to develop and implement economic policies. This course can help you build a strong foundation in mathematics and problem-solving, which are essential skills for success as an Economist.

See salaries and explore the career path for Economist