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Philip Ramsden and Phil Chaffe

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

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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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What's inside

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

Syllabus

Module 1Indices and Surds
Recognise and use the laws of indices for all rational exponents
Use and manipulate surds, including rationalising the denominator
Read more
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

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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
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
Show steps
  • Review decimal, binary, octal, and hexadecimal systems
  • Learn to convert numbers between systems
  • Practice solving problems using different number systems
Organize Your Course Materials
Stay organized and improve your learning efficiency by compiling and reviewing your course materials regularly.
Show steps
  • 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
Supplement your course materials by reading a comprehensive book that covers the key concepts of A-level mathematics.
Show steps
  • Read through the relevant chapters of the book.
  • Work through the practice exercises provided in the book.
Seven other activities
Expand to see all activities and additional details
Show all ten activities
Master algebraic techniques
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
Prepare for the course by reviewing the laws of indices and working with surds.
Show steps
  • 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
Gain a better understanding of polynomial manipulation techniques through guided tutorials.
Browse courses on Polynomials
Show steps
  • 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
Sharpen your problem-solving abilities by practicing solving various types of inequalities.
Browse courses on Inequalities
Show steps
  • 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
Forming a study group allows you to connect with peers, discuss concepts, and gain diverse perspectives, enhancing your comprehension of the course material.
Show steps
  • 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
Demonstrate your comprehension of coordinate geometry by solving a comprehensive set of problems.
Browse courses on Coordinate Geometry
Show steps
  • 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
Apply your knowledge of mechanics by creating a simulation that demonstrates the principles of motion.
Browse courses on Mechanics
Show steps
  • 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.

Reading list

We've selected 17 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in A-level Mathematics for Year 12 - Course 1: Algebraic Methods, Graphs and Applied Mathematics Methods.
Provides a comprehensive introduction to mathematical methods used in the physical sciences, covering topics such as vector calculus, differential equations, and complex analysis. It useful reference for students who want to learn more about the mathematical methods used in the course.
Provides a comprehensive introduction to linear algebra, covering topics such as vector spaces, matrices, and linear transformations. It useful reference for students who want to learn more about the mathematical foundations of the course.
Provides a comprehensive introduction to mathematical methods used in physics and engineering, covering topics such as vector calculus, differential equations, and complex analysis. It useful reference for students who want to learn more about the mathematical methods used in the course.
Provides a comprehensive overview of advanced algebra, covering topics such as groups, rings, fields, and modules. It useful reference for students who want to learn more about the mathematical foundations of the course.
Provides a comprehensive introduction to linear algebra, covering topics such as vector spaces, matrices, and linear transformations. It useful reference for students who want to learn more about the mathematical foundations of the course.
Covers the syllabus of the new A-Level and is excellent for the Core of Mathematics for Advanced Level, for the IB Diploma and for students who are preparing for further mathematics courses at university.
Provides a comprehensive introduction to mathematical statistics, covering topics such as probability, random variables, and statistical inference. It useful reference for students who want to learn more about the statistical methods used in the course.
Provides a comprehensive introduction to statistics, covering topics such as probability, random variables, and statistical inference. It useful reference for students who want to learn more about the statistical methods used in the course.
Provides a comprehensive introduction to discrete mathematics, covering topics such as sets, logic, and graph theory. It useful reference for students who want to learn more about the mathematical foundations of the course.
Provides a rigorous introduction to calculus, covering topics such as limits, derivatives, integrals, and differential equations. It useful reference for students who want to learn more about the mathematical foundations of the course.
Provides a comprehensive review of mathematics, covering topics such as algebra, trigonometry, and calculus. It useful reference for students who want to brush up on their mathematical skills before taking the course.
Provides a comprehensive review of pre-calculus, covering topics such as algebra, trigonometry, and analytic geometry. It useful reference for students who want to brush up on their mathematical skills before taking the course.
Provides a gentle introduction to calculus, covering topics such as limits, derivatives, and integrals. It useful reference for students who want to learn more about the basics of calculus.
Provides a gentle introduction to algebra, covering topics such as polynomials, equations, and inequalities. It useful reference for students who want to learn more about the basics of algebra.
Provides a gentle introduction to trigonometry, covering topics such as angles, triangles, and trigonometric functions. It useful reference for students who want to learn more about the basics of trigonometry.
Provides a gentle introduction to calculus, covering topics such as limits, derivatives, and integrals. It useful reference for students who want to learn more about the basics of calculus.

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