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Advanced Mathematics 1

  • Description
  • Outcome
  • Certification
  • This free online training explores complex numbers and equations, polynomial equations, conics, advanced trigonometry, differentiation, antiderivatives, and vectors in 2- and 3-space. This course is both an ideal study-aid for students to improve their skills in their spare time or for anyone interested in exploring the world of mathematics.

  • Upon completion of this course you will understand nominal, discrete and continuous data in frequency tables. You will know the product rule and you will be able to easily perform calculations of differentiation. You will gain a good knowledge of antiderivatives including Hyperbolic functions, partial fractions, linear substitution, odd and even powers. You will understand the relationship between graphs and their antiderivatives. You will be able to calculate complex numbers using addition, subtraction, multiplication and division. You will be familiar with DeMoivre's Theorom, polar form multiplication and division. This course will teach you how to calculate conics, degrees, radians, inverse circular functions, polynomial equations and much more.

  • All Alison courses are free to study. To successfully complete a course you must score 80% or higher in each course assessments. Upon successful completion of a course, you can choose to make your achievement formal by purchasing an official Alison Diploma, Certificate or PDF.

    Having an official Alison document is a great way to share your success. Plus it’s:

    • Ideal for including in CVs, job applications and portfolios
    • An indication of your ability to learn and achieve high results
    • An incentive to continue to empower yourself through learning
    • A tangible way of supporting the Alison mission to empower people everywhere through education.

Advanced Mathematics 1
  • Free

  • 3-4 Hours

  • XSIQ

  • Assessment

  • Certification

  • 50 Pts

Modules List( 17 )
  • Module
    1
    Creating a frequency table from data
    • Creating a frequency table from data This free online course covers types of data such as nominal, discrete and continuous data, and how to create frequency tables from data. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
    • Frequency and graphs - overview
    • Nominal data
    • Discrete data
    • Continuous data
    • Frequency tables with nominal data
    • Frequency tables with discrete data
    • Frequency tables - discrete data and summary statistics
    • Mean from frequency tables - discrete data
    • Interpreting column graphs
    • Family size cumulative frequency
  • Module
    2
    Differentiation - Product rule
    • Differentiation - Product rule This free online course covers the product rule for antiderivatives. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
    • Product Rule
    • Example 1
    • Example 2
    • Example 3
  • Module
    3
    Antiderivatives
    • Antiderivatives This free online course covers topics related to antiderivatives such as standard antiderivative types, hyperbolic functions, and partial fractions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
    • Review of Standard Antiderivatives
    • Standard Antiderivative Types
    • Type 2 - Hyperbolic Functions
    • Type 3 - Partial Fractions
    • Example 2
    • Type 5 - Linear Substitution
  • Module
    4
    Antiderivatives of circular functions
    • Antiderivatives of circular functions This free online course covers the topic of the antiderivatives of circular functions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
    • Type 4 - Inverse Circular Functions
    • Examples 1 and 2
    • Examples 3 and 4
    • Examples 5 and 6
    • Type 6 - Odd and Even Powers
    • Odd Powers
    • Even Powers
  • Module
    5
    Antiderivatives and their graphs
    • Antiderivatives and their graphs This free online course covers the relationship between the graphs of functions and their antiderivatives. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
    • Relationships Between Graphs of Functions and their Antiderivatives
    • Original and Antiderivative Functions
    • Graphs of Antiderivatives
    • Examples 1 and 2
    • Examples 3 and 4
    • Examples 5 and 6
  • Module
    6
    Complex numbers 1
    • Complex numbers 1 This free online course covers topics related to complex numbers such as the addition, subtraction, multiplication, and division of complex numbers. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
    • Introduction
    • Operations with Complex Numbers
    • Addition and Subraction of Complex Numbers
    • Multiplication of Complex Numbers by a Constant
    • Multiplication of Complex Numbers by Another Complex Number
    • Division and Complex Conjugates
    • Division of Complex Numbers
    • Argand Diagram
  • Module
    7
    Complex numbers 2
    • Complex numbers 2 This free online course covers topics related to complex numbers such as the polar form multiplication, and division and the conversion between polar form and cartesian form. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
    • Polar form
    • Conversion between polar form and cartesian form
    • DeMoivre's Theorem
    • Polar form multiplication - example 1
    • Polar form division - example 1
    • Polar form multiplication - example 2
    • Polar form division - example 2
  • Module
    8
    Conics (elipses and hyperbolae)
    • Conics (elipses and hyperbolae) This free online course covers topics graphs of hyperbolae and ellipses and the transformation of hyperbolae. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
    • Graphs of Ellipses
    • Examples
    • Graphs of Hyperbolae
    • Example 1
    • Example 2
    • Example 3
    • Example 4
    • Transformations of hyperbolae
    • Translations
  • Module
    9
    Degrees and radians
    • Degrees and radians This free online course covers the conversion of radian and degree measures. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
    • Exact Values
    • Conversions of Radian and Degree Measures
  • Module
    10
    Inverse circular functions
    • Inverse circular functions This free online course covers derivatives of inverse circular functions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
    • Derivatives of Inverse Circular Functions
    • Example 2
    • Example 3
  • Module
    11
    Polynomial equations
    • Polynomial equations This free online course covers solutions to polynomial equations and the Fundamental Theorem of Algebra. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
    • Solution of Polynomial Equations
    • Example
    • The Fundamental Theroem of Algebra
    • Equations
    • Examples
  • Module
    12
    Reciprocal function graphs
    • Reciprocal function graphs This free online course covers graphs of reciprocal functions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
    • Graphs of Reciprocal Functions
    • Example 1
    • Example 2
    • Example 3
  • Module
    13
    Vectors in 2 and 3 dimensions
    • Vectors in 2 and 3 dimensions This free online course covers topics related to scalars. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
    • Vector Definition
    • Symbols Used to Represent Vectors
    • Magnitude of a Vector
    • Zero Vector
    • Subtracting Vectors
    • Equal vectors
    • Parallel Vectors
    • Vectors in Cartesian Form
    • Position Vectors
    • The Cartesian Plane
    • Linear Dependence and Independence
    • Unit Vector
    • Multiplying by a Scalar
    • Linear Dependence and Independence Example
  • Module
    14
    Scalar products of vectors
    • Scalar products of vectors This free online course covers topics such as scalar and vector resolutes, and finding the angle between two vectors. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
    • Scalar and vector resolutes
    • Scalar resolutes
    • Vector resolutes
    • Vector resolute examples
    • Scalar (or dot) Product
    • Using the Dot Product in Vector Proofs
    • Example 1
    • Finding the Angle Between Two Vectors
    • Example 2 (midpoints)
    • Perpendicular Vectors
    • Inclination to the x or y axis
    • Example 3 (midpoints)
    • Example 4 (Co-linear points)
  • Module
    15
    Symmetry and periodicity
    • Symmetry and periodicity This free online course covers topics related to symmetry and periodicity. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress. 
    • Use of Symmetric, Periodic and Complementary Relationships of Circular Functions
    • Symmetry Example 1
    • Example 2
    • Example 3
    • Periodicity
    • Complementary Relationships
    • Complementary Relationship Examples
  • Module
    16
    Trigonometric identities
    • Trigonometric identities This free online course covers topics related to reciprocal circular functions, inverse circular functions, and trigonometric identities. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.
    • Reciprocal Circular Functions
    • Inverse Circular Functions
    • Trigonometric Identities
  • Assessment
    • Assessment
    • Advanced Mathematics 1 Assessment
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