Hester Catharina van Dyk

Education Affordable quality GEDeducare Curricula for home education, academies & learning centres. The aim of GEDeducare Curricula is to lay the foundations to give the semi-dependent students in South Africa a broader knowledge of GED®. ​GEDeducare curricula supports students from the ages of 13, using this learning program and require a tutor/invigilator/parent to grade the students tasks to aid with their learning experience!

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Louise Badenhorst


Mathematical reasoning

****TUTORS AND PARENTS - Registrations for next year opens in week 45!*******

The learning application is aimed at semi-dependent students giving the parent or tutor more time to assist with their other student/child.

GEDeducare supports students from the ages of 13, using this Academic Curricula learning program. require a tutor/invigilator/parent to grade the students tasks to aid with their learning experience!

Students progress from GEDeducare to GEDonline - providing the student is able to work independently-meaning without 
help from a tutor for about 3-4 hours per day. 

We encourage the more mature student (age 16/17<) that work independently to use The GED-online  Academy learning application to pass their GED®! 

*PDF Course Books and Task Books now available with the Tutor & Parent login.  Here Tutors will find information regarding their term schedules and exam schedules. School terms:

Tutor login: The login can be requested from

Parent login:  The login can be requested from

Video Tutorials with permission from Mometrix Jay Willis raises funds for children with muscular dystrophy.

High school students can join The GEDeducare Academy and is ideal for students with learning disabilities such as ADHD/ADD or Dyslexia.

Join us on our BIG mission to democratize education with technology!

* The content were especially selected from multiple sources to give the GEDeducare student a good foundation when using this learning application.  To avoid plagiarism, each site used has been carefully referenced/acknowledged.  A full list of references can be found either beneath each activity and or under the 'citing internet sources' topic of each subject.

See also:how to use Google tools for Citation and doing Research on the Internet. New innovations to Google Apps for Education make it easy and convenient for students to search for material that is, "free to use, share, or modify, even commercially".

Reminder: The GED Math examinations are Multiple Choice Questions!


For students using a laptop or computer, use Chrome as your browser. Students using a tablet; Puffin browser. Ensure you have Adobe Flash Player loaded! This will ensure you don't have any issues with the program.

Find us at or Send your query with childs name&surname&age to:

For any comments, please email us on

You could also ask to join the Facebook group st: SA Home Schoolers doing American SAT and GED School leaving Certificate

Students new to the Academy can now watch the introduction video! Each Tutorial has a task that needs to be completed and submitted to the academy! The tests are done online once the student feels confident about their knowledge of the course content.

Watch the student video here: 



We encourage students to go to  or for additional help with math!

The GED® Mathematical Reasoning Test focuses on two major content areas: quantitative problem solving and algebraic problem solving. 

Given these priorities, the GED® Mathematical Reasoning Test adheres to the following parameters:

  • Approximately 45 percent of the content in the test focuses on quantitative problem solving, and approximately 55 percent focuses on algebraic problem solving.

  • The test includes items that test procedural skill and fluency as well as problem solving.

  • The contexts within which problem solving skills are measured were taken from both academic and workforce contexts.

  • Approximately 50 percent of the items are written to a Depth of Knowledge cognitive complexity level of 2.

  • Approximately 30 percent of the items are aligned to a Mathematical Practice standard in addition to a content indicator.

  • The statistics and data interpretation standards are also measured in the GED® Social Studies and Science Tests.

  • Candidates are provided with an on-screen calculator, the Texas Instruments TI-30XS Multiview scientific calculator, for use on most of the items on the 2014 GED® Mathematics Test. They are also given a calculator and reference sheet.

As of Friday, February 21, 2014, the standard time allowance on the GED® test - Mathematical Reasoning was increased by 25 minutes.

  • The time allowance for GED Ready™ - Mathematical Reasoning was also increased by 13 minutes.

  • Students who took either of these tests before February 21 received an email from GED Testing Service with instructions for receiving a free retake.


Term 1

1. Math Basics

1.1 Lesson 1: Operations Basics

  1. Addition and Subtraction
  2. Associative Property
  3. Distributive Property
  4. Exponents and Roots
  5. Integers, Decimals, and Fractions
  6. Multiplication and Division
  7. Order of Operations

1.2 Lesson 2: Factors and Multiples

  1. Greatest Common Factor
  2. Least Common Multiple
  3. Multiples
  4. Multiples and Least Common Multiples
  5. Prime Numbers, Factoring, and Prime Factorization

1.3 Lesson 3: Unit Conversions

  • Rates and Unit Rates


2. Fractions

2.1Lesson 1: Fraction Basics

  1. Changing Mixed Numbers to Improper Fractions
  2. Converting Improper Fractions to Mixed Numbers
  3. Fractions of a Whole
  4. Improper Fractions and Mixed Numbers
  5. Ordering Fractions
Term 2

2.2Lesson 2: Fraction Operations

  1. Adding and Subtracting Fractions
  2. Converting Improper Fractions to Mixed Numbers and Decimals
  3. Converting Mixed Numbers to Decimals and Improper Fractions
  4. Converting Percentages to Decimals and Fractions
  5. Multiplying and Dividing Fractions


3. Decimals

3.1 Lesson 1: Decimal Basics

  1. Decimals
  2. Ordering Decimals

3.2 Lesson 2: Decimal Operations

  1. Adding and Subtracting Decimals
  2. Changing a Number from Standard Form to Scientific Notation
  3. Converting Decimals to Fractions and Percentages
  4. Converting Decimals to Improper Fractions and Mixed Numbers
  5. Dividing Decimals
  6. Multiplying Decimals
  7. Scientific Notation


4. Solving Equations

4.1 Lesson 1: Equation Basics

  1. Absolute Value
  2. Arithmetic Sequences
  3. Solving an Equation Using Four Basic Operations
  4. Solving Equations Using Addition and Subtraction
  5. Solving Equations Using Multiplication and Division
  6. Solving Equation with Absolute Value
Term 3

4.2 Lesson 2: Inequalities

  1. Equations and Inequalities
  2. Graphing Solutions to Linear Inequalities
  3. Linear Inequalities
  4. Solving Absolute Value Inequalities
  5. Solving Inequalities Using All four Basic Operations

4.3 Lesson 3: Linear System of Equations

  1. Comparison of Methods for Solving System of Equations
  2. Linear Equations Basics
  3. System of Linear Equations
  4. System of Equations Basics

4.4 Lesson 4: Graphing of Linear Equations and Functions

  1. Changing Constants in Graphs of Functions: Linear Functions
  2. Changing Constants in Graphs of Functions: Quadratic Equations
  3. Graphing Absolute Value Equations
  4. Graphing Linear Equations
  5. Graphing the Inverse of a Function
  6. Graphs of Functions
  7. Solutions of a Quadratic Equation on a Graph
  8. Using a Graph

4.5 Lesson 5: Word Problems

  1. Right Triangle Word Problems
  2. Word Problems and Addition
  3. Word Problems and Division
  4. Word Problems and Multiplication
  5. Word Problems and Subtraction
Term 4

5. Geometry

5.1 Lesson 1: Angle Basics

  1. Angles
  2. Geometric Symbols: Angles

5.2 Lesson 2: Triangles

  1. Area and Perimeter of a Triangle
  2. Measurements for Similar Triangles
  3. Measurements for Similar Triangles – Continued
  4. Measurements for Similar Triangles – Continued II
  5. Proof that a Triangle is 180 Degrees
  6. Similar Triangles

5.3 Lesson 3: Circles

  1. Area and Circumference of a Circle
  2. Finding Measurements for Parts of a Circle
  3. Unit Circles and Standard Position

5.4 Lesson 4: Volume and Surface Area of 3D Shapes

  1. 3D Geometric Shapes
  2. Volume and Surface Area of a Cube
  3. Volume and Surface Area of a Pyramid
  4. Volume and Surface Area of a Rectangular Solid
  5. Volume and Surface Area of a Circular Cone
  6. Volume and Surface Area of a Circular Cylinder
  7. Volume and Surface Area of a Sphere


6. Probability, Statistics, Percentages, Ratios, and Proportions

6.1 Lesson 1: Probability

  • Theoretical and Experimental Probability

6.2 Lesson 2: Percentages, Ratios, and Proportions

  1. Calculation of a Percentage
  2. Computation with Percentages
  3. Finding the Percentage Decrease
  4. Finding the Percentage Increase
  5. Percentages
  6. Proportions
  7. Proportions and Percents
  8. Proportions in the Real World
  9. Ratios and Percentages

Algebra, Functions, and Patterns

Patterns are a simpler mathematical application, and involve detecting and foretelling a sequence of figures accurately. Functions and Algebra are frequently paired together, as high school students typically learn about functions as part of their Pre-Algebra curriculum. Functions are a type of equation that seek to assess how two numbers connect based on a given variable. Variables are a distinct part of Algebra, which can be defined as a mathematical system driven by variables, equations, and numeric associations.


Number Operations and Number Sense

The Number Operations and Number Sense section of the Mathematical Reasoning test evaluates how well you can identify the numbers you see, and how well you can solve basic arithmetic problems. For the latter, you’ll have to utilize division, addition, multiplication, and subtraction. With the former, you’ll be expected to demonstrate that you know what numbers mean when you see them—what they’re for, how much they’re worth, and how different numbers compare with each other. This knowledge category is the simplest subject you’ll find on this part of the exam.


Data Analysis, Statistics, and Probability

Statistics represents the mathematical process used for making logical predictions based on the numbers involved. It goes hand in hand with Probability, which is used to predict the frequency of a given event. Data analysis is exactly as it says on the tin—your ability to interpret numerical data presented to you.


Measurement and Geometry

Geometry deals with the study and calculation of shapes. With Geometry-based questions, you’ll find subject matter related to angles, points, and much more. Measurement involves Geometry on a three-dimensional basis, and will likely ask you to find quantities such as perimeters, areas, distances, and volumes, among other things. Here is where you’ll likely have to refer to your formula sheet quite a bit, as well as do some drawing to get to your answers.


While this study guide isn’t 100 percent comprehensive, we hope it will be of great help to you as you prepare for this important next step in your academic and/or professional careers.












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They may not be used or reproduced without the express written permission of ACE or GED Testing Service.

*GED® is a registered trademark of the American Council on Education (ACE) and administered exclusively by GED Testing Service LLC under license.


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