GCSE Maths Teachers Pack V11

By Clive W. Humphris

An enhanced eBook published in full colour. Now including extensive interactive content enabling exploration by inserting any values that would occur in a real situation whereby the graphics are redrawn to reflect those changes.

Calculations can be also tested against any standard subject textbook to compare the results.

Interactive Technology when used in the classroom can motivate passive students by encouraging their active participation where STEM subjects are ideally suited to Mobile Interactive Technology.

Students are more likely to be comfortable with technology they understand i.e. their phone and can interact with, often preferring 'Learning-by-Doing' over traditional pencil and paper methods.

Full colour graphics that are redrawn for every input change will make the learning experience more enjoyable and effective as it encourages experimentation of real world situations as almost any practical values are accepted.

Students who struggle to be fully engaged in normal classroom activity can often achieve the unexpected once sat in front of a digital screen where they can learn without the embarrassment of full class exposure.

Mobile Interactive Technology can bring any STEM textbook to life by inserting printed values from the book into their mobile device and comparing the results.

Colourful visual presentation assists the learning process as students will more likely remember, thereby increasing their personal confidence as they believe they are learning more as a result. Knowing the content is on their phone encourages them to dip-in in a spare moment more than open a traditional textbook.

Conclusion: Students will spend more time engaged with the Mobile Interactive Technology than with a traditional textbook.

For each topic group students can TEST THEIR UNDERSTANDING by considering an open question whereby their ease of answering will provide an indication of personal progress.
 

• Language: English
• Publisher: eptsoft
• Release date: Nov 24, 2018
• ISBN: 9781386434849

Clive W. Humphris

Clive W. Humphris M0DXJ: Ex Technology Teacher. Software Developer, Author and Director of eptsoft limited. Married with two children and four grandchildren.Apprentice Instrument Maker at Marconi’s with Senor Technical Management roles in Radio Rentals and Alcatel Business Systems before starting eptsoft providing educational software to schools colleges and universities worldwide since 1992.Interests outside of developing digital products for eptsoft, include Running, Walking and Reading.

Book preview

GCSEMathsTeachersApp600

Table of Contents

Introduction

Number Systems

Number Conversion

Number Types

Compound Measures

Roots

Angles and Parallels

Triangle Ratios

Triangle Angles

Percentages

Ratios

Fractions

Vectors

Geometry

Circle Angles

Area

Surface Area and Symmetry

Volume

Laws

Algebra 0

Algebra 1

Algebra 2

Mathematical Rules

Powers and Indices

Simplifying

Linear Equations

Graphing

Slope and Translation

Curves and Angle Conversion

Data Analysis

GCSE Maths Teachers Pack V11

by Clive W. Humphris 

Portable Learning, Reference and Revision Tools.

Copyright by eptsoft limited 2018

All rights reserved.

Acknowledgement

Our thanks and appreciation goes to John D. Ransley MIEE from Whitbourne in Worcestershire for all his help and expert guidance in developing this eBook and additional app content.

Introduction

An enhanced eBook published in full colour. Now including extensive interactive content enabling exploration by inserting any values that would occur in a real situation whereby the graphics are redrawn to reflect those changes.

Calculations can be also tested against any standard subject textbook to compare the results.

Interactive Technology when used in the classroom can motivate passive students by encouraging their active participation where STEM subjects are ideally suited to Mobile Interactive Technology.

Students are more likely to be comfortable with technology they understand i.e. their phone and can interact with, often preferring 'Learning-by-Doing' over traditional pencil and paper methods.

Full colour graphics that are redrawn for every input change will make the learning experience more enjoyable and effective as it encourages experimentation of real world situations as almost any practical values are accepted.

Students who struggle to be fully engaged in normal classroom activity can often achieve the unexpected once sat in front of a digital screen where they can learn without the embarrassment of full class exposure.

Mobile Interactive Technology can bring any STEM textbook to life by inserting printed values from the book into their mobile device and comparing the results.

Colourful visual presentation assists the learning process as students will more likely remember, thereby increasing their personal confidence as they believe they are learning more as a result. Knowing the content is on their phone encourages them to dip-in in a spare moment more than open a traditional textbook.

Conclusion: Students will spend more time engaged with the Mobile Interactive Technology than with a traditional textbook.

For each topic group students can TEST THEIR UNDERSTANDING by considering an open question whereby their ease of answering will provide an indication of personal progress.

8 8 2012-01-02T12:20:00Z 2012-03-20T10:02:00Z 5 718 4097 eptsoft 34 8 5031 9.3821

NUMBER CONVERSION: Rounding Numbers.

Interactive Content!

The number of decimal places is the number of figures after the decimal point. It is normal to round a decimal number to n decimal places to make it more readable. Obviously this reduces the accuracy of the original number.

The process of manual number rounding is to look at the next figure after n, (this is the decider figure) if the decider is five or greater, increase the preceding figure by one. Discard any figures after n.

Rounding numbers containing decimal fractions to whole numbers can be useful when estimating. The accuracy of the estimate will depend largely on the magnitude of the whole number relative to the fractional part.

For example, the fractional part of the value 2.4 has considerably more significance than say, 120.4. Estimating by rounding provides is a useful check on the value of the final calculation.

8 8 2012-01-02T12:20:00Z 2012-03-20T10:02:00Z 5 718 4097 eptsoft 34 8 5031 9.3821

NUMBER CONVERSION: Significant Figures.

The number of significant figures is counted from the first non-zero figure and applies to both the whole and decimal parts and determines the accuracy of the number. Number rounding is also applied and so the result could be shown with less than the number of significant figures specified.

Whenever values are multiplied or divided the answer should never be considered more accurate than the one with the least number of significant digits, and so it will ease your calculations if round them to the same format.

There are difficulties when using computers or calculators with significant numbers, caused by trailing zeros being stripped off the value stored in the microprocessor register. Each digit has a numeric value and a positional value, therefore a trailing zero on the fractional part of a number when written means zero.

For example, 0.120 could be any numerical value of 0.120 ± 0.0005, the same converted digital value would be 0.120 truncated to 0.12 ± 0.005. The important point is that errors can arise in the accuracy of the calculation. There are many instances when using electronic computations that numbers do not accurately reflect those generated through manual calculations. For most practical applications these rounding errors can be ignored.

8 8 2012-01-02T12:20:00Z 2012-03-20T10:02:00Z 5 718 4097 eptsoft 34 8 5031 9.3821

NUMBER CONVERSION: Exponent To Ordinary Form.

Numbers expressed in exponent form, is a shorthand way of writing very large or very small numbers.

Conversion to ordinary form is carried out by shifting the decimal point the required number of places left or right indicated by the positive or negative nature of the exponent part of the number.

Using the Equation Editor input each of the examples and try modifying the values and number format.

8 8 2012-01-02T12:20:00Z 2012-03-20T10:02:00Z 5 718 4097 eptsoft 34 8 5031 9.3821

NUMBER CONVERSION: Standard Form or Index (SI) To Ordinary Form.

With Standard Form numbers the 'index value' indicates the base number multiplied or divided by ten to the power of that value. This is also known as Standard Index, abbreviated to SI commonly called Scientific Notation.

Positive indexes multiply by ten, a negative index divides by 10. This is the same as shifting the decimal point left or right and inserting the required number of zeros.

As is often the case in mathematics there are some rules to be obeyed. The base can be a number between 1 and 10, but not ten itself i.e. 9.9 is OK. The index of which is the power, shown as a positive or negative integer.

For this topic you should avoid inputting whole numbers e.g. 6 or 6.0 for base values, as your computer will truncate any decimal part and treat it as an integer number, thereby generating an error message. This is a software problem that has to be worked around, caused by number types used in the conversion. You could use say 6.0001 which would still return a high level of accuracy.

8 8 2012-01-02T12:20:00Z 2012-03-20T10:02:00Z 5 718 4097 eptsoft 34 8 5031 9.3821

NUMBER CONVERSION: Ordinary to Standard Form or Index (SI).

Standard Form or Standard Index (SI) numbers have only one whole number before the decimal point followed by the decimal figures to the required accuracy.

The index shows that number expressed to the power of 10. The number of times the value is required to be multiplied or divided by ten is shown by the number index value.

Positive index values mean multiply and division occurs whenever the index is negative.

Try inputting values both greater and less than 1. For example 456.1234 and .0004516.

8 6 2012-01-02T14:13:00Z 2012-03-20T10:06:00Z 4 676 3857 eptsoft 32 7 4736 9.3821

NUMBER TYPES: Rational and Irrational Numbers.

Interactive Content!

A rational number is one that can be expressed in the form of a fraction, the decimal equivalent of which can be determined by dividing the denominator into the numerator, a half or 1/2 is a rational number, 1/3 is not a rational number and therefore irrational.

The square root of two will produce an irrational number.

Irrational numbers cannot be determined accurately using a calculator or computer. This is because values are stored in the microcomputer registers as binary numbers and rounding will take place as the numbers are converted.

As irrational numbers theoretically have an infinite number of decimal places they cannot be contained within the registers and therefore will either be rounded