Resources and information for General Maths Units 1&2 at CSHS

Complete the above activities. You may need to wait until you get home and have access to a milk carton, soft drink can and an old text book.

clipped from www.intmath.com

A Geometric Sequence is formed by multiplying a starting number (a₁) by a number r, called the common ratio.

Example:

5, 10, 20, 40, 80, 160, has a₁ = 5, r = 2.

Here, we start with 5 and multiply by 2 each time to get the next number in the progression.

The n-th term of a Geometric Sequence is given by: a_n = a₁r^n-1

Example:

Find the 50^th term of the geometric progression 5, 10, 20, 40, 80, …

Answer

The Sum of a Geometric Sequence

The sum to n terms of a Geometric Sequence means:

a₁ + a₁r + a₁r² + a₁r³ + … + a₁r^n-1

We can find the sum of this series by using our CAS and Sigma Notation

Example:

A king once promised a prince anything he wanted because he saved the princess’s life. The prince requested one grain of rice on the first square of a chess board, 2 on the second, 4 on the third, 8 on the fourth square, etc.

How much rice is there if one grain of rice weighs 20 mg?

Answer

Some further problems for you to practice:

Question 1

Question 2

Please view the following clips before moving on. You may need to refer to these clips before answering the questions given below:

clipped from www.math.montana.edu

Summation, or Sigma, Notation

There are many situations in which we need to sum or add a large number of numbers. Because this happens so often, mathematicians have adopted some notation — called summation notation or sometimes sigma notation (because the Greek letter sigma is used) for use in this
situation

There are many situations in which we need to sum or add a large number of numbers. Because this happens so often, mathematicians have adopted some notation — called summation notation or sometimes sigma notation (because the Greek letter sigma is used) for use in this situation. Computer algebra systems like Maple, Mathematica, and the TI-Nspire CAS have similar notation.

We illustrate this notation with an example. Suppose that we want to find the sum

1 + 4 + 9 + … + 10,000

Notice that we are adding 100 terms. We will use the notation a_j for the j-th term in this sum. Notice that the terms can be described by the formula

a_j = j²

Using summation notation this sum is written

Questions:

1. What is the difference between a sequence and a series?
2. What is an arithmetic sequence/series?

clipped from www.math.montana.edu

An index variable: In this case the index variable is j.
This variable is used to number or label each term.

A number indicating the start of the sum — that is, the number
of the first term. In this case the start is 1. The start is usually
either zero or one but it can be anything. For example, we often start
a summation with the current year.

A formula describing each term. In this case the j-th
term is j².

A number indicating the end of the sum — that is, the number
of the last term. In this case the end is 100.

The upper case Greek letter sigma which is the Greek equivalent of the
English letter ess is used to denote summation.

Look at your CAS window to see how summation is denoted for your CAS system.

clipped from www.math.montana.edu

Check Your Understanding

Write the sum

1 + 2 + 3 + ... + 10

using sigma notation and then compute it using your computer algebra system.
answer

Write the sum

1 + 2 + 3 + ... + 100

using sigma notation and then compute it using your computer algebra system.
answer

Write the sum

1 + 3 + 5 + ... + 99

using sigma notation and then compute it using your computer algebra system.
answer

Write the sum

1 + 2 + 4 + 16 + ... + 512

using sigma notation and then compute it using your computer algebra system.
answer

Write the sum

1 + (1/2) + (1/4) + ... + (1/1024)

using sigma notation and then compute it using your computer algebra system.
answer

Attempt the following questions:

The following clip is an introduction to Density. Concentration is another term for density when we have 2 or more liquids compared – think of cordial in a glass.

Other density and concentration questions:

1.

2.

3.

4.

5.

6.

Your task:

1. Prepare a short commercial about your Sports Drink. You only have this period to complete this task.
2. Make your commercial as you go. Open iMovie straight away and start collecting images and audio you will use.
3. Address the questions in the image below. The following link may help you with this.
   • What ingredients go into all sports drinks
4. Highlight your drinks key ingredients. How much of each ingredient will be present in your new drink? What units of measurement will you mention in your commercial?
5. Share your commercial to quicktime and upload to your youtube account (create one of these if you don’t already have one). Studywiz me the url for your commercial. Include your name in the title of your Studywiz message.

In this entry you will find all the resources and information necessary to successfully complete your Investigative Report into The Community Garden.

Your report will consist of 2 parts. Part A will require you to extend on some of the tasks you have already completed this term and present it as a presentation. Part B requires you to analyse a new design for the Community Garden using some of the skills you have developed this term and present a written report.

The image below is to be used for Part A Section 5 of your report: Area Calculations

Investigative Report Assessment Information

Due Date: Friday 29th August

The attached document is the Design Project Rubric (Updated version 14/8/8) that will be used to assess your Design Project. Please read this document and message me any questions you have.

An effective way to communicate your queries about the task would be to edit this document with another coloured font, save it (with  your name and ‘queries’ in the title) and attach it to your message.

Due Date: Frigay 29th August

Investigate and respond to the following questions in your workbook:

1. What is a regular prism? (play the animation)
2. Officially a prism doesn’t have what?
3. The general formula for the volume of a regular prism is?
4. The formulae for the following shapes:
   • Cylinder
   • Sphere
   • Cone
5. What is a polyhedron?

Some basic formulae

Practice questions:

1. Simple rectangular box questions ( attempt three of these). Solutions.
2. Other more difficult problems:

Capacity

Convert the following volumes to units of capacity:

A harder problem:

Check your answers using this online conversion tool. Note: You also have access to a conversion calculator through your Widgets.

Test yourself using the online quiz

Some definitions:

In this investigation you will learn about interior and exterior angles of polygons. Complete the tasks in the Angles in Polygons Worksheet in your workbooks. You will need to download the Ti-Nspire document: Angles in polygons using you Ti Computer Link software on a PC.

In this entry you will find out how to insert lines of best fit to bivariate data by hand but using your CAS. The following CAS documents will also help you decide what a good line of best fit is. Download the .tns file to your CAS using your Computer Link software on a PC. The MS Word documet will provide further instructions and questions for you to answer.

Answer the following questions in your workbook