There are links to lots of revision resources for the Area and Volume topic in my previous post from today. Revision links for the Sequences and Polygons topics will be posted shortly.

Don’t forget the test is next Thursday. 16th Oct

These are the things you need to be able to do for the Area and Volume topic. The grade is in brackets.

• Find the area of a triangle, parallelogram, kite and trapezium (D)
• Find the area and perimeter of compound shapes (D)
• Calculate the circumference of a circle to an appropriate degree of accuracy (D)
• Find the perimeter of a semicircle (C)
• Calculate the area of a circle to an appropriate degree of accuracy (D)
• Find the area of a semicircle (C)
• Calculate volumes of triangular prisms, parallelogram-based prisms and cylinders (C)
• Convert between measures of volume (C)
• Solve problems involving surface areas of prisms and cylinders (C)
• Convert between measures of area (C)
• Calculate volumes of spheres and Cones (A)
• Calculate areas of sectors and segments (A)
• Calculate the length of arcs (A)

This list is taken from the Module 5 contents list on Mathsduck.

Below are some links to revision resources that may be useful for revision for the Area and Volume section.

Mymaths.co.uk lessons

Area of a Parallelogram

Area of a triangle

Area of a Trapezium

Circumference of a circle

Area of a circle

Volume of prisms

Volume of a cylinder

Surface area of prisms

Volume of spheres, cones and pyramids

Arcs and sectors

Don’t forget you can use the online homework for practice too.

Video tutorials

These are direct links to relevant video tutorials.

Area and perimeter of circles (emaths.co.uk)

Geometry of a circle (mathcentre.ac.uk)

Area of trapeziums

Area of paralleogram

Area of triangle

Download explanations document

You can download an explanation sheet as a Word document. This includes explanations of how to work out areas and volumes. Worked examples and some exam style questions for you to try.

Other resources

There are links to other revision resources on the Mathsduck GCSE revision page and don’t forget you can look at the blog posts from each lesson. To find the relevant posts use the tag cloud or search box on the right of this page or choose the Chapter 1 category.

Revision links for the other other 2 topics (sequences and polygons) will be posted shortly.

We then continued to work on finding the formula for the nth term of sequences. This is detailed in the post from last lesson.

Definitions

Here are some definitions of words you need to know.

Term - a number or variable (letter) or the product of a number and variable(s). e.g. 3, x, 3x

nth term - this phrase is used to describe a ‘general’ term in a sequence. You can use the nth term to find the terms of a sequence. The nth term might look something like 2n + 4,  n - 2 or n² + 6

Term-to-term rule - the rule that describes the difference between terms in a sequence. e.g. +3 or -5

Linear sequence - a sequence where the differences between the terms are all the same.

Using the nth term to find a sequence

we can find the terms of a sequence if we know the nth term.

Given the nth term 2n + 3

We find the first term by replacing n with 1 in the formula. So the first term is

2 x 1 + 3 = 5

In the same way we can find the second term by replacing n with 2 in the formula

2 x 2 + 3 = 7

We can do this for every term. For example the 100th term would be

2 X 100 + 3 = 203

So the first five terms in this sequence whose nth term is  2n + 3 are

5, 7, 9, 11, 13, …

The term to term rule for this sequence is + 2, because you add 2 to each term to find the next.

Finding the nth term

To find the formula for the nth term of a sequence you use the formula as below.

You need to complete the worksheet called ‘Polygon Geometry’.

You must describe the shapes using keywords such as triangle, equilateral, trapesium etc. Then you must calculate (or write down) the size of the angles.

You can work on the sheet and I suggest you do so in pencil.

The sheet looks like this:

If you don’t have the sheet for any reason you can Download it here.

The password to open the file is the short name of Mr Dolan’s classroom.

Homework due: Wednesday 8th oct 2008

The sum of the interior angles of a polygon is the total of all the inside angles added together. You can find the sum of interior angles for both regular and irregular shapes.

The sum of the interior angles is found by dividing up the polygon into triangles from one vertex and then multiplying the number of triangles by 180° (the sum of the angles in a triangle).

Here are some examples:

We also looked at how we can find the size of one of the interior angles in a regular polygon. You cannot find the interior angle of an irregular polygon this way because the angles are different.

We looked at the following two methods. either can be used.

This is the explanation we had on the board during the lesson.

The homework is online at Mymaths.co.uk and can be found at

mymaths.co.uk/gold/volume/volumeMovieOH.html

You will need to sign in with the schools login details and then your personal login and password so that your mark is recorded.

If you get stuck don’t forget to look at the relevent mymaths lesson and if you still need help see me before it is due in.

Please remember that although the homework is online you can (and probably will need to) do some working on paper or in the back of your books.

Homework due: Wednesday 1st Oct 2008

To find the surface area of a cylinder we have to understand that if you flatten out a cylinder the shape of the net is made up from two circles (of equal size) that are the ends and a rectangle where the length is the length of the cylinder and the width is the circumference of the circle at the end.

A cylinder like this:

Has a net like this:

So to work out the surface area you find the area of the circle, double it for the two circles. Then find the area of the rectangle and add together all three to find the total surface area.

You can see more explanation and examples on the Mymaths lesson about surface area.