School has decided to have a school wide math contest on 4/6/2014 (the midterm exam day) and all Math class students will take part in this contest. We have decided to use the contest in place of the midterm exam.

We will teach today, have the math contest next time, and use the lesson after the contest to go over the contest questions.

Up to now the three kinds of transformations we have talked about: Reflection, Rotation, and Translation, all do not change the figure’s shape and size. They are called rigid transformation. Today we talk about enlargement where the shape remains but the size changes. And an enlargement transformation can increase (when the scale fact is bigger than 1) and reduce (when the scale factor is less than 1) the size. And there must be a center of enlargement.

Lastly, we talked about the combination of multiple transformations and how to identify each transformation involved and fully describe it.

Homework:

Page 122: #14, #15, #17, #18, #19, #20.

We study transformations. A transformation, also known as a mapping, transforms a figure into another figure. Today we focus on reflection, rotation, and translation.

We cover the solutions of right-angled triangles with sin, cos, tan applications and how to apply them to solve simple real world problems.

Just want to point out for parents, our teaching about trigonometry is very basic, we are not going to go more than what we have taught so far.

Homework:

Page 108, #9, #11, #18, #19, #24, #26, #28, #31, #32, #33, #38

We start with measurement for spheres. Two important formulae to remember:

Volume of a sphere with radius r is: 4/3 pi r^3

Surface area of a sphere with radius of r is: 4 pi r^2

We then talk about areas of similar figures and volumes of similar solids.

In general, if the ratio of the corresponding lengths of two similar figures is a / b, then the ratio of their areas is ( a / b )^2.

And if the ratio of the corresponding lengths of two similar solids is a / b, then:

• the ratio of their volumes is ( a / b )^3;
• the ratio of their total surface areas is ( a / b )^2.

Knowing the above formulae, as well as the ones we learned last time, allows us to make various calculations in terms of finding the area or volume of some real world objects.

Homework:

Page 97: 42, 43, 44, 46, 49, 52, 53, 56, 59, 61

We study similar triangles, which have the same shape, but not the size. When two triangles are similar, their corresponding angles are the same, and their corresponding sides are proportional. The constant ratio is called the scale factor.

Two triangles ABC and XYZ, they are similar if:

• Angle X = Angle A, and Angle Y = Angle B (which implies that Angle Z = Angle C. This is AAA) or
• XY / AB = YZ / BC = ZX / CA   (This is three sides are proportional. SSS) or
• XY/AB = ZX / CA ,and Angle X = Angle A  (this is two sides with including angle. SAS)

We can use the above three rules to decide if two triangles are similar.

We now start Chapter 9 on Mensuration, about measurement.

We first study sectors in a circle, the arcs. For a sector facing an angle X, we have the following:

Length of arc / circle circumference = X / 360  and Area of sector / Area of the circle = X / 360

From the above, we can further derive the relationship between the length of the arc (say a) with the area of the sector (say A) on a circle with the radius r as:

A = ar / 2

We then study the volumes and surface areas of a cone and a pyramid where both volume has the formulae of:

V = (1/3) * Base Area * Height

Armed with the formula for sectors/arcs, we can calculate the surface are for a cone.

Below is this week’s homework:

Page 84, # 8 – #22

Page 89, #3 – #5, #8, #10, #41, #45, #48, #51, #58, #60

Today starts the 2013-2014 Spring semester. Welcome back, old and new students.

We will be on the subject of geometry for a while. Today we covered congruent triangles. Three rules for deciding if two triangles are congruent:

1. SAS: two sides and the included angles. It is important that the angle has to be one between the two sides;

2. AAS: two angles and a corresponding side. With two angles the same, the third ones have to be identical as well. So it is important to see if the sides are indeed the corresponding ones.

3. SSS: side-side-side.

4. RHS: right angle hyptenuse and side. This one is for right-angled triangle.

We did some proof problems using the above rules.

Homework: Page 81-84, #1 – #6