A-Math Quiz

This post is specially posted for JH1 Accelerated Mathematics Students, because the content will be based on the proofs you have to learn. (Can be found in Pink Handout too, but I'll give more examples on Number 3 in case you do not know what is Counter-Example)

1. Proof of Sum of Interior Angles bounded by // lines

2. Proof of Exterior Angle Property

Let a, b and c be angles in a triangle and d be the exterior angle beside c.

Prove that a + b = d

a + b + c = 180 (sum of angles in a triangle)

d + c = 180 (adj. angles on a straight line)

Since a + b + c = d + c = 180,

cancelling out c, we get a + b = d.

Therefore, a + b = d. (Proven!)

3. Giving a Counter-Example

This means giving an example which disproves something.

Let's consider the number pattern: 2, 4, 8, 16, 32, ... ...

Show that T(n) = 2n is incorrect.

*Use examples*

Let n be 3.

So, T(3) = 2(3)

= 6

*Include Concluding Sentence":

However, it is shown that the third term is 8 and not 6, so this formula is incorrect. (Proven!)

Example: (By the way, I made it so it is very easy)

Pattern: 9, 27, 81, 243, 729, ... ...

(a) Show that T(n) = 9n is wrong.

(b) What is the correct formula for this pattern?

ANSWER:

(a) Let n be 3.

T(3) = 9(3)

= 27

The third term is 81 but the answer I get is 27. Therefore it is wrong.

(b) 9^n (9 to the power of n)

4. Rewriting algebraic Formula

Ok that's all I can help you. Please remember all that.

For MA104 students, if you want to learn, ask from the A-Math Students, including me.

Hope I'm not spamming the class blog! :):):)

Goldwin