T-QAD Day 5 @ 19 April 2020

Notes: Indices

Example 1:   

Simplify 

Solution : 

Example 2 :

T-QAD

Question 1 : Q1/D5/190420

Question 2 : Q2/D5/190420

                                                                                                    

Answers T-QAD 16 April 2020

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Geometric Progression Part 1 - The n-th term

Geometric Progression

Assalamualaikum darling semua....

let us recap again the lesson yesterday.

Geometric progression is a special type of sequence that will relate within one term and the term next to it.

Geometric Progression will have :  Common Ratio , r.  

How to get it?

 r = t₂/t_{1  or}

   = t₃/t_{2  or}

                = t₄/t_{3  and other}

_{in general...}   r = t_n-1/t_n

Simply by dividing the second term with the first term.

The Rule- To find the n^th

For any given question, The main steps are:

1. Check the sequence whether it is a geometric progression(GP) or arithmetic progression(AP).

2. Identify the common different,d-(AP) or common ratio,r-(GP)

3. Identify the first term

Let say you are given a question : 

Example 1: Find the 10^th term of the sequence:  2, 4, 8, ...

let us solve it step by step...

Step 1 :   Check whether the sequence is AP or GP.

So, it is a Geometric Progression(GP).

Step 2: Since it is a GP, so the r = 2.

Step 3: The first term, a = 2.

Solution:

Example 2 : Find the number of terms of the sequence :  2 , 6 , 18 , …. 486 

Start with : Determine whether it is GP or AP? (Very important, so that we use the correct formula)

So, it is a Geometric Progression(GP).

Step 2: Since it is a GP, so the r = 3.

Step 3: The first term, a = 2.

Solution:

Further exercise :

Download Module Progression (If you don't have it) : MODULE

Solve Question page 13 & 14.

If you have finish learning the lesson, please continue and fill in the feed back.

(This is also the attendance)

FEEDBACK 

OK guyss.. happy learning.. #studyADDMATHathome

                

T-QAD Day 4 @ 16 April 2020

Question 1 : Q1/D4/160420

A quadratic equation x² + px + 9 = 2x  has two equal roots.

Find the possible values of p.

                                                                                                         (3 marks)

Question 2 : Q2/D4/160420

(a)          Solve the following quadratic equation:

               3x² + 5x – 2 = 0

(b)          The quadratic equation hx² + kx + 3 = 0, ,

               where h and k are constants, has two equal roots.

Express h in terms of k.  

                                                                                                         (4 marks)

Answers T-QAD 15 April 2020

Check your answer and fill in the form to record your marks.

MyMarks 

T-QAD Day 3 @ 15 April 2020

Question 1 : Q1/D3/150420

Solve the simultaneous equations  

2x + y = 1 and 2x² + y² +xy = 5.

Give your answers correct to three decimal places.

                                                                                                         (5 marks)

Question 2 : Q2/D3/150420

Solve the following simultaneous equations:

2x – y  – 3 = 0    and        2x² – 10x  + y + 9 = 0

                                                                                                         (5 marks)

Answers T-QAD 14 April 2020

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                 MyMarks

1.  (a) 5                               (1 mark)

      (b) { -3, -1, 1, 3 }         (1 mark)

               Review :

               (a) the object of -1 is 5

               (b) Range is the set of images

2.  (a)   {w, x, z}                            (1 mark)

     (b)   Many to one relation        (1 mark)

Review :

               (a)  Range is the set of images

               (b) Object 2 and object 3 have the same image, x. This is many to one relation.

T-QAD Day 2 @ 14 April 2020

Question : Q1/D2/140420

Question : Q2/D2/140420

Answers : T-QAD Day 1 @ 13 April 2020

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 MyMARKS

T-QAD Day 1 @ 13 April 2020

Question:    Q1/D1/130420

The diagram shows the sector OPQ with centre O.

Find, (use Phi=3.142)

a) Angle POQ, in terms of phi radian.

b) the perimeter, in cm, sector OPQ. 

                                                                    (4 marks)

Question: Q2/D1/130420

Diagram shows the sectors OAB and ODC with center O.

It is given that OA = 4 cm, the ratio of OA : OD = 2:3 and the area of the shaded region is 11.25 cm²
Find,
a) the length, in cm, of OD,
b) θ,  in radians
                                                (4 marks)

Arithmetic Progression : Part 3

How are you? Hopefully all of you guys are in good condition.
#stayathome #studyathome


This post will be the last part of arithmetic progression, which is finding the sum of the n^th terms.

Firstly, what does it mean by sum of n^th terms?

In simple explanation, if we have an arithmetic sequence such as

2, 5, 8, 11, 14, 17, 20, …

Question : Find the sum of the first 6 terms.

The question actually asks you to find….

The sum of     2 + 5 + 8 + 11 + 14 + 17

                       = 57

Very simple right?

But, because it is a very special sequence, which have a common difference, then we may apply a formula to find the sum of it.

We will use two formula.

First Formula:  

What is a? Recall from previous lesson:

a is the first term. So a = 2.

Next, what is d ?  d is the common difference, so

                d = 5 - 3 

                   = 2 

What is n? n is number of terms that we want to sum.

From the formula;   S₆ = (6/2) (2(2) + (6-1)3)
                                     = 57

The same answer right? So, if you know the number of terms, the first term, and the common difference, then just use this formula. If you have a few numbers in the list, maybe you can simply list it and sum all of them, but what happen if you have many terms to be added such as 50 terms?

Then this formula can be applied.

Second Formula: 

We can use this formula when we know the last term to be summed. From the example :
the first term a, a= 2. Number of term to be added, n = 6. The 6^th is , l = 17.

so, 

        = 57

So, exactly using all the methods, the answer still the same.
Choose wisely while you want to answer the question.

Good Luck.

Task 1: 
Read and copy the notes....
Then...
Fill this form . FORM

Next, Try as many as questions you can. You may copy the questions.
(Try to use both methods for each question)
click HERE to proceed with the exercise.

Task 2: Try the quiz
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Task 3: 
Enrichment
Try questions from your module page 7 - 10.  Module
This is the Answer. You may refer to it if you have any problem.
ANSWER.

Task 4:
Time to test your understanding

#QUIZ 2  code:  828919 . Due date 16 April 2020 before 11.45pm.

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Task 5: 
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