O-Level Additional Math

PSLE marks the graduation of Primary school students and their entry into Secondary schools as teenagers. Discuss all issues about Secondary schooling here.
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mathtuition88
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积少成多:Doing at least one Maths question per day.

Post by mathtuition88 » Sat May 18, 2013 1:41 pm

积少成多: How can doing at least one Maths question per day help you improve!

We all know the saying “an apple a day keeps the doctor away“. Many essential activities, like eating, exercising, sleeping, needs to be done on a daily basis.

Mathematics is no different!

Here is a surprising fact of how much students can achieve if they do at least one Maths question per day. (the question must be substantial and worth at least 5 marks)

This study plan is based on the concept of 积少成多, or “Many little things add up“. Also, this method prevents students from getting rusty in older topics, or totally forgetting the earlier topics. Also, this method makes use of the fact that the human brain learns during sleep, so if you do mathematics everyday, you are letting your brain learn during sleep everyday.

Let’s take the example of Additional Mathematics.

Exam is on 24/25 October 2013.
Let’s say the student starts the “One Question per day” Strategy on 20 May 2013

Days till exam: 157 days (22 weeks or 5 months, 4 days)

So, 157 days = 157 questions (or more!)
Read the full article at:
http://mathtuition88.com/2013/05/18/how ... tion-stud/

lost boy
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Re: Secondary School Mathematics

Post by lost boy » Sat May 18, 2013 4:24 pm

Hi, ps help to solve sec one math

1) the sum of first n terms of a series is (n^2 + 2n) for all values of n. find the first three terms of the series.

2. Find the sum of the even numbers from 50 to 100 inclusive.

3. Write down the nth term and the sum of the first n terms of an arithmetic progression whose first term is a and whose common difference is d. Use these formulae to find the sum of all the numbers between 100 and 200 that are divisible by 7.

4. In the arithmetic progression whose first term is -27,the tenth term is equal to the sum of the first nine terms. Calculate the common difference.

5. The sum of the first 6 terms of an arithmetical progression is 55.5 and the sum of the next 6 terms is 145.5. Find the common difference and first term.


Thanks . Ps show me the working.

jieheng
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Re: Secondary School Mathematics

Post by jieheng » Sat May 18, 2013 7:13 pm

lost boy wrote:Hi, ps help to solve sec one math

1) the sum of first n terms of a series is (n^2 + 2n) for all values of n. find the first three terms of the series.
1)

Sn (Sum of first n terms) = n^2 + 2n

T1 (1st term) = S1 (Sum of first term) = 1 + 2 = 3

S2 (Sum of first 2 terms) = 2^2 + 2*2 = 4 + 4 = 8

T2 (2nd term) = S2 - S1 = 8 -3 = 5

S3 = 3^2 + 2*3 = 9 + 6 = 15

T3 = S3 - S2 = 15 - 8 = 7

jieheng
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Re: Secondary School Mathematics

Post by jieheng » Sat May 18, 2013 7:27 pm

lost boy wrote:Hi, ps help to solve sec one math

3. Write down the nth term and the sum of the first n terms of an arithmetic progression whose first term is a and whose common difference is d. Use these formulae to find the sum of all the numbers between 100 and 200 that are divisible by 7.
3)

a = first term , d = common difference

Tn (nth term) = a + (n-1)*d

Sn (sum of first n terms) = (n/2)*[ 2a + (n-1)*d ]


1st no that is divisible by 7 is 105

Last no that is divisible by 7 is 196

105 , 112 , ...................................... , 196

a = 105 , d = 7

Tn = a + (n-1)*d
196 = 105 + (n-1)*7
(n-1) = 13
n = 14

Sn = (n/2)*[ 2a + (n-1)*d ]

S14 = (14/2)*[2*105 + (14-1)*7] = 2107

jieheng
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Re: Secondary School Mathematics

Post by jieheng » Sat May 18, 2013 7:31 pm

lost boy wrote:Hi, ps help to solve sec one math

2. Find the sum of the even numbers from 50 to 100 inclusive.



a = first term , d = common difference

Tn (nth term) = a + (n-1)*d

Sn (sum of first n terms) = (n/2)*[ 2a + (n-1)*d ]

a = 50 , d = 2

Tn = a + (n-1)*d

100 = 50 + (n-1)*2

n = 26

Sn = (n/2)*[ 2a + (n-1)*d ]

S26 = (26/2)*[2*50 + (26-1)*2] = 1950


jieheng
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Re: Secondary School Mathematics

Post by jieheng » Sat May 18, 2013 7:37 pm

lost boy wrote:Hi, ps help to solve sec one math

4. In the arithmetic progression whose first term is -27,the tenth term is equal to the sum of the first nine terms. Calculate the common difference.
4)

a = -27 , d = common difference

Tn (nth term) = a + (n-1)*d

T10 = -27 + (10-1)*d = -27 + 9d

Sn = (n/2)*[ 2a + (n-1)*d ]

S9 = (9/2)*[2(-27) + (9-1)*d] = (9/2)[-54 + 8d] = -243 + 36d

T10 = S9

-27 + 9d = -243 + 36d

27d = 216

d = 6

jieheng
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Re: Secondary School Mathematics

Post by jieheng » Sat May 18, 2013 8:41 pm

lost boy wrote:Hi, ps help to solve sec one math


5. The sum of the first 6 terms of an arithmetical progression is 55.5 and the sum of the next 6 terms is 145.5. Find the common difference and first term.

5)

a = first term , d = common difference

Sn (sum of first n terms) = (n/2)*[ 2a + (n-1)*d ]

S6 = (6/2)*[ 2a + (6-1)*d ] = 55.5
6a + 15d = 55.5 ------ (1)

Sum of next 6 terms = Sum of first 12 terms - Sum of first 6 terms = S12 - S6

S12 - S6 = 145.5
(12/2)*[ 2a + (12-1)d ] - 55.5 = 145.5
12a + 66d = 201 ----- (2)

Solving equations (1) and (2) ,

a = 3 , d = 2.5

lost boy
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Re: Secondary School Mathematics

Post by lost boy » Sat May 18, 2013 9:44 pm

Thanks JieHeng! Your help is much appreciated.

S-H
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Re: 积少成多:Doing at least one Maths question per day.

Post by S-H » Tue May 21, 2013 9:16 pm

mathtuition88 wrote:积少成多: How can doing at least one Maths question per day help you improve!

We all know the saying “an apple a day keeps the doctor away“. Many essential activities, like eating, exercising, sleeping, needs to be done on a daily basis.

Mathematics is no different!

Here is a surprising fact of how much students can achieve if they do at least one Maths question per day. (the question must be substantial and worth at least 5 marks)

This study plan is based on the concept of 积少成多, or “Many little things add up“. Also, this method prevents students from getting rusty in older topics, or totally forgetting the earlier topics. Also, this method makes use of the fact that the human brain learns during sleep, so if you do mathematics everyday, you are letting your brain learn during sleep everyday.

Let’s take the example of Additional Mathematics.

Exam is on 24/25 October 2013.
Let’s say the student starts the “One Question per day” Strategy on 20 May 2013

Days till exam: 157 days (22 weeks or 5 months, 4 days)

So, 157 days = 157 questions (or more!)
Read the full article at:
http://mathtuition88.com/2013/05/18/how ... tion-stud/

Well said!! Thank you for the advice. Will follow and hope to see improvement in my maths for my '0' level exam!

mathtuition88
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Re: 积少成多:Doing at least one Maths question per day.

Post by mathtuition88 » Tue May 21, 2013 9:32 pm

S-H wrote:

Well said!! Thank you for the advice. Will follow and hope to see improvement in my maths for my '0' level exam!
I am glad that you find the advice helpful!
All the best for your O level exams!

Perseverance can grind an iron rod into a needle, not to mention acing your O level exams!

(This legend is about Li Bai (李白), a great poet in Tang Dynasty. Li Bai was naughty and disliked study when he was a child. One day he saw an old woman grinding an iron rod on a big stone when he was playing by a river. Driven by curiosity, Li Bai came up and asked,
"What are you doing, granny?"
"Grinding an iron rod," said the old women without stopping grinding.
"Then what for?" he asked again.
"To make a sewing needle," was the answer.
"What?!" little Li Bai was puzzled, "you want to grind so big a rod into a needle? It will take many years."
"This doesn't matter. As long as I persevere in doing so, there is nothing you cannot achieve in the world. Certainly I can make a needle from the rod." Deeply moved by what the old woman said, Li Bai took effort to study since then and finally became one of the greatest poets in China.)

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