PSLE marks the graduation of Primary school students and their entry into Secondary schools as teenagers. Discuss all issues about Secondary schooling here.
mathtuition88
BlackBelt Posts: 901
Joined: Thu Apr 25,
Total Likes:16

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

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!)
http://mathtuition88.com/2013/05/18/how ... tion-stud/

lost boy
OrangeBelt Posts: 65
Joined: Tue Nov 27,

### Re: Secondary School Mathematics

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
BrownBelt Posts: 613
Joined: Thu Mar 24,
Total Likes:3

### Re: Secondary School Mathematics

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
BrownBelt Posts: 613
Joined: Thu Mar 24,
Total Likes:3

### Re: Secondary School Mathematics

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
BrownBelt Posts: 613
Joined: Thu Mar 24,
Total Likes:3

### Re: Secondary School Mathematics

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
BrownBelt Posts: 613
Joined: Thu Mar 24,
Total Likes:3

### Re: Secondary School Mathematics

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
BrownBelt Posts: 613
Joined: Thu Mar 24,
Total Likes:3

### Re: Secondary School Mathematics

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
OrangeBelt Posts: 65
Joined: Tue Nov 27,

### Re: Secondary School Mathematics

Thanks JieHeng! Your help is much appreciated.

S-H
BrownBelt Posts: 564
Joined: Mon Feb 08,
Total Likes:1

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

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!)
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
BlackBelt Posts: 901
Joined: Thu Apr 25,
Total Likes:16

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

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!