11 plus series summation questions
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11 plus series summation questions
Hi,
I see the following question in a “Non-Routine Maths problems” for 11+
Find the sum of the integers from 1 to 1000.
1+2+3+4…………………………………………….+998+999+1000=?
I know the answer is simply n(n-1)/2 i.e 1000*999/2 … and that because I have a degree in applied Maths. My question is…. how is this an 11 plus question? How is a 10 year old suppose to think of this without have to used some advance maths summation result?
Funny enough my daughter came across the solution herself whilst reading “Women in Science” – 50 Fearless Pioneers who changed the world. I was pretty impressed she recognised that was the solution right in the middle of Maryam Mirzakhani's brief biography.
I see the following question in a “Non-Routine Maths problems” for 11+
Find the sum of the integers from 1 to 1000.
1+2+3+4…………………………………………….+998+999+1000=?
I know the answer is simply n(n-1)/2 i.e 1000*999/2 … and that because I have a degree in applied Maths. My question is…. how is this an 11 plus question? How is a 10 year old suppose to think of this without have to used some advance maths summation result?
Funny enough my daughter came across the solution herself whilst reading “Women in Science” – 50 Fearless Pioneers who changed the world. I was pretty impressed she recognised that was the solution right in the middle of Maryam Mirzakhani's brief biography.
Re: 11 plus series summation questions
Isn't this the one some young genius (Leibnitz? Pascal? Fermat?) is supposed to have solved in an instant when his teacher set it to keep the class occupied for an hour?
I would agree that in an 11+ it would only be likely to be solved either by someone similarly with a quick brain who spots that they can add two copies of the numbers together in matching pairs 1+1000, 2+999 ..... 1000+1 , realise that they have 1000 * 1001 and halve it - or who has read widely in enrichment maths and been shown it before. Maybe it's the scholarship question.....
I would agree that in an 11+ it would only be likely to be solved either by someone similarly with a quick brain who spots that they can add two copies of the numbers together in matching pairs 1+1000, 2+999 ..... 1000+1 , realise that they have 1000 * 1001 and halve it - or who has read widely in enrichment maths and been shown it before. Maybe it's the scholarship question.....
Re: 11 plus series summation questions
Hi,
Just thought i would drop an update here.....and a answer to my own question.
First a correction to the above, the solution is n(n+1)/2 and NOT n(n-1)/2.
This question is actually related to Triangular numbers. Precisely, the sum of first n numbers is the nth triangular number.
so essentially in the question above, we are to calculate the 1000th Triangular number. Notice that the formular for the nth triangular number and the sum of the first n numbers are the same. The visual below may be helpful.
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Just thought i would drop an update here.....and a answer to my own question.
First a correction to the above, the solution is n(n+1)/2 and NOT n(n-1)/2.
This question is actually related to Triangular numbers. Precisely, the sum of first n numbers is the nth triangular number.
so essentially in the question above, we are to calculate the 1000th Triangular number. Notice that the formular for the nth triangular number and the sum of the first n numbers are the same. The visual below may be helpful.
@
@@
@@@
@@@@
@@@@@
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Re: 11 plus series summation questions
Sometimes the maths questions at the end of the paper are put there to keep the students occupied who have almost finished the paper and who might otherwise become restless and distract the other students.
Dd1 had this question as the last one in a Maths paper a few years ago. DG
Dd1 had this question as the last one in a Maths paper a few years ago. DG