Monday, August 1, 2011

Level Test (review) part 2

Objectives:
to clarify, consolidate and analyse common conceptual and careless errors committed by students during level test.

Individually, please identify one possible error in each of the error analysis solutions shown below. eg. Conceptual error due to misquoting of (a+b)^2 law. It should be a^2+2ab+b^2 NOT a^+b^2. You may correct part of OR all the errors found in each solution.
In total, you should complete 5 work in all.

A

B

C

D

E

1. A): There are missing brackets, instead of 5m+n/m+n. It is meant to be 5(m+n) because we need to multiply 5 by both sides of the equation

B): It is a conceptional error, you cannot cancel out the m

C): Carless mistake, he/she forgot to mutliply the -3 by 7

D):The student multiplied 3(2a+1) first before doing the square when it is meant to be the other way round.

E): Conceptional error, in y (6x-9y) it is meant to be 6xy-9y^2. There are another conceptional error, it is meant to be a positive 9y^2 not a negative and the x is meant to be a y

2. a.missing brackets and wrong sign.5(m+n)-4m+n

b.you cannot cancel out m.

c.he forgot to multiply the 3. should be 7x-21-20-7x=-41

Nicholas Tan
Choy Rui Zhi
Part 1(a,b,c)

3. a: Negative and negative makes positive and the answer could be simplified. the answer is m=2N
b: the answer could not be simplified
c: 7(x-3)=7x+21 but the answer that is shown is 7x+3
d: the student should square the bracketed sum then multiply
e: 9y*y=9y^2. Not 9xy

4. A: Careless error. The equation should be (5m+5m-m+n)/m+n and not (5m+n-m-n)/m+n

B: Conceptual and careless error. The equation should be (5m+5m-m+n)/m+n and not (5m+n-m-n)/m+n and m/m+n cannot be simplified to become 1/n.

C: Conceptual error. The 7 is to be multiplied by x and 3 resulting in 7x-21 and not 7x-3.

D: Conceptual error. The equation should have been squared first before being multiplied so it should have been 3(4a^2+1) = 12a^2+1.

5. A: The answer is not simplified
B: m/n+n is not equal to 1/n
C: There is a minus sign before (20-7x), hence, -X- = +. so it becomes 7x + 7x
D: The numbers in the bracket should be squared before being multiplied by 3
E: When y is multiplied by y, the answer is y^2 and the is no square in (-3y)

6. Charles O&#39;Rourke8/04/2011 08:52:00 AM

1.careless for using wrong sign
2.conceptual error because you cannot cancel out numbers or values in fractions.
3.careless error because he did not multiply 3 by 7
4.careless for not changing the + to a - in the (6a+3)^2
5.careless,y(6x-9y) should be 6xy-9y^2

7. Question A - Conceptual error

When a negativer is multiplied by another negative, it becomes a positive. (Law : Like terms equal positive).

The - [(5/m+n) - (4m-n/m+n)] works out to be :

[5m+5n-4m+n/m+n].

5-1(4m-n) would result in a positive of n and not a negative.

The 5 refers to both the m and n, not just the m only.

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Question B - Conceptual error

The student has a conceptual error. He should only be able to cancel if the + and - sign are multiplication and division.
The student has cancelled off when the operation is addition and minus.

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Question C - Conceptual error

The student when expanding 7(x-3) only multiplied the 7 and x and did not multiply the 7 and 3. And when -1(20-7x), -1 x -7x = 7x. When a negative is multiplied with another negative number, it becomes a positive.

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Question D - Careless error

The student did not change the positive sign of the operation to a negative one after the positive value has been multiplied by a negative operation.

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Question E - Careless Error

The student has multiplied a y with a y and wrote it as xy instead of y^2.

When the student had mutliplied (-3y)^2, the student wrote 9x instead of 9y.

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Shawn Liew Hong Wei

8. A: It is supposed to be 5(m+n) or 5m+5n not 5m+n
B: m/n+n is not 1/n
C: The 7 did not multiply by 3 in the bracket.
D: Did not power by 2 first.
E: 3y became 9x.

9. D) The power must be done first, which means -3(2a+1)^2 and the power is [(2a+1)^2] that must be done first before it multiply by -3 so it would be 2a^2+4a+1 then you multiply by -3.
The answer is also wrong as the person forget the rul of (-)(+)=(-)
so if -3(2a^2+4a+1) = -16a^2-12a-3)
so the person is wrong.
E ) he has two errors in his answer first is (-3y)^2 = -9x ? the answer has become from y to x.
And it is (-3)^2 = to 9x not a negative number. the rule is (-)(-)=(+)

10. E: Careless error. (-3y)^2 is 9y^2 and not 9y^2.

11. A) The answer is 5m+5n-4m+n/m+n . The negative should be changed to a positive . Move the negative sign to the numerator of the fraction so it will become - (4m-n) . In this case we take - x 4m = -4m and - x -n = n so the numerator becomes 4m+n . The next error is that when 5 is changed into a fraction, the numerator becomes 5(m+n) which is 5m+5n but they think the numerator is 5m+n as when m+n is moved to the numerator it would look like 5m+n so this is a careless error .
B) This is a error that he has to seek a teacher for help as it is a conceptual error .
C)7(x-3) when expanded is 7 x x - 7 x -3 which is equal to 7x + 21 . -(20-7x) when expanded is - times 20 which is equal to -20 and - times -7x is 7x so the answer is +7x-20 . The answer is 7x+21+7x-20 and when simplified is 14x + 1 .
D) The student should have squared (2a+1) which will be (4a^2+1) then multiply it by -3 and negative 3 times positive 4a^2 is -12a^2 as when a negative number is multiplied by a positive number, it becomes a negative number and the same thing happens when -3 is multiplied by +1 so -3(2a+1)^2 is equal to -12a^2-3 . The final answer is 0 .
E) The answer for y(6x-9y) is 6xy-9y^2 so it must be a conceptual error as to how he got 9xy .+(-3y) when expanded is +x-3y which is equal to -3y so it must also be another conceptual error as to how he got 9x^2 .

12. A: Careless error, missing brackets made the person confused
B: Conceptual error. He cancelled the m.
C: Careless error. He did not multiply the negative 3 by negative 7. The answer should be 1.
D: Conceptual error. He multiplied the numbers in the brackets before squaring them.
E: Careless mistakes. He did not do y*y, instead he did y*x. He also mistook y for x and did the last part wrong. The correct answer should be 18xy - 9y^2.

13. A) It is suppose to be 5(m+n)=5m+5n
B) It is a conceptional mistake as m cannot be canceled
C)It is a conceptional mistake as the 3 should be multiplied and - x -= +
D) Conceptional mistake. He should square the number first
E)It is a carless mistake as the 9xy is suppose to 9y^2 and the 9x^2 is suppose to be 9y^2

14. a) In terms of fractions you can say 5m+5n / m + n as if you factorise it will still end up with a 5. Therefore (5m + 5n - (4m - n) ) / m + n removing the brackets "- n " would become "+ n" as after you minus n from 4n it is the same as adding n to 5m + 5n. So 5m - 4m would = to m. 5n + n = 6n
This person made a careless mistake by forgetting to change the minus sign to a plus. Even so, he/she did not continue simplifying it.

b)This person made the same mistaking as the person who has done question A, but she simplified it at the end. When cannot "cancel" when there is a "+" sign in the fraction. There are "imaginary" brackets on the numerator and denominator thus we must do (m+n) first and cannot "cancel" the M's

c) This person also made the same mistake about no changing "-" to "+" after removing the brackets. he/she also forget to times 7 to 3 when she did the step 7(x * 3)

d)This person firstly should have did 3(2a +1)(2a+1) = 3(4a^2+2a+2a+1) = 12a^2 + 12a + 3
When this person removed the brackets, she did not change the plus to minus to as adding on the the subtracting number is as good as subtracting each number from 3 + 12a^2

e)This person done some thing wrong, y(9y) does not equal to 9xy, where did the x come from? it would be 9y^2. and where did the (-3y) go? it should be 12xy +6xy + 9y^2 -3y