## 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. 1.The n should have been multiplied by 5.
2.The n should not be canceling out each other.
3.The 7 should not negative but positive.
4.(6a+3) when squared is not 36a squared+9.
5.-3y cannot be changed to -9x square

2. A.The n at the numerator is to be multiplied by 5.
B.The m at the numerator cannot be cancelled with the m at the denominator cannot be canceled at the last part.
C.When removing the bracket,the -7 should become +7.
D.It should be -(36a^2+9) then -36a^2-9
E.It should be 9y^2 not 9xy and -3y should not be worked to -9x square

3. 1. The sign is wrong , -x - = + and they did not multiply the n by 5 .
2.They can not just cancel out the n .
3. The 7 was not multiplied by the 3 and the 7x is positive not negative
4. The ^2 needs to be done first by using the identity then multiplying by the number outside the brackets
5.The expansion for the y outside the bracket is wrong and the expansion for the sign is wrong and the number is wrong ( -3y)

4. A) Error with the sign conversion (-)(-) = (+). (-)(4m-n/m+n) should be 4 m+n.

B) Error in division .Just like using numbers, addition and subtraction can't use this method of canceling. It should eb just 2n+m/m+n.

C) Error in sign conversion. Just like A) (-)(-)=(+) which in this case is (-)(20-7x) which is -20+7x.

D) Error in power sign. The power sign should be taken out first before removing the brackets. It should be in this order -3(2a+1) = -3(4a^2+1)=-12a^2-1

E) Error in multiplication. I should be y(6x-9y) = 6xy-9y^2 not 9xy.

5. A) There is error with the sign, negative times negative equals positive. So it should be 4m+n. Another problem is that, the n should have been multiplied by 5

B) the m cannot be canceled out just like that, it must be a cross multiplication

C) -(20-7x).. before the bracket, there is a 'invisible 1' and when it is multiplied by 1, the signs need to change too because negative times negative equals positive. so it should be, -20+7x

D) The power sign should be done first before multiplying the numbers in the bracket, and the signs are wrong, (-)(+) = (-), it should be -36^2-9

E) it is -(-3y), how can it become 9x^2? Numbers in the question cannot be changed.

6. 1.should be 4m+n, not 4m-n
2.cancelling cannot be used in addition in the denominator and numerator of the fraction
3.7 must be positive, not negative
4.power sign must be taken out first
5.-3y is not 9x^2

7. 1. It should be 4m+n because if you have 3-(2-1), that would be 3-2+1.
2. You can not cancel in addition
3. 7(x-3) = 7x - 21 not 7x - 3 and then conversion error. It should be20 + 7x
4. Power sign comes first
5. -3y isn't 9x^2. Y is not X

8. A) The sign is wrong it should be 4m+n not 4m-n.
B)You cannot cancel addition but can cancel when it is multiplication or division.
C)The sign convention is wrong as (-) X (-) = (+) so it should be 7x-3-20+7x
D)The sign convention is again wrong. When there is a negative outside the bracket always remember there is a 1 there thus you have to take note of the sign convention and thus its should be (6a-3)^2
E) It should be 9y^2 and -3y is also not 9y^2

9. A) <5m+n> The 5 must be also multiplied with the n resulting in 5n.
the -n in 4m-n /m+n after it is in one fraction must become +n since - x - = +

B) the m cannot be canceled out since one of them is addition .Cancelation only occurs when both are in multiplication.

C) the result is not 7x -3. the 7 is also multiplied by -3 resulting in -21
and -(20-7x) will result in -+20--70x which will result in = -20+70x

D) < 3(2a+1)^2 > the square belongs to the values in the brackets not including the 3 in multiplication.thus the process of squaring must occur before multiplying with 3.

E) the expression to the right should result in +6xy -9y^2 not +6xy-9xy.
<>
for (E)

I think it is a (-3y) the whole squared since the brackets will be redundant if they are not in multiplication or other similar processes.
So the correct answer (-3y)^2 will result in (9)(y^2)