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) It should be 5(m+n) because 5 is multiplied by both m and n.
B) It cannot be further simplified from the final fraction
C) The 3 in the first bracket should also be multiplied by 7.
D) (6a+3)^2 is not (36a^2+9), instead it should be (36a^2+36a+9)
E) 9y multiplied by y is 9y^2, not 9xy...

2. A. '5m+n' where did the positive n come from?
B. Same as A.
C. '7(x-3)' the answer for that equation should be '7x-21'. Which means, only x was multiplied by 7.
D. (6a+3)^2 should be (6a-3)^2.
E. Where did 9x^2 come from?

3. A: It should be [5m+5n-4m+n/m+n = m+6n/m+n]
C: It should be [7x-21-20-7x=14x-41]
D: It should be [ 3=12a^2-3(4a^2+4a+1 = -12a]
E: It should be [12xy+6xy-9y^2+9y^2]

4. A) must put brackets around m+n when multiplied by 5
B) unable to simplify the final answer
C) did not multiply the numbers in brackets
D) did not multiply with the negative sign when multiplying with 3
E) when multiplying y and (6x-9y) answer is not 6xy and 9xy

5. A)
-(4m-n/m+n) = -4m+n/-m+n , not -4m-n/m+n
B)
m/m+n cannot be simplified any further
C)
-(20-7x) = -20+7x , not -20-7x
D)
-(6a+3)^2 = -(35a^2+36a+9) = -35a^2-36a-9 , not -36a^2+9
E)
y(6x-9y) = 6xy-9y^2 , not 6xy-9xy

6. abiyyu arif rahman8/02/2011 08:17:00 AM

A: 5 is not multiplied by n.
B: since the denominator is M+N, you cannot cancel M with M
C: the last minus should be a plus
D: the last plus should be a minus
E: 9xy should have been 9y^2

7. Kat Yong Jie answered and then8/02/2011 08:17:00 AM

B. Should not cancel the 2 "m"s. E.g. 5/5+8 does not = ⅛.

C. Forgotten to x7 of 3 in 7(x-3) and change the operation in 20-7x to 20+7x

D. Did not use the parking lot format. It should be (6a+3)^2 = 6a^2+36a+9

E. Change the operation of (-3y) to (+3y)

8. A: Although it is correct to bring the 5 on top and multiply it by the denominator, it is a must to bracket it or else there is only 1n and it is supposed to be 5n.
B: It is for the same error as A however it is not possible for m to divide by m+another number. like 3 divided by 3+4, it is not correct.
C: When 7 multiply by (x-3), it is not 7x-3 because the 7 also applies to the 3 since it is in a bracket form. And for the bracketed 20-7x, the minus sign and minus sign cross so it is supposed to be + instead.
D: It is supposed to square it first, then multiply it by 3 and because of this error, the answer is wrong.
E: There was a careless mistake when (-3y) was changed to 9x^2 and when y(6x-9y) where one part was changed to 9xy instead of 9y^2.

9. For A, the person should simplify the numbers further.
For B, the numbers should not be cancelled when they are being divided, eg. 4/2+2=1 but when it is cancelled the answer would not be the same eg. 4/4+2 cancelled=1/1+2=1/3 so the answer is not the same.
For C, the person has forgotten to simplify the -3, it should be -21, the numbers on the right also has a problem which shows that -7x should be +7x as -x-=+.
For D, the person also did not times the - with the +3, thus the +3 should be -3.
For E, the person did not show us properly how he had got -9x^2, he started out with-3y but ended up with -9x^2, he might have miscopied the numbers.

10. A: The error is at the 5m+n. It should be 5m+5n. Also the equation can be further simplified to m+4n/m+n.

B: The error is at the cancellation. The m cannot be cancelled out and thus the answer should be m/m+n but the n should be a 5n so the answer is m+4n/m+n.

C: There are two errors in this equation. Firstly, the 3 should have been multiplied by 7 which will give 21. Secondly, the minus sign in front of the 7x at the back should be a plus sign since the minus sign multiplied the minus sign outside the bracket.

D: (2a+1)^2 should have been done before 3(2a+1).

E: The 9xy should have been 9y^2 as the 9y was multiplied by y.

11. A) They did not distribute the minus sign. They did not also multiply the 5 with m+n.
(5m+5n-4m+n)/m+n
B) The same mistakes as A but you cannot cancel like that, so the answer is the same.
C) They did not follow the distributive law.
7(x-3)-(20-7x)
7x-21-20+7x
D) They wrongly distribute the minus sign. And they also should square it first.
3+12a^2-3(2a+1)^2
(2a+1)(2a+1)=4a^2+4a+1
3+12a^2-3(4a^2+4a+1)
3+12a^2-12a^2-12a-3
=-12a
E) I think it is some careless mistakes.
12xy+y(6x-6y)+(-3y)
12xy+6xy-6y^2-3y
18xy-6y^2-3y

12. A/B : It should be (5m+5n-4m+n)/(m+n)=(m+6n)/(m+n)

C : It should be 7x-21-20+7x=14x-41

D : It should be 3+12a^2-(36a^2+36a+9)
=3+12a^2-36a^2-36a-9
=-6-24a^2-18a

E : It should be 12xy+6xy-9y^2-3y=18xy-9y^2-3y

13. A:When 5 becomes 5(m+n),there must be a bracket(as shown).
B:We should be able to simplify the final answer
C:The number '3' in he brakets is not multiplied
D:(6ax3)^2 is not 36a^2+9,but it is (36a^2+36a+9)
E:9y x y equals to 9y^2,not 9xy

14. A) it should be (5m+5n-4m-n)/m+n NOT (5m+n-4m-n)/m+n

c) It should be 7x-21 - 20+7x NOT 7x-3 - 20-7x

D) 3(2a+1)^2 should be multiplied by the power first then by three.

E) (3y) should not become -9x^2 in the next line but it should be -3y

15. kaneko yoshiki8/02/2011 08:23:00 AM

a) Conceptual error: he took 5(m+n) but in the end, did 5(m)+n.
b) Conceptual error: m/m+n is not 1/n. let's say that m is 3 and n is 2. 3/3+2 is not 1/2. that's why
c) conceptual error. 7(x-3) is not 7x-3, it is 7x-21. also, -(20-7x) is - 20+7x
d) conceptual error: 3(2a+11)^2 is then 3(4a^2+121). then it becomes 12a^2+363
e) y(6x-9y)+(-3y) is 6xy-9Y^2-3y

16. Question A:
His equation: 5m+n-4m-n / m+n

Should be: [5(m+n)]-(4m-n) / m+n
=(5m+5n) -(4m-n) / m+n
= 5m+5n - 4m+n / m+n
= m+6n / m+n

Question C:
His equation: 7(x-3)-(20-7x)
=7x-3 - 20-7x

Should be: [7x-3(7)]-(20-7x)
=(7x-21) -(20-7x)
= 7x-21 - 20+7x
= 14x-41

Question D:
=-36a^2-9

He did : -(6a+3)^2
=-36a^2+9

Question E:
Should be : (-3)^2
= +9
But he did: (-3)^2
=(-9)

17. (A) and (B) There is no brackets.It should be 5(m+n)-(4m-n)/m+n
(C) The person forgot to multiply the 3 with 7 to get 21 and the person forgot to change the - sign into a + sign for 20+7x
(D) The power to has to be multiplied first then the number outside of the brackets.
(E) The (3y) should be -3y after removing brackets

18. a) It should be 5(m+n)-4m-n/m+n.
b) m/m+n does not equal to 1/n because if we change it into numbers for example, 1/1+2, it does not equal to 1/2. The equation 5m+n-4m-n/m+n is also wrong so the final answer is wrong
c) He only expanded the x but not the 3
d) He expanded the 3(2a+1)^2 first when he should have squared it first
e) y(6x-9Y)+(-3y) does not equal to 6xy-9x-9x^2, it should be equal to 6xy-9y^2-9y^2

19. For the mistake in A, we need to make the denominator the same for both 5 and 4m-n/m+n. 5 = 5/1. We can multiply the denominator, which is 1, by m+n. The result of that is m+n. We must do the same to the numerator. 5 multiplied by m+n equals to 5m+5n. So the answer is 5m+5n-4m-n/m+n.
For the mistake in B, the student should not have cancelled out the m.
For the mistake in C, the -3 should be multiplied by 7, so it should be 7x-21.
For the mistake in D, the person should have done (2a+1)^2 before doing 3(2a+1).

20. (A) 5 - 4m-n/m+n = 5 (m+n)-4m-n/m+n
(B) 5m+5n-4m-n/m+n = 5m+5n-4m-n = m+4n
(C) 7x-21-20-7x = -41
(D) 3+12a^2-3(2a+1)^2 = 3+12a^2 - 2a^2+2a+1
=4+10a^2+2a
(E) 12xy+y(6x-9y)+(-3y) = 12xy+6xy-9y^2-3y
=18xy-9y^2-3y

21. (A) When 5 is multiplied by m+n, it should be 5(m+n) and hence, the results should be 5m+5n and not 5m + n
(B) The 5 multiplied by (m+n) is not 5n + m but 5n + 5m. Also, m/m+n the ms cannot be cancelled out as.. Example : Let's say m = 3 and n = 2. This way, m/m+n = 3/5 while 1/n = 1/2. Hence, this is wrong.
(C) The 3 was not multiplied by the 7 and the negative sign behind the brackets were not used to make the -7x positive. Hence, the answer should be 14x - 41
(D) -3(2a+1)^2 Has been interpreted wrongly. Ignoring the power first, -3(2a +1) = -6a - 3. (-6a-3)^2 does not equals to 36a^2 + 9. This is a conceptual error of the parking lot.
(E) y * 9y is 9y^2 and not 9xy. And where did the 9x^2 come from?