**Objectives**:

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

**Task:**

**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**

A) It should be 5(m+n) because 5 is multiplied by both m and n.

ReplyDeleteB) 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...

A. '5m+n' where did the positive n come from?

ReplyDeleteB. 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?

A: It should be [5m+5n-4m+n/m+n = m+6n/m+n]

ReplyDeleteC: 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]

A) must put brackets around m+n when multiplied by 5

ReplyDeleteB) 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

A)

ReplyDelete-(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

A: 5 is not multiplied by n.

ReplyDeleteB: 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

A. Changing of operation sign in 4m-n. It should be 4m+n.

ReplyDeleteB. 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)

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.

ReplyDeleteB: 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.

For A, the person should simplify the numbers further.

ReplyDeleteFor 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.

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.

ReplyDeleteB: 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.

A) They did not distribute the minus sign. They did not also multiply the 5 with m+n.

ReplyDelete(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

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

ReplyDeleteC : 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

A:When 5 becomes 5(m+n),there must be a bracket(as shown).

ReplyDeleteB: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

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

ReplyDeletec) 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

a) Conceptual error: he took 5(m+n) but in the end, did 5(m)+n.

ReplyDeleteb) 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

Question A:

ReplyDeleteHis 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:

Instead of: -(6a+3)^2

=-36a^2-9

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

=-36a^2+9

Question E:

Should be : (-3)^2

= +9

But he did: (-3)^2

=(-9)

(A) and (B) There is no brackets.It should be 5(m+n)-(4m-n)/m+n

ReplyDelete(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

a) It should be 5(m+n)-4m-n/m+n.

ReplyDeleteb) 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

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.

ReplyDeleteFor 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).

(A) 5 - 4m-n/m+n = 5 (m+n)-4m-n/m+n

ReplyDelete(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

(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

ReplyDelete(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?