BY MR JOHARI

**Context**

Below shown the solution posted by the secondary 3 students during the 4th February 2013 Maths Quiz C.

There are errors in the solution posted.

**Focus**

Error Analysis and Peer Evaluation

Individual Effort

**Task**

You are required to

**post**the following as a**comment**:
(i) Nature of error - conceptual or carelessness (be very specific in your description)

example - careless error due to arithmetic (addition)

example - conceptual error due to error in (a + b)^2 = a^2 + b^2.

(2) Correction to the error

Ensure that your solution is concise and correct.

1) The division sign changed to a multiplication sign, this is a conceptual error as when u convert cuberoot to ^1/3 it does not change the sign

ReplyDelete2a) Conceptual error 32^2 ≠ 2^5+x, instead it should be 2^5x

2c) Careless error 3^2≠2, 3^2=9

3a) Careless error 64≠2^5, 64=2^6

3c) Careless error 16≠2^5, 16=2^4

Good observation - sometimes there is a fine line between carelessness n conceptual errors.

Delete1. Careless & Conceptual. He changed the divide sign to multiplication. He also made another mistake. If he continues, he should have add 1/3 to 3 instead of multiplying it, as m^n + m^b = m^n+b

ReplyDelete2a. Conceptual. 32^x should be 2^5x. The 5 and x should be multiplied together instead of added.

2c. Careless. 3/9 is not 1/2 it is 1/3

3a. Careless. 64 is not 2^5, it is 2^6.

3c. Careless. 1/16 should be 2^-4 not 2^-5.

1) It is a conceptual error, as when he changed ÷3√m it became x3^1/3, it should retain its divide sign as it is only changing its form not the equation.

ReplyDeletem^x=m^3÷m^1/3xm^5

m^x=m^7 2/3

x=7 2/3

2a)concept error 32^x ≠ 2^5+x, 32^x =(2^5)^x

32^x =(2^5)^x

32^x=(2^x)^5

(3)^5= 243

2c) careless error 3^2= 9 ≠ 6 so instead of 1/2 you should get 1/3

3/4^x=3/(2^x)^2=3/3^2=3/9=1/3

3a)careless error 64 = 2^6 not 2^5

64 = 2^6

2^5x=2^6

5x=6

x=1.2

3c) Careless error 16 = 2^4 16 ≠ 2^5

2^5x=1/2^4

2^5x=2^-4

5x=-4

x=-0.8

1) Conceptual error . Even if we change cube root to an index of 1/3 , the sign does not change and remains as divide

ReplyDelete2) Conceptual error . 32 = 2^5 . But the x is the index of 32 so , the x is multiplied together with the 5 to become 2^5x

2c) Careless error . 3/3^2 is not half , instead it if 3/9 which is 1/3

3) Careless error . 2^5 is 32 , not 64 . So it is actually 5x =6

3c) Careless error . 16 is 2^4 or in this case 1/16 is 2^-4 .

1) Conceptual error . Even if we change cube root to an index of 1/3 , the sign does not change and remains as divide

ReplyDelete2) Conceptual error . 32 = 2^5 . But the x is the index of 32 so , the x is multiplied together with the 5 to become 2^5x

2c) Careless error . 3/3^2 is not half , instead it if 3/9 which is 1/3

3) Careless error . 2^5 is 32 , not 64 . So it is actually 5x =6

3c) Careless error . 16 is 2^4 or in this case 1/16 is 2^-4 .

Q1) Careless. "m^3 / m^1/3" is changed to "m^3 x m^1/3" thus getting the wrong solution. Else, the solution would be m^3 / m^1/3 x m^5 = m^7/1/3 where x = 7 and 1/3 .

ReplyDeleteQ2a) Conceptual error. 32^x = (2^5)^x which is 2^5x instead of 2^5+x . Solution would be (2^x)^5 = 3^5 = 243.

Q2c) Careless error. 3/3^2 is not 1/2 , instead its 3/3^2 = 3/9 = 1/3

Q3a) Careless error. 64 is not 2^5 , it should be 2^6, thus 5x = 6 and x = 1.2.

Q3c) Careless error. 16 is not 2^5 , it should be 2^4, thus 5x = -4 which x = -0.8.

1) Conceptual error. He mistook the a^m x a^n = a^m+n law.

ReplyDeletem^3 x m^1/3 x m^5 = m^3+1/3+5 = m^7/2/3

2a) Careless error. He converted 32^x as 2^5+x while the proper conversion should be 2^5x

2^5x = (2^x)^5 = 3^5 = 243

2c) Careless error. 3^2 does not equal 6

3/3^2 = 3/9 = 1/3

3a) Careless error. 64 does not equal to 2^5. Instead it should be 2^6

2^5x = 2^6

5x = 6

x= 1/1/5

3c) Careless error. 1/16 does not equal to 2^-5. instead it should be 2^-4

2^5x = 2^-4

5x = -4

x = -4/5

1) Careless error: when converting 3√m to m^1/3, he changed the sign from ÷ to x.

ReplyDeleteOn the second line, m^3 x m^1/3, he multiplied the index instead of adding. Conceptual error

Correction:

m^x = m^3 ÷ 3√m x m^5

m^x = m^3 ÷ m^1/3 x m^5

x = 3 - 1/3 + 5

x = 7 2/3

2a) Conceptual error. 32^x ≠ 2^5+x. Instead, 32^x = 2^5x.

Correction:

32^x = 2^5x = (2^x) ^ 5 = 3^5 = 243

2c) Careless error 3^2 ≠ 6. Instead, 3^2 = 9

Correction:

3/4^x = 3/(2^2)^x = 3/9 = 1/3

3a) Careless error. 64 ≠ 2^5. Instead, 64 = 2^6

Correction:

32^x = 64

2^5x = 2^6

5x = 6

x = 1.2

3c) Careless error. 16 ≠ 2^5. Instead, 16 = 2^4

Correction:

32^x = 1/16

2^5x = 2^-4

5x = -4

x = -0.8

This comment has been removed by the author.

ReplyDelete1) Conceptual error because the division sign was change to multiplication sign.

ReplyDeleteIt should be:

m^x = m^3 ÷ ∛m x m^5

m^x = m^3 ÷ m^1/3 x m^5

x = m - 1/3 + 5

x = 23/3

2a) Conceptual error because 32^x ≠ 2^5+x.

It should be:

32^x = (2^5)^x = (2^x)^5 = 3^5 = 243

2c) Careless error due to division.

It should be:

3/4^x = 3/(2^x)^2 = 3/3^2 = 1/3

3a) Careless error because 64 ≠ 2^5

It should be:

32^x = 64

2^5x = 2^6

5x = 6

x = 6/5

3c) Careless error because 1/16 ≠ 2^-5

It should be:

32^x = 1/16

2^5x = 2^-4

5x = -4

x = -4/5

1) Conceptual, division sign does not change to multiplication

ReplyDeleteConceptual, when multiplying , it is not 3x1/3, but 3+1/3

2) Conceptual, 32^x = 2^5^x, not 2^5+x

2c) Careless, 3^2 != 6

3) Careless, 64 != 2^5

3c) Careless, 1/16 != 2^-5

1. Conceptual error. Wrong concept of the laws of indices.

ReplyDeleteRight answer:

m^x = m^3 / 3√m x m^5

m^x = m^3 / m^1/3 x m^5

m^x = m^3-(1/3)+5

x=7 2/3

2a. Conceptual error. 32 does not equal to 2^5+x but 2^5x.

Right answer:

32^x = 2^5x

= (2^x)^5

= 243

2c. Careless error due to the error in 3/3^2 = 1/2

Right answer:

3 / 4^x = 3 / (2^x)^2

= 3/3^2

= 3/9

= 1/3

3a. Careless error due to the error in 64 = 2^5

Right answer:

32^x = 64

2^5x = 2^6

5x = 6

x = 1 1/5

3c. Careless error due to the error in 1/16 = 2^-5

Right answer:

32^x = 1/16

2^5x = 2^-4

5x = -4

x = -4/5

1. Conceptual error. m^3 / √m is not equals to m^3 * m ^1/3. The sign does not change from * to / when changing the cube root to a power. Also, m^3 * m^1/3 = m^(3+1/3). The powers need to be added when multiplying.

ReplyDelete2a. Conceptual error. 32^x = (2^5)^x = 2^5x. Not 32^x = (2^5)^x = 2^(5+x). The powers need to be multiplied and not added in this case.

2c. Careless error. 3/3^2 = 3/9 = 1/3. Not 3/3^2 = 3/6 = 1/2

3a. Careless error. 64 = 2^6 not 2^5

3c. Careless error. 1/16 = 2^-4 not 2^-5

1)

ReplyDeletecarelessness

m^x=m^3 / m^1/3 *m^5

m^x=m^(3-1/3+5)

m^x=m^23/3

x=23/3=7+2/3

2a)

conceptual error

32^x=2^5^x=(2^x)^5=3^5=243

2c)

carelessness

3/3^3=3/9=1/3

3a)

conceptual error

32^x=(2^5)^x

(2^5)^x=64=2^6

x=6/5

3c)

carelessness

2^5x=2^-4

x=-4/5

q1) conceptual error: sign should remain as multiplication sign not change into divide, law of indices states that m^3 x m^1/3 should be m^4/3 and not m.

ReplyDeleteq2a) conceptual error: 32^2 ≠ 2^5+x, instead it should be 2^5x

q2c) careless error 3/3^2 is not 1/2, expand before simplifying, instead answer should be 3/9 = 1/3

q3) Careless error: 64 ≠2^5 instead is equal to 2^6

3c) Careless error: 1/16 ≠ 2^-5, instead is equal to 2^-4. Thus 5x=-4, therefore value of x=-0.8

Part 2:

ReplyDelete1)

m^x = m^7 2/3

x=7 2/3

2a)

32^x = (2^x)^5

= (3)^5

=243

2c)

3/4^x = 3/(2^x)^2

=3/3^2

=1/3

3a)

32^x = 64

2^5x = 2^6

x = 1.2

3c)

32^x = 1/16

2^5x = 2^-4]

x = -0.8

test post

ReplyDelete1.Conceptual error. m^1 x m^2 = m^1+2.

ReplyDeleteIt should not be multiplied, which in this case shows m^3 x m^1/3, which should be m^3+1/3 and not m^3 x 1/3.

m^x = m^ 8 1/3

therefore, x = 8 1/3

2a) Conceptual error. 32^2 ≠ 2^5+2, but instead (2^5)^x.

(2^x)^5

= (3)^5

= 243

2c) Careless Error. 3^2 = 9, not 6.

3/ 3^2 = 3/ 9

= 1/3

3a) Careless error. 64 = 2^6, not 2^5

2^5x = 2^6

5x = 6

x = 1.2

3c) Careless error, 1/16 = 2^-4, not 2^-5

2^5x = 2^-4

5x = -4

x = -4/5

1. CE m^3 / √m is not equals to m^3 * m ^1/3. The sign does not change from * to / when changing the cube root to a power. Also, m^3 * m^1/3 = m^(3+1/3).

ReplyDelete2a. CE32^x = (2^5)^x = 2^5x. Not 32^x = (2^5)^x = 2^(5+x).

2c. CM 3/3^2 = 3/9 = 1/3. Not 3/3^2 = 3/6 = 1/2

3a. CM64 = 2^6 not 2^5

3c. CM 1/16 = 2^-4 not 2^-5

1. Conceptual error. When he changed the cube root, the divide sign should not change to multiply sign. Both the indices of m should not be multiplied to each other, it should be added instead.

ReplyDelete2a. Conceptual. Since 32 is 2^5 and x is the index of 32 in the question, x should be the index of (2^5) and so x will be multiplied into the index of 2.

2c. Careless. 3^2 is not 3*2. 3^2 = 9.

3a. Careless. 64 ≠ 2^5. 64 = 2^6

3c. Careless. 16 ≠ 2^5. 16 = 2^4

1) Conceptual ERROR.He accidentally changed the division sign into a multiplication sign.

ReplyDelete2a) Conceptual ERROR 32^x doesn't equal to 2^5+x . It should be 2^5x since (x^m)^n =x^mn

2c) Conceptual ERROR. 3^2 is 9 not 6 since x^m doesn't equal to xm

3a) Careless ERROR 2^5= 32 NOT 64. 2^5=64

3c) Careless ERROR. 16 = 2^4 not 2^5

1. CE

ReplyDeletem^x=m^3÷m^(1/3)*m^5

=m^(3-1/3+5)

=m^(7+2/3)

therefore, x=7 2/3

2. CE

32^x=(2^5)^x=(2^x)^5

=3^5=243

3. CL

3/(3^2)=1/3

4. CL

32^x=64

2^5x=2^6

x=1.2

5. CL

32^x=1/16

2^5x=2^-4

x=-0.8