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.

Q1) Conceptual error, changed division sign to multiplication sign when changing cube root to fractional exponent)

ReplyDeleteSolution:

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

m^x = m^7 2/3

x = 7 2/3

Q2a) Conceptual error (32^x ≠ 2^5+x)

Solution:

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

Q2c) Careless error (3^2 ≠ 6)

Solution:

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

Q3a) Careless error (64 ≠ 2^5)

Solution:

32^x = 64

2^5x = 2^6

x = 1 1/5

Q3c) Careless error (1/16 ≠ 2^-5)

Solution:

32x = 1/16

32x= 16^-1

2^5x = 2^-4

x = -4/5

1) Conceptual error. Changed division sign into multiplication sign after changing cube root into a fractional exponent.

ReplyDeleteSolution:

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

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

m^x=m^7 2/3

x= 7 2/3

2a) Conceptual Error. 32^x ≠ 2^5+x, 32^x=(2^x)^5

Solution:

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

2c) Careless Error. 3^2 ≠ 6, 3^2=9

Solution:

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

3a) Careless Error. 64=2^6, 64≠ 2^5

Solution:

32^x=64

(2^5)^x=2^6

2^5x=2^6

5x=6

x=1 1/5

3c) Careless Error. 1/16 ≠ 2^-5, 1/16=2^-4

32^x=1/16

2^5x=2^-4

5x=-4

x=-4/5

Q1. Conceptual error.m^3 X m^(1/3) ≠ m

ReplyDeletem^x = m^3 / m^(1/3) X m^5

m^x = m^8/m^(1/3)=m^7 2/3

x=7 2/3

Q2a.Conceptual error 32^x ≠ 2^(5+x)

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

Q2c.Carelessness 3/3^2 ≠ 1/2

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

3a. Carelessness 2^5 ≠ 64

32^x = 64

2^5x = 2^6

5x = 6

x = 1 1/5

3b.Carelessness 1/16 ≠ 2^-5

32x = 1/16

32x = 2^-4

2^5x = 2^-4

5x = -4

x = -4/5

Question 1

ReplyDeleteConceptual error due to m^x = m^3 x m^/3 x m^5

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

= m^2 2/3 x m^5

= m^7 2/3

x = 7 2/3

Question 2a

Conceptual error: 32^x ≠ 2^5+x

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

Question 2C

Careless error : 3/3^2 ≠ 1/2

3/9 = 1/3

Question 3A

Careless error: 64 ≠ 2^5

32^x = 64

2^5x = 2^6

5x = 6

x = 6/5

Question 3C

Careless error: 1/16 ≠ 2^-5

32^x = 1/16

32^x = 2^-4

5x = -4

x = -4/5

1) Conceptual error. Changed division sign into multiplication sign after changing cube root into a fractional exponent.

ReplyDeleteSolution:

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

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

m^x=m^7 2/3

x=7 2/3

2a) Conceptual Error. 32^x ≠ 2^5+x, 32^x=(2^x)^5

Solution:

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

2c) Careless Mistake. 3^2 ≠ 6, 3^2=9

Solution:

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

3a) Careless Mistake. 64=2^6, 64≠ 2^5

Solution:

32^x=64

(2^5)^x=2^6

2^5x=2^6

5x=6

x=1 1/5

3c) Careless Error. 1/16 ≠ 2^-5, 1/16=2^-4

32^x=1/16

2^5x=2^-4

5x=-4

x=-4/5

1) Conceptual error

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

=m^3-1/3+5

=m^7 2/3

x= 7 2/3

2a) Conceptual Error

32^x=(2^x)^5

=(3)^5

=243

3a) Careless Error

32^x=64

(2^5)^x=2^6

2^5x=2^6

5x=6

x=6/5

3c) Careless Error

32^x=1/16

2^5x=2^-4

5x=-4

x=-4/5

1. Careless error; changed the division sign to multiplication sign in process of changing the term to indices.

ReplyDeleteSolution:

m^x = m^3 ÷ m^1/3 x m^5

m^x = m^(7 2/3)

x = 7 2/3

2a. Conceptual error; when expanding 32^x, used multiplication law instead of power law.

Solution:

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

2c. Careless error; multiplied 3 by 2 in 3^2 instead of 3 to the power of 2.

Solution:

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

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

Solution:

32^x = 64

2^5x = 2^6

5x = 6

x = 6/5

x = 1 1/5

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

Solution:

32^x = 1/16

2^5x = 2^-4

5x = -4

x = -4/5

1) Conceptual error: mᵡ = m³ x m^1/3 x m⁵ (division sign changed to multiplication sign after changing cube root to fraction)

ReplyDeletesolution:

mᵡ = m³ ÷ ∛m x m⁵

mᵡ = m³ ÷ m^1/3 x m⁵

mᵡ = m^5 8/3

∴ x = 7 2/3

2)

a) Conceptual error: 32ᵡ ≠ 2⁵⁺ᵡ

solution:

32ᵡ = 2⁵ᵡ

= (2ᵡ)⁵

= 243

c) Careless error: 3/3² ≠ 1/2

solution:

3/4ᵡ = 3/2²ᵡ

= 3/9

= 1/3

3)

a) Careless error: 64 ≠ 2⁵

solution:

32ᵡ = 64

2⁵ᵡ = 2⁶

∴ 5x = 6

x = 6/5

c) Careless error: 1/16 ≠ 2⁻⁵

32ᵡ = 1/16

32ᵡ = 2⁻⁴

2⁵ᵡ = 2⁻⁴

∴ 5x = -4

x = -4/5

Q1: Careless Error (changed division sign to multiplication sign while converting fractional indices)

ReplyDeleteConceptual Error ( (m^3) x (m^1/3) ≠ m , should be (m^3) x (m^1/3) = M^3 1/3)

Solution:

m^x = m^3 ÷ m^1/3 x m^5

m^x = (m^2 2/3) x (m^5)

m^x = m^7 2/3

x = 7 2/3

Q2a: Conceptual Error (32^x ≠ 2^x+5 , should be 32^x = 2^5x)

Solution:

32^x = 2^5x

= (2^x)^5

= 3^5

= 243

Q2c: Careless Error (3/3^2 ≠ 1/2, should be 3/3^2 = 1/3)

Solution:

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

= 3/3^2

= 3/9

= 1/3

Q3a: Careless Error (64 ≠ 2^5 , should be 64 = 2^6)

Solution:

32^x = 64

2^5x = 2^6

5x = 6

x = 6/5

x = 1 1/5

Q3c: Careless Error (1/16 ≠ 2^-5 , should be 1/16 = 2^-4)

Solution:

32^x = 1/16

2^5x = 2^-4

5x = -4

x = -4/5

1. Conceptual error

ReplyDeletem^x = m^3 / m^(1/3) x m^5

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

m^x =m^7 2/3

x= 7 2/3

2a. Conceptual Error

32^x=(2^x)^5

32^x=(3)^5

x=243

3a. Careless

32^x=64

(2^x)^5=2^6

2^5x=2^6

5x=6

x=6/5

3c. Careless

32^x=16^-1

2^5x=2^-4

5x=-4

x=-4/5

Questions 2a to 3c I have forgotten how to do therefore I didn't know the answer.. But I have relearnt the steps and redid the quiz on my own and got full marks :OO

ReplyDelete