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Common Errors in Secondary Mathematics
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Common Errors Committed by the
Students in Secondary Mathematics
Errors that students often make in doing secondary mathematics during their practice and during the examinations and their remedial measures are well explained here stp by step.
Some Common Errors in Mathematics
Conceptual Errors
2(a+b) = 2a +2b
Due to this statement students get an impression that everything works like this. Here is whole list , in which this does not work.
Incorrect 
Correct 
(a + b)^{2} = a^{2} + b^{2} 
(a + b)^{2} = a^{2} + b^{2} + 2ab 






sin(x + y) = sinx + siny 
sin(x + y) = sinx cosy + cosx siny 
Improper use of square root
Students seem to be under misconception that which is incorrect.
The proper working is as under
x^{2} – 4 = 0
⇒ x^{2} = 4
⇒
⇒
* Improper use of power of trigonometric functions
Incorrect 
Correct 
sin^{n}x
= sinx^{n} 
sin^{n}x = (sinx)^{n}^{} 
Incorrect 
Correct 
cos85^{o}
= sin(90^{o} – 5^{o}) = sin5^{o} 
cos85^{o}
= cos(90^{o} – 5^{o}) = sin5^{o} or cos85^{o}
= sin(90^{o} – 85^{o}) = sin5^{o} 
*Incorrect solution of quadratic equation
Solve :
3x^{2} = x
Incorrect 
Correct 
3x^{2}
= x ⇒ 3x = 1 ⇒ x = 1/3 Here students
divide both side by x without realising that x could be 0 also 
3x^{2}
= x ⇒ 3x^{2} –
x = 0 ⇒ x(3x  1) = 0 Either x = 0 or
3x – 1 = 0 x = 0, 1/3 Both values of
x satisfy the given equation; hence both are the solution of quadratic
equation. 
Procedural Errors
Procedural knowledge means the knowledge regarding how to do something. This can also be understood as mathematical skills. Rectification of procedural errors requires practice and feedback.
Following are some of the common procedural errors that the students commit:
A). Many a time, students decide that parentheses are not needed at certain steps. They fail to understand the importance of parentheses.
Example 1: Square of 3x.
Incorrect 
Correct 
(3x)^{2}
= 3x^{2} 
(3x)^{2}
= (3)^{2 }(x)^{2} = 9x^{2} 
Here students
are failed to follow the procedure of BODMAS 
Example 2: Square of 2
Incorrect 
Correct 
(2)^{2}
2^{2} =  4 
(2)^{2}
= 4 
Example 3: Solve for x:
Incorrect 
Correct 
⇒ 5x + 15 = 6 ⇒ 5x = 9 ⇒ x = 9/5 
⇒ 5x  45 = 6 ⇒ x =  51/5 
B) Improper Distribution
Example 1: Simplify: 3(2x^{2 } 6)
Incorrect 
Correct 
3(2x^{2 }
6) = 6x^{2}  6 
3(2x^{2 }
6) = 6x^{2}  18 
Incorrect 
Correct 
2(3x5)^{2} =(6x10)^{2}
= 36x^{2}  120x + 100 
2(3x5)^{2} = 2(9x^{2}
– 30x + 25)
= 18x^{2} – 60x + 50 
Incorrect 
Correct 


Incorrect 
Correct 
Area of
the rectangle having length and breadth 6cm and 5cm respectively is 6 Ñ… 5 =
30 cm^{2} 
Area of
the rectangle having length and breadth 6cm and 5cm respectively is 6cm x 5cm
= 30 cm^{2} 
Incorrect 
Correct 
BC = AC = K

BC = AC = K

Incorrect 
Correct 
(7x – 3)^{2}
= 7x^{2} – 3^{2} = 7x^{2} – 9 
(7x – 3)^{2}
= (7x)^{2}  2× 7x × 3– 3^{2} = 49x^{2} – 42x + 9 
Incorrect 
Correct 
Since the given equation has equal roots. ∴ Discriminant = 0 ⇒ b^{2} – 4ac = 0 ⇒ (k + 1)^{2}  4×
(k + 4) × 1 = 0 ⇒ k^{2} + 1  4k + 4 = 0 ⇒ k^{2}  5k +
k + 5 = 0 ⇒ k(k – 5) + 1(k – 5) = 0 ⇒ (k – 5) (k + 1) = 0
K = 5 or k = 1 
Since the given equation has equal roots. ∴ Discriminant = 0 ⇒ b^{2} – 4ac = 0 ⇒ (k + 1)^{2}  4× (k + 4) × 1 = 0 ⇒ k^{2} + 2k + 1  4k  16 = 0 ⇒ k^{2}  2k  15 = 0 ⇒ k^{2}  5k + 3k  15 = 0 ⇒ k(k – 5) + 3(k – 5) = 0 ⇒ (k – 5) (k + 3) = 0 ⇒ k = 5 or k =  3 
S. No. 
Common Errors 
Reasons 
Remedial Measures 
1 
Sometime students used ASA rule 
Connot differentiate congruency
and similarity rules 
Congruency rules are: SSS, SAS, ASA, AAS, RHS Similarity Rules are: SSS, SAS, AAA, AA 
2 
AB = DE BC = EF AC = DF 
Cannot understand the congruency
and similarity rule properly. 
Two triangles are congruent then
corresponding angles and sides are equal. Two triangles are similar then
corresponding angles are equal and sides are proportional. 
3 
If DE  BC then

Cannot differentiate between
similarity and Basic Proportionality theorem 
DE  BC, then first prove that △ADE ~ △ABC

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