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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 = a2 + b2 |
(a + b)2 = a2 + b2 + 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
x2 – 4 = 0
⇒ x2 = 4
⇒
⇒
* Improper use of power of trigonometric functions
Incorrect |
Correct |
sinnx
= sinxn |
sinnx
= (sinx)n |
Incorrect |
Correct |
cos85o
= sin(90o – 5o) = sin5o |
cos85o
= cos(90o – 5o) = sin5o or cos85o
= sin(90o – 85o) = sin5o |
*Incorrect solution of quadratic equation
Solve :
3x2 = x
Incorrect |
Correct |
3x2
= x ⇒ 3x = 1 ⇒ x = 1/3 Here students
divide both side by x without realising that x could be 0 also |
3x2
= x ⇒ 3x2 –
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
= 3x2 |
(3x)2
= (3)2 (x)2 = 9x2 |
Here students
are failed to follow the procedure of BODMAS |
Example 2: Square of -2
Incorrect |
Correct |
(-2)2
-22 = - 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(2x2 - 6)
Incorrect |
Correct |
3(2x2 -
6) = 6x2 - 6 |
3(2x2 -
6) = 6x2 - 18 |
Incorrect |
Correct |
2(3x-5)2 =(6x-10)2
= 36x2 - 120x + 100 |
2(3x-5)2 = 2(9x2
– 30x + 25)
= 18x2 – 60x + 50 |
Incorrect |
Correct |
|
|
Incorrect |
Correct |
Area of
the rectangle having length and breadth 6cm and 5cm respectively is 6 Ñ… 5 =
30 cm2 |
Area of
the rectangle having length and breadth 6cm and 5cm respectively is 6cm x 5cm
= 30 cm2 |
Incorrect |
Correct |
BC = AC = K
|
BC = AC = K
|
Incorrect |
Correct |
(7x – 3)2
= 7x2 – 32 = 7x2 – 9 |
(7x – 3)2
= (7x)2 - 2× 7x × 3– 32 = 49x2 – 42x + 9 |
Incorrect |
Correct |
Since the given equation has equal roots. ∴ Discriminant = 0 ⇒ b2 – 4ac = 0 ⇒ (k + 1)2 - 4×
(k + 4) × 1 = 0 ⇒ k2 + 1 - 4k + 4 = 0 ⇒ k2 - 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 ⇒ b2 – 4ac = 0 ⇒ (k + 1)2 - 4× (k + 4) × 1 = 0 ⇒ k2 + 2k + 1 - 4k - 16 = 0 ⇒ k2 - 2k - 15 = 0 ⇒ k2 - 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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