Basics of Simplification

Simplification

We must learn to do the basic calculations faster. It saves few
seconds from each question. And at the end, we find that at
least 5-10 minutes have been saved.
What to do for faster basic calculation:
1. Remember the tables upto30-40.
2. Learn the method of multiplication.
3. Learn the method of addition - substraction in a single
line or column.
4. Learn the method of approximation.
5. Learn to compare two fractions.
6. Remember square roots, squares, cubes and cube
roots.
7. Remember fractional value of percentage.
8. Remember decimal values of reciprocals.
9. Do calculations mentally. Don’t write unnecessary
steps.
10. Learn the laws of surds and indices.
Directions (Q. 1-51): What will come in place of the
question mark(?) in the following equations?
11. VBODMAS Rule:
V stands for Vinculum or bar
B Stands for brackets and operation of brackets in
the order (), {}, []
O stands for “of”
D stands for division (÷)
M stands for multiplication (×)
A stands for addition (+)
S stands for substraction (-)
12. Some algebraic formulae:
1. (a + b)2 = a2 + b2 + 2ab
2. (a – b)2 = a2 + b2 – 2ab
3. (a + b)2 + (a – b)2 = 2(a2 + b2)
4. (a + b)2 – (a – b)2=4ab
5. (a + b) (a – b) = a2 – b2
6. (a + b)3 = a3 + 3a2b + 3ab2 + b3
7. (a – b)3 = a3 – 3a2b + 3ab2 – b3
8. a3 + b3 = (a + b) (a2 – ab + b2 )
9. a3 – b3 = (a – b) (a2 + ab + b2)