Tenth Grade Math Practice

Introduction to tenth grade math practice problem:

              Mathematics interacted well with all other branches of Science and Social Sciences and new fields such as Operations Research, Industrial Mathematics, Mathematics of Computation, Mathematical Statistics, Mathematical Biology, Mathematical Modeling, Cryptology, and Mathematical Economics etc. The tenth grade mathematics includes number theory, quadratic equation, greatest common divisor, least common divisor, factorization, and data handling etc. In this article we shall do some tenth grade practice problem.


Tenth grade math example practice problem


Example:

Find the L.C.M of 12(x–1)3 and 15(x–1) (x+2)2

Solution:

Lowest degree which is exactly divisible by the given polynomials and whose coefficient of the highest degree term has the same sign as the sign of the coefficient of the highest degree term in their product.

12(x–1)3 = 22 × 3 (x –1)3

15 (x–1) (x + 2)2 = 5 × 3 (x – 1) (x + 2)2

L.C.M. = 22 × 3 × 5 (x – 1)3 (x + 2)2 = 60 (x – 1)3 (x + 2)2

Example:

Find the L.C.M. of 6x2y, 9x2yz, 12x2y2z

Solution: 6x2y = 2 × 3 × x2 y

9xy2z = 32 x2 yz

12x2y2z= 22 × 3x2 y2z

L.C.M. = 22 × 32 × x2y2z = 4 × 9 x2y2z

L.C.M. = 36x2y2 z

Example:

Find the square root of

x2 – 4 = x2 – 22 = (x–2) (x+2)

x2 + x – 6 = x2 + 3x – 2x – 6 = x (x+3) – 2 (x+3) = (x+3) (x–2)

x2 + 5x + 6 = x2 + 3x + 2x – 6 = x (x+3) + 2 (x+3) = (x+3) (x+2)

Hence (x2 – 4) (x2 + x – 6) (x2 + 5x + 6)

= (x + 2) (x + 3) (x – 2) (x + 3) (x + 2) (x – 2)

= (x–2)2 (x + 2)2 (x + 3)2 = [(x – 2) (x + 2) (x + 3)]2

Therefore the required square root is (x – 2) (x + 2) (x + 3)


Tenth grade math example practice problem


Practice Problem 1:

Find the L.C.M. of x3 + 1, x2 – 1, (x + 1)2

Answer:

L.C.M. = (x + 1)2 (x – 1) (x2 – x + 1)

Practice Problem 2:

Find square root of x2 + 10x + 25

Answer:

x + 5