# 10th Grade Math Problems

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10th grade math syllabus include
·        Arithmetic

·        Algebra
·        Geometry
·        Mensuration
·        Trigonometry

Examples of 10th grade math problems: -

·         From arithmetic: -

Example 1: - A mixed fertilizer contains urea and cow manure in the ration of 2 : 5. Find out the weight of the components required to produce 28 quintals of mixed fertilizer.

Analysis of data: - Urea: cow manure = 2 : 5

Therefore proportional part of urea in the mixed fertilizer = 2 / 7

And that of cow manure in the mixed fertilizer = 5 / 7

In mathematical language the problem is

i)             28 x (2 / 7)
ii)            28 x (5 / 7)

Solution: -
i)             28 x (2 / 7)= 4 x 2 = 8
ii)            28 x (5 / 7)= 4 x 5 = 20

Answer: - Weight of urea= 8 quintals and weight of cow manure = 20 quintals.

·         From Algebra: -

Example  :-  Find the H.C.F. and L.C.M. of the following two expressions:

1st expression = 4 p^2 q r^3
2nd expression = 6 p^3 q^2 r^4

H.C.F.

i) H.C.F. of the coefficients is 2
ii) The highest common powers of the variables are 2 for p, 1 for q and 3 for r.
Therefore, the required H.C.F. = 2 p^2 q r^3

L.C.M.

i) The L.C.M. of the co-efficient = 2 x 2 x 3 = 12
ii) The highest powers of the variables are 3 for p, 2 for q and 4 for r.
Therefore, the required L.C.M. = 12 p^3 q^2 r^4