  Grade 7 - Algebra-Expressions-and-Equations

(Sample Printed worksheet)

1)Find the sum of following polynomials
 A) 2p3 + q3 - 14pq - 2q and -p3 - 10q3 + 9p2q + 2pq - 12p + 12q - 18 B) 9x2y - 3xy2 - 8x + 14y - 16 and 12x3 + 4y3 - 12x2y - 4xy + 9
 2) Find value of a from equation (a - 5)2 - (a + 3)2 = -64Hint : Use identity (a+b) (a-b) = a2 - b2
 3) If a + b = 11,������b + c = 12, and������c + a = 13,then what is the value of a + b + c?
 4) Deborah bought a total of 17 hens and ducks. He got a discount of $0.90 for each hen and a discount of$ 1.10 for each duck. She saved $16.90 in total. How many ducks did she buy?  5) If f(x) = x2, find the value of . Fill in the blanks 6)If y = -1 , ( -2y2 - 8y - 1) - ( -4y2 + 8y - 6) =  7) Ages of Karen and Sharon are in ratio 2:7 . If sum of their ages is 45 years, age of Sharon is years. Choose correct answer(s) from given choice 8)If 2x + 2 = 24, what is the value of 2x - 2?  a. 23 b. 17 c. 20 d. 27 9)Brian earns$ x daily and spends \$ y per week. What is his saving for 7 weeks ?
 a. 7x + 49y b. 49x -7y c. 7x - 49y d. 49x + 7y
10)A poultry farm produced 14q2 + 2q + 3 eggs in a year. It packaged 2q2 - 5q + 8 eggs and sent them to market while 9q2 + 9q - 2 eggs got destroyed. How many eggs are left with the poultry farm?
 a. -3q2 - 2q - 3 b. 3q2 + 2q - 3 c. 3q2 - 2q - 3 d. 3q2 - 2q + 3

1)
A) p3 - 9q3 + 9p2q - 12pq - 12p + 10q - 18
Step 1
To add polynomial 2p3 + q3 - 14pq - 2q and -p3 - 10q3 + 9p2q + 2pq - 12p + 12q - 18, first place like terms in same columns and add as usual.
Like this:
 2p3 + q3 - 14pq - 2q -p3 - 10q3 + 9p2q + 2pq - 12p + 12q - 18 p3 - 9q3 + 9p2q - 12pq - 12p + 10q - 18

Using columns helps us to match the like terms together in a complicated sum
Step 2
Therefore the sum of polynomial 2p3 + q3 - 14pq - 2q and -p3 - 10q3 + 9p2q + 2pq - 12p + 12q - 18 is p3 - 9q3 + 9p2q - 12pq - 12p + 10q - 18
B) 12x3 + 4y3 - 3x2y - 3xy2 - 4xy - 8x + 14y - 7
Step 1
To add polynomial 9x2y - 3xy2 - 8x + 14y - 16 and 12x3 + 4y3 - 12x2y - 4xy + 9, first place like terms in same columns and add as usual.
Like this:
 9x2y - 3xy2 - 8x + 14y - 16 12x3 + 4y3 - 12x2y - 4xy + 9 12x3 + 4y3 - 3x2y - 3xy2 - 4xy - 8x + 14y - 7

Using columns helps us to match the like terms together in a complicated sum
Step 2
Therefore the sum of polynomial 9x2y - 3xy2 - 8x + 14y - 16 and 12x3 + 4y3 - 12x2y - 4xy + 9 is 12x3 + 4y3 - 3x2y - 3xy2 - 4xy - 8x + 14y - 7

2) a = 5

3) 18

4) 8

5) 2x + b

6)
7)
8) c. 20
9) b. 49x -7y
10) c. 3q2 - 2q - 3