ANSWER KEY - ALGEBRA
I. Write algebraic expressions for the following
a. The sum of 3 times a and 3 times y = 3a +3y
b. The product of 5 and z subtracted from 8 times y = 8y – 5z
2
c. 2 of 10 times l = 4l (i.e 2 * 10 * l)
5
5
d. 6 times c decreased from b = b – 6c
e. Out of Rs. 80 pocket money Ram spent x Rs on food , Rs. 43 on gifts and Rs. y on
clothes = x+43+y = 80
II.
Separate the constants and variables in the following terms
a. -25a2b - Constant = -25; Variable = a2b
b. 98xyz - Constant = 98 ; Variable = xyz
c. 202 - Constant = 202
d. xy - Constant = -1 ; Variable = xy
e. 4mn - Constant = 4; Variable = mn
III.
Write the terms in each of the following expressions
a. –m2n +n2m – mnl – Terms are –m2n, n2m, – mnl
b. 200a2 – 500b2 +c2 - Terms are 200a2, – 500b2 c2
c. a2b2c2 – abc2 – abc - Terms are a2b2c2, – abc2 – abc
d. -5a - 6q -8c - Terms are -5a, -6q, - 8c
e. -6x + 3y - Terms are -6x , 3y
IV.
Write algebraic expressions using the following terms
a. pqr, - 15p2, 12q2r - Expression is 12q2r – 15p2 +pqr
b. abc, - 3a2b, -abc - Expression is abc – 3a2b -abc
c. -9ax + 14d2, - 15ade – Expression is 14d2 -15ade -9ax
V.
Write true or false and correct the false statements
a. 9y has two terms 9 and y – False
Correct Statement - 9y is one term
b. 2x is a binomial - False
y
Correct Statement - 2x/y is a monomial
c. The literal coefficient of -4x2e is -4 - False
Correct Statement – The literal coefficient is x2e
d. m3n2z = m*3*n*2*z – False
Correct Statement - m*m*m*n*n*z
VI. Identify the type of algebraic expression
a. -3abc +c2 – 5ab - Trinomial – Three terms
b. 9 * a*a*b +c = Binomial – Two Terms
c. 5 * z*y*b = Monomial – One Term
d. 3y – 2y ÷ z = _Binomial – Two Terms (2y/ z is one term)
e. 2*a*b + 4 ÷ 7 * b +9 =Trinomial – Three terms ( 4/7b is one term)
VII.
Write the coefficient of
a. g2 in – 29g2h2k2 – Coefficient is -29h2k2
b. 25 in 25x3y2z – Coefficient is x3y2z
c. m3 in 42m3nq – Coefficient is 42nq
VIII.
Write the numeral coefficient in the following terms
a. 42b2n2m
Literal coefficient – b2n2m
Numeral coefficient - 42
b. 58l3m3n
Literal coefficient – l3m3n
Numeral coefficient - 58
c. -2p2q2xyz
Literal coefficient - p2q2xyz
Numeral coefficient - -2
IX. Write the factors of
a. 8m2n2 - Factors are 8/9, m, m, n, n
9
b. 50abc – Factors are 50, a, b, c
c. –l2m2n2 – Factors are -1 , l, l, m, m, n, n
X. Write in order by arranging numeral factors and literal factors in alphabetical
order.
a. zal52 – 10alz
b. x9ca2 – 18acx
c. 5a2n3d – 30adn
XI. Identify like and unlike terms in the following
a. 5ax, -5b2y, 6by2, 7xa, 2ax 7
Like terms – 5ax, 7xa, 2ax
Unlike terms - -5b2y, 6/7by2
b. x2y3, – 5x3y, 8x3y2, -4x2y3, -x2y3 Like terms – x2y3, -4x2y3, -x2y3
Unlike terms - – 5x3y, 8x3y2
c. 3a2, -5a, -a2, 5a2, 8a3 Like terms – 3a2, -a2, 5a2
Unlike terms - -5a, 8a3
XII.
Substitute and find the value of the following algebraic expressions
a. 2xy where x = 8 and y = 2
= 2 *8 *2
= 32
Answer = 32
b. 3kz where k = 4 and z = 6
2
3
3 * 4* 6
2
=3*4*3
=36
Answer = 36
c. 6a – 7d where a = 5 and d = 3
= 6* 5 – 7 *3
= 30 – 21
=9
Answer =9
XIII.
Expand the following
a. d4m3e2 = d* d* d* m* m* m* e* e
b. f3x2l – f* f* f* x * x* l
c. dn3e2 – d* n* n* n* e* e
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