An algebraic expression containing three terms is called a
A. monomial
B. binomial
C. trinomial
D. All of these
Monomial is for one term
Binomial is for two terms
and trinomial is for three terms.
Number of terms in the expression 3x2y – 2y2z – z2x + 5 is
A. 2
B. 3
C. 4
D. 5
There are total 4 terms which are in addition or subtraction.
The terms of expression 4x2 – 3xy are:
A. 4x2 and –3xy
B. 4x2 and 3xy
C. 4x2 and –xy
D. x2 and xy
The terms are added to form expressions and negative sign is included in the term
Factors of –5x2 y2 z are
A. – 5 × x × y × z
B. – 5 × x2× y × z
C. – 5 × x × x × y × y × z
D. – 5 × x × y × z2
we can just contract this option and we’ll find the original expression.
Coefficient of x in – 9xy2z is
A. 9yz
B. – 9yz
C. 9y2z
D. – 9y2z
coefficient of any variable is everything in multiplication with that variable in that term.
Which of the following is a pair of like terms?
A. –7xy2z, – 7x2yz
B. – 10xyz2, 3xyz2
C. 3xyz, 3x2y2z2
D. 4xyz2, 4x2yz
The two are like terms because they have same algebraic factors.
Identify the binomial out of the following:
A. 3xy2 + 5y – x2y
B. x2y – 5y – x2y
C. xy + yz + zx
D. 3xy2 + 5y – xy2
The first and last terms are actuall one term and therefore there total two terms which makes it binomial.
The sum of x4 – xy + 2y2 and –x4+ xy+2y2 is
A. Monomial and polynomial in y
B. Binomial and Polynomial
C. Trinomial and polynomial
D. Monomial and polynomial in x
By adding we get 4y2 which is a monomial and polynomial in y.
The subtraction of 5 times of y from x is
A. 5x – y
B. y – 5x
C. x – 5y
D. 5y – x
x minus 5 times of y.
– b – 0 is equal to
A. –1 × b
B. 1 – b – 0
C. 0 – (–1) × b
D. – b – 0 – 1
Both are equal to -b
The side length of the top of square table is x. The expression for perimeter is:
A. 4 + x
B. 2x
C. 4x
D. 8x
perimeter is 4 times side.
The number of scarfs of length half metre that can be made from y metres of cloth is :
A. 2y
B.
C. y + 2
D.
we get the answer by dividing y by 1/2.
123x2y – 138x2y is a like term of :
A. 10xy
B. –15xy
C. –15xy2
D. 10x2y
Since,
123x2y – 138x2y
= x2y(123 – 138)
= x2y(-15)
= -15x2y
The like term of -15x2y is 10x2y, since they both have same algebraic factors.
The value of 3x2 – 5x + 3 when x = 1 is
A. 1
B. 0
C. –1
D. 11
3(1)2 – 5(1) + 3 = 1
The expression for the number of diagonals that we can make from one vertex of a n sided polygon is:
A. 2n + 1
B. n – 2
C. 5n + 2
D. n – 3
Since there are n corners out of which you cannot take the two neighboring corners and one itself, so there are n-3 diagonals.
The length of a side of square is given as 2x + 3. Which expression represents the perimeter of the square?
A. 2x + 16
B. 6x + 9
C. 8x + 3
D. 8x + 12
length * 4 = Perimeter in case of a square.
Fill in the blanks to make the statements true.
Sum or difference of two like terms is ______ .
a like term
4x – 2x = 2x where R.H.S is a like term.
Fill in the blanks to make the statements true.
In the formula, area of circle = πr2, the numerical constant of the expression πr2 is _____ .
π
π is constant and other are variables.
Fill in the blanks to make the statements true.
3a2b and –7ba2 are _____ terms.
like
Same algebraic factors a2b
Fill in the blanks to make the statements true.
–5a2b and –5b2a are ______ terms.
unlike
Different Algebraic factors
Fill in the blanks to make the statements true.
In the expression 2πr, the algebraic variable is ______ .
r
r is variable and rest is constant.
Fill in the blanks to make the statements true.
Number of terms in a monomial is ______.
one
As per the definition of monomial.
Fill in the blanks to make the statements true.
Like terms in the expression n(n + 1) + 6 (n – 1) are ____ and _____.
n, 6n
n(n + 1) + 6 (n – 1) = n2 + n+ 6n – 6
Hence n and 6n are like terms
Fill in the blanks to make the statements true.
The expression 13 + 90 is a _____ .
constant
13+90 = 103.
Fill in the blanks to make the statements true.
The speed of car is 55 km/hrs. The distance covered in y hours is ______.
55y
distance = speed x time
Fill in the blanks to make the statements true.
x + y + z is an expression which is neither monomial nor ________ .
binomial
Its trinomial.
Fill in the blanks to make the statements true.
If (x2y + y2 + 3) is subtracted from (3x2y + 2y2 + 5), then coefficient of y in the result is _______ .
2x2
3x2y + 2y2 + 5 - x2y - y2 – 3
= 2x2y + y2 + 2
2x2 is the coefficient required.
Fill in the blanks to make the statements true.
– a – b – c is same as – a – (________).
b + c
when bracket is opened both the equations are exactly same.
Fill in the blanks to make the statements true.
The unlike terms in perimeters of following figures are ______ and _____.
2y, 2y2
Perimeter of fig.1 = 2x + 2x + y + y = 4x + 2y
Perimeter of fig.2 = x + x + y2 + y2 = 2x + 2y2
Fill in the blanks to make the statements true.
On adding a monomial ________ to – 2x + 4y2 + z, the resulting expression becomes a binomial.
2x or -4y2 or -z
Since, each of the three will cancel out a term in the expression
Fill in the blanks to make the statements true.
3x + 23x2 + 6y2 + 2x + y2 + ______ = 5x + 7y2.
(-23x2)
5x + 7y2- 3x - 23x2 - 6y2 - 2x - y2
= 23x2
Fill in the blanks to make the statements true.
If Rohit has 5xy toffees and Shantanu has 20yx toffees, then Shantanu has _____ . more toffees.
15xy
Difference 20xy – 5xy = 15xy
State whether the statements given are True or False.
x is a polynomial.
True
Because it has more than one term.
State whether the statements given are True or False.
(3a – b + 3) – (a + b) is a binomial.
False
It comes out to be 2a – 2b + 3 which is a trinomial.
State whether the statements given are True or False.
A trinomial can be a polynomial.
True
A Polynomial has more than one term, so 3 terms is also a polynomial.
State whether the statements given are True or False.
A polynomial with more than two terms is a trinomial.
False
It can be a trinomial only when it has exactly 3 terms.
but more than 2 means it could 3,4,5 or anything greater.
State whether the statements given are True or False.
Sum of x and y is x + y.
True
State whether the statements given are True or False.
Sum of 2 and p is 2p.
False
Sum of 2 and p is 2 + p.
State whether the statements given are True or False.
A binomial has more than two terms.
False
It does not have more than 2 terms rather it has exactly 2 terms.
State whether the statements given are True or False.
A trinomial has exactly three terms.
True
This is how we define trinomial.
State whether the statements given are True or False.
In like terms, variables and their powers are the same.
True
The variables and their powers we call them algebraic factors and they are same in case of like terms.
State whether the statements given are True or False.
The expression x + y + 5x is a trinomial.
False
It is a binomial because two of them are like terms that is x and 5x
so the expression could be written as
6x + y.
State whether the statements given are True or False.
4p is the numerical coefficient of q2 in – 4pq2.
False
numerical coefficient of q2 is – 4p.
There should be a negative sign too.
State whether the statements given are True or False.
5a and 5b are unlike terms.
True
Because they have different variables.
State whether the statements given are True or False.
Sum of x2 + x and y + y2 is 2x2 + 2y2.
False
Their sum is x2 + x + y + y2
It cannot be further simplified to 2x2 + 2y2
State whether the statements given are True or False.
Subtracting a term from a given expression is the same as adding its additive inverse to the given expression.
True
Because additive inverse and subtracting term are exactly same.
State whether the statements given are True or False.
The total number of planets of Sun can be denoted by the variable n.
False
The no. of planets is constant and not variables. There are 8 no. of planets and we don’t assign variables to constants.
State whether the statements given are True or False.
In like terms, the numerical coefficients should also be the same.
False
In like terms only the numerical coefficient could be different, otherwise everything is same.
State whether the statements given are True or False.
If we add a monomial and binomial, then answer can never be a monomial.
False
In some situation it might become a monomial.
example: x and -x + y
if we add them
we get x – x + y = y
and we got a monomial.
State whether the statements given are True or False.
If we subtract a monomial from a binomial, then answer is at least a binomial.
False
it could a monomial too.
we use ‘at least’ for expression with least no. of term.
therefore, it is at least a monomial.
State whether the statements given are True or False.
When we subtract a monomial from a trinomial, then answer can be a polynomial.
True
It can be a polynomial and with that it can also be binomial.
State whether the statements given are True or False.
When we add a monomial and a trinomial, then answer can be a monomial.
False.
It can be a binomial if the monomial cancel one term of trinomial else it would be a polynomial but it can never be a monomial.
Write the following statements in the form of algebraic expressions and write whether it is monomial, binomial or trinomial.
(a) x is multiplied by itself and then added to the product of x and y.
(b) Three times of p and two times of q are multiplied and then subtracted from r.
(c) Product of p, twice of q and thrice of r.
(d) Sum of the products of a and b, b and c and c and a.
(e) Perimeter of an equilateral triangle of side x.
(f) Perimeter of a rectangle with length p and breadth q.
(g) Area of a triangle with base m and height n.
(h) Area of a square with side x.
(i) Cube of s subtracted from cube of t.
(j) Quotient of x and 15 multiplied by x.
(k) The sum of square of x and cube of z.
(l) Two times q subtracted from cube of q.
(a) x2 + xy Binomial
(b) r-(3p×2q)
r – 6pq Binomial
(c) p×2q×3r
6pqr monomial
(d) ab + bc + ca Trinomial
(e) 3x Monomial
(f) 2(p+q) = 2p+2q
(g) monomial
(h) x2 monomial
(i) t3 - s3 binomial
(j) monomial
(k) x2 – z3 binomial
(l) q3 – 2q binomial
Write the coefficient of x2 in the following:
(i) x2 – x + 4
(ii) x3 – 2x2 + 3x + 1
(iii) 1 + 2x + 3x2 + 4x3
(iv) y + y2x + y3x2 + y4x3
(i) 1
(ii) -2
(iii) 3
(iv) y3
Find the numerical coefficient of each of the terms:
(i) x3y2z, xy2z3, –3xy2z3, 5x3y2z, –7x2y2z2
(ii) 10xyz, –7xy2z, –9xyz, 2xy2z, 2x2y2z2
(i) x3y2z - 1
xy2z3 - 1
–3xy2z3 - -3
5x3y2z - 5
–7x2y2z2 - -7
(ii) 10xyz - 10
–7xy2z - -7
–9xyz - -9
2xy2z - 2
2x2y2z2 - 2
Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial.
(a) 3x2yz2 – 3xy2z + x2yz2 + 7xy2z
(b) x4 + 3x3y+3x2y2–3x3y–3xy3+y4– 3x2y2
(c) p3q2r + pq2r3 + 3p2qr2 – 9p2qr2
(d) 2a + 2b+2c–2a–2b–2c – 2b + 2c + 2a
(e) 50x3 – 21x + 107 + 41x3 – x + 1 – 93 + 71x–31x3
(a) 4x2yz2 + 4xy2z
Binomial
(b) x4 + y4 - 3x3y
Trinomial
(c) p3q2r + pq2r3 - 6p2qr2
Trinomial
(d) 2a - 2b + 2c
Trinomial
(e) 60x3 – 49x + 15
Trinomial
Add the following expressions:
(a) p2 – 7pq – q2 and – 3p2 – 2pq + 7q2
(b) x3–x2y–xy2 –y3 and x3 –2x2y+3xy2+4y
(c) ab + bc + ca and – bc – ca – ab
(d) p2 – q + r, q2 – r + p and r2 – p + q
(e) x3y2 + x2y3 +3y4 and x4 + 3x2y3 + 4y4
(f) p2qr + pq2r + pqr2 and – 3pq2r –2pqr2
(g) uv – vw, vw – wu and wu – uv
(h) a2 + 3ab – bc, b2 + 3bc – ca and c2 + 3ca – ab
(i) p4 + 2p2 + -17p + p2 and
(j) t – t2 – t3 – 14; 15t3 + 13 + 9t – 8t2; 12t2 – 19 – 24t and 4t – 9t2 + 19t3
(a) p2 – 7pq – q2 – 3p2 – 2pq + 7q2
-2p2 – 9pq + 6q2
(b) x3–x2y–xy2 –y3 + x3 –2x2y+3xy2+4y
2x3–3x2y–2xy2 –y3 +4y
(c) ab + bc + ca – bc – ca – ab
0
(d) p2 – q + r + q2 – r + p + r2 – p + q
p2 + q2 + r2
(e) x3y2 + x2y3 +3y4 + 1x4 + 3x2y3 + 4y4
x3y2 + 4x2y3 +7y4 + x4
(f) p2qr + pq2r + pqr2 - 3pq2r –2pqr2
p2qr -2pq2r - pqr2
(g) uv – vw, vw – wu + wu – uv
0
(h) a2 + 3ab – bc + b2 + 3bc – ca + c2 + 3ca – ab
a2 + b2 + c2 + 2ab + 2bc + 2ca
(i)
=
(j) t – t2 – t3 – 14 + 15t3 + 13 + 9t – 8t2 + 12t2 – 19 – 24t + 4t – 9t2 + 19t3
= -10t -6t2 + 33t3 – 20
= 33t3 - 6t2 – 10t – 20
Subtract
(a) –7p2qr from – 3p2qr.
(b) –a2 – ab from b2 + ab.
(c) –4x2y – y3 from x3 + 3xy2 – x2y.
(d) x4 + 3x3y3 + 5y4 from 2x4 – x3y3 + 7y4.
(e) ab – bc – ca from – ab + bc + ca.
(f) –2a2 – 2b2 from – a2 – b2 + 2ab.
(g) x3y2 + 3x2y2 – 7xy3 from x4 + y4 + 3x2y2 – xy3.
(h) 2(ab + bc + ca) from –ab – bc – ca.
(i) 4.5x5 –3.4x2+5.7 from 5x4–3.2x2–7.3x.
(j) 11 – 15y2 from y3 – 15y2 – y – 11.
(a) – 3p2qr – (–7p2qr)
– 3p2qr + 7p2qr
4p2qr
(b) b2 + ab – (–a2 – ab)
b2 + ab + a2 + ab
b2 + 2ab + a2
(c) x3 + 3xy2 – x2y – (–4x2y – y3)
x3 + 3xy2 – x2y + 4x2y + y3
x3 + 3xy2 + 3x2y + y3
(d) 2x4 – x3y3 + 7y4 – (x4 + 3x3y3 + 5y4)
2x4 – x3y3 + 7y4 – x4 - 3x3y3 - 5y4
x4 – 4x3y3 + 2y4
(e) – ab + bc + ca – (ab – bc – ca)
–2ab + 2bc + 2ca
(f) – a2 – b2 + 2ab – (–2a2 – 2b2)
– a2 – b2 + 2ab + 2a2 + 2b2
a2 + b2 + 2ab
(g) x4 + y4 + 3x2y2 – xy3 – (x3y2 + 3x2y2 – 7xy3)
x4 + y4 + 3x2y2 – xy3 – x3y2 - 3x2y2 + 7xy3
x4 + y4 - x3y3 + 6xy3
(h) –ab – bc – ca – (2(ab + bc + ca))
-3ab – 3bc – 3ca
(i) 5x4–3.2x2–7.3x – (4.5x5 –3.4x2+5.7)
5x4–3.2x2–7.3x – 4.5x5 + 3.4x2 - 5.7
– 4.5x5 + 5x4 + 0.2x2 – 7.3x – 5.7
(j) y3 – 15y2 – y – 11 – (11 – 15y2)
y3 – 15y2 – y – 11 – 11 + 15y2
y3 – y – 22
(a) What should be added to x3 + 3x2y + 3xy2 + y3 to get x3 + y3?
(b) What should be added to 3pq + 5p2q2 + p3 to get p3 + 2p2q2 + 4pq?
(a) x3 + y3 – x3 - 3x2y - 3xy2 – y3
3x2y – 3xy2
(b) p3 + 2p2q2 + 4pq – (3pq + 5p2q2 + p3)
p3 + 2p2q2 + 4pq – 3pq - 5p2q2 - p3
-3p2q2 + pq
(a) What should be subtracted from 2x3 – 3x2y + 2xy2 + 3y3 to get x3 – 2x2y + 3xy2 + 4y3?
(b) What should be subtracted from –7mn + 2m2 + 3n2 to get m2 + 2mn + n2?
(a) Let’s consider the first term to be A and second term to be B.
According to question
A – x = B
i.e., there is a x which is subtracted from A to get B
So x=A – B
2x3 – 3x2y + 2xy2 + 3y3 - x3 + 2x2y - 3xy2 - 4y3
= x3 – 2x2y + 3xy2 + 4y3
(b) Let’s consider the first term to be A and second term to be B.
According to question
A – x = B
i.e., there is a x which is subtracted from A to get B
So x=A – B
–7mn + 2m2 + 3n2 - m2 - 2mn - n2
= -9mn + m2 + 2n2
How much is 21a3 – 17a2 less than 89a3 – 64a2 + 6a + 16?
89a3 – 64a2 + 6a + 16 – (21a3 – 17a2)
= 89a3 – 64a2 + 6a + 16 - 21a3 + 17a2
= 68a3 – 47a2 + 6a + 16
How much is y4 – 12y2 + y + 14 greater than 17y3 + 34y2 – 51y + 68?
first is greater than second and we need to find the difference.
y4 – 12y2 + y + 14 – (17y3 + 34y2 – 51y + 68)
y4 – 12y2 + y + 14 – 17y3 - 34y2 + 51y – 68
= y4 – 17y3 - 46y2 + 52y – 54
How much does 93p2 – 55p + 4 exceed 13p3 – 5p2 + 17p – 90?
93p2 – 55p + 4 - 13p3 + 5p2 - 17p + 90
= - 13p3 + 9p2 - 72p + 94
To what expression must 99x3 – 33x2 – 13x – 41 be added to make the sum zero?
99x3 – 33x2 – 13x – 41
To make the sum zero we can just add the negative of any expression to the expression
= -99x3 + 33x2 + 13x + 41
Subtract 9a2 – 15a + 3 from unity.
Unity means 1.
∴ 1 – (9a2 – 15a + 3)
= -9a2 + 15a – 2
Find the values of the following polynomials at a = – 2 and b = 3:
(a) a2 + 2ab + b2
(b) a2 – 2ab + b2
(c) a3 + 3a2b + 3ab2 + b3
(d) a3 – 3a2b + 3ab2 – b3
(e)
(f)
(g)
(h) a2 + b2 – ab – b2 – a2
(a) a2 + 2ab + b2
(-2)2 + 2(-2)(3) + (3)2
= 1
(b) (-2)2 – 2(-2)(3) + (3)2
= 25
(c) (-2)3 + 3(-2)2(3) + 3(-2)(3)2 + (3)3
= 1
(d) (-2)3 – 3(-2)2(3) + 3(-2)(3)2 – (3)3
= -125
(e)
=
(f)
=
(g)
=
(h) (-2)2 + (3)2 – (-2)(3) – (3)2 – (-2)2
= 6
Find the values of following polynomials at m = 1, n = –1 and p = 2:
(a) m + n + p
(b) m2 + n2 + p2
(c) m3 + n3 + p3
(d) mn + np + pm
(e) m3 + n3 + p3 – 3mnp
(f) m2n2 + n2p2 + p2m2
(a) 1-1+2
= 2
(b) 12 + (-1)2 + 22
= 6
(c) (1)3 + (-1)3 + 23
= 8
(d) (1)(-1) + (-1)(2) + (2)(1)
= -1
(e) 13 + (-1)3 + 23 – 3(1)(-1)(2)
= 14
(f) (1)2(-1)2 + (-1)2(2)2 + (2)2(1)2
= 9
If A = 3x2 – 4x + 1, B = 5x2 + 3x – 8 and C = 4x2 – 7x + 3, then find:
(i) (A + B) – C
(ii) B + C – A
(iii) A + B + C
(i) (3x2 – 4x + 1 + 5x2 + 3x – 8) – 4x2 + 7x – 3
= 4x2 + 6x – 10
(ii) 5x2 + 3x – 8 + 4x2 – 7x + 3 – 3x2 + 4x – 1
= 6x2 – 6
(iii) 3x2 – 4x + 1 + 5x2 + 3x – 8 + 4x2 – 7x + 3
= 12x2 – 8x – 4
If P = –(x – 2), Q = –2(y +1) and R = –x + 2y, find a, when P + Q + R = ax.
P = –(x – 2)
Q = –2(y +1)
R = –x + 2y,
According to question P + Q + R = ax.
- (x – 2) –2(y +1) –x + 2y = ax
= -x +2 -2y – 2 -x + 2y = ax
= -2x = ax
= a = -2
From the sum of x2 – y2 – 1, y2 – x2 – 1 and 1 – x2 – y2 subtract – (1 + y2).
Sum
x2 – y2 – 1 + y2 – x2 – 1 + 1 – x2 – y2
= -x2 – y2 – 1
Subtract
-x2 – y2 – 1 + 1 + y2
= x2
Subtract the sum of 12ab –10b2 –18a2 and 9ab + 12b2 + 14a2 from the sum of ab + 2b2 and 3b2 – a2.
(ab + 2b2 + 3b2 – a2) – (12ab –10b2 –18a2 + 9ab + 12b2 + 14a2)
= 3b2 + 3a2 – 20ab
Each symbol given below represents an algebraic expression:
= 2x2 + 3y, = 5x2 + 3x, = 8y2 – 3x2 + 2x + 3y
The symbols are then represented in the expression:
Find the expression which is represented by the above symbols.
(2x2 + 3y) + (5x2 + 3x) – (8y2 – 3x2 + 2x + 3y)
= 10x2 – 8y2 +x
Observe the following nutritional chart carefully:
Write an algebraic expression for the amount of carbohydrates in ‘g’ for
(a) y units of potatoes and 2 units of rajma (b) 2x units tomatoes and y units apples.
(a) 1unit potato is 22gm carbohydrates
y unit = 22y gm carbohydrates
2 units rajma gives 60×2 gm carbohydrates
22y + 120 is the expression for carbohydrates.
(b) 1 unit tomatoes have 4gm carbohydrates
2x unit will have 2x×4 unit carbohydrates i.e., 8x gm carbohydrates.
Similarly, y unit apples will have 14y gm carbohydrates.
⇒ 8x + 14y is the required expression.
Arjun bought a rectangular plot with length x and breadth y and then sold a triangular part of it whose base is y and height is z. Find the area of the remaining part of the plot.
initial area = xy
area sold =
remaining area =
Amisha has a square plot of side m and another triangular plot with base and height each equal to m. What is the total area of both plots?
Area of square plot = m2
Area of triangular plot =
total area =
=
A taxi service charges ₹ 8 per km and levies a fixed charge of ₹ 50. Write an algebraic expression for the above situation, if the taxi is hired for x km.
1km is 8
x km will be 8x rs.
and a fixed charge of 50 is applied in all journeys.
⇒ 8x + 50 is the required expression.
Shiv works in a mall and gets paid ₹ 50 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks.
total working hours in two weeks = 7 + x
1 hours pays Rs. 50
⇒ (7+x)50 is the required expression.
Sonu and Raj have to collect different kinds of leaves for science project. They go to a park where Sonu collects 12 leaves and Raj collects x leaves. After some time Sonu loses 3 leaves and Raj collects 2x leaves. Write an algebraic expression to find the total number of leaves collected by both of them.
total no. of leaves collected by Sonu = 12 -3
total no. of leaves collected by Raj = x + 2x
⇒ total no. of leaves = (12-3)+(x+2x)
= 9 + 3x
A school has a rectangular play ground with length x and breadth y and a square lawn with side x as shown in the figure given below. What is the total perimeter of both of them combined together?
Total perimeter = x + x + x + y + x + y
Total perimeter = 4x + 2y
The rate of planting the grass is ₹ x per square metre. Find the cost of planting the grass on a triangular lawn whose base is y metres and height is z metres.
total area of lawn =
rate for 1 sq. m = Rs. x.
Total Rate =
This is the required expression
Find the perimeter of the figure given below:
perimeter = 5x – y + 2(x+y) + (5x-y) + 2(x+y)
= 14x + 2y
In a rectangular plot, 5 square flower beds of side (x + 2) metres each have been laid (see figure given below). Find the total cost of fencing the flower beds at the cost of ₹ 50 per 100 metres:
perimeter of 1 square bed = 4(x+2)
perimeter of 5 square bed = 20(x+2)
Rate for 100 m = Rs. 50
Rate for 1 m = Rs.
Rate for 20(x+2) m =
Required expression = 10(x+2)
A wire is (7x – 3) metres long. A length of (3x – 4) metres is cut for use. Now, answer the following questions:
(a) How much wire is left?
(b) If this left out wire is used for making an equilateral triangle. What is the length of each side of the triangle so formed?
(a) Wire left = (7x - 3) – (3x-4)
wire left = 4x + 1
(b) Side length =
Rohan's mother gave him ₹ 3xy2 and his father gave him ₹ 5(xy2+2). Out of this total money he spent ₹ (10–3xy2) on his birthday party. How much money is left with him?
total money received = 3xy2 + 5(xy2+2)
= 8xy2 + 10
(i) A triangle is made up of 2 red sticks and 1 blue sticks . The length of a red stick is given by r and that of a blue stick is given by b. Using this information, write an expression for the total length of sticks in the pattern given below:
(ii) In the given figure, the length of a green side is given by g and that of the red side is given by p.
Write an expression for the following pattern. Also write an expression if 100 such shapes are joined together.
(a) there are total 18 side with length r and total 6 sides with length b.
∴ 18r+ 6b is the required expression
(b) for 1 figure 2g+2p
for 100 → 200g+200p
The sum of first n natural numbers is given by Find
(i) The sum of first 5 natural numbers.
(ii) The sum of first 11 natural numbers.
(iii) The sum of natural numbers from 11 to 30.
(i) n=5
(ii) n=11
(iii) result at n=30 - result at n = 10
15×30 + 15 – (50+5)
= 410
The sum of squares of first n natural numbers is given by or Find the sum of squares of the first 10 natural numbers.
put n = 10 in any one of the equation
= 385
The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of
(a) Table of 7
(b) Table of 10
(c) Table of 19
(a) Table of 7
put n = 7
55× 7 = 385
(b) Table of 10
put n = 10
55× 10 = 550
(c) Table of 19
put n = 19
55× 19 = 1045
If = 2x + 3, x + 7 and = x – 3, then find the value of :
i.
ii.
If = 2x + 3, x + 7 and = x – 3
(i)
Put x= 6 in 2x+3 in triangle shape.
x = 3/2 in square shape
and x = 1 in circle.
(2×6+3)+()-(1-3)
(ii)
= 1
If and = x + 6, then find the value of:
i.
ii.
(i)
=
(ii)
=
Translate each of the following algebraic expressions
4b – 3
Three subtracted by four times b.
Translate each of the following algebraic expressions
8(m + 5)
eight times the sum of m and five.
Translate each of the following algebraic expressions
Seven divided by the difference of 8 and x.
Translate each of the following algebraic expressions
seventeen times quotient of sixteen divided by w.
(i) Critical Thinking Write two different algebraic expressions for the word phrase “ of the sum of x and 7.”
(ii) What’s the Error? A student wrote an algebraic expression for “5 less than a number n divided by 3” as What error did the student make?
(iii) Write About it Shashi used addition to solve a word problem about the weekly cost of commuting by toll tax for ₹ 15 each day. Ravi solved the same problem by multiplying. They both got the correct answer. How is this possible?
(i) ‘of is used for multiplication’
(ii) the resultant of difference is divided by n.
correct =
(iii) Multiplication is just repetitive addition.
either we add it many times or just multiply it ones.
Challenge Write an expression for the sum of 1 and twice a number n. If you let n be any odd number, will the result always be an odd number?
1+2n
now if n is odd
then yes the expression will always be odd
because 2n will always be even. (even if n is odd or even)
so even plus 1 will always be odd.
Critical Thinking Will the value of 11x for x = –5 be greater than 11 or less than 11? Explain.
In 11x when we put x = -5
then 11(-5) = -55
this is a negative number and so its definitely less than 11.
Match Column I with Column II in the following:
Column I
1. The difference of 3 and a number squared
let n be the number
3-n2
2. 5 less than twice a number squared
let n be the number
2n2 - 5
3. Five minus twice the square of a number
let n be the number
5 – 2n2
4. Four minus a number multiplied by 2
let x be the number
4 – 2x
5. Seven times the sum of a number and 1
let n be the number
7(n+1)
6. A number squared plus 6
let n be the number
n2+6
7. 2 times the sum of a number and 6
2(n+6)
8. Three less than the square of a number
n2 – 3
At age of 2 years, a cat or a dog is considered 24 “human” years old. Each year, after age 2 is equivalent to 4 “human” years. Fill in the expression [24 + 4(a – 2)] so that it represents the age of a cat or dog in human years. Also, you need to determine for what ‘a’ stands for. Copy the chart and use your expression to complete it.
In each blank put a as the respective age and find the resultant on right.
Express the following properties with variables x, y and z.
(i) Commutative property of addition
(ii) Commutative property of multiplication
(iii) Associative property of addition
(iv) Associative property of multiplication
(v) Distributive property of multiplication over addition
(i) a+b = b+a
(ii) ab = ba
(iii) a+(b+c) = (b+c)+a
(iv) a(bc) = (ab)c
(v) a(b+c) = ab+bc