Fundamental Concepts & Operations on Algebraic Expressions - ICSE STD 8 MATHS Questions

Q 1[1 Mark Question Answer]1 Mark

Subtract $a^3-3 a^2$ from $b^3-3 b^2$.

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Q 2[1 Mark Question Answer]1 Mark

Identify monomial, binomial and trinomial from : $8 a \div 9 b-2 a^2 \times b^2$

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Q 3[1 Mark Question Answer]1 Mark

Identify monomial, binomial and trinomial from : $\frac{x^2-2 y^2+z^2}{3}$

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Q 4[1 Mark Question Answer]1 Mark

Identify monomial, binomial and trinomial from : $x y+y z+z x$

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Q 5[1 Mark Question Answer]1 Mark

Identify monomial, binomial and trinomial from : $\frac{a}{3}+\frac{b}{6}$

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Q 6[2 Mark Question Answer]2 Marks

Divide : $\left(x^6-y^6\right)$ by $(x-y)$

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Q 7[2 Mark Question Answer]2 Marks

Subtract the sum of $4 x^2+7 x y+3 y^2+1$ and $2 x^2-5 x y-2 y^2+8$ from $9 x^2-8 x y+11 y^2$.

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Q 8[2 Mark Question Answer]2 Marks

Subtract : $7 x^3-6 x^2 y+9 x y^2-2 y^3$ from $3 x^2 y-2 x^3+y^3-5 x y^2$

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Q 9[2 Mark Question Answer]2 Marks

Subtract : $1-x+2 x^2-x^3$ from $2 x^3-x^2+3 x+2$

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Q 10[2 Mark Question Answer]2 Marks

Subtract : $5 x^2+x-11$ from $x^2-2 x+8$

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Q 11[3 marks sum]3 Marks

Find the quotient and remainder : $\left(6 a^2-31 a+47\right)$ is divided by $(2 a-5)$

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Q 12[3 marks sum]3 Marks

The product of two numbers is $\left(x^6-y^6\right)$. If one of the numbers is $(x-y)$, then find the other.

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Q 13[3 marks sum]3 Marks

There are $(3 x+5 y)$ shelves in a library and in each shelve there are $(5 x+3 y)$ books. How many books are there in the library?

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Q 14[3 marks sum]3 Marks

Multiply : $\left(3 x^5-7 x^3+2 x^2-x+4\right)$ by $\left(x^3-2 x^2+3 x-1\right)$

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Q 15[3 marks sum]3 Marks

Multiply : $\left(8 x^4-3 x^2+9 x-8\right)$ by $\left(2 x^2-5 x+3\right)$

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Q 16[4 marks sum]4 Marks

What must be subtracted from $8 x^4+14 x^3-2 x^2+7 x-8$ so that the resulting polynomial is exactly divisible by $\left(4 x^2+3 x-2\right)$ ?

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Q 17[4 marks sum]4 Marks

Find the quotient and remainder : $\left(3 t^5+7 t^4-11 t^3+8 t^2-32 t+5\right)$ is divided by $\left(2+3 t+t^2\right)$

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Q 18[4 marks sum]4 Marks

Find the quotient and remainder : $\left(2 x^4-x^3+10 x^2+8 x-5\right)$ is divided by $\left(x^2-x+6\right)$

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Q 19[4 marks sum]4 Marks

Divide : $\left(16 x^4-81 y^4\right)$ by $(2 x-3 y)$

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Q 20[4 marks sum]4 Marks

Divide : $\left(x^6-8\right)$ by $\left(x^2-2\right)$

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Q 21[5 marks sum]5 Marks

Show by division method that $\left(2 a^2-a+3\right)$ is a factor of $\left(6 a^5-a^4+4 a^3-5 a^2-a-15\right)$.

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Q 22[5 marks sum]5 Marks

Find the quotient and remainder : $\left(x^6+3 x^2+10\right)$ is divided by $\left(x^3+1\right)$

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Q 23MCQ1 Mark

$(2 x+5)(2 x-5)=$ ?

A
$\left(4 x^2+10 x-25\right)$
B
$\left(4 x^2-10 x+25\right)$
✓
$\left(4 x^2-25\right)$
D
$\left(4 x^2+25\right)$

Answer: C.

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Q 24MCQ1 Mark

$(2 x+3)(3 x-1)=$ ?

A
$\left(6 x^2-7 x+3\right)$
B
$\left(6 x^2-7 x-3\right)$
✓
$\left(6 x^2+7 x-3\right)$
D
$\left(6 x^2+8 x-3\right)$

Answer: C.

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Q 25MCQ1 Mark

$(x+5)(x-3)=$ ?

A
$x^2+2 x+15$
✓
$x^2+2 x-15$
C
$x^2+5 x-15$
D
$x^2-3 x-15$

Answer: B.

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Q 26MCQ1 Mark

$\left(3 q+7 p^2-2 r^3+4\right)-\left(4 p^2-2 q+7 r^3-3\right)=$ ?

✓
$\left(3 p^2+5 q-9 r^3+7\right)$
B
$\left(-3 p^2-5 q+9 r^3-7\right)$
C
$\left(11 p^2+q+5 r^3+1\right)$
D
$\left(p^2+2 q+5 r^3+1\right)$

Answer: A.

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Q 27MCQ1 Mark

The sum of $(6 a+4 b-c+3),(2 c-5 a-6),(2 b-3 c+4)$ and $(11 b-7 a+2 c-1)$ is

A
$(-6 a+6 b+c-4)$
✓
$(-6 a+17 b)$
C
$(-3 a+14 b-3 c+2)$
D
$(4 a-6 b+2)$

Answer: B.

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Fundamental Concepts & Operations on Algebraic Expressions question types

Fundamental Concepts & Operations on Algebraic Expressions questions

Generate a Fundamental Concepts & Operations on Algebraic Expressions paper free

Fundamental Concepts & Operations on Algebraic Expressions MATHS - Fundamental Concepts & Operations on Algebraic Expressions

Fundamental Concepts & Operations on Algebraic Expressions question types

Fundamental Concepts & Operations on Algebraic Expressions questions

Generate a Fundamental Concepts & Operations on Algebraic Expressions paper free