Finding the Value of an Expression

Q. Let a>0, and let P(x) be a polynomial with integer coefficients such that P(1)=P(3)=P(5)=P(7)=a , and P(2)=P(4)=P(6)=P(8)=-a. The smallest possible value of a =5× Q. what is Q

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value of 2 raised to the power of100

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Question 9

What should be the value of 'a' if the value of $2x^2+x-a$ equals to 5, when x = 0?

Q.

If z = 10, find the value of $z^3-3(z-10)$

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Question 1 (iii)

If m = 2, find the value of:
9 - 5m

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Question 2 (ii)

If p = -2, find the value of:
$-3p^2+4p+7$

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Question 66 (a)

Find the value of the given polynomial at a = -2 and b = 3.

$a^2+2ab+b^2$

Q.

Question 7 (iii)

Simplify these expressions and find their values if
x = 3, a = -1, b = -2:
3a + 5 - 8a + 1

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Question 46

Answer True/False.

2x - 5 > 11 is an equation.

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Question 86 (ii)

The sum of first n natural numbers is given by $\frac{1}{2}{n}^2+\frac{1}{2}n$. Find

The sum of first 11 natural number

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If

Solve the following problems. Draw Venn diagrams for each of them.

Q.

Question 3 (i)

Find the value of the following expression, when x = -1:
2x - 7

Q.

The solution of the equation 4x + 5 = 29

1. x = -6

2. x = 6

3. x = 0

4. x = -3

Q. Find the value of expression:
3a - 4b - 8 + 5a + 2b, if a = 3 and b = 7.

1. 2

Q.

Will the value of $11x$ for $x=-5$ be greater than $11$ or less than $11?$ Explain.

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Question 3 (iii)

Find the value of the following expression, when x = -1:
$x^2+2x+1$

Q.

Explain how to solve inequalities.

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Question 67 (d)

Find the value of the given polynomial at m = 1, n = -1 and p = 2

mn + np + pm

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Question 95 (iii)

Write About It:

Shashi used addition to solve a word problem about the weekly cost of commuting by toll tax for Rs 15 each day. Ravi solved the same problem by multiplying. They both got the correct answer. How is this possible?

Q. Evaluate the algebraic expression $a{x}^2+b{y}^2-c{z}^2$,

for $x=1$, $y=-1$, $z=2$, $a=-2$, $b=1$ & $c=-2$

1. 5
2. -9
3. 7
4. 11

Q.

Question 88

The sum of the multiplication table of natural number n is given by $55\times n$, Find the sum of

(a) Table of 7
(b) Table of 10
(c) Table of 19

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Question 66 (d)

Find the value of the given polynomial at a = -2 and b = 3.

$a^3-3a^{2}b+3a{b}^2-b^3$

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Question 7 (ii)

Simplify these expression and find their values if x = 3, a = -1, b = -2:
2 - 8x + 4x + 4

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Question 5 (iii)

When a = 0, b = -1, find the value of the given expression:
$2a^{2}b+2a{b}^2+ab$

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Question 66 (g)

Find the value of the given polynomial at a = -2 and b = 3.

$\frac{a}{b}+\frac{b}{a}$

Q.

$7$ relatives of a man comprise $4$ ladies and $3$ gentlemen.His wife has also $7$ relatives, $3$ of them are ladies and $4$ gentlemen. In how many ways can they invite a dinner party of $3$ ladies and $3$ gentlemen so that there are $3$ of the mans relatives and $3$ of the wifes relatives?

1. $485$

2. $500$

3. $486$

4. $102$

Q.

Find the value of expression $(a-b)(a^2+ab)$ when a = 3 and b = 2?

1. 16

2. 54

3. 20

4. 15

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Question 66 (f)

Find the value of the given polynomial at a = -2 and b = 3.

$\frac{a^2-b^2}{3}$

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Question 87

The sum of squares of first n natural numbers is given by $\frac{1}{6}n(n+1)(2n+1)$ or $\frac{1}{6}(2n^3+3n^2+n)$. Find the sum of squares of the first 10 natural numbers.

Q.

Simplify the expressions and find the value if x is equal to 2

(i) x + 7 + 4 (x − 5) (ii) 3 (x + 2) + 5x − 7

(iii) 6x + 5 (x − 2) (iv) 4 (2x −1) + 3x + 11