Question 12 Marks
Write three expressions each having 4 terms.
AnswerThree expressions each having 4 terms are as follow:
(i) $4 x^2-3 y^2+9 x-8 y$ (ii) $4 x^2-3 x y+4 x+13$ (iii) $5 x^3-5 x^2-5 x-5$
View full question & answer→Question 22 Marks
Group the like terms together from the following
12x, 12, -25x, -25, -25y, 1, x, 12у, у
Answer(i) 12x,25x, x are like terms, since they have same algebraic factor i.e. x.
(ii) 12,25, 1 are like terms as they all are constant.
(iii) -25 y, 12 y, y are like terms, since they have same algebraic factor i.e. y.
View full question & answer→Question 32 Marks
What are the terms in the following expressions? Show how the terms are formed. Draw a tree diagram for each expression.
$2 x^2 y$
View full question & answer→Question 42 Marks
What are the terms in the following expressions? Show how the terms are formed. Draw a tree diagram for each expression.
(ii) 7mn - 4
Question 52 Marks
What are the terms in the following expressions? Show how the terms are formed. Draw a tree diagram for each expression.
(i) $8 y+3 x^2$
AnswerIn $8 y+3 x^2$, the terms are $8 y$ and $3 x^2$.
The term 8 y is formed by multiplying the variable y by 8. The term 13 x^2 is formed by first multiplying the variable x with itself to get $x^2$ and then multiplying $x^2$ by 3. View full question & answer→Question 62 Marks
Describe how the following expressions are obtained?
(iii) $4 x^2-5 x$
View full question & answer→Question 72 Marks
(i) If $z=10$, find the value of $z^3-3(z-10)$.
(ii) p = -10 find the value of $p^2-2 p-100$.
Answer(i) When z = 10 then
the value of $z^3-3(z-10)=(10)^3-3(10-10)$
= 10 × 10 × 10 - 3 × 0
= 1000 - 0 = 1000
Hence, the value of the given expression is 1000.
(ii) When p = -10 then the value of
$p^2-2 p-100=(-10)^2-2 \times(-10)-100$
= (-10) × (-10) + 20 - 100
= 100 + 20 - 100 = 20
Hence, the value of the given expression is 20.
View full question & answer→Question 82 Marks
Simplify these expressions and find their values, If x = 3, a = -1, b = -2.
(v) 2a - 2b - 4 - 5 + a
Answer(v)The simplified expression is 3a - 2b - 9 and its required value is -8.
View full question & answer→Question 92 Marks
Simplify these expressions and find their values, If x = 3, a = -1, b = -2.
(iv) 10 - 3b - 4 - 5b
Answer(iv)The simplified expression is 6 - 8b and its required value is 22.
View full question & answer→Question 102 Marks
Simplify these expressions and find their values, If x = 3, a = -1, b = -2.
(iii) 3a + 5 - 8a + 1
Answer(iii)The simplified expression is - 5a + 6 and its required value is 11.
View full question & answer→Question 112 Marks
Simplify these expressions and find their values, If x = 3, a = -1, b = -2.
(ii) 2 - 8x + 4x + 4
Answer(ii) We have, 2 - 8x + 4x + 4 = - 8x + 4x + 2 + 4
= x(- 8 + 4) + 6 = - 4x + 6
On putting x = 3 in - 4x + 6 we get
- 4x + 6 = - 4(3) + 6 = - 12 + 6 = - 6
Hence, the simplified expression is - 4x + 6 and its required value is -6.
View full question & answer→Question 122 Marks
Simplify these expressions and find their values, If x = 3, a = -1, b = -2.
(i) 3x - 5 - x + 9
Answer(i) We have, 3x - 5 - x + 9 = 3x - x - 5 + 9
= x(3 - 1) + 4
= 2x + 4
On putting x = 3 ln 2x + 4 we get
2x + 4 = 2(3) + 4
= 6 + 4 = 10
Hence, the simplified expression is 2x + 4 and its required value is 10.
View full question & answer→Question 132 Marks
Simplify the expressions and find the value, if x is equal to 2.
4(2x - 1) + 3x + 11
Question 142 Marks
Simplify the expressions and find the value, if x is equal to 2.
6x + 5(x - 2)
Question 152 Marks
Simplify the expressions and find the value, if x is equal to 2.
3(x - 2) + 5x - 7
Answer15
Hence, the simplified expression is 8x - 1 and its required value is 15.
View full question & answer→Question 162 Marks
Simplify the expressions and find the value, if x is equal to 2.
x + 7 + 4(x - 5)
AnswerWe have, x + 7 + 4(x - 5) = x + 7 + 4x - 20
= x + 4x + 7 - 20
= x(1 + 4) - 13 = 5x - 13
On putting x = 2in * 5x - 13 we get
5x - 13 = 5(2) - 13 = 10 - 13 = -3
Hence, the simplified expression is 5x - 13 and its required value is -3.
View full question & answer→Question 172 Marks
When a = 0 and b = -1 , find the value of the given expressions.
$2 a^2+b^2+1$
AnswerWhen a = 0 and b = -1 then
the value of $2 a^2+b^2+1=2(0)^2+(-1)^2+1$
= 2 × 0 + 1 + 1 = 0 + 1 + 1 = 2
View full question & answer→Question 182 Marks
Find the value of the following expressions when x = - 1
$2 x^2-x-2$
AnswerOn putting $x=-1$ in $2 x^2-x-2$, we get
$2 x^2-x-2=2(-1)^2-(-1)-2$
$\begin{array}{l}=2 \times 1+1-2 \\ =2+1-2=3-2=1\end{array}$
View full question & answer→Question 192 Marks
Find the value of the following expressions when x = - 1
$x^2+2 x+1$
AnswerOn putting $x=-1$ in $x^2+2 x+1$, we get
$\begin{aligned} x^2+2 x+1 & =(-1)^2+2(-1)+1 \\ & =1-2+1=2-2=0\end{aligned}$
View full question & answer→Question 202 Marks
If p = - 2 then find the value of
$-2 p^3-3 p^2+4 p+7$
AnswerDo same as part (ii) Ans. 3
View full question & answer→Question 212 Marks
If p = - 2 then find the value of
$-3 p^2+4 p+7$
AnswerOn putting $p=-2$ in $-3 p^2+4 p+7$, we get
$-3 p^2+4 p+7=-3(-2)^2+4(-2)+7$
= - 3(4) - 8 + 7 = - 12 - 8 + 7
= -20 + 7 - 13
View full question & answer→Question 222 Marks
Identify like terms in the following:
$\begin{array}{l}\text { 10pq, } 7 p, 8 q,-p^2 q^2,-7 q p,-100 q,-23,12 q^2 p^2, \\ -5 p^2, 41,2405 p, 78 q p, 13 p^2 q, q p^2, 701 p^2\end{array}$
AnswerLike terms are 10 pq, -7qp and 78qp (have same algebraic factors p, q);
7 p and 2405 p (have same algebraic factor p);
8q and-100q (have same algebraic factor q);
$-p^2 q^2$ and $12 q^2 p^2$ (have same algebraic factors $p, p, q, q)$;
-23 and 41 (both are constants); $-5 p^2$ and $701 p^2$
(have same algebraic factors $p, p$ ) $; 13 p^2 q, q p^2$
(have same algebraic factors p, p, q).
View full question & answer→Question 232 Marks
Identify like terms in the following:
$\begin{array}{l}-x y^2,-4 y x^2, 8 x^2, 2 x y^2, 7 y,-11 x^2,-100 x,-11 y x, \\ 20 x^2 y,-6 x^2, y, 2 x y, 3 x\end{array}$
AnswerLike terms are
$-x y^2$ and $2 x y^2$ (have same algebraic factors $x, y, y$ );
$-4 y x^2$ and $20 x^2 y$ (have same algebraic factors $x, x, y$ );
$8 x^2,-11 x^2$ and $-6 x^2$ (have same algebraic factors $x, x$ );
7 y and y (have same algebraic factors y);
-100x and 3x (have same algebraic factor x);
-11 yx and 2xy (have same algebraic factors x, y).
View full question & answer→Question 242 Marks
State whether a given pair of terms is of like or unlike terms.
$12 x z, 12 x^2 z^2$
Answer$12 x z, 12 x^2 z^2$ are unlike terms, since algebraic factors are not same. [in $12 x z$, algebraic factors are $x, z$ and in $12 x^2 z^2$, algebraic factors are $x, x, z, z]$
View full question & answer→Question 252 Marks
State whether a given pair of terms is of like or unlike terms.
$4 m^2 p, 4 m p^2$
Answer$4 m^2 p, 4 m p^2$ are unlike terms, since algebraic factors are not same. [in $4 m^2 p$, algebraic factors are $m, m, p$ and in $4 m p^2$, algebraic factors are $\left.m, p, p\right]$
View full question & answer→Question 262 Marks
State whether a given pair of terms is of like or unlike terms.
14xy, 42yx
Answer14xy, 42 yx are like terms, since algebraic factors x and y are same.
View full question & answer→Question 272 Marks
State whether a given pair of terms is of like or unlike terms.
-29x, -29y
Answer(- 29x -29 y are unlike terms, since algebraic factors are not same. [ in - 29x, algebraic factor is x and in-29 y algebraic factor is y]
View full question & answer→Question 282 Marks
State whether a given pair of terms is of like or unlike terms.
$-7 x, \frac{5}{2} x$
Answer$-7 x, \frac{5}{2} x$ are like terms, since algebraic factor $x$ is same.
View full question & answer→Question 292 Marks
State whether a given pair of terms is of like or unlike terms.
1,100
Answer1,100 are like terms, since both are constant.
View full question & answer→Question 302 Marks
Identify terms and factors in the expressions given below:
$0.1 p^2+0.2 q^2$
AnswerIn the expression $0.1 p^2+0.2 q^2$, terms are $01 p^2$ and $0.2 q^2$, factors of 0.1 $p^2$ are 0.1, p, p and factors of $0.2 q^2$ are 0.2, q, q.
View full question & answer→Question 312 Marks
Identify terms and factors in the expressions given below:
$\frac{3}{4} x+\frac{1}{4}$
AnswerIn the expression $\frac{3}{4} x+\frac{1}{4}$, terms are $\frac{3}{4} x, \frac{1}{4}$ and factors of $\frac{3}{4} x$ are $\frac{3}{4}$, x and factor of $\frac{1}{4}$ is $\frac{1}{4}$.
View full question & answer→Question 322 Marks
Identify terms and factors in the expressions given below:
1.2ab - 2.4b + 3.6a
AnswerIn the expression 1.2ab - 2.4b + 3.6a terms are 1.2ab, -2.4b and 3.6a and factors of 1.2ab are 1.2, a, b, factors of -2.4b are -2.4, b and factors of 3.6a are 3.6, a.
View full question & answer→Question 332 Marks
Identify terms and factors in the expressions given below:
pq + q
AnswerIn the expression pq + q terms are pq, q and factors of pq are p, q and factor of q is q.
View full question & answer→Question 342 Marks
Identify terms and factors in the expressions given below:
$x y+2 x^2 y^2$
AnswerIn the expression $x y+2 x^2 y^2$, terms are xy, $2 x^2 y^2$ and factors of xy are x, y and factors of $2 x^2 y^2$ are 2, x, x, y, y.
View full question & answer→Question 352 Marks
Identify terms and factors in the expressions given below:
$5 y+3 y^2$
AnswerIn the expression $5 y+3 y^2$, terms are 5y, $3 y^2$ and factors of 5 y are 5, y and factors of $3 y^2$ are 3, y, y.
View full question & answer→Question 362 Marks
Identify terms and factors in the expressions given below:
(- 4x + 5y)
AnswerIn the expression - 4x + 5y terms are - 4x 5y and factors of - 4x are -4, x and factors of 5 y are 5, y.
View full question & answer→Question 372 Marks
Identify terms and factors in the expressions given below:
(- 4x + 5)
AnswerIn the expression - 4x + 5 terms are - 4x 5 and factors of - 4x are-4, x and factor of 5 is 5.
View full question & answer→Question 382 Marks
Identify the terms and their factors in the following expressions. Show that the terms and factors by tree diagrams.
$-a b+2 b^2-3 a^2$
View full question & answer→Question 392 Marks
Identify the terms and their factors in the following expressions. Show that the terms and factors by tree diagrams.
$5 x y^2+7 x^2 y$
View full question & answer→Question 402 Marks
Identify the terms and their factors in the following expressions. Show that the terms and factors by tree diagrams.
$y-y^3$
View full question & answer→Question 412 Marks
Identify the terms and their factors in the following expressions. Show that the terms and factors by tree diagrams.
$1+x+x^2$
AnswerWe have, $1+x+x^2$
Here, terms are 1, x and $x^2$. Factor of 1 is 1, factor of x is x and factors of $x^2$ is x, x. Now, to show terms and factors, tree diagram is given below.
View full question & answer→Question 422 Marks
Identify the terms and their factors in the following expressions. Show that the terms and factors by tree diagrams.
x - 3
AnswerWe have, x - 3
Here, terms are x and -3. Factor of x is x and factor of-3 is-3. Now, to show terms and factors, tree diagram is given below.
View full question & answer→Question 432 Marks
Answer(i) $\frac{87}{2}$
(ii) 1
View full question & answer→Question 442 Marks
Observe the following nutritional chart carefully
| Food Item (per unit = 100g) | Carbohydrates |
| Rajma | 60 g |
| Cabbage | 5 g |
| Potato | 22 g |
| Carrot | 11 g |
| Tomato | 4 g |
| Apples | 14 g |
Write an algebraic expression for the amount of carbohydrates (in grams) for
(i) y units of potatoes and 2 units of rajma.
(ii) 2x units tomatoes and y units apples.
Answer(i) 22y + 120
(ii) 8x + 14y
View full question & answer→Question 452 Marks
Write the coefficient of y in the following expressions.
(i) 4xy + 4x
(ii) $4 x^2 y-6 x$
Answer(i) Given, $4 x y+4 x$
Term containing $y$ is $4 x y$.
So, the coefficient of $y$ is $4 x$.
(ii) Given, $4 x^2 y-6 x$
Term containing $y$ is $4 x^2 y$.
So, the coefficient of $y$ is $4 x^2$.
View full question & answer→Question 462 Marks
Write the coefficient of x in the following expressions.
(i) 3x - 4y
(ii) $4 x y^2-3 y^3$
Answer(i) Given, 3x - 4y
Term containing x is 3x.
So, the coefficient of x is 3.
(ii) Given, $4 x y^2-3 y^3$
Term containing $x$ is $4 x y^2$.
So, the coefficient of $x$ is $4 y^2$.
View full question & answer→Question 472 Marks
Write the following into algebraic expression.
(i) x cube plus two times y square.
(ii) x cube minus three times x square.
Answer(i) Given, x cube plus two times y square.
Algebraic expression will be $x^3+2 y^2$.
(ii) Given, x cube minus three times x square.
Algebraic expression will be $x^3-3 x^2$.
View full question & answer→
