myhelper: of class 8

Showing posts with label of class 8. Show all posts

S.chand publication New Learning Composite mathematics solution of class 8 Chapter 12 Mensuration Exercise 12B

Exercise 12B

Find area of the following polygons

OPEN IN YOUTUBE

Question 1

ΔABE-

Area₁$=\frac{1}{2}\times 12\times 30$

=180cm²

Area₂$=\frac{1}{2}h(a+b)$

$=\frac{1}{2}\times 15\times (30+24)$

=405cm²

Total area=Area₁+Area₂

=180+405=585cm²

OPEN IN YOUTUBE

Question 2

Sol :

ΔPQU-

Area₁$=\frac{1}{2}\times 40\times 15$

=300 cm²

In rectangle QRTU

Area₂=40×28=1120cm²

In ΔRST-

Area₃$=\frac{1}{2}\times 40 \times 15$

=300cm²

∴Total area=Area₁+Area₂+Area₃

=300+1120+300=1720cm²

OPEN IN YOUTUBE

Question 3

Sol :

ABCDEF is a hexagonal figure.

∴A regular hexagon can be divided into a equilateral triangle

∴Area of ABCDEF=6×Area of one triangle

$=6\times \left[\frac{\sqrt{3}}{4}\times (sides)^2\right]$

$=6\left[\frac{\sqrt{3}}{4}\times 8^2\right]$

$=6\times \frac{\sqrt{3}}{4}\times 8\times 8$

=6×1.732×2×8

=166.272m²

OPEN IN YOUTUBE

Question 4

Sol :

EI=5cm ,HI=8cm

EF=6cm ,GH=3cm

Join O and G

OG=8cm=IH

IOGH is a rectangle

∴EFGO is a trapezium

∴Area of IEFGH=Area of IOGH+Area of EFGO

$=(8×3)+\frac{1}{2}\times (6+8) \times 2$

=24+$\frac{1}{2}\times 14 \times 2$

=24+14

=38 cm²

OPEN IN YOUTUBE

Question 5

Sol :

ΔRSV-

Area₁$=\frac{1}{2}\times \text{Base}\times \text{Height}$

$=\frac{1}{2}\times 8\times 10$

=40cm²

Trapezium STUV-

Area₁$=\frac{1}{2}\times \text{h}\times (8+14)$

[∵RO=10

RP=17

∴OP=h=17-10=7cm]

$=\frac{1}{2}\times 7 \times 22$

=77

∴Area=Area₁+Area₁

=40+77=117cm²

OPEN IN YOUTUBE

Question 6

Sol :

Let ,ABCP is a rectangle

∴A₁=(4×10)=40cm²

Let,

EFQD is a rectangle

∴A₂=(9×8)=72cm²

PC and QD join "O"

∴POQG is a rectangle

∴PO=GQ=15-8=7cm

PG=27-10=17cm

∴Area=7×17=119cm²

Now , ΔODC➝

OD=27-(10+9)=27-19=8cm

OC=PO-PC=7-4=3cm

∴Area$=\frac{1}{2}\times 8\times 3$=12

∴Area of PCDQG➝

A₃=119-12=107cm²

∴Total Area=A₁+A₂+A₃

=40+72+107

=219cm²

OPEN IN YOUTUBE

Question 7

Find the area of the hexagon ABCDFF in two ways:

(a) By splitting into two congruent triangles and a rectangle.

(b) By splitting into two congruent trapeziums.

Sol :

(a)

⇒ABCDEF is a hexagon, by splitting into two congruent by BF and CE

∴BCEF is rectangle

ABF ,DCE are triangle

ABF , DCE are triangle

∴Area of BCEF=A₁=(7×10)=70cm²

Area of ABF=A₂=$=\frac{1}{2}\times 10\times 4$=20cm²

ΔABF=ΔDCF=20

∴Total area of ABCDEF=70+20+20=110cm²

(b)

ABCDEF is hexagon splitting by AD into two congruent trapezium

ABCD and ADEF are trapezium

∴Area of ABCD=A₁$=\frac{1}{2}h(a+b)$

[h=OC$=\frac{10}{2}$=5

a=7 , b=15]

$=\frac{1}{2}5(7+15)$

$=\frac{1}{2}\times 5\times 22$

=55cm²

∴Area of ABCD=Area of ADEF=55cm²

∴Total area of ABCDEF=55+55=110cm²

OPEN IN YOUTUBE

Question 8

The perimeter of a square and a rectangle hexagon are equal. Find the ratio of the area of the hexagon to the area of the square.

Sol :

Perimeter of a square=4a

Perimeter of a regular hexagon=6b

ATQ,

4a=6b

∴$\frac{a}{b}=\frac{6}{4}$

∴$b=\frac{4a}{6}$

Now,

Area of hexagon : Area of square

$=6\times \frac{\sqrt{3}}{4}\times b^2$ : a²

$=\dfrac{6\times \frac{\sqrt{3}}{4}\times \frac{4a}{6}\times \frac{4a}{6}}{a^2}$

$=\frac{2\sqrt{3}}{3}$

=2√3:3

S.chand publication New Learning Composite mathematics solution of class 8 Chapter 6 Factorisation of Algebraic Expressions Exercise 6F

Exercise 6F

Q1 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 1

Factorise the following:

y² + 4y + 3

Sol :
=y²+3y+y+3

=y(y+3)+1(y+3)

=(y+1)(y+3)

Q2 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 2

a² + 12a + 27

Sol :

=a²+9a+3a+27

=a(a+9)+3(a+9)

=(a+3)(a+9)

Q3 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 3

(3) x² + 12x + 32

Sol :
=x²+8x+4x+32
=x(x+8)+4(x+8)

=(x+8)(x+4)

Q4 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 4

p² – 11p + 24

Sol :
=p² – 11p + 24

=p(x-8)-3(x-8)

Q5 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 5

x² – 15x + 44

Sol :

=x²–15x+44
=x(x-11)-4(x-11)

=(x-11)(x-4)

Q6 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 6

m² – 15m + 56

Sol :
=m² – 15m + 56
=m(m-8)-7(m-8)

=(m-8)(m-7)

Q7 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 7

x² + x – 30

Sol :

=x²+x–30

=x(x+6)-5(x+6)

=(x+6)(x-5)

Q8 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 8

a² – 3a – 18

Sol :

=a²–6a+3a–18

=a(a-6)+3(a-6)

=(a-6)(a+3)

Q9 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 9

b² –b – 56

Sol :

=b² –b – 56

=b(b-8)+7(b-8)

=(b-8)(b+7)

Q10 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 10

t² – 20t – 125

Sol :

=t²–20t–125

=t(t-25)+5(t-25)

=(t-25)(t+5)

Q11 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 11

u² – 7u – 30

Sol :

=u² – 7u – 30

=u(u-10)+3(u-30)

Q12 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 12

x² – 43x + 42

Sol :

=x²–42x-x+42
=x(x-42)-1(x-12)

=(x-4²)(x-1)

Q13 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 13

k² + 12k – 160

Sol :

=k²+20k-8k-160

=k(k+20)-8(k+20)

Q14 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 14

x² + 5x – 24

Sol :

=x² + 5x – 24

=x(x+8)-3(x+8)

=(x+8)(x-3)

Q15 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 15

c²– 19c + 78

Sol :

=c²–13c-9c+78
=c(c-13)+9(c-13)
=(c-13)(c+9)

Q16 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 16

y²+ 2y – 48

Sol :

=y²+8y-6y–48

=y(y+8)-6(y+8)

=(y+8)(y-6)

Q17 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 17

a² + 9a – 36

Sol :

=a²+12a-3a-36

=a(a+12)-3(a+12)

=(a+12)(a-3)

Q18 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 18

m² – 3m – 40

Sol :

=m²–5m+2m–10

=m(m-5)+2(m-5)

=(m-5)(m+2)

Q19 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 19

t² – 17t – 84

Sol :

=t²–21t+4t-84

=t(t-21)+4(t-21)

=(t-21)(t+4)

Q20 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 20

x² – 13x – 68

Sol :

=x²– 13x – 68

=x(x-17)-4(x-17)

=(x-17)(x-4)

Q21 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

OPEN IN YOUTUBE

Question 21

u² + 6u – 112

Sol :
=u² + 6u – 112

=u(u+4)-8(u+14)

=(u+14)(u-8)

S.chand publication New Learning Composite mathematics solution of class 8 Chapter 5 Algebraic Expressions Exercise 5F

Exercise 5F

OPEN IN YOUTUBE

Question 1

Divide:

(a) 7a+7b by 7

Sol :
$=\frac{7a+7b}{7}=\frac{7(a+b)}{7}$
=a+b

(b) ax+ay by a

Sol :

$=\frac{ax+ay}{a}=\frac{a(x+y)}{a}$
=x+y

Sol :

$=\frac{6y-2}{2}=\frac{2(3y-1)}{2}$
=3y-1

(d) b–a by b

Sol :
$=\frac{b-a}{b}=\dfrac{b\left(1-\frac{a}{b}\right)}{b}$
$=1-\frac{a}{b}$

OPEN IN YOUTUBE

Question 2

(a) 8y–8 by -8

Sol :
$=\frac{8y-8}{-8}=\frac{8(y-1)}{-8}$
=-y+1

(b) 6x⁴+3x³+3x² by 3x²

Sol :
$=\frac{6x^4+3x^3+3x^2}{3x^2}$

$=\frac{3x^2(2x^2+x+1)}{3x^2}$

=2x²+x+1

Sol :
$=\frac{25x^8-20x^5}{5x^3y^3}=\frac{5x^5(5x^3-4)}{5x^3y^3}$

$=\frac{x^2}{y^3}(5x^3-4)$

$=\frac{5x^4}{y^3}-\frac{4x^2}{y^3}$

(d) x²y²z²–xyz+1 by xyz

Sol :

$=\frac{x^2y^2z^2-xyz+1}{xyz}=\frac{x^2y^2z^2}{xyz}-\frac{xyz}{xyz}+\frac{1}{xyz}$

$xyz-1+\frac{1}{xyz}$

$=xyz+\frac{1}{xyz}-1$

OPEN IN YOUTUBE

Question 3

Express each quotient as a sum.

(a) $\frac{35a^5+28a^4b^2-14a^3b^3}{-7a^2}$

Sol :

$=\frac{35a^5+28a^4b^2-14a^3b^3}{-7a^2}$

$=-5a^3-4a^2b^2+2ab^3$

(b) $\frac{16x^2y-48xy^2+8x^2y^2}{8x^2y^2}$

Sol :

$=\frac{16x^2y-48xy^2+8x^2y^2}{8x^2y^2}$

$=\frac{2}{y}-\frac{6}{x}+1$

OPEN IN YOUTUBE

Question 4

Evaluate

$\frac{x}{y}$ when $=\frac{x+y}{y}=21$

Sol :

$=\frac{x+y}{y}=21$

x+y=21y

x=21y-y=20y

$\frac{x}{y}=20$

S.chand publication New Learning Composite mathematics solution of class 8 Chapter 5 Algebraic Expressions Exercise 5E

Exercise 5E

OPEN IN YOUTUBE

Question 1

Simplify:

(a) $\frac{9x^7}{3x^5}$
Sol :

=3x^7-5=3x²

(b) $\frac{-20y^{12}}{4y^8}$
Sol :

=-5y^12-8=-5y⁴

(c) $\frac{-15a^7}{-3a^{15}}$

Sol :

=5a^7-15=5a^-8

$=\frac{5}{a^8}$

(d) $\frac{18x^4y^2}{9x^3y}$
Sol :

=2xy

OPEN IN YOUTUBE

Question 2

(a) $\frac{-35x^8y^9}{-7x^3y^2}$
Sol :

=5x⁵y⁷

(b) $\frac{48a^2b^2c^4}{-12abc^3}$

Sol :
=-4abc

(c) $\frac{10x^{20}y^7z^4}{0.1x^{16}y^3z^9}$
Sol :

=100x⁴y⁴z^-5

$=\frac{100x^4y^4}{z^5}$

(d) $\frac{0.6a^4b^3c^2}{0.3ab^5c^7}$

Sol :

=2a³b^-2c^-5

$=\frac{2a^3}{b^2c^5}$

OPEN IN YOUTUBE

Question 3

(a) $\frac{(3a^3b)(5ab^3)}{(5ab)(6ab^7)}$
Sol :

$=\frac{3\times a^3 \times b\times 5\times a\times b^3}{5\times a\times b\times 6\times a\times b^7}$

$=\frac{a^2}{2b^4}$

(b) $\frac{4ab(-7a^3b^7)}{-14a^2b^2}$

Sol :

$=4\times a\times b \times (-7)\times a^3 \times b^7$
=2a²b⁶

(c) $\frac{(5a^2b)^2(-100b^3)}{(5^2b)^2}$

Sol :

$=\frac{5^2 \times a^4 \times b^2 \times (-100)\times b^3}{5^4 b^2}$

=-4a⁴b³

(d) $\frac{(-2x^2y)^3}{(6xy^2)^2}$

Sol :

$=\frac{-8x^6y^3}{36x^2y^4}=\frac{-2x^4}{9y}$

(e) $\frac{(3x^2)^3(3y)}{(3x)^3(3x)^2}$

Sol :

$=\frac{3\times 3\times 3\times 3\times x^6\times y}{3\times 3\times 3\times 3^2\times x^2\times x^3 }=\frac{xy}{3}$

(f) $\frac{(-2pq^2)^8}{(4p^2q)^4}$
Sol :

$=\frac{-2^8 \times p^8 \times q^{16}}{2^8 \times p^8 \times q^4}$

=q¹²

S.chand publication New Learning Composite mathematics solution of class 8 Chapter 5 Algebraic Expressions Exercise 5B

Exercise 5B

OEN IN YOUTUBE

Question 1

Find the product of the following pairs of monomials.

(a) 5, 2x

Sol :

=5×2x=10

(b) -3y, 4y

Sol :

=-12y²

Sol :

=-6p×8pqr=48p²qr

(d) 12p⁵, -5p

Sol :

=12p⁵×-5p=-60p⁶

OEN IN YOUTUBE

Question 2

Find the area of a rectangle whose length is 6x³y² units and breadth is 3xy² units.

Sol :

Length of rectangle=6x³y²

Breadth of rectangle=3xy²

∴Area of rectangle=Length×Breadth

=6x³y²×3xy²

=18x⁴y⁴

OEN IN YOUTUBE

Question 3

Simplify:

(a) (3y³ ) (-3y²)

Sol : -9y⁵

(b) (-8x⁵) (2x)

Sol : -16x⁶

Sol : +12m³n³

(d) (x⁴) (x³) (x)

Sol : x⁸

(e) (-4a) (5ab) (3b)

Sol : -60a²b²

(f) (-x³y²) (xy) (2y)

Sol : -2x⁴y⁴

(g) (-1/3 a³) (9a) (-2a⁴)

Sol : 6a⁸

(h) (-q)³ (2q)²

Sol : -4q⁵

(i) (2x)² (3x)³

Sol : 108x⁵

(j) (-4z) (-5z²)³

Sol : 500z⁷

(k) (-3y)² (-3y)³

Sol : -243y⁵

(l) (-0.5a²b) (-2ab)³

Sol : 4a⁵b⁴

OEN IN YOUTUBE

Question 4

Find a monomial equivalent to the given expression.

(a) ( 4a³b²) (3a³b⁴) + (2ab)⁶

Sol :

=12a⁶b⁶+64a⁶b⁶

=76a⁶b⁶

(b) (4x³) (2x)⁴ – (7x)² (3x⁵)

Sol :

=64x⁷-147x⁷

=-83x⁷

Sol :

=-30p²q²+14p²q²+60p²q²

=44p²q²

(d) (- 3xyz) (4x²yz) – (5y²) (2xz²) (-x²)

Sol :

=-12x³y²z²+10x³y²z²

=-2x³y²z²

Exercise 12B

Find area of the following polygons

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Exercise 6F

Q1 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 1

Factorise the following:

Q2 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 2

Q3 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 3

Q4 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 4

Q5 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 5

Q6 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 6

Q7 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 7

Q8 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 8

Q9 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 9

Q10 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 10

Q11 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 11

Q12 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 12

Q13 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 13

Q14 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 14

Q15 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 15

Q16 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 16

Q17 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 17

Q18 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 18

Q19 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 19

Q20 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 20

Q21 | Ex-6F | Class 8 | SChand | New Learning Composite maths | Factorisation of Algebraic Expressions | myhelper

Question 21

Exercise 5F

Question 1

Question 2

Question 3

Question 4

Exercise 5E

Question 1

Question 2

Question 3

Exercise 5B

Question 1

Question 2

Question 3

Question 4

Contact Form