The Class 8 is an important year in a student’s life and Maths is one of the subjects that require dedication, hard work, and practice. It’s a subject where you can score well if you are well-versed with the concepts, remember the important formulas and solving methods, and have done an ample amount of practice. Worry not! Home Revise is here to make your Class 8 journey even easier. It’s essential for students to have the right study material and notes to prepare for their board examinations, and through Home Revise, you can cover all the fundamental topics in the subject and the complete NCERT Class 8 Maths Book syllabus.
1. Evaluate:
(i) 3-2 (ii) (-4)-2 (iii) (1/2)-5
Solution:
(i) 3-2 = (1/3)2
= 1/9
(ii) (-4)-2 = (1/-4)2
= 1/16
(iii) (1/2)-5 = (2/1)5
= 25
= 32
2. Simplify and express the result in power notation with a positive exponent:
(i) (-4)4 ÷(-4)8
(ii) (1/23 )2
(iii) -(3)4 ×(5/3)4
(iv) (3-7 ÷3-10 )×3-5
(v) 2-3 ×(-7)-3
Solution:
(i)
= (-4)5 /(-4)8
= (-4)5-8
= 1/(-4)3
(ii) (1/23 )2
= 12 /(23 )2
= 1/23×2 = 1/26
(iii) -(3)4 ×(5/3)4
= (-1)4 ×34 ×(54 /34 )
= 3(4-4) ×54
= 30 ×54 = 54
(iv) 
= (3-7 /3-10 )× 3-5
= 3-7 – (-10) × 3-5
= 3(-7+10) ×3-5
= 33 ×3-5
= 3(3+-5)
= 3-2
=1/32
(v) 2-3 ×(-7)– 3
= (2×-7)-3
(Because am ×bm = (ab)m )
= 1/(2×-7)3
= 1/(-14)3
3. Find the value of:
(i) (30 +4-1 )×22
(ii) (2-1 ×4-1 )÷2– 2
(iii) (1/2)-2 +(1/3)-2 +(1/4)-2
(iv) (3-1 +4-1 +5-1 )0
(v) {(-2/3)-2 }2
Solution:
(i)(30 +4– 1 )×22 = (1+(1/4))×22
= ((4+1)/4 )×22
= (5/4)×22
= (5/22 )×22
= 5×2(2-2)
= 5×20
= 5×1 = 5
(ii)(2-1 ×4-1 )÷2-2
= [(1/2)×(1/4)] ÷(1/4)
= (1/2×1/22 )÷ 1/4
= 1/23 ÷1/4
= (1/8)×(4)
= 1/2
(iii) (1/2)-2 +(1/3)-2 +(1/4)-2
= (2-1 )-2 +(3-1 )-2 +(4-1 )-2
= 2(-1×-2) +3(-1×-2) +4(-1×-2)
= 22 +32 +42
= 4+9+16
=29
(iv) (3-1 +4-1 +5-1 )0
= 1
(v) {(-2/3)-2 }2 = (-2/3)-2×2
= (-2/3)-4
= (-3/2)4
= 81/16
4. Evaluate:
(i) (8-1 ×53 )/2-4
(ii) (5-1 ×2-2 )×6-1
Solution:
(i) (8-1 ×53 )/2-4
=
= 2×125 = 250
(ii) (5-1 ×2-2 )×6-1
= (1/10)×1/6
= 1/60
5. Find the value of m
for which 5
m
÷ 5-3
= 55
Solution:
5 m ÷ 5-3 = 55
5(m-(-3) ) = 55
5m+3 =55
Comparing exponents on both sides, we get
m+3 = 5
m = 5-3
m = 2
6. Evaluate:
(i)
(ii)
Solution:
(i)
= 3-4
= -1
(ii)
=
=
=
= 512/125
7. Simplify the following:
(i)
(ii)
Solution:
(i)
=
=
(ii)
=
=
=
=
= 1×1×3125
= 3125
1. Express the following numbers in standard form.
(i) 0.0000000000085
(ii) 0.00000000000942
(iii) 6020000000000000
(iv) 0.00000000837
(v) 31860000000
Solution:
(i) 0.0000000000085 = 0.0000000000085×(1012 /1012 ) = 8.5 ×10-12
(ii) 0.00000000000942 = 0.00000000000942×(1012 /1012 ) = 9.42×10-12
(iii) 6020000000000000 = 6020000000000000×(1015 /1015 ) = 6.02×1015
(iv) 0.00000000837 = 0.00000000837×(109 /109 ) = 8.37×10-9
(v) 31860000000 = 31860000000×(1010 /1010 ) = 3.186×1010
2. Express the following numbers in the usual form.
(i) 3.02×10-6
(ii) 4.5×104
(iii) 3×10-8
(iv) 1.0001×109
(v) 5.8×1012
(vi) 3.61492×106
Solution:
(i) 3.02× 10-6 = 3.02/106 = 0 .00000302
(ii) 4.5× 104 = 4.5× 10000 = 45000
(iii) 3× 10-8 = 3/108 = 0.00000003
(iv) 1.0001× 109 = 1000100000
(v) 5.8× 1012 = 5.8× 1000000000000 = 5800000000000
(vi) 3.61492× 106 = 3.61492× 1000000 = 3614920
3. Express the number appearing in the following statements in standard form.
(i) 1 micron is equal to 1/1000000 m.
(ii) Charge of an electron is 0.000, 000, 000, 000, 000, 000, 16 coulomb.
(iii) Size of bacteria is 0.0000005 m
(iv) Size of a plant cell is 0.00001275 m
(v) Thickness of a thick paper is 0.07 mm
Solution:
(i) 1 micron = 1/1000000
= 1/106
= 1×10-6
(ii) Charge of an electron is 0.00000000000000000016 coulombs
= 0.00000000000000000016× 1019 /1019
= 1.6× 10-19 coulomb
(iii) Size of bacteria = 0.0000005
= 5/10000000 = 5/107 = 5×10-7 m
(iv) Size of a plant cell is 0.00001275 m
= 0.00001275×105 /105
= 1.275×10-5 m
(v) Thickness of a thick paper = 0.07 mm
0.07 mm = 7/100 mm = 7/102
= 7×10-2
mm
4. In a stack, there are 5 books, each having a thickness of 20 mm and 5 paper sheets, each having a thickness of 0.016 mm. What is the total thickness of the stack?
Solution:
Thickness of one book = 20 mm
Thickness of 5 books = 20×5 = 100 mm
Thickness of one paper = 0.016 mm
Thickness of 5 papers = 0.016×5 = 0.08 mm
Total thickness of a stack = 100+0.08 = 100.08 mm
= 100.08×102 /102 mm
mm