NCERT Class 7 Maths Formulas and Examples
Class 7 NCERT Maths
100 Important Questions with Answers
1. Integers
1. Find: (-8) + 15
Answer: 7
2. Find: (-12) - (-7)
Answer: -5
3. Find: (-6) × (-9)
Answer: 54
4. Find: 72 ÷ (-8)
Answer: -9
5. Simplify: (-5) + (-8) + 12
Answer: -1
6. Find: 18 - [(-4) + 7]
Answer: 15
7. What is the additive inverse of -17?
Answer: 17
8. What is the multiplicative identity?
Answer: 1
2. Fractions and Decimals
9. Add: 2/3 + 1/6
Answer: 5/6
10. Subtract: 7/8 - 3/8
Answer: 1/2
11. Multiply: 3/5 × 10/9
Answer: 2/3
12. Divide: 4/5 ÷ 2/5
Answer: 2
13. Convert 0.75 into a fraction.
Answer: 3/4
14. Add: 3.45 + 2.7
Answer: 6.15
15. Multiply: 2.5 × 0.4
Answer: 1
16. Divide: 6.4 ÷ 0.8
Answer: 8
3. Data Handling
17. Find the mean of 5, 7, 9, 11, 13.
Answer: 9
18. Find the range of 4, 9, 12, 18, 20.
Answer: 16
19. A coin is tossed once. What is the probability of getting a head?
Answer: 1/2
20. A die is thrown once. What is the probability of getting 4?
Answer: 1/6
21. What is the probability of getting an even number on a die?
Answer: 1/2
22. Find the mean of 10, 20, 30, 40.
Answer: 25
23. Find the range of 15, 22, 8, 30, 17.
Answer: 22
24. What is the probability of getting a number greater than 4 on a die?
Answer: 1/3
4. Simple Equations
25. Solve: x + 8 = 20
Answer: x = 12
26. Solve: x - 7 = 15
Answer: x = 22
27. Solve: 5x = 45
Answer: x = 9
28. Solve: x/4 = 7
Answer: x = 28
29. Solve: 3x + 5 = 20
Answer: x = 5
30. Solve: 2x - 7 = 13
Answer: x = 10
31. Solve: 4x + 3 = 19
Answer: x = 4
32. The sum of a number and 9 is 25. Find the number.
Answer: 16
5. Lines and Angles
33. What is the complement of 35°?
Answer: 55°
34. What is the supplement of 75°?
Answer: 105°
35. Two angles of a linear pair are 65° and x°. Find x.
Answer: 115°
36. If one vertically opposite angle is 80°, find the other.
Answer: 80°
37. Two complementary angles are x° and 40°. Find x.
Answer: 50°
38. Two supplementary angles are 120° and x°. Find x.
Answer: 60°
39. If two parallel lines are cut by a transversal, what can be said about corresponding angles?
Answer: They are equal.
40. If one angle formed by two intersecting lines is 125°, what is its vertically opposite angle?
Answer: 125°
6. The Triangle and Its Properties
41. Find the third angle of a triangle having angles 60° and 70°.
Answer: 50°
42. Two angles of a triangle are 90° and 35°. Find the third angle.
Answer: 55°
43. What is the sum of the angles of a triangle?
Answer: 180°
44. Find the exterior angle if the two opposite interior angles are 50° and 70°.
Answer: 120°
45. Can 3 cm, 4 cm and 8 cm form a triangle?
Answer: No, because 3 + 4 < 8.
46. Can 5 cm, 6 cm and 8 cm form a triangle?
Answer: Yes.
47. What are the angles of an equilateral triangle?
Answer: 60°, 60°, 60°
48. A triangle has sides 5, 5 and 8 cm. What type of triangle is it based on its sides?
Answer: Isosceles triangle.
7. Congruence of Triangles
49. What does congruent mean?
Answer: Having the same shape and the same size.
50. Name the four important congruence criteria.
Answer: SSS, SAS, ASA and RHS.
51. Two triangles have all three corresponding sides equal. Which criterion applies?
Answer: SSS.
52. Two right triangles have equal hypotenuse and one corresponding side equal. Which criterion applies?
Answer: RHS.
53. If △ABC ≅ △PQR, which side corresponds to AB?
Answer: PQ.
54. If two triangles are congruent and one has a side of 7 cm, what is the corresponding side of the other triangle?
Answer: 7 cm.
8. Comparing Quantities
55. Find 25% of 200.
Answer: 50
56. Convert 3/5 into a percentage.
Answer: 60%
57. Convert 40% into a fraction.
Answer: 2/5
58. A shirt costs ₹500 and is sold for ₹600. Find the profit.
Answer: ₹100
59. For Question 58, find the profit percentage.
Answer: 20%
60. An article bought for ₹800 is sold for ₹720. Find the loss.
Answer: ₹80
61. Find the loss percentage in Question 60.
Answer: 10%
62. Find the simple interest on ₹2,000 at 5% per annum for 2 years.
Answer: ₹200
63. Find the amount in Question 62.
Answer: ₹2,200
64. A number increases from 100 to 120. Find the percentage increase.
Answer: 20%
9. Rational Numbers
65. Add: 1/2 + 3/4
Answer: 5/4
66. Subtract: 5/6 - 1/3
Answer: 1/2
67. Multiply: 2/3 × 3/5
Answer: 2/5
68. Divide: 3/4 ÷ 1/2
Answer: 3/2
69. What is the additive inverse of 5/7?
Answer: -5/7
70. What is the multiplicative inverse of -3/8?
Answer: -8/3
71. Is 0 a rational number?
Answer: Yes, 0 = 0/1.
72. Compare 2/3 and 3/4.
Answer: 3/4 > 2/3.
10. Practical Geometry
73. What instrument is generally used to draw circles and arcs?
Answer: Compass.
74. What instrument is used to measure angles?
Answer: Protractor.
75. What is the perpendicular bisector of a line segment?
Answer: A line that passes through its midpoint and is perpendicular to it.
76. Which information is sufficient to construct a triangle using SSS?
Answer: The lengths of all three sides.
77. Which criterion uses two sides and the included angle?
Answer: SAS.
78. Which criterion is used for two right triangles when their hypotenuse and one corresponding side are equal?
Answer: RHS.
11. Perimeter and Area
79. Find the perimeter of a rectangle with length 12 cm and breadth 5 cm.
Answer: 34 cm
80. Find the area of the same rectangle.
Answer: 60 cm²
81. Find the perimeter of a square of side 8 cm.
Answer: 32 cm
82. Find the area of a square of side 8 cm.
Answer: 64 cm²
83. Find the area of a triangle with base 10 cm and height 6 cm.
Answer: 30 cm²
84. Find the area of a parallelogram with base 15 cm and height 4 cm.
Answer: 60 cm²
85. A rectangle has area 72 cm² and length 9 cm. Find its breadth.
Answer: 8 cm
86. A square has perimeter 36 cm. Find its side.
Answer: 9 cm
12. Algebraic Expressions
87. Simplify: 3x + 5x
Answer: 8x
88. Simplify: 7a - 3a + 2a
Answer: 6a
89. Expand: 3(x + 4)
Answer: 3x + 12
90. Expand: 5(2x - 3)
Answer: 10x - 15
91. What are the terms in 5x + 3y - 7?
Answer: 5x, 3y, -7.
92. Are 4x and 7x like terms?
Answer: Yes.
13. Exponents and Powers
93. Find: 2⁵
Answer: 32
94. Find: 3⁴
Answer: 81
95. Simplify: 2³ × 2⁴
Answer: 2⁷ = 128
96. Simplify: 5⁶ ÷ 5²
Answer: 5⁴ = 625
97. Simplify: (2³)²
Answer: 2⁶ = 64
14. Symmetry
98. How many lines of symmetry does a square have?
Answer: 4.
99. How many lines of symmetry does an equilateral triangle have?
Answer: 3.
100. What is the order of rotational symmetry of a square?
Answer: 4.
Important Formula Sheet
Mean = Sum of observations ÷ Number of observations
Probability = Favourable outcomes ÷ Total outcomes
Area of triangle = ½ × base × height
Area of rectangle = length × breadth
Perimeter of rectangle = 2(length + breadth)
Area of square = side²
Perimeter of square = 4 × side
Simple Interest = (Principal × Rate × Time) ÷ 100
Profit = Selling Price - Cost Price
Loss = Cost Price - Selling Price
Profit % = (Profit ÷ Cost Price) × 100
Loss % = (Loss ÷ Cost Price) × 100
Sum of angles of a triangle = 180°
Linear pair = 180°
Complementary angles = 90°
Supplementary angles = 180°
aᵐ × aⁿ = aᵐ⁺ⁿ
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
(aᵐ)ⁿ = aᵐⁿ
F + V - E = 2
Comments
Post a Comment