Module 01 Mathematics 100 important sentences for Revision

1. Basic Arithmetic

1. Mathematics is the science of numbers and quantities.
2. Addition combines two or more quantities into one.
3. Subtraction finds the difference between two numbers.
4. Multiplication is repeated addition of the same number.
5. Division splits a number into equal parts.
6. The order of operations follows BODMAS rule.
7. BODMAS means Brackets, Orders, Division, Multiplication, Addition, Subtraction.
8. A fraction shows a part of a whole.
9. The numerator is the number above the fraction line.
10. Below the fraction line the number is called denominator.

2. Factions and Decimals

11. Like fractions have the same denominator.
12. Unlike fractions have different denominators.
13. To add fractions, make denominators the same.
14. Improper fractions have numerators larger than denominators.
15. Mixed fractions combine whole numbers and fractions.
16. Decimal numbers are fractions with denominators as powers of ten.
17. To convert a fraction to a decimal, divide numerator by denominator.
18. To convert a decimal to percentage, multiply by 100.
19. 0.75 equals ¾ or 75%.
20. 1/5 equals 0.2 or 20%.

3. Ratios and Proportions

21. A ratio compares two quantities by division.
22. A proportion shows two ratios are equal.
23. Ratios can be simplified like fractions.
24. Direct proportion means both quantities increase together.
25. Inverse proportion means one quantity increases, the other decreases.
26. Example: speed and time are inversely proportional.
27. Example: distance and time are directly proportional.
28. Cross multiplication is used to solve proportions.
29. Percentage = (part ÷ whole) × 100.
30. Ratio 2:3 means for every 2 of one, there are 3 of another.

4. Powers and Roots

31. A power or index shows repeated multiplication.
32. .
33. Any number to power zero equals one.
34. A square is a number multiplied by itself.
35. A number multiplied by itself twice is called cube.
36. Square root is the number that produces a given number when multiplied by itself.
37. Cube root gives a number whose cube equals the original number.
38. .
39. .
40. Indices follow rules of addition and subtraction in powers.

5. Algebra Basics

41. Algebra uses symbols to represent unknown quantities.
42. A variable is a letter that represents a number.
43. A term is a combination of numbers and variables.
44. A coefficient is the number multiplied by a variable.
45. Like terms have the same variable and power.
46. Unlike terms have different variables or powers.
47. Equation is a statement showing two expressions are equal.
48. To solve an equation, isolate the variable.
49. Linear equations have variables raised to power one.
50. Simultaneous equations have two or more unknowns solved together.

 6. Algebraic Operations

51. To expand brackets, multiply each term inside by the outside term.
52. To factorize, take out common terms or use identities.
53. .
54. .
55. .
56. Substitution means replacing variables with actual numbers.
57. Formula rearrangement changes the subject of formula.
58. Transposition moves terms across the equal sign by changing signs.
59. Check solutions by substituting values back in the equation.
60. Quadratic equations have variables squared (power of 2).

7. Geometry – Angles and Triangles

61. knowledge of shapes, sizes, and properties of space is geometry.
62. A line is straight with no thickness.
63. An angle is formed when two lines meet.
64. Angles are measured in degrees (°).
65. Right angle equals 90 degrees.
66. Straight line equals 180 degrees.
67. Full circle equals 360 degrees.
68. Acute angle is less than 90 degrees.
69. The Obtuse angle is greater than 90 but less than 180 degrees.
70. Complementary angles add up to 90 degrees.

8. Triangles and Circles

71. The sum of angles in a triangle is always 180 degrees.
72. An equilateral triangle has all sides equal.
73. An isosceles triangle has two sides equal.
74. A scalene triangle has all sides unequal.
75. Pythagoras theorem: .
76. It applies only to right-angled triangles.
77. Hypotenuse is the side opposite the right angle.
78. Circumference of circle = .
79. Area of circle = .
80. Diameter equals twice the radius.

9. Areas and Volumes

81. The Area of rectangle = length × width.
82. The Area of triangle = ½ × base × height.
83. The Area of parallelogram = base × height.
84. Formula of The Area of trapezium = ½ × (sum of parallel sides) × height.
85. The Volume of cube = side³.
86. The Volume of cuboid = length × width × height.
87. The Volume of cylinder = πr²h.
88. The Volume of cone = ⅓πr²h.
89. The Volume of sphere = 4/3πr³.
90. The Surface area of sphere = 4πr².

10. Trigonometry and Statistics

91. Trigonometry relates angles to sides in a triangle.
92. Sine = opposite ÷ hypotenuse.
93. Cosine = adjacent ÷ hypotenuse.
94. Tangent = opposite ÷ adjacent.
95. .
96. The inverse of sine gives angle from ratio.
97. Graphs visually represent data or equations.
98. Formula of Mean = sum of all values ÷ number of values.
99. Median is the middle value in ordered data.
100. Mode is the value that appears most often.