Mathematics is an essential subject that plays an important role in a student’s school life. Class 9 is a crucial year in a student’s education as it sets the foundation for higher-level mathematics. In this article, will provide All important maths formulas for class 9 students that will help them to solving the problems also with these formulas student will be understand the mathematical concepts of class 9.
Geometry Formulas for Class 9
Geometry formulas are mathematical equations that are used to calculate length, area, volume, angles, and other properties of geometric shapes. There are diffrent types of geometry formulas for class 9 that are used to calculate different parameters of geometric shapes. Here are some common geometry formulas include:
Geometry Shapes Formulas for Class 9
| Geometric Formulas | Area | Perimeter |
|---|---|---|
| Rectangle | A= l × w, Where l= length and w= width | P = 2 × (l+w ), Where l= length and W= width |
| Triangle | A = (1⁄2) × b × h, Where b= base and h= height | P = a + b + c, Where, a,b,c are the sides of the triangle |
| Trapezoid | A = (1⁄2) × h × (b1+ b2), Where, b1, b2 are length of parallel sides of trapezoid. | P = a + b + c + da,b,c,d are the sides of the trapezoid |
| Parallelogram | A = b × h, Where b= base and h= height | P = 2 (a+b)a and b are the sides of the parallelogram |
| Circle | A = π r2 Where, r= radius of cicle | C = 2 π r |
| Rectangular Prism | V = l × w × h, Where l = length, w=width and h=height | SA = 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height, respectively. |
Algebra Formulas for Class 9
Algebra formulas are the base of higher level algebraic studies. It involves understanding the algebraic expressions and solving the equations expressions. By learning the algebra formulas, students are enabled to solve equations and find their solutions. Apart from mathematics, these formulas are most important to develop skills applicable in Many different professions and disciplines like medicine, engineering, chemistry, budgeting and so on. Here are some important algebra formulas for class 9.
| 1. (a + b)2 = a2 + 2ab + b2 |
| 2. (a − b)2 = a2 − 2ab + b2 |
| 3. (a + b)(a – b) = a2 – b2 |
| 4. (x + a)(x + b) = x2 + (a + b)x + ab |
| 5. (x + a)(x – b) = x2 + (a – b)x – ab |
| 6. (x – a)(x + b) = x2 + (b – a)x – ab |
| 7. (x–a)(x–b) = x2 – (a+b)x + ab |
| 8. (a + b)3 = a3 + b3 + 3ab(a + b) |
| 9. (a – b)3 = a3 – b3 – 3ab(a – b) |
| 10. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz |
| 11. (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz |
| 12. (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz |
| 13. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz |
| 14. x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz − xz) |
| 15. x2 + y2 = 12[(x + y)2 + (x – y)2] |
| 16. (x + a)(x + b)(x + c) = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc |
| 17. x3 + y3 = (x + y)(x2 – xy + y2) |
| 18. x3 – y3 = (x – y)(x2 + xy + y2) |
| 19. x2 + y2 + z2 − xy – yz –zx = 1/2[(x − y)2 + (y − z)2 + (z − x)2] |
Surface Area and Volume Formulas for Class 9
Surface area and volume formulas are used to solve the surface area as well as volume of different dimensional geometric shapes. Here are some important surface area and volume formulas for class 9.
| Shape | Surface Area | Volume |
|---|---|---|
| Cube | 6a2a = side of the cube | a3 |
| Cone | πr(l+r) where, r=radius of basel=slant height Also, l2=h2+r2, where h is the height of cone | (1/3)πr2h |
| Cylinder | 2πr(h+r)r = radius of circular basesh = height of cylinder | πr2h |
| Cuboid | 2(lb + bh +lh)l= length, b=breadth, h=height | lbh |
| Sphere | 4πr2 | (4/3)πr3 |
Also check: Important Maths Formulas for Class 8
Heron’s Formula for class 9
Heron’s formula, also known as Hero’s formula, is used to calculate the area of a triangle when the lengths of all three sides are known. The formula is named after Hero of Alexandria, a Greek mathematician who first described it in his book “Metrica” around 60 AD.
The formula for the area (A) of a triangle with sides of length a, b, and c is:
A = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle, given by:
s = (a + b + c)/2
So, to use Heron’s formula to find the area of a triangle with sides of length a, b, and c, you would first calculate the semi-perimeter s, and then plug in the values of s, a, b, and c into the formula for the area.
For example, if a triangle has sides of length 6 cm, 8 cm, and 10 cm, we can use Heron’s formula to find its area as follows:
s = (6 + 8 + 10)/2 = 12
A = √(12(12-6)(12-8)(12-10)) = √(12 × 6 × 4 × 2) = 24 cm^2
Therefore, the area of triangle is 24 square centimeters.
Also Check: Integral Formulas
Polynomial Formula for Class 9
Here is a brief list of important polynomial formulas that are applicable in finding the roots of polynomial equations.
| S.NO | Polynomial Formulas |
|---|---|
| 1 | (x + y)2 = x2 + 2xy + y2 |
| 2 | (x – y)2 = x2 – 2xy + y2 |
| 3 | (x + y) (x – y) = x2 – y2 |
| 4 | (x + a) (x + b) = x2 + (a + b) x + ab. |
| 5 | (x + a) (x – b) = x2 + (a – b) x – ab. |
| 6 | (x – a) (x + b) = x2 + (b – a) x – ab. |
| 7 | (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx |
| 8 | (x + y)3 = x3 + y3 + 3xy(x + y) |
| 9 | (x – y)3 = x3 – y3 – 3xy(x – y) |
| 10 | x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx) |
Statistics formula for class 9
Here are some important statistics formulas for Class 9:
Mean = (sum of data values) / (number of data values)
Median:
For an odd number : Median = (n + 1) / 2, here n is the number of data values.
For an even number of data values : Median = (n / 2)th value + [(n / 2) + 1]th value / 2
Mode: The mode of a set of data is the value that occurs most frequently. If no value occurs more than once, the set has no mode.
Range = Largest value – Smallest value Variance = [(sum of squared deviations from the mean) / (number of data values – 1)]
Standard Deviation = √Variance
These are some of the important statistics formulas that you will learn in Class 9. As you continue to study statistics, you will learn more advanced techniques for analyzing and interpreting data.
Probability Formula for Class 9
Probability = (number of favorable outcomes) / (number of possible outcomes)
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