List of Math Formulas for Grade 10
Here are some important math formulas for 10th-grade students:
1. Properties of Logarithms
The following properties of logarithms can be used to simplify expressions and solve equations involving logarithms:
log(ab) = log a + log b
log(a/b) = log a – log b
log ab = b log a
2. Trigonometric Identities
The following trigonometric identities are important for solving trigonometry problems:
sin2 x + cos2 x = 1
1 + tan2 x = sec2 x
1 + cot2 x = sec2 x
3. Sum and Difference Formulas
The sum and difference formulas can be used to find the sine, cosine, or tangent of the sum or difference of two angles:
sin(a ± b) = sin a cos b ± cos a sin b
cos(a ± b) = cos a cos b ∓ sin a sin b
tan(a ± b) = (tan a ± tan b)/(1 ∓ tan a tan b)
4. Binomial Theorem
The Binomial Theorem can be used to expand the power of a binomial expression:
(a + b)n = C(n, 0)an bo + C(n, 1)a(n-1) b1 + … + C(n, r)a(n-r) br + … + C(n, n)a0 bn
5. Permutations and Combinations
The formulas for permutations and combinations are important for counting problems:
Permutations: P(n, r) = n!/(n-r)!
Combinations: C(n, r) = n!/[(n-r)! r!]
6. Quadratic Formula
The roots of a quadratic equation ax2 + bx + c = 0 can be found using the quadratic formula:
x = (-b ± sqrt(b2 – 4ac))/2a
7. Distance Formula
The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by the formula:
d = sqrt((x2 – x1)2 + (y2 – y1)2)
These formulas cover a range of topics such as algebra, trigonometry, probability, and geometry, and are essential for 10th-grade students to master as they prepare for more advanced math courses.