## 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 a^{b} = b log a

### 2. Trigonometric Identities

The following trigonometric identities are important for solving trigonometry problems:

sin^{2} x + cos^{2} x = 1

1 + tan^{2} x = sec^{2} x

1 + cot^{2} x = sec^{2} 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)a^{n} b^{o} + C(n, 1)a^{(n-1)} b^{1} + … + C(n, r)a^{(n-r)} b^{r} + … + C(n, n)a^{0} b^{n}

### 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 ax^{2} + bx + c = 0 can be found using the quadratic formula:

x = (-b ± sqrt(b^{2} – 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.