Grade 10 Math Formula

Slope Formula

m = (y2 - y1) / (x2 - x1); calculates the steepness (slope) of a line given two points.

Slope-Intercept Form

y = mx + b; represents a linear relation, where m is the slope and b is the y-intercept.

Standard Form of a Linear Equation

Ax + By + C = 0; represents a linear relation, often used for systems of equations.

Distance Formula

d = √((x2 - x1)² + (y2 - y1)²); calculates the distance between two points.

Midpoint Formula

M = ((x1 + x2)/2, (y1 + y2)/2); calculates the midpoint of a line segment.

Standard Form of a Quadratic Equation

y = ax² + bx + c; the graph is a parabola, determining the direction based on a.

Vertex Form of a Quadratic Equation

y = a(x - h)² + k; easily identifies the vertex of the parabola.

Factored Form of a Quadratic Equation

y = a(x - r)(x - s); easily identifies the x-intercepts of the parabola.

Quadratic Formula

x = (-b ± √(b² - 4ac)) / (2a); solves for the roots of a quadratic equation.

Discriminant

Δ = b² - 4ac; determines the number of real roots of a quadratic equation.

Pythagorean Theorem

a² + b² = c²; relates the lengths of sides of a right-angled triangle.

Sine Ratio (SOH)

sin(θ) = Opposite / Hypotenuse; relates angle to side lengths in a right triangle.

Cosine Ratio (CAH)

cos(θ) = Adjacent / Hypotenuse; relates angle to side lengths in a right triangle.

Tangent Ratio (TOA)

tan(θ) = Opposite / Adjacent; relates angle to side lengths in a right triangle.

Area of a Rectangle/Square

A = l × w; calculates area based on length and width.

Area of a Triangle

A = (1/2)bh; calculates area of any triangle.

Area of a Circle

A = πr²; calculates area of a circle based on its radius.

Circumference of a Circle

C = 2πr or C = πd; calculates the distance around a circle.

Volume of a Prism/Cylinder

V = A_base × h; calculates volume based on area of base and height.

Volume of a Pyramid/Cone

V = (1/3) A_base × h; calculates volume based on area of base and height.

Volume of a Sphere

V = (4/3)πr³; calculates the volume of a sphere.

Surface Area of a Rectangular Prism

SA = 2(lw + lh + wh); calculates the total surface area of a rectangular prism.

Surface Area of a Cylinder

SA = 2πr² + 2πrh; calculates the total surface area of a cylinder.

Surface Area of a Sphere

SA = 4πr²; calculates the total surface area of a sphere.

Vertex Form of a Quadratic Equation

y = a(x - h)² + k;

easily identifies the vertex of the parabola.

Difference of Squares Formula a2−b2=(a−b)(a+b)a2−b2=(a−b)(a+b)

a² - b² = (a - b)(a + b); used for factoring binomials where two perfect squares are subtracted.

Discriminant

\Delta = b^2 - 4ac; determines the number of real roots of a quadratic equation.