A relation connects two sets using ordered pairs, while a function is a special relation where each input has exactly one unique output.
Multiply radian measure by 180/π. For example, π radians = 180°. This conversion is essential for solving trigonometric equations.
Argand plane represents complex numbers graphically with the x-axis as real part and y-axis as imaginary part. Example: a+ib corresponds to (a,b).
If one event occurs in m ways and another in n ways, then both occur in m×n ways. This forms the basis of permutations.
It states (x+y)^n = Σ(nCr) x^(n-r) y^r for r=0 to n, where nCr are binomial coefficients from Pascal's triangle.
The (r+1)th term is T_(r+1) = nCr x^(n-r) y^r. For middle term(s), use n/2 or (n/2)+1 based on n even/odd.
Circle with center (h,k) and radius r: (x-h)² + (y-k)² = r². For center at origin: x² + y² = r².
A degenerate conic occurs when the plane passes through the vertex of the cone, producing a point, a line, or intersecting lines.
The derivative at a point equals the slope of the tangent line to the curve at that point. It measures instantaneous rate of change.
Mean deviation uses absolute deviations from mean, while standard deviation uses squared deviations, giving more weight to outliers.
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A relation connects two sets using ordered pairs, while a function is a special relation where each input has exactly one unique output.
Multiply radian measure by 180/π. For example, π radians = 180°. This conversion is essential for solving trigonometric equations.
Argand plane represents complex numbers graphically with the x-axis as real part and y-axis as imaginary part. Example: a+ib corresponds to (a,b).
If one event occurs in m ways and another in n ways, then both occur in m×n ways. This forms the basis of permutations.
It states (x+y)^n = Σ(nCr) x^(n-r) y^r for r=0 to n, where nCr are binomial coefficients from Pascal's triangle.
The (r+1)th term is T_(r+1) = nCr x^(n-r) y^r. For middle term(s), use n/2 or (n/2)+1 based on n even/odd.
Circle with center (h,k) and radius r: (x-h)² + (y-k)² = r². For center at origin: x² + y² = r².
A degenerate conic occurs when the plane passes through the vertex of the cone, producing a point, a line, or intersecting lines.
The derivative at a point equals the slope of the tangent line to the curve at that point. It measures instantaneous rate of change.
Mean deviation uses absolute deviations from mean, while standard deviation uses squared deviations, giving more weight to outliers.