Parametric: x and y defined by a parameter. | Implicit: x and y related by an equation.

Vectors: Have magnitude and direction. | Scalars: Have only magnitude.

Dot Product: Results in a scalar. | Cross Product: Results in a vector (in 3D).

Circle: Constant radius in all directions. | Ellipse: Varying radius (major and minor axes).

Ellipse: Sum of distances to foci is constant. | Hyperbola: Difference of distances to foci is constant.

Velocity: Vector with magnitude and direction. | Speed: Scalar, magnitude of velocity.

Position Vector: Indicates location. | Velocity Vector: Indicates rate of change of position.

Matrix Addition: Element-wise addition, commutative. | Matrix Multiplication: Rows by columns, not commutative.

Line: x and y change linearly with t. | Circle: x and y change sinusoidally with t.

Explicit: y is isolated on one side (y = f(x)). | Implicit: x and y are intertwined in an equation.

1. Substitute t=a into x(t) to find x-coordinate. 2. Substitute t=a into y(t) to find y-coordinate. 3. Position is (x(a), y(a)).

1. Find the derivative of x(t) with respect to t. 2. Find the derivative of y(t) with respect to t. 3. v(t) = <x'(t), y'(t)>.

1. Evaluate x'(a) and y'(a). 2. Speed = sqrt((x'(a))^2 + (y'(a))^2).

1. Find the derivative of x'(t) with respect to t. 2. Find the derivative of y'(t) with respect to t. 3. a(t) = <x''(t), y''(t)>.

1. Check for x^2 and y^2 terms. 2. If both are present and have the same coefficient, it's a circle. 3. If both are present and have different coefficients but the same sign, it's an ellipse. 4. If one is present, it's a parabola. 5. If both are present with opposite signs, it's a hyperbola.

1. Ensure A and B have the same dimensions. 2. Add corresponding elements: (A+B)[i,j] = A[i,j] + B[i,j].

1. For matrix [[a, b], [c, d]], multiply ad and bc. 2. Subtract: determinant = ad - bc.

1. Let x = rcos(t). 2. Let y = rsin(t).

1. Add the x-components: a + c. 2. Add the y-components: b + d. 3. Result: u + v = <a+c, b+d>.

1. Complete the square for both x and y terms. 2. Rewrite the equation in the form (x-h)^2 + (y-k)^2 = r^2.

$x = r \cos(t)$, $y = r \sin(t)$

$||v|| = \sqrt{a^2 + b^2}$

$v(t) = r'(t) = <\frac{dx}{dt}, \frac{dy}{dt}>$

$Speed = ||v(t)|| = \sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2}$

$a(t) = v'(t) = r''(t) = <\frac{d^2x}{dt^2}, \frac{d^2y}{dt^2}>$

$det([[a, b], [c, d]]) = ad - bc$

$(x-h)^2 + (y-k)^2 = r^2$

$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$

$\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$ or $\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1$

$x = f(t), y = g(t)$