Algebra and Coordinate Geometry Rules

Flashcards covering algebra exponent rules, binomial expansions, square root approximations, and coordinate geometry formulas from the review sheet.

$$x + x$$

$$2x$$

$$x \times x$$

$$x^2$$

$$x^a \times x^b$$

$$x^{a+b}$$

$$\frac{x^a}{x^b}$$

$$x^{a-b}$$

$$x^{\frac{1}{2}}$$

$$\sqrt{x}$$

$$x^{\frac{1}{3}}$$

$$\sqrt[3]{x}$$

$$x^{-1}$$

$$\frac{1}{x}$$

$$\frac{1}{x^{-1}}$$

$$x$$

$$(x^a)^b$$

$$x^{ab}$$

$$(xy)^a$$

$$x^a y^a$$

$$(x^a y^b)^c$$

$$x^{ac} y^{bc}$$

$$(x^a \sqrt{y})^b$$

$$x^{ab} y^{\frac{b}{2}}$$

$$x^a + x^b$$

Leave as is

$$x^a - x^b$$

Leave as is

$$x^a + y^a$$

Leave as is

$$x^a y^b$$

Leave as is

$$\frac{x^a}{y^b}$$

Leave as is

$$(x+y)^2$$

$$x^2 + 2xy + y^2$$

$$(x-y)^2$$

$$x^2 - 2xy + y^2$$

$$(2x-y)^2$$

$$4x^2 - 4xy + y^2$$

$$(x-2y)^2$$

$$x^2 - 4xy + 4y^2$$

$$(x^2 + y^2)^2$$

$$x^4 + 2x^2 y^2 + y^4$$

$$(x^2 - y^2)^2$$

$$x^4 - 2x^2 y^2 + y^4$$

$$(x^2 y^2)^2$$

$$x^4 y^4$$

$$(3x^2)^2$$

$$9x^4$$

$$(3 + x^2)^2$$

$$9 + 6x^2 + x^4$$

$$(2x^2)^3$$

$$8x^6$$

$$(x^2 y^3)^3$$

$$x^6 y^9$$

$$\sqrt{2}$$

$$\approx 1.4$$

$$\sqrt{3}$$

$$\approx 1.7$$

$$\sqrt{5}$$

$$\approx 2.2$$

Slope / Gradient Formula ($m$)

$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\Delta y}{\Delta x}$$

Slope of Parallel Lines

$m_1 = m_2$ (same slope)

Slope of Perpendicular Lines

$m_1 = -\frac{1}{m_2}$ (negative reciprocal)

Vertical Lines

Equation $x = a$ (slope is undefined)

Horizontal Lines

Equation $y = b$ (slope $m = 0$)

$$x\text{-intercept}$$

Let $y = 0$ then solve for $x$

$$y\text{-intercept}$$

Let $x = 0$ then solve for $y$

Quadratic Formula

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Distance Formula (between 2 points)

$$D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

Value of $y = x^2$ when $x = 4$

$$y = 16$$

Value of $y = x^2$ when $x = -4$

$$y = 16$$

Value of $y = -x^2$ when $x = 4$

$$y = -16$$

Value of $y = -x^2$ when $x = -4$

$$y = -16$$