Algebra 1 Formulas for CST Preparation

Questions and Answers

What is the standard form of a linear equation?

Ax + By + C = 0 (correct)

D = R * T

y = mx + b

y - y1 = m(x - x1)

What formula is used to complete the square?

C = (B/2)^2

What does D = R * T represent?

Distance = (Rate)(Time)

What is the slope-intercept form of a line?

y = mx + b Signup and view all the answers

What is the point-slope form of a line?

y - y1 = m(x - x1) Signup and view all the answers

How is the slope calculated when given two points?

m = (y2 - y1)/(x2 - x1) Signup and view all the answers

What is the Work Formula?

1/Time 1 + 1/ Time 2 = 1/ Total Time Signup and view all the answers

What is the standard form of a quadratic equation?

Ax^2 + Bx + C = 0 Signup and view all the answers

When lines are parallel, what do they have?

The same slope Signup and view all the answers

When lines are perpendicular, they have what kind of slopes?

Reciprocal slopes with opposite signs Signup and view all the answers

What defines a function?

Passes the Vertical Line test Signup and view all the answers

What does not define a function?

Does not pass the vertical line test Signup and view all the answers

What does 'm' represent in the context of lines?

Slope Signup and view all the answers

What does 'b' stand for in linear equations?

Y intercept Signup and view all the answers

What is a coordinate pair?

(x,y) Signup and view all the answers

What is slope defined as?

Rise over run Signup and view all the answers

The Quadratic Formula is derived from what?

Completing the square Signup and view all the answers

What is a like term?

Same variable and same exponent Signup and view all the answers

What happens when you multiply variables with exponents?

You add the exponents Signup and view all the answers

What are the steps for completing the square?

<ol> <li>Make sure A term is '1'. 2. Move C term to the right. 3. Complete square on the left with (b/2)^2 and add to both sides. 4. Factor the left, simplify the right. 5. Take the square root of both sides. 6. Solve for X.</li> </ol> Signup and view all the answers

Study Notes

Linear Equations and Forms

Standard Form: (Ax + By + C = 0) represents linear equations.
Slope-Intercept Form: (y = mx + b) is used for easy graphing; (m) indicates slope, and (b) indicates the y-intercept.
Point-Slope Form: (y - y_1 = m(x - x_1)) applies when a point and slope are given.

Functions and Slope

Definition of a Function: Passes the vertical line test; each (x) only corresponds to one (y).
Not a Function: Fails the vertical line test; more than one (y) value for a single (x).

Slope Calculations

Slope Formula: (m = \frac{y_2 - y_1}{x_2 - x_1}) determines slope between two points.
Slope Interpretation: Slope is defined as rise over run; the change in (y) over the change in (x).

Quadratic Functions

Standard Form of Quadratic Equation: Expressed as (Ax^2 + Bx + C = 0).
Quadratic Formula: Derived from completing the square on the standard form of a quadratic.

Completing the Square

Method for Completing the Square:
- Ensure (A) term equals 1; if not, divide.
- Move (C) term to the right side.
- Complete the square using ((\frac{b}{2})^2) and add this to both sides.
- Factor the left side and simplify the right side.
- Take the square root of both sides and solve for (X).

Distance and Rate

Distance Formula: (D = R \times T) calculates distance based on rate and time.

Work Formula

Work Equation: (\frac{1}{\text{Time 1}} + \frac{1}{\text{Time 2}} = \frac{1}{\text{Total Time}}) calculates combined work rates of two individuals.

Relationships between Lines

Parallel Lines: Have the same slope (e.g., ( \frac{1}{2} ) and ( \frac{1}{2} )).
Perpendicular Lines: Have slopes that are reciprocals with opposite signs (e.g., (-\frac{5}{4}) and (\frac{4}{5})).

Exponents and Like Terms

Like Terms: Terms that share the same variable and exponent.
Multiplying Variables: When multiplying, add the exponents of the variables.

Coordinate Pairs

Definition: A coordinate pair is represented as ((x,y)).
Slope Interpretation: Slope is articulated as the rise over run, or change in (y) over change in (x).

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Description

This quiz covers essential formulas from Algebra 1 that are crucial for understanding linear equations and graphing. Each card presents a formula along with its definition to assist in mastering the material for CST assessments. Perfect for quick revision and exam preparation!