MATH 1 EOC - MUST KNOWS

A comprehensive set of practice flashcards covering the 'Must Knows' for the Math 1 End of Course exam, including linear and exponential functions, quadratics, systems, and key formulas.

What is the formula for calculating the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$?

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

In the linear equation $y = mx + b$, what do $m$ and $b$ represent?

$m$ represents the slope and $b$ represents the $y$-intercept.

What characterizes the growth or decay of an exponential function $y = a(b)^x$?

Growth occurs when $b > 1$ and decay occurs when $0 < b < 1$. house

What are the exponential growth and decay formulas involving a rate $r$?

Growth: $y = a(1 + r)^x$; Decay: $y = a(1 - r)^x$

How can you distinguish between a linear and an exponential table?

Linear tables have a constant addition pattern ($a + d$, $a + 2d$), while exponential tables have a constant multiplication pattern or ratio ($a \times b$, $a \times b^2$).

What is the explicit formula for an arithmetic sequence?

$$a_n = a_1 + (n - 1)d$$

What is the explicit formula for a geometric sequence?

$$a_n = a_1 \times r^{(n-1)}$$

When solving an equation, what is the result if the variables cancel out and you are left with a false statement like $3 = 5$?

No solution

When solving an equation, what is the result if the variables cancel out and you are left with a true statement like $4 = 4$?

Infinite solutions

What is the definition of a function in terms of inputs and outputs?

A relation where one input has exactly one output; on a table, there are no repeated $x$ values with different $y$ values.

What test is used on a graph to determine if it is a function?

Vertical Line Test

What is the rule for flipping the inequality sign when solving an inequality?

Flip the sign if you multiply or divide by a negative number.

How are the symbols $<$ and $>$ represented on a number line graph?

With an open circle

How are the symbols $\text{≤}$ and $\text{≥}$ represented on a number line graph?

With a closed circle

What are the three possible types of solutions for a system of equations?

One solution (lines intersect), No solution (lines are parallel), and Infinite solutions (same line).

What are the three common methods for solving systems of equations?

Graphing, substitution, and elimination

In a quadratic function $y = ax^2 + bx + c$, how does the value of $a$ determine the direction of the parabola?

If $a > 0$, the parabola opens up; if $a < 0$, the parabola opens down.

What is another term for the $x$-intercepts of a quadratic function?

Zeros

How is the Interquartile Range (IQR) calculated in statistics?

$$IQR = Q_3 - Q_1$$

What does a larger spread in data indicate regarding variability?

More spread means more variability.

What is the Pythagorean Theorem, and when can it be used?

$a^2 + b^2 = c^2$; it can only be used for right triangles.

What are the exponent rules for multiplication, division, and power to a power?

Multiply: add exponents ($x^m \times x^n = x^{m+n}$); Divide: subtract exponents ($x^m / x^n = x^{m-n}$); Power to power: multiply exponents ($(x^m)^n = x^{mn}$).

What is a key test tip for identifying functions from a list of ordered pairs?

Watch for repeated $x$ values; if an $x$ repeats with a different $y$, it is not a function.