AK STAR Math Grade 9 flashcards
AK STAR Math Grade 9 · Build recall with a focused review session.
32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Irrational number
- A real number that cannot be written as a ratio of two integers; its decimal expansion is infinite and non-repeating, such as pi or the square root of 2.
- Scientific notation
- A number expressed as a product of a factor between 1 and 10 and a power of 10, useful for very large or small values.
- Product of powers rule
- When multiplying expressions with the same base, keep the base and add the exponents, so a^m times a^n equals a^(m+n).
- Rationalizing a denominator
- Rewriting a fraction so no radical remains in the denominator, usually by multiplying numerator and denominator by the same radical or conjugate.
- Unit rate
- A rate in which the second quantity is one unit, found by dividing the first quantity by the second, such as miles per one hour.
- Slope formula
- The slope of a line through two points equals the change in y divided by the change in x: m = (y2 - y1)/(x2 - x1).
- Slope-intercept form
- The equation y = mx + b, where m is the slope and b is the y-intercept, used to graph and compare linear relationships.
- Quadratic formula
- For ax^2 + bx + c = 0 with a not zero, x = (-b plus or minus the square root of b^2 - 4ac) divided by 2a.
- Discriminant
- The expression b^2 - 4ac in the quadratic formula; its sign tells whether the equation has two, one, or no real solutions.
- System of equations
- Two or more equations with the same variables; a solution makes every equation true at the same time and is found by graphing, substitution, or elimination.
- Zero product property
- If a product of factors equals zero, then at least one factor must equal zero, allowing factored quadratic equations to be solved.
- Difference of squares
- A polynomial of the form a^2 - b^2, which factors as the product of (a + b) and (a - b).
- Inequality solution
- A value or set of values that makes an inequality true; multiplying or dividing by a negative number reverses the inequality symbol.
- Function notation
- The notation f(x) names the output of function f for input x, so f(3) means the output when the input equals 3.
- Domain and range
- The domain is the set of all allowed input values of a function; the range is the set of all resulting output values.
- Rate of change
- The amount one quantity changes relative to another, often the slope of a graph, calculated as change in output divided by change in input.
- Linear function
- A function whose graph is a straight line and whose equation can be written as y = mx + b, showing a constant rate of change.
- Exponential function
- A function of the form y = a times b^x with b positive and not equal to 1, showing repeated multiplication by a constant factor.
- Vertical line test
- A rule that a graph represents a function only if no vertical line crosses the graph at more than one point.
- Transformations of functions
- Shifts, stretches, compressions, and reflections that change a parent function's graph; adding outside the function moves it vertically.
- Pythagorean theorem
- In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: a^2 + b^2 = c^2.
- Distance formula
- The distance between points (x1, y1) and (x2, y2) equals the square root of (x2 - x1)^2 plus (y2 - y1)^2.
- Midpoint formula
- The midpoint of a segment with endpoints (x1, y1) and (x2, y2) is ((x1 + x2)/2, (y1 + y2)/2).
- Congruent figures
- Figures that have exactly the same size and shape; corresponding sides and angles are equal, and one can be mapped onto the other by rigid motions.
- Similar figures
- Figures with the same shape but not necessarily the same size; corresponding angles are equal and corresponding side lengths are proportional.
- Volume of a cylinder
- The volume of a cylinder equals the area of its circular base times its height, V = pi times r^2 times h.
- Parallel line slopes
- Parallel lines lie in the same plane and never intersect; their slopes are equal, while perpendicular lines have slopes that multiply to negative one.
- Line of best fit
- A straight line that models the trend in a scatter plot, chosen to be as close as possible to the data points and used for prediction.
- Correlation coefficient
- A number from negative one to one that measures the strength and direction of a linear relationship between two variables.
- Two-way table
- A table that organizes data about two categorical variables by showing counts for each combination of categories in rows and columns.
- Mean absolute deviation
- The average distance between each data value and the mean, found by averaging the absolute differences; it measures spread.
- Sample space
- The set of all possible outcomes of a probability experiment, such as heads and tails for one coin toss.