FAST Math Grade 8 flashcards
FAST Math Grade 8 · 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.
- Rational number
- A number that can be written as a fraction a/b where a and b are integers and b is not zero. Its decimal form terminates or repeats.
- Irrational number
- A real number that cannot be written as a fraction of two integers. Its decimal form is non-terminating and non-repeating, such as the square root of 2 or pi.
- Scientific notation
- A way to write very large or very small numbers as N times 10 to a power, where N is at least 1 and less than 10.
- Negative exponent rule
- For any nonzero base a and positive integer n, a raised to the negative n equals 1 divided by a raised to the n.
- Cube root of negative number
- The cube root of a negative number is negative because a negative number multiplied by itself three times gives a negative product. For example, the cube root of negative 27 is negative 3.
- Slope formula
- The slope of a line through two points equals the change in y divided by the change in x: (y2 minus y1) divided by (x2 minus x1).
- Perpendicular line slopes
- Two nonvertical lines are perpendicular exactly when their slopes are negative reciprocals, so the product of the slopes equals negative one.
- Inequality reversal rule
- When you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality symbol to keep it true.
- System with no solution
- A system of two linear equations has no solution when the lines are parallel: the equations have the same slope but different y-intercepts.
- Square of a binomial
- The square of (a plus b) equals a squared plus 2ab plus b squared. The middle term is essential; the result is not a squared plus b squared.
- Point-slope form
- An equation of a line written as y minus y1 equals m times (x minus x1), where m is the slope and the point (x1, y1) lies on the line.
- Function
- A rule that assigns exactly one output value to each input value. On a graph, it passes the vertical line test: no vertical line meets the graph twice.
- Rate of change
- The change in the output divided by the change in the input over an interval. For a linear function it equals the slope and is constant.
- Linear function
- A function of the form y equals mx plus b whose graph is a straight line. Its table shows constant first differences and its rate of change is constant.
- Exponential function
- A function of the form y equals a times b to the x power, where a is the initial value and b is the growth or decay factor. Successive outputs have a constant ratio.
- Initial value of a function
- The output when the input is zero, written f of zero. On a graph it is the y-intercept; in a table it is the value paired with input zero.
- Comparing functions
- To compare functions given as equations, tables, graphs, or descriptions, compare their rates of change (slopes) and their initial values (y-intercepts).
- Rigid transformation
- A translation, reflection, or rotation. It changes a figure's position or orientation but preserves all side lengths and angle measures, producing a congruent figure.
- Dilation
- A transformation that enlarges or reduces a figure by a scale factor about a center point. Angles stay equal and lengths multiply by the scale factor, producing similar figures.
- Pythagorean theorem
- In a right triangle, the sum of the squares of the two leg lengths equals the square of the hypotenuse length: a squared plus b squared equals c squared.
- Converse of Pythagorean theorem
- If a triangle's side lengths satisfy a squared plus b squared equals c squared, where c is the longest side, then the triangle is a right triangle.
- Distance formula
- The distance between two points equals the square root of the sum of the squared differences of their x-coordinates and y-coordinates. It comes from the Pythagorean theorem.
- Volume of a cone
- The volume of a cone equals one third times pi times the radius squared times the height. Three such cones fill a cylinder with the same base and height.
- Similar figures
- Figures with equal corresponding angle measures and proportional corresponding side lengths. The scale factor equals the ratio of any pair of corresponding lengths.
- Scatter plot association
- A description of paired data by direction (positive or negative), form (linear or nonlinear), and strength (strong or weak), based on how closely points follow a pattern.
- Line of best fit
- A line drawn through a scatter plot that comes closest to the overall pattern of points and can be used to estimate or predict values.
- Two-way table
- A table that displays counts of two categorical variables, with rows for one variable's categories and columns for the other, plus totals.
- Conditional relative frequency
- A ratio found by dividing a cell count by its row or column total. It gives the proportion with one trait among those in a particular category.
- Probability of independent events
- When two events do not affect each other, the probability that both occur equals the product of their individual probabilities.
- Interquartile range
- The difference between the third quartile and the first quartile. It measures the spread of the middle half of the data and is not affected by outliers.
- Break-even point
- The value of the variable at which two cost or income expressions are equal. It is found by setting the expressions equal and solving the resulting equation.
- Counterexample
- A single case that makes a general statement false. One counterexample disproves a claim, but confirming examples never prove a claim is always true.