TExES Math 4-8 (115) flashcards
TExES Math 4-8 (115) · Build recall with a focused review session.
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- 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 ratio of two integers; its decimal form neither terminates nor repeats, such as π or √2.
- Least common multiple
- The smallest positive number that is a multiple of two or more given numbers; it is found by using the greatest power of each prime factor.
- Greatest common factor
- The largest number that divides evenly into two or more given numbers; it is found by multiplying the shared prime factors.
- Percent change
- The ratio of the amount of change to the original amount, expressed as a percent; calculated as (new minus old) divided by old times 100%.
- Order of operations
- A standard sequence for evaluating expressions: grouping symbols, exponents and roots, multiplication and division left to right, then addition and subtraction left to right.
- Slope
- The constant rate of change of a line, calculated as the change in y divided by the change in x between two points.
- Slope-intercept form
- The equation y = mx + b, where m is the slope and b is the y-intercept of the line.
- Quadratic formula
- For ax² + bx + c = 0, the solutions are x equals negative b plus or minus the square root of b² minus 4ac, all divided by 2a.
- Discriminant
- The expression b² − 4ac in the quadratic formula; its sign indicates whether the quadratic has two, one, or no real solutions.
- Arithmetic sequence
- A sequence with a constant difference between consecutive terms; the nth term is a₁ + (n − 1)d.
- Exponential function
- A function of the form y = ab^x, where b is positive and not 1; it models repeated multiplication such as growth or decay.
- Pythagorean theorem
- In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: a² + b² = c².
- Similar figures
- Figures with equal corresponding angles and proportional corresponding side lengths; scale factor k changes lengths by k and areas by k².
- Midpoint formula
- The midpoint of a segment with endpoints (x₁,y₁) and (x₂,y₂) is ((x₁+x₂)/2, (y₁+y₂)/2), which lies exactly halfway between the endpoints.
- Complementary angles
- Two angles whose measures add to exactly 90 degrees; they do not need to be adjacent or part of the same figure.
- Surface area
- The total area of all the faces or surfaces of a three-dimensional figure, measured in square units.
- Dilation
- A transformation that enlarges or reduces a figure by a scale factor from a fixed center point; it preserves shape but not necessarily size.
- Independent events
- Events in which the occurrence of one does not affect the probability of the other; for such events, P(A and B) equals P(A) times P(B).
- Complement rule
- The probability that an event does not occur equals 1 minus the probability that it does occur: P(not E) = 1 − P(E).
- Interquartile range
- The difference between the third quartile and the first quartile; it measures the spread of the middle 50 percent of a data set.
- Correlation coefficient
- A number between −1 and 1 that describes the strength and direction of a linear association between two variables.
- Normal distribution
- A symmetric, bell-shaped distribution; about 68 percent of values lie within one standard deviation of the mean, 95 percent within two, and 99.7 percent within three.
- Mathematical modeling
- The process of representing a real-world situation with mathematics, solving the resulting problem, and interpreting and checking the solution in context.
- Counterexample
- A single case that makes a general mathematical statement false; it is sufficient to disprove a conjecture.
- Multiple representations
- Describing the same mathematical idea using words, tables, graphs, equations, or diagrams to deepen understanding and support problem solving.
- Deductive reasoning
- Reasoning from accepted statements such as definitions and previously proven theorems to a logically certain conclusion.
- Zone of proximal development
- Vygotsky's term for the range of tasks a learner can complete with guidance but not yet independently; scaffolding is provided within this zone.
- Formative assessment
- Assessment used during instruction to monitor student understanding and adjust teaching; examples include exit tickets, questioning, and quick quizzes.
- Concrete-representational-abstract
- An instructional sequence that introduces a concept with manipulatives, then drawings or diagrams, then symbolic notation.
- Summative assessment
- Assessment administered at the end of a unit or course to evaluate achievement against learning goals, such as a final exam or major project.
- Differentiation
- Adjusting content, process, or product in response to student readiness, interests, and learning profiles so all students can access learning.