Math Vocabulary

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Across
  1. 4. Function An exponential function in mathematics is a function of the form 𝑓 ( 𝑥 ) = 𝑎 ⋅ 𝑏^𝑥. 𝑎 is a constant (called the coefficient), 𝑏 is the base of the exponential function, which is a positive real number, and 𝑏 ≠ 1, and 𝑥 is the exponent, which can be any real number.
  2. 5. A specific case or instance that disproves a general statement or proposition. It demonstrates that the statement is not universally true. For example, if a statement claims that "all prime numbers are odd," finding the prime number 2, which is even, serves as a counterexample, showing that the original statement is false. Some approaches to this are starting from known facts, axioms, or previously proven statements and using logical steps to arrive directly at the statement to be proved, assuming the opposite of the statement to be proved, and then showing that this assumption leads to a contradiction, or proving that the contrapositive of the statement is true. For a statement of the form "If P, then Q," its contrapositive is "If not Q, then not P."
  3. 7. Root A number value that, when multiplied by itself, gives the original number. If 𝑦 is the square root of 𝑥, then that means 𝑦^2 = 𝑥
  4. 9. An algebraic expression that consists of exactly two terms and are combined with either a plus sign or a minus sign. Examples: a+b, a-b, 3x + 2, a^2 - 4b, 5 - 7x
  5. 10. The absence of contradictions within a set of statements, axioms, or a logical system. For example, if x+y=2 and 2x−y=1, then this system of equalities is __________ because the solution of 𝑥 = 1, 𝑦 = 1 satisfies both equations.
  6. 11. A process where a quantity increases at a rate proportional to its current value. This is commonly expressed with the equation: 𝑁 ( 𝑡 ) = 𝑁 0 𝑒^𝑘𝑡. N(t) is the quantity at time 𝑡, 𝑁 0 is the initial quantity at time 𝑡 = 0, 𝑘 is the growth constant, a positive real number that represents the rate of growth, and 𝑒 is the base of the natural logarithm.
  7. 12. Variation A linear relationship between two variables where one variable is a constant multiple of the other. If one variable changes, the other changes proportionally. This relationship can be expressed using the equation 𝑦 = 𝑘𝑥.
  8. 14. If no set of values for the variables that satisfies all the equations simultaneously. For example, if x+y=2 and x+y=3, the system of equalities is ____________ because there are no values of 𝑥 and 𝑦 that can satisfy both equations at the same time.
  9. 16. An algebraic expression that consists of only one term. Examples: 7, 3x, -2a^2, 5xy^3, 4x^2n^3
  10. 17. A line that separates different regions in a coordinate plane, often in the context of inequalities or systems of linear equations. For a linear equation in two variables, like 𝑦 = 𝑚 𝑥 + 𝑏, the boundary line represents all the solutions of that equation. It divides the plane into two halves.
  11. 19. Not divisible by 2. If 1=2×0+1, then one is not an even number. If −5=2×(−3)+1, than -5 is not an even number.
  12. 20. The set of all possible x-values (inputs) that can be used in the equation of the line. In the linear equation 𝑦 = 𝑚 𝑥 + 𝑏, the domain can be all real numbers unless specified otherwise, meaning any real number can be plugged in for 𝑥. The domain defines the range of inputs for which the line exists.
  13. 21. Divisible by 2. If 2=2×1, then 2 is not odd. If −4=2×(−2), then -4 is not odd.
  14. 23. The distance of a number from zero on the number line, regardless of direction. If 𝑥 is positive or zero, ∣ 𝑥 ∣ = 𝑥. If 𝑥 is negative, ∣ 𝑥 ∣ = − 𝑥 (which is positive).
  15. 24. An ordered list of numbers, objects, or other mathematical elements arranged in a specific order, following a particular rule or pattern. A sequence in which the difference between consecutive terms is constant. For example, the sequence 2,5,8,11,14 has a common difference of 3. The sequence 3,9,27,81 has a common ratio of 3.
Down
  1. 1. Function A function that maps complex numbers to complex numbers. if 𝑧 = 𝑥 + 𝑖𝑦 is a complex number (where 𝑥 and 𝑦 are real numbers, and 𝑖 is the imaginary unit with 𝑖^2 = − 1), then a complex function 𝑓 is a rule that assigns each complex number 𝑧 in its domain to a complex number 𝑤 in its codomain, often expressed as 𝑤 = 𝑓 ( 𝑧 ).
  2. 2. A special number that can be calculated from a square matrix and provides important information about the matrix.For a 2x2 matrix, 𝐴 = ( 𝑎, 𝑏, 𝑐, 𝑑 ) The determinant of matrix 𝐴 is given by the formula det ⁡ ( 𝐴 ) = 𝑎 𝑑 − 𝑏 𝑐
  3. 3. An expression consisting of variables (also known as indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Examples: 2x^2 + 3y + 4z + 5, 5x^3 + 2xy + 7q^2 - 4y + 1
  4. 6. An operation that changes a figure or function in some way. Translation: Shifting a shape or graph without changing its size or orientation. Rotation: Turning a shape around a fixed point by a certain angle. Reflection: Flipping a shape over a line (axis) to create a mirror image. Scaling: Changing the size of a shape, either enlarging or shrinking it, while maintaining its proportions.
  5. 8. The set of y-values (outputs) that the line can take. In the equation of a line like 𝑦 = 𝑚 𝑥 + 𝑏, the range is determined by the slope and y-intercept, indicating all possible heights (y-values) the line can reach across its domain (x-values).
  6. 13. A statistical measure that describes the extent to which two variables change together. +1 indicates a perfect positive correlation (as one variable increases, the other also increases). -1 indicates a perfect negative correlation (as one variable increases, the other decreases). 0 indicates no correlation (the variables do not have a linear relationship).
  7. 15. A fixed value that does not change.In an algebraic expression, a constant is a term that does not contain any variables. For example, in the expression 3𝑥 + 5, the number 5 is a constant term because it does not change regardless of the value of 𝑥.
  8. 18. A process where a quantity increases at a rate proportional to its current value. This is commonly expressed with the equation: 𝑁 ( 𝑡 ) = 𝑁 0 𝑒^𝑘𝑡. N(t) is the quantity at time 𝑡, 𝑁 0 is the initial quantity at time 𝑡 = 0, 𝑘 is the growth constant, a positive real number that represents the rate of growth, and 𝑒 is the base of the natural logarithm.
  9. 22. A numerical or constant quantity placed before and multiplying a variable in an algebraic expression. in the polynomial 2𝑥^2 + 3𝑥 + 4, the coefficients are 2, 3, and 4. Here, 2 is the coefficient of 𝑥^2, 3 is the coefficient of 𝑥, and 4 is the constant term (which can also be considered a coefficient of 𝑥^0).