8th Grade Algebra

  1. What is a variable in algebra? A variable in algebra is a letter or symbol that represents an unknown quantity.
  2. What is an equation? An equation is a statement that two expressions are equal.
  3. What is the order of operations in algebra? The order of operations in algebra is the set of rules used to evaluate expressions: parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right).
  4. What is a term in algebra? A term in algebra is a number, variable, or product of a number and variables.
  5. What is a coefficient? A coefficient is the numerical factor of a term.
  6. What is a constant in algebra? A constant in algebra is a value that does not change.
  7. What is a solution to an equation? A solution to an equation is a value that makes the equation true when substituted for the variable.
  8. What is a system of equations? A system of equations is a set of two or more equations with the same variables.
  9. What is a linear equation? A linear equation is an equation of a straight line, in which the variables have a degree of one.
  10. What is slope? Slope is the measure of the steepness of a line.
  11. What is the slope-intercept form of a linear equation? The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
  12. What is the point-slope form of a linear equation? The point-slope form of a linear equation is y – y1 = m(x – x1), where (x1, y1) is a point on the line and m is the slope.
  13. What is a function? A function is a relation between two sets in which each input value is associated with a unique output value.
  14. What is a domain in a function? The domain of a function is the set of input values for which the function is defined.
  15. What is a range in a function? The range of a function is the set of output values that the function produces.
  16. What is an inverse function? An inverse function is a function that undoes another function.
  17. What is a quadratic function? A quadratic function is a function of the form y = ax^2 + bx + c, where a, b, and c are constants and a is not equal to zero.
  18. What is a parabola? A parabola is the graph of a quadratic function, which is a symmetric curve that opens either upwards or downwards.
  19. What is a vertex of a parabola? The vertex of a parabola is the point at which the parabola changes direction.
  20. What is the axis of symmetry of a parabola? The axis of symmetry of a parabola is the line that passes through the vertex and divides the parabola into two symmetric halves.
  21. What is the quadratic formula? The quadratic formula is x = (-b ± sqrt(b^2 – 4ac)) / 2a, which is used to find the solutions to a quadratic equation.
  22. What is a radical? A radical is a symbol used to indicate the square root of a number or expression.
  23. What is a rational exponent? A rational exponent is an exponent that is a fraction, where the numerator represents the power and the denominator represents the root.
  24. What is a polynomial? A polynomial is a sum of terms, where each term consists of a coefficient and a variable raised to a power.
  1. What is factoring in algebra? Factoring in algebra is the process of writing a polynomial as a product of simpler polynomials or factors. This allows us to simplify expressions, solve equations, and find zeros of functions. Factoring involves finding common factors, using the distributive property, and factoring by grouping or using special formulas. It is an important skill in algebra and is used in many applications, such as finding the roots of quadratic equations, simplifying fractions, and solving word problems.
  2. What is a quadratic equation? A quadratic equation is an equation of degree 2 that can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.
  3. What is the discriminant of a quadratic equation? The discriminant of a quadratic equation is the expression b^2 – 4ac that appears under the square root in the quadratic formula. It helps determine the number and nature of the solutions of the equation.
  4. What is a complex number? A complex number is a number of the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.
  5. What is the conjugate of a complex number? The conjugate of a complex number a + bi is the complex number a – bi. It is obtained by changing the sign of the imaginary part.
  6. What is a system of linear inequalities? A system of linear inequalities is a set of two or more linear inequalities with the same variables. Its solution is the set of all points that satisfy all the inequalities simultaneously.
  7. What is an absolute value? The absolute value of a number is its distance from zero on the number line. It is always non-negative and is denoted by vertical bars, such as |x|.
  8. What is a logarithm? A logarithm is the inverse function of exponential functions. It is denoted by log and has a base, such as log base 10 or log base e (natural logarithm).
  9. What is a function notation? Function notation is a way of writing a function using a symbol, such as f(x), where f is the name of the function and x is the independent variable.
  10. What is a vertical line test? The vertical line test is a method used to determine if a graph represents a function. It involves drawing a vertical line through the graph and checking if it intersects the graph at more than one point.
  11. What is a polynomial function? A polynomial function is a function of the form f(x) = a_n x^n + a_{n-1} x^{n-1} + … + a_1 x + a_0, where a_n, a_{n-1}, …, a_1, a_0 are constants and n is a non-negative integer. It is a type of function that can have multiple roots and is used in many areas of mathematics and science.
  12. What is a slope-intercept form? Slope-intercept form is a way of writing the equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.
  13. What is the point-slope form of the equation of a line? The point-slope form of the equation of a line is y – y1 = m(x – x1), where m is the slope and (x1, y1) is a point on the line.
  14. What is a system of equations? A system of equations is a set of two or more equations with the same variables. Its solution is the set of all values of the variables that satisfy all the equations simultaneously.
  15. What is a matrix? A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is often used to represent systems of linear equations and transformations in mathematics.
  16. What is a determinant? A determinant is a scalar value associated with a square matrix. It is used to determine if the matrix is invertible and to find the solutions of systems of linear equations.
  17. What is a rational expression? A rational expression is an expression of the form p(x)/q(x), where p(x) and q(x) are polynomials and q(x) ≠ 0.
  18. What is a radical expression? A radical expression is an expression of the form √x or x^(1/2), where x is a non-negative real number.
  19. What is the Pythagorean Theorem? The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
  20. What is the FOIL method? The FOIL method is a mnemonic device used to multiply two binomials. It stands for First, Outer, Inner, Last, and involves multiplying the first terms, outer terms, inner terms, and last terms, and then adding the results.
  21. What is a logarithmic function? A logarithmic function is a function of the form f(x) = log_a(x), where a is the base of the logarithm and x is a positive real number. It is the inverse function of an exponential function and is often used to represent growth and decay.
  22. What is a radical equation? A radical equation is an equation that contains a radical expression, such as √x, and involves solving for the value of the variable.
  23. What is a quadratic function? A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0. It is a type of polynomial function and has a parabolic graph.
  24. What is a domain of a function? The domain of a function is the set of all values of the independent variable for which the function is defined. It is often represented using interval notation.
  25. What is a range of a function? The range of a function is the set of all values of the dependent variable that the function can produce. It is often represented using interval notation.
  26. What is a linear inequality? A linear inequality is an inequality that can be written in the form ax + by > c or ax + by < c, where a, b, and c are constants and x and y are variables.
  27. What is a compound inequality? A compound inequality is an inequality that consists of two or more inequalities joined by the words “and” or “or”.
  28. What is a simultaneous equation? A simultaneous equation is a set of two or more equations with the same variables. Its solution is the set of all values of the variables that satisfy all the equations simultaneously.
  29. What is an absolute value equation? An absolute value equation is an equation that contains an absolute value expression, such as |x|, and involves solving for the value of the variable.
  30. What is a rational function? A rational function is a function of the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomials and q(x) ≠ 0. It can have vertical asymptotes and holes in its graph.
  31. What is a linear programming problem? A linear programming problem is a type of optimization problem that involves maximizing or minimizing a linear objective function subject to linear constraints. It is often used in economics and operations research.
  32. What is a function notation? Function notation is a way of representing a function using symbols, such as f(x), where f is the name of the function and x is the independent variable.
  33. What is the inverse of a function? The inverse of a function is a function that undoes the action of the original function. It is often denoted as f^(-1)(x).
  34. What is the slope of a line? The slope of a line is a measure of its steepness and is given by the formula m = (y2 – y1)/(x2 – x1), where (x1, y1) and (x2, y2) are two points on the line.
  35. What is the midpoint formula? The midpoint formula is a formula used to find the midpoint of a line segment between two points. It is given by the formula [(x1 + x2)/2, (y1 + y2)/2].
  36. What is the distance formula? The distance formula is a formula used to find the distance between two points in a coordinate plane. It is given by the formula √[(x2 – x1)^2 + (y2 – y1)^2].
  37. What is a function table? A function table is a table that shows the input and output values of a function. It is often used to graph functions and find patterns.
  38. What is the standard form of a linear equation? The standard form of a linear equation is ax + by = c, where a, b, and c are constants and a and b are not both zero.
  39. What is a direct variation? A direct variation is a relationship between two variables where one variable is a constant multiple of the other, such as y = kx.
  40. What is an inverse variation? An inverse variation is a relationship between two variables where the product of the variables is a constant, such as xy = k.
  41. What is a quadratic formula? The quadratic formula is a formula used to find the solutions of a quadratic equation of the form ax^2 + bx + c = 0. It is given by x = (-b ± √(b^2 – 4ac))/2a.
  42. What is a system of equations? A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all the equations simultaneously.
  43. What is a coefficient? A coefficient is a number that multiplies a variable in a term, such as 3x or -2y.
  44. What is a linear function? A linear function is a function of the form f(x) = mx + b, where m and b are constants and x is the independent variable. It has a straight-line graph.
  45. What is the point-slope form of a linear equation? The point-slope form of a linear equation is y – y1 = m(x – x1), where m is the slope and (x1, y1) is a point on the line.
  46. What is the slope-intercept form of a linear equation? The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
  47. What is a radical expression? A radical expression is an expression that contains a radical symbol, such as √x. It represents the square root of a number or expression.
  48. What is a perfect square? A perfect square is a number that is the square of an integer, such as 4, 9, or 16.
  49. What is a quadratic equation? A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. It can have one or two real solutions or two complex solutions.
  50. What is a function? A function is a relation between two sets of numbers, where each input corresponds to exactly one output. It can be represented by a graph, an equation, or a table.
  51. What is a monomial? A monomial is a polynomial with only one term, such as 3x or -2y^2.
  52. What is a piecewise function? A piecewise function is a function that is defined by multiple equations, with each equation applying to a different interval or “piece” of the domain.
  53. What is a matrix? A matrix is a rectangular array of numbers or variables arranged in rows and columns. It is used to represent systems of linear equations and perform various operations in algebra.
  54. What is a complex number? A complex number is a number of the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1).
  55. What is a polynomial function? A polynomial function is a function of the form f(x) = anxn + an-1xn-1 + … + a1x + a0, where n is a non-negative integer and a0, a1, …, an are coefficients.
  56. What is a rational function? A rational function is a function of the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomials and q(x) is not zero.
  57. What is a quadratic inequality? A quadratic inequality is an inequality that can be written in the form ax^2 + bx + c > 0 or ax^2 + bx + c < 0, where a, b, and c are constants and a ≠ 0.
  58. What is a linear inequality? A linear inequality is an inequality that can be written in the form ax + by > c or ax + by < c, where a, b, and c are constants and a and b are not both zero.
  59. What is a greatest common factor (GCF)? The greatest common factor (GCF) of two or more numbers or expressions is the largest number or expression that divides them evenly.
  60. What is a least common multiple (LCM)? The least common multiple (LCM) of two or more numbers or expressions is the smallest number or expression that is a multiple of all of them.
  61. What is a synthetic division? Synthetic division is a method used to divide a polynomial by a linear factor of the form x – a, where a is a constant. It is a shortcut method for long division.