Questions and Answers
What is the rational number that can be written as a fraction with an integer in the numerator and the denominator?
What is the value of r in the equation r^n = a, where n ≥ 2?
What is the value of a^(1/n), where a > 0 and n ≥ 2?
What is the radical symbol that indicates the nth root of a?
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What is a surd?
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What is the property of simplifying surds that states √(a) × √(b) = √(ab)?
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What is the purpose of rationalising the denominator?
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What is the law of exponents that states a^m × a^n = a^(m+n)?
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What is the formula for exponential growth or decay?
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What is the purpose of rationalizing denominators?
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What is the formula for a^(-m)?
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What is the purpose of the zero-product property in solving quadratic surd equations?
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What is the formula for a^(m/n)?
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What is the first step in identifying the variables in an exponential growth or decay problem?
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What is the first step in solving surd equations?
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What is the set of natural numbers represented by?
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What is the purpose of converting surds to exponential notation?
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What is the formula for exponential growth or decay?
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What is the formula for population growth?
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What is the purpose of completing the square?
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What is the purpose of checking solutions in surd equations?
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What is the formula for compound interest?
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What is the quadratic formula used for?
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What is the formula for the quadratic formula?
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What is the first step in solving quadratic equations by completing the square?
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What is the definition of a^0?
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What is the definition of a^(-n)?
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What is the definition of √(a)?
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What is the formula to determine the roots of a quadratic equation?
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What type of roots does a quadratic equation have when b^2 - 4ac > 0?
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What is the first step in solving a quadratic equation by substitution?
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What is the purpose of the discriminant in a quadratic equation?
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What type of roots does a quadratic equation have when b^2 - 4ac < 0?
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What is the last step in finding the quadratic equation given the roots?
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When is the discriminant of a quadratic equation equal to zero?
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What is the purpose of the substitution method in solving quadratic equations?
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What happens when the discriminant is a perfect square?
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What is the second step in finding the quadratic equation given the roots?
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What is the nature of the roots of a quadratic equation if the discriminant Δ is less than 0?
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What is the formula for the discriminant Δ of a quadratic equation in standard form?
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What is the first step in solving a quadratic inequality?
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What is the purpose of a table of signs in solving a quadratic inequality?
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What is the graphical representation of a quadratic inequality?
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What is the purpose of solving simultaneous linear equations?
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What method is commonly used to solve systems of simultaneous equations with linear and non-linear equations?
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What is required to solve for the values of n unknown variables?
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What is the main difference between solving quadratic equations and quadratic inequalities?
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What is the purpose of sign analysis in solving quadratic inequalities?
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What is the first step in solving a system of equations using substitution?
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What is the purpose of equating the two equations in the elimination method?
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What is the final step in solving word problems?
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What is the effect of a positive value of q on the graph of y = ax^2 + q?
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What is the effect of a negative value of a on the graph of y = ax^2 + q?
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What is the effect of a positive value of p on the graph of y = a(x + p)^2 + q?
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What is the purpose of assigning variables to unknown quantities in word problems?
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What is the role of problem-solving strategies in real-world applications?
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What is the purpose of drawing the graph of each equation on the same system of axes in solving graphically?
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What is the axis of symmetry of the graph of y = a(x + p)^2 + q?
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What is the effect of q on the graph of a quadratic function?
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What is the axis of symmetry for the graph of f(x) = a(x + p)^2 + q?
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How do you shift the graph of a quadratic function 2 units to the right?
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What is the formula for the average gradient of a curve between two points A and C?
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What is the general form of a hyperbolic function?
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What is the effect of a on the shape of the graph of a quadratic function?
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What is the range of the graph of a quadratic function when a > 0?
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What is the formula for finding the y-intercept of a quadratic function?
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What is the turning point of the graph of f(x) = a(x + p)^2 + q?
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What is the domain of the graph of a quadratic function?
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What is the effect of a positive value of q on the graph of f(x) = 1/x + q?
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What is the effect of a negative value of p on the graph of f(x) = a/(x + p) + q?
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What is the domain of the function f(x) = a/(x + p) + q?
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What is the effect of a positive value of a on the graph of f(x) = a/x + q?
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What is the horizontal asymptote of the function f(x) = a/x + q?
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What is the effect of a positive value of b on the graph of f(x) = ab^x + q?
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What is the effect of a negative value of a on the graph of f(x) = ab^x + q?
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What is the vertical asymptote of the function f(x) = a/(x + p) + q?
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What is the effect of a positive value of p on the graph of f(x) = a/(x + p) + q?
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What is the axes of symmetry intersect at in the graph of f(x) = a/(x + p) + q?
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What is the value of $a^{-rac{1}{n}}$?
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What is the property of surds that states $\sqrt[n]{a} \times \sqrt[n]{b} = \sqrt[n]{ab}$?
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What is the purpose of rationalising the denominator?
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What is the value of $a^{rac{m}{n}}$?
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What is the law of exponents that states $a^m \times a^n = a^{m+n}$?
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What is the definition of a surd?
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What is the value of $\sqrt[n]{a^m}$?
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What is the property of surds that states $\frac{\sqrt[n]{a}}{\sqrt[n]{b}} = \sqrt[n]{\frac{a}{b}}$?
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What is the purpose of identifying the variables in an exponential growth or decay problem?
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What is the result of multiplying a rational number by its reciprocal?
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What is the formula for determining the roots of a quadratic equation?
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What is the set of numbers that includes all rational and irrational numbers?
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What type of roots does a quadratic equation have when b^2 - 4ac > 0?
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What is the formula used to find the solutions of a quadratic equation?
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What is the purpose of completing the square in solving quadratic equations?
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What is the purpose of making a substitution in solving quadratic equations?
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What is the first step in finding the quadratic equation given the roots?
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What is the result of raising a number to the power of 0?
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What is the formula used to find the roots of a quadratic equation by completing the square?
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What is the discriminant of a quadratic equation?
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What is the definition of a surd?
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What happens when the discriminant is a perfect square?
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What is the purpose of the quadratic formula in solving quadratic equations?
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What is the purpose of identifying restrictions in the substitution method?
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What is the last step in finding the quadratic equation given the roots?
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What is the result of raising a number to a negative power?
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What type of roots does a quadratic equation have when the discriminant is less than 0?
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What is the second step in finding the quadratic equation given the roots?
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What is the purpose of raising both sides of the equation to the power corresponding to the root when solving surd equations?
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What is the formula for exponential growth or decay?
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What is the purpose of converting surds to exponential notation?
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What is the definition of a^0?
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What is the purpose of checking solutions in surd equations?
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What is the formula for a^(m/n)?
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What is the purpose of factorizing quadratic equations in surd form?
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What is the definition of a^(-m)?
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What is the purpose of applying exponent laws when solving surd equations?
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What is the first step in solving surd equations?
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What is the nature of the roots of a quadratic equation if Δ = 0?
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What is the purpose of the discriminant Δ in a quadratic equation?
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What is the first step in solving a quadratic inequality?
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What is the purpose of a table of signs in solving a quadratic inequality?
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What is the graphical representation of a quadratic inequality?
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What method is commonly used to solve systems of simultaneous equations with linear and non-linear equations?
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What is required to solve for the values of n unknown variables?
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What is the formula for the discriminant Δ of a quadratic equation in standard form?
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What is the purpose of solving quadratic inequalities?
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What is the main difference between solving quadratic equations and quadratic inequalities?
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What is the purpose of solving simultaneous linear equations?
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What is the effect of q on the graph of y = ax^2 + q?
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What is the first step in solving a word problem?
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What is the purpose of translating words into algebraic expressions in a word problem?
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What is the effect of a on the shape of the graph of y = ax^2 + q?
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What is the purpose of solving systems of equations?
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What is the effect of p on the graph of y = a(x + p)^2 + q?
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What is the purpose of substitution in solving quadratic equations?
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What is the purpose of elimination in solving quadratic equations?
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What is the purpose of solving quadratic equations?
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What is the effect of q on the graph of a quadratic function?
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What is the range of a quadratic function if a > 0?
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How do you find the y-intercept of a quadratic function?
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What is the formula for the turning point of a quadratic function in the form f(x) = a(x + p)^2 + q?
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What is the axis of symmetry for a quadratic function in the form f(x) = a(x + p)^2 + q?
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How do you shift a quadratic function m units to the right?
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What is the formula for the average gradient between two points on a curve?
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What is the purpose of the average gradient formula?
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What is the general form of a hyperbolic function?
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What is the purpose of finding the average gradient between two points on a curve?
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What is the effect of a change in p on the graph of y = a/(x + p) + q?
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What is the domain of the function y = a/(x + p) + q?
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What is the effect of a change in q on the graph of y = a/(x + p) + q?
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What is the range of the function y = a/(x + p) + q?
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What is the axis of symmetry of the graph of y = a/(x + p) + q?
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What is the effect of a change in a on the graph of y = a/(x + p) + q?
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What is the equation of the vertical asymptote of the graph of y = ab^x + q?
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What is the effect of a change in q on the graph of y = ab^x + q?
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What is the domain of the function y = ab^x + q?
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What is the effect of a change in b on the graph of y = ab^x + q?
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What is the value of $a^{-rac{1}{n}}$?
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What is the value of $a^{rac{m}{n}}$?
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What is the purpose of rationalising the denominator?
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What is the property of simplifying surds that states $\sqrt[n]{a} \times \sqrt[n]{b} = \sqrt[n]{ab}$?
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What is the value of $a^{rac{1}{n}}$?
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What is the definition of a surd?
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What is the purpose of the laws of exponents?
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What is the formula for $a^{rac{m}{n}}$ in terms of radicals?
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What is the purpose of exponent laws in algebra?
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What is the result of raising both sides of an equation to the power corresponding to the root in solving surd equations?
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What is the formula for exponential growth or decay?
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What is the purpose of factorizing a quadratic equation in solving surd equations?
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What is the definition of a^0?
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What is the purpose of converting surds to exponential notation in solving surd equations?
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What is the result of substituting a solution back into the original equation in solving surd equations?
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What is the purpose of isolating the surd in solving surd equations?
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What is the definition of a^(-m)?
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What is the formula for population growth?
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What is the first step in identifying the variables in an exponential growth or decay problem?
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What is the purpose of converting percentage rates into decimal form in exponential growth or decay problems?
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What is the set of real numbers represented by?
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What is the formula to determine the roots of a quadratic equation?
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What is the formula for completing the square in a quadratic equation?
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What happens when the discriminant is less than 0?
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What is the purpose of the discriminant in a quadratic equation?
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What is the purpose of the quadratic formula?
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What is the definition of a^(1/n) in exponential notation?
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What is the first step in solving a quadratic equation by substitution?
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What is the formula for a^(-m) in exponential notation?
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What type of roots does a quadratic equation have when b² - 4ac = 0?
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What is the last step in finding the quadratic equation given the roots?
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What is the purpose of rationalizing the denominator in a surd expression?
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What is the formula for the discriminant Δ of a quadratic equation in standard form?
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What is the formula for the discriminant Δ of a quadratic equation in standard form?
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What type of roots does a quadratic equation have when b² - 4ac > 0?
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What is the purpose of solving quadratic equations by completing the square?
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What is the purpose of the substitution method in solving quadratic equations?
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When is the discriminant of a quadratic equation equal to zero?
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What is the nature of the roots of a quadratic equation if the discriminant Δ is equal to 0?
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What is the purpose of solving a quadratic inequality?
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What is the formula for the discriminant Δ of a quadratic equation in standard form?
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What is the first step in solving a quadratic inequality?
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What is required to solve for the values of n unknown variables?
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What is the purpose of a table of signs in solving a quadratic inequality?
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What is the graphical representation of a quadratic inequality?
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What method is commonly used to solve systems of simultaneous equations with linear and non-linear equations?
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What is the nature of the roots of a quadratic equation if the discriminant Δ is greater than 0?
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What is the purpose of solving simultaneous linear equations?
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What is the effect of a positive q on the graph of y = a/(x + p) + q?
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What is the domain of the function y = a/(x + p) + q?
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What is the effect of a negative p on the graph of y = a/(x + p) + q?
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What is the range of the function y = a/(x + p) + q?
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What is the effect of a on the shape of the graph of y = a/(x + p) + q?
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What is the equation of the vertical asymptote of the graph of y = a/(x + p) + q?
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What is the equation of the horizontal asymptote of the graph of y = a/(x + p) + q?
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What is the effect of q on the graph of y = ab^x + q?
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What is the effect of a on the shape of the graph of y = ab^x + q?
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What is the effect of p on the graph of y = ab^(x + p) + q?
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What is the first step in solving a system of linear equations using the substitution method?
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What is the purpose of writing a set of equations when solving a word problem?
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What is the effect of the parameter q on the graph of a parabolic function of the form y = ax^2 + q?
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What is the purpose of solving simultaneous linear equations in real-world applications?
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What is the effect of the parameter a on the shape of a parabolic function of the form y = ax^2 + q?
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What is the final step in solving a system of linear equations using the substitution method?
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What is the purpose of solving quadratic equations in real-world applications?
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What is the effect of the parameter p on the graph of a parabolic function of the form y = a(x + p)^2 + q?
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What is the first step in solving a word problem?
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What is the purpose of solving systems of linear equations in real-world applications?
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What is the effect of the value of q on the graph of a quadratic function?
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What is the domain of a quadratic function?
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What is the turning point of a quadratic function in the form f(x) = a(x + p)^2 + q?
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What is the axis of symmetry of a quadratic function in the form f(x) = a(x + p)^2 + q?
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How do you shift a quadratic function 2 units to the right?
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What is the average gradient of a curve between two points?
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What is the formula for the average gradient of a curve?
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What is a hyperbolic function?
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What is the purpose of finding the equation of a parabola from the graph?
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What is the effect of a negative value of a on the shape of a quadratic function?
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What is the value of a^(1/n) when a > 0 and n ≥ 2?
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What is the property of surds that states √(a) × √(b) = √(ab)?
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What is the purpose of rationalising the denominator in a surd expression?
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What is the value of a^(-1/n) when a > 0 and n ≥ 2?
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What is the value of a^(m/n) when a > 0, m ∈ ℤ, and n ∈ ℤ, n ≠ 0?
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What is the property of rational exponents that states a^(m/n) = √(a^m)^(1/n)?
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What is the purpose of expressing surds in exponential notation?
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What is the value of a^(m/n) when a < 0, m ∈ ℤ, and n ∈ ℤ, n ≠ 0?
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What is the purpose of isolating the surd in surd equations?
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What is the formula for exponential growth or decay?
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What is the purpose of checking solutions in surd equations?
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What is the formula for a^(-m)?
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What is the purpose of rationalizing the denominator?
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What is the formula for a^(m/n)?
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What is the first step in solving quadratic surd equations?
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What is the purpose of applying the exponent laws in surd equations?
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What is the formula for population growth?
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What is the purpose of converting surds to exponential notation?
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What is the first step in solving a quadratic equation using the completing the square method?
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What is the purpose of the quadratic formula?
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What is the set of whole numbers represented by?
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What is the formula to find the final amount in an exponential growth or decay problem?
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What is the definition of a^m × a^n?
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What is the purpose of converting percentages into decimal form in exponential growth or decay problems?
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What is the formula to determine the roots of a quadratic equation?
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What is the formula to find the square root of a?
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What type of roots does a quadratic equation have when b^2 - 4ac = 0?
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What is the purpose of the discriminant in a quadratic equation?
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What is the formula to find the value of x in a quadratic equation using the quadratic formula?
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What is the purpose of the discriminant in a quadratic equation?
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What is the definition of a rational number?
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What is the first step in solving a quadratic equation by substitution?
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What happens when the discriminant is a perfect square?
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What is the nature of the roots of a quadratic equation if the discriminant Δ is less than 0?
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What is the formula for the discriminant Δ of a quadratic equation in standard form?
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When is the discriminant of a quadratic equation equal to zero?
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What is the last step in finding the quadratic equation given the roots?
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What type of roots does a quadratic equation have when b^2 - 4ac > 0?
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What is the nature of the roots of a quadratic equation if the discriminant Δ is equal to 0?
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What is the purpose of solving a quadratic inequality?
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How do you determine the critical values in a quadratic inequality?
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What is the purpose of the table of signs in solving a quadratic inequality?
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What is the formula for the discriminant Δ of a quadratic equation in standard form?
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What type of roots does a quadratic equation have when b^2 - 4ac is greater than 0?
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What is the graphical representation of a quadratic inequality?
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What is the purpose of sign analysis in solving quadratic inequalities?
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What method is commonly used to solve systems of simultaneous equations with linear and non-linear equations?
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What is required to solve for the values of n unknown variables?
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What is the first step in solving a system of linear equations using substitution?
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What is the purpose of solving word problems in mathematics?
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What is the effect of a positive value of q on the graph of the parabolic function y = ax^2 + q?
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What is the purpose of assigning variables to unknown quantities in word problems?
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What is the effect of a negative value of a on the graph of the parabolic function y = ax^2 + q?
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What is the purpose of checking the solution in word problems?
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What is the effect of a positive value of p on the graph of the parabolic function y = a(x + p)^2 + q?
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What is the purpose of solving systems of linear equations?
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What is the first step in solving a word problem?
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What is the purpose of solving quadratic equations?
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What is the effect of q on a quadratic function?
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What is the domain of a quadratic function?
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What is the formula for finding the y-intercept of a quadratic function?
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What is the turning point of the quadratic function f(x) = a(x + p)^2 + q?
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What is the axis of symmetry of the quadratic function f(x) = a(x + p)^2 + q?
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How do you shift a quadratic function m units to the right?
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What is the formula for the average gradient of a curve between two points?
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What is the formula for the average gradient of a curve f(x) between points P(a, f(a)) and Q(a + h, f(a + h))?
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What is the name of the function of the form y = a/x + q?
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What is the purpose of the average gradient in a curve?
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What is the effect of q on the graph of y = 1/x + q?
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What is the effect of a on the graph of y = a/x?
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What is the equation of the horizontal asymptote of y = a/(x + p) + q?
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What is the domain of y = a/(x + p) + q?
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What is the effect of p on the graph of y = a/(x + p) + q?
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What is the range of y = a/(x + p) + q?
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What is the equation of the vertical asymptote of y = a/(x + p) + q?
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What is the effect of q on the graph of y = ab^x + q?
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What is the effect of a on the graph of y = ab^x + q?
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What is the equation of the horizontal asymptote of y = ab^x + q?
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