Questions and Answers
What is the value of r in the equation r^n = a, where n ≥ 2?
What is the value of a^(-1/n)?
What is the value of a^(m/n)?
What is the purpose of rationalising the denominator?
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What is the condition for the radicand in a radical symbol when n is even?
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What is the rule for negative exponents?
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What is the purpose of rationalizing denominators?
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What is the formula for exponential growth or decay?
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What is the main goal when solving surd equations?
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What is the power of a power rule?
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What is the purpose of writing surds in exponential notation?
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What is the formula for fractional exponents?
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What is the final step when solving surd equations?
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What is the key consideration when raising both sides of the equation to the power to eliminate the surd?
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What is the exponential growth model used for?
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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 formula for converting a square root to an exponent?
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What is the set of natural numbers represented as?
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What is the formula for solving a quadratic equation using the completing the square method?
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What is the purpose of completing the square in quadratic equations?
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What is the formula for an exponential growth or decay problem?
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What is the first step in solving a quadratic equation using the quadratic formula?
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What is the definition of $a^0$?
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What is the formula for the quadratic formula derived from?
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What is the purpose of the quadratic formula?
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What is the formula for determining the roots of a quadratic equation?
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What condition is required for a quadratic equation to have two distinct real roots?
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What is the purpose of making a substitution when solving a quadratic equation?
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What is the first step in finding the quadratic equation given the roots?
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What is the discriminant of a quadratic equation?
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What type of roots does a quadratic equation have if the discriminant is less than zero?
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What is the condition for a quadratic equation to have exactly one real root?
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What is the purpose of identifying restrictions in the substitution method?
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What is the final step in solving a quadratic equation by substitution?
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What type of roots does a quadratic equation have if the discriminant is a perfect square?
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What does a discriminant value of Δ < 0 indicate about the roots of a quadratic equation?
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What is the formula for calculating the discriminant of a quadratic equation in standard form?
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What is the purpose of creating a table of signs when solving quadratic inequalities?
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What is the general method for solving quadratic inequalities?
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What is the purpose of determining critical values when solving quadratic inequalities?
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What is the result of solving a quadratic equation when the discriminant is Δ = 0?
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What is the graphical representation of a quadratic inequality?
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What is the purpose of analyzing the sign of each factor on intervals defined by the critical values?
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What is the main difference between solving quadratic equations and quadratic inequalities?
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What is the general method for solving systems of simultaneous equations?
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What is the effect of a on the shape of the graph of f(x) = a(x + p)^2 + q?
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What is the domain of the function f(x) = a(x + p)^2 + q?
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What is the range of the function f(x) = a(x + p)^2 + q when a > 0?
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What is the equation of the axis of symmetry for the function f(x) = a(x + p)^2 + q?
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What is the formula to find the y-intercept of the function f(x) = a(x + p)^2 + q?
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How do you shift the equation of a parabola 3 units to the right?
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What is the formula to find the average gradient between two points on a curve?
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What is the effect of p on the graph of f(x) = a(x + p)^2 + q?
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What is the effect on the graph of the function y = ab^(x+p) + q if p > 0?
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What is the turning point of the function f(x) = a(x + p)^2 + q?
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What is the formula to find the x-intercept of the function f(x) = a(x + p)^2 + q?
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What is the range of the function y = ab^(x+p) + q if a > 0?
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What is the formula for the depreciated value using simple depreciation?
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What is the effect of compound depreciation on the depreciation amount?
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Why do we use timelines in finance?
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What happens to the interest rate when amounts are compounded more than once per annum?
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What is the effect of a negative value of b on the function f(x)?
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What is the horizontal asymptote of the function y = ab^(x+p) + q?
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What is the average gradient of a curve between points P(a, f(a)) and Q(a + h, f(a + h))?
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What is the main purpose of solving systems of linear equations?
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What is the effect of q > 0 on the graph of y = a/x + q?
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What is the key difference between simple and compound depreciation?
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What is the first step in solving a word problem using algebraic equations?
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What is the definition of a quadratic sequence?
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What is the value of the horizontal asymptote for the graph of y = a/(x + p) + q?
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What is the formula for finding the annual depreciation rate (i) for compound decay?
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What is the effect of a > 0 on the graph of y = ab^x + q?
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What is the general form of the nth term of a quadratic sequence?
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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 q > 0 on the graph of a parabolic function?
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What is the effect of p > 0 on the graph of y = a/(x + p) + q?
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What is the main difference between the substitution and elimination methods for solving systems of linear equations?
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What is the point of intersection of the axes of symmetry for the graph of y = a/(x + p) + q?
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What is the purpose of checking the solution in a problem-solving strategy?
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What is the advantage of using algebraic equations to model real-world problems?
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What is the range of the function y = a/(x + p) + q?
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What is the equation of the vertical asymptote for the graph of y = a/(x + p) + q?
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What is the benefit of using a problem-solving strategy?
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What is the average gradient of a curve at a point P(a, f(a))?
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What is the term for the point where the two graphs intersect in a graphical solution of a system of linear equations?
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What is the formula for the probability of the union of three events A, B, and C?
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What is the characteristic of mutually exclusive events?
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What is the purpose of tree diagrams?
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What is the formula for the probability of two independent events A and B?
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What is the structure of a two-way contingency table?
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What is the formula for the probability of an event A given event B (A if B)?
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What is the condition for two events A and B to be independent?
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What is the purpose of using tree diagrams in probability?
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What is the formula for calculating the probability of a specific path in a tree diagram?
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What is the purpose of using contingency tables in probability?
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What is the correct approach when interest rates change or additional deposits/withdrawals are made in a compound interest problem?
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What is the formula for calculating the accumulated value in a compound interest problem?
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What is the difference between nominal and effective interest rates?
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What is the formula for calculating the effective interest rate?
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What is the formula for calculating the probability of two independent events?
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What is the formula for calculating the conditional probability of event A given event B?
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What is the concept of mutually exclusive events in probability?
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What is the formula for calculating the probability of the union of two events A and B?
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What is the concept of the sample space in probability?
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What is the formula for calculating the probability of the complement of an event A?
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What is the value of a^(1/n), where a > 0 and n is a positive integer?
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What is the result of multiplying a^(m/n) by a^(p/n)?
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What is the condition for the radicand in a radical symbol when n is odd?
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What is the purpose of simplifying surds?
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What is the purpose of rationalizing the denominator?
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What is the definition of a surd?
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What is the purpose of converting surds into exponential notation when solving surd equations?
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What is the result 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 nature of the roots of a quadratic equation if the discriminant Δ is less than 0?
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What is the key consideration when raising both sides of the equation to the power to eliminate the surd?
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How do you determine the critical values when solving a quadratic inequality?
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What is the formula for exponential growth or decay?
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What is the purpose of creating a table of signs when solving quadratic inequalities?
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What is the purpose of rationalizing the denominator?
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What is the general method for solving systems of simultaneous equations with linear and non-linear equations?
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What is the formula for converting a surd to an exponential?
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What is the main goal when solving surd equations?
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What is the result of solving a quadratic equation when the discriminant Δ is equal to 0?
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What is the purpose of determining the nature of the roots of a quadratic equation?
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What is the power of a power rule?
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What is the application of exponential growth models in real-world scenarios?
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What is the formula for calculating the discriminant of a quadratic equation in standard form?
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What is the purpose of creating a table of signs when solving quadratic inequalities?
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What is the importance of checking solutions when solving surd equations?
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What is the graphical representation of a quadratic inequality?
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What is the condition for a quadratic equation to have exactly one real root?
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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 definition of a^0, where a is not equal to zero?
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What is the formula for exponential growth or decay?
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What is the condition for a quadratic equation to have exactly one real root?
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What is the purpose of identifying restrictions in the substitution method?
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What is the formula for determining the roots of a quadratic equation using the quadratic formula?
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What is the effect of a on the shape of the graph of f(x) = a(x + p)^2 + q?
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What is the purpose of creating a table of signs when solving quadratic inequalities?
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What is the formula for determining the roots of a quadratic equation in the form ax^2 + bx + c = 0?
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What is the condition for a quadratic equation to have exactly one real root?
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What is the purpose of identifying restrictions in the substitution method?
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What is the nature of the roots of a quadratic equation when the discriminant Δ is greater than zero?
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What is the final step in solving a quadratic equation by substitution?
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What is the formula for finding the quadratic equation given the roots r_1 and r_2?
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What is the purpose of making a substitution when solving a quadratic equation?
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What is the type of roots a quadratic equation has when the discriminant Δ is a perfect square?
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What is the first step in finding the quadratic equation given the roots?
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What is the condition for a quadratic equation to have two complex conjugate roots?
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What is the main goal of solving a system of linear equations?
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What is the result of substituting the solution back into the original equation in the elimination method?
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What is the purpose of drawing the graph of each equation in the graphical method?
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What is the key step in solving word problems using algebraic equations?
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What is the definition of a quadratic sequence?
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What is the general form of a quadratic sequence?
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What is the effect of q on the graph of a quadratic function y = ax^2 + q?
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What is the purpose of solving systems of equations in real-world applications?
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What is the first step in solving a word problem using algebraic equations?
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What is the purpose of checking the solution in a word problem?
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What is the effect of a negative value of a on the graph of f(x) = a(x + p)^2 + q?
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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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What is the effect of a horizontal shift of p units to the right on the graph of f(x) = a(x)^2 + q?
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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 turning point of the graph of f(x) = a(x + p)^2 + q?
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What is the range of the graph of f(x) = a(x + p)^2 + q if a > 0?
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What is the effect of a vertical shift of q units upwards on the graph of f(x) = a(x)^2 + q?
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What is the domain of the function f(x) = a(x + p)^2 + q?
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What is the y-intercept of the graph of f(x) = a(x + p)^2 + q?
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What is the formula for the gradient of the tangent to the curve at a point?
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What is the formula for the average gradient of a curve f(x) with points P(a, f(a)) and Q(a + h, f(a + h))?
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What is the effect of q on the graph of y = a/x + q?
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What is the domain of the function 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 vertical asymptote 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 + q?
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What is the horizontal asymptote of the function y = ab^x + 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 axis of symmetry of the function y = a/(x + p) + q?
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What is the condition for a quadratic equation to have exactly one real root?
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What is the effect of b on the direction of the function f(x) = ab^(x+p) + q, assuming a > 0?
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What is the effect of a change in p on the graph of f(x) = ab^(x+p) + q?
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What is the effect of a change in q on the graph of f(x) = ab^(x+p) + q?
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What is the domain of the function f(x) = ab^(x+p) + q?
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What is the range of the function f(x) = ab^(x+p) + q, assuming a > 0?
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What is the formula for simple depreciation?
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What is the formula for compound depreciation?
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What is the purpose of using timelines when working with compound interest?
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What happens to the depreciation amount each year in simple depreciation?
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What happens to the depreciation amount each year in compound depreciation?
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What is the formula for the probability of three events A, B, and C occurring?
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What is the definition of mutually exclusive events?
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What is the purpose of a tree diagram?
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When calculating the accumulated value, what should you do when interest rates change or additional deposits/withdrawals are made?
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What is the formula for the probability of two independent events A and B occurring?
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What is the formula for Simple Interest?
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What is the purpose of a contingency table?
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What is the formula for Compound Interest?
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What is the formula for the Effective Interest Rate?
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What is the formula for the probability of an event A given event B?
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What is the formula for the probability of independent events?
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What is the condition for two events A and B to be independent?
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What is the formula for the probability of dependent events?
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What is the formula for calculating the probability of a specific path in a tree diagram?
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What is the definition of Mutually Exclusive Events?
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What is the purpose of the intersection rule for three events?
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What is the formula for the probability of a desired outcome in a tree diagram?
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What is the purpose of Venn Diagrams?
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What is the result of the intersection of two independent events?
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What is the purpose of calculating the accumulated value at the end of each period?
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What is the value of a^(1/n) when n is a positive integer?
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What is the result of simplifying (√(a) × √(b)) if a and b are positive integers?
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What is the purpose of rationalizing the denominator in a surd expression?
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What is the value of a^(-m/n) when a is a positive integer and m and n are integers?
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What is the result of raising a surd to a power?
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What is the condition for a radicand to have real roots when n is even?
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What is the result of multiplying two surds with the same root?
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What is the result of dividing a surd by another surd?
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What is the result 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 determining the roots of a quadratic equation in the form ax^2 + bx + c = 0?
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What is the purpose of converting percentage rates into decimal form before using them in the exponential growth or decay formula?
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What type of roots does a quadratic equation have if the discriminant is greater than zero?
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What is the purpose of converting surds into their exponential form?
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What is the result of applying the formula for exponential growth or decay to find the final amount?
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What is the step in the substitution method for solving quadratic equations where you identify a common factor or repeated expression?
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What is the formula for exponential growth or decay?
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What is the main goal when solving quadratic equations using the completing the square method?
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What is the formula for finding the quadratic equation given the roots r_1 and r_2?
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What is the key consideration when isolating the surd on one side of the equation?
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What is the condition for a quadratic equation to have exactly one real root?
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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 checking the solution by substituting back into the original equation?
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What is the result of applying the power of a power rule?
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What is the purpose of identifying restrictions in the substitution method for solving quadratic equations?
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What is the condition required for a quadratic equation to have two distinct real roots?
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What is the formula for fractional exponents?
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What is the result of solving a quadratic equation when the discriminant is Δ = 0?
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What type of roots does a quadratic equation have if the discriminant is a perfect square?
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What is the final step in solving a quadratic equation by substitution?
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What is the condition for a quadratic equation to have two distinct real roots?
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What is the purpose of creating a table of signs when solving quadratic inequalities?
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What is the purpose of rationalizing denominators?
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What is the purpose of making a substitution when solving a quadratic equation?
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What is the general method for solving quadratic inequalities?
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What is the definition of a^0?
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What is the main difference between solving quadratic equations and quadratic inequalities?
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What is the discriminant of a quadratic equation in the form ax^2 + bx + c = 0?
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What is the nature of the roots of a quadratic equation when the discriminant Δ is greater than 0?
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What is the effect of a on the shape of the graph of f(x) = a(x + p)^2 + q?
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What is the purpose of determining critical values when solving quadratic inequalities?
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What is the formula for calculating the discriminant of a quadratic equation in standard form?
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What is the result of solving a quadratic equation when the discriminant is Δ = 0?
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What is the purpose of creating a table of signs when solving quadratic inequalities?
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What is the graphical representation of a quadratic inequality?
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What is the condition for a quadratic equation to have two distinct real roots?
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What is the purpose of analyzing the sign of each factor on intervals defined by the critical values?
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What is the general method for 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 first step in solving a system of linear equations using substitution?
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What is the purpose of making a substitution when solving a quadratic equation?
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What is the definition of a quadratic sequence?
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What is the effect of q on the graph of the function y = ax^2 + q?
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What is the purpose of identifying variables in a word problem?
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What is the general method for solving systems of simultaneous equations?
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What is the purpose of solving systems of linear equations?
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What is the result of solving a quadratic equation when the discriminant is Δ = 0?
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What is the purpose of solving quadratic inequalities?
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What is the graphical representation of a quadratic inequality?
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What is the effect of the value of a on the shape of the graph of f(x) = a(x + p)^2 + q?
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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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What is the turning point of the graph of f(x) = a(x + p)^2 + q?
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What is the effect of the value of p on the graph of f(x) = a(x + p)^2 + q?
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What is the range of the function f(x) = a(x + p)^2 + q when a > 0?
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What is the purpose of finding the y-intercept when sketching the graph of f(x) = a(x + p)^2 + q?
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How do you find the x-intercept of the graph of f(x) = a(x + p)^2 + q?
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What is the purpose of finding the domain of the function f(x) = a(x + p)^2 + q?
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What is the average gradient of the curve at point P when h = 0?
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What is the average gradient of a curve between two points?
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What is the effect of q on the graph of y = a/x + q?
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What is the formula for calculating the average gradient of a curve between two points A(x_A, y_A) and C(x_C, y_C)?
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What is the domain of the function y = a/(x + p) + q?
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What is the horizontal asymptote 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 + 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 formula for the average gradient?
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What is the vertical asymptote of the function 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 the function y = a/(x + p) + q?
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If b > 1, what is the nature of the function f(x)?
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What is the effect of a change in p on the graph of y = ab^(x+p) + q?
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What is the range of the function y = ab^(x+p) + q when a > 0?
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What is the formula for simple depreciation?
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What is the key characteristic of compound depreciation?
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How do you find the annual depreciation rate (i) for simple or compound decay?
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What is the purpose of timelines in compound interest?
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What happens to the depreciation amount each year in compound depreciation?
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What is the horizontal asymptote of the function y = ab^(x+p) + q?
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What is the domain of the function y = ab^(x+p) + q?
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What is the formula for the probability of three events A, B, and C occurring?
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What is the condition for two events to be independent?
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What is the purpose of a tree diagram?
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What is the formula for the probability of a specific path in a tree diagram?
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What is the purpose of a contingency table?
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What is the formula for the probability of an event A given event B?
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What is the condition for two events to be mutually exclusive?
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What is the purpose of the independence test in a contingency table?
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What is the formula for calculating the probability of an event A?
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What is the purpose of drawing a tree diagram?
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What is the purpose of breaking down periods when calculating the accumulated value of an investment or loan?
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What is the formula for calculating the accumulated value of an investment or loan using compound interest?
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What is the difference between independent and dependent events?
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What is the formula for calculating the effective interest rate?
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What is the purpose of the addition rule for mutually exclusive events?
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What is the formula for calculating the conditional probability of event A given event B?
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What is the purpose of creating a Venn diagram?
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What is the formula for calculating the probability of two events that are not mutually exclusive?
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What is the purpose of calculating the accumulated value at the end of each period?
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What is the formula for calculating the nominal interest rate?
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What is the value of $a^{1/n}$?
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What is the result of multiplying $\sqrt[n]{a}$ and $\sqrt[n]{b}$?
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What is the value of $a^{-1/n}$?
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What is the purpose of rationalizing the denominator in a surd expression?
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What is the value of $\sqrt[n]{a^m}$?
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What is the result of dividing $\sqrt[n]{a}$ by $\sqrt[n]{b}$?
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What is the condition for the radicand in a radical symbol when $n$ is even?
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What is the formula for the product of powers?
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What is the value of $a^{mn}$ in terms of $(a^m)^n$?
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Solve for $x$ in the equation $\sqrt{x} = 2$.
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What is the value of $a^{rac{m}{n}}$ in terms of $\sqrt[n]{a^m}$?
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Solve for $x$ in the equation $x^2 = 16$.
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What is the purpose of writing surds in exponential notation?
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Solve for $x$ in the equation $\sqrt{x+2} = 3$.
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What is the formula for exponential growth or decay?
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What is the key consideration when raising both sides of the equation to the power to eliminate the surd?
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What is the result of solving a quadratic equation when the discriminant is = 0?
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What is the condition for a quadratic equation to have exactly one real root?
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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 creating a table of signs when solving quadratic inequalities?
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How do you determine the critical values when solving quadratic inequalities?
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What is the general method for solving quadratic inequalities?
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What is the purpose of graphing the quadratic function when solving quadratic inequalities?
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What type of roots does a quadratic equation have if the discriminant Δ is a perfect square?
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What is the formula for calculating the discriminant of a quadratic equation in standard form?
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What is the purpose of determining the sign of each factor on intervals defined by the critical values?
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What is the general method for solving systems of simultaneous equations?
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What is the main difference between solving quadratic equations and quadratic inequalities?
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What is the condition for a quadratic equation to have two distinct real roots?
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What is the purpose of making a substitution when solving a quadratic equation?
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What type of roots does a quadratic equation have if the discriminant is a perfect square?
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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 formula for determining the roots of a quadratic equation?
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What is the purpose of completing the square in 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 purpose of identifying restrictions in the substitution method?
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What is the formula for exponential growth or decay?
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What is the set of rational numbers represented as?
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What is the formula for calculating the discriminant of a quadratic equation in standard form?
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What type of roots does a quadratic equation have if the discriminant is Δ > 0?
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What is the definition of a^(-n)?
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What is the formula for solving a quadratic equation using the quadratic formula?
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What is the final step in solving a quadratic equation by substitution?
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What is the condition for a quadratic equation to have exactly one real root?
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What is the purpose of the quadratic formula?
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What is the formula for converting a square root to an exponent?
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What is the rule for negative exponents?
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What is the set of real numbers represented as?
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What is the main goal of solving word problems?
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What is the characteristic of a quadratic sequence?
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What is the effect of q on the graph of the function y = ax^2 + q?
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What is the first step in solving a system of equations using the substitution method?
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What is the purpose of solving systems of equations?
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What is the graphical representation of a system of equations?
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What is the purpose of using mathematical models in real-world applications?
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What is the general form of a quadratic sequence?
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What is the purpose of solving quadratic equations?
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What is the method of solving a system of equations by making one variable the subject of both equations?
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What is the formula for the average gradient of a curve f(x) between two points P(a, f(a)) and Q(a + h, f(a + h))?
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What is the effect of q on the graph of y = a/x + q?
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What is the domain of the function y = a/(x + p) + q?
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What is the horizontal asymptote 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 f(x) = a(x + p)^2 + 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 turning point of the function f(x) = a(x + p)^2 + q?
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What is the vertical asymptote of the function y = a/(x + p) + q?
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What is the axis of symmetry of the function f(x) = a(x + p)^2 + q?
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What is the formula for the exponential function of the form y = ab^x + 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 range of the function f(x) = a(x + p)^2 + q when a > 0?
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How do you find the y-intercept of the function f(x) = a(x + p)^2 + q?
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What is the axes of symmetry of the graph of y = a/(x + p) + 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 f(x) = a(x + p)^2 + q?
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What is the formula to find the average gradient of a curve between two points A(x_A, y_A) and C(x_C, y_C)?
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What is the purpose of finding the average gradient of a curve?
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What is the domain of the function f(x) = a(x + p)^2 + q?
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How do you shift the graph of f(x) = a(x + p)^2 + q by m units to the right?
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What is the effect of b on the direction of the function f(x) = ab^(x+p) + q, assuming a > 0?
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What is the effect of a change in p on the graph of the function f(x) = ab^(x+p) + q?
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What is the range of the function f(x) = ab^(x+p) + q when a > 0?
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What is the formula for simple depreciation?
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What is the characteristic of compound depreciation?
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How is the annual depreciation rate (i) found for simple or compound decay?
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What is the purpose of using timelines in compounding?
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What happens to the interest rate when compounding occurs more than once a year?
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What is the horizontal asymptote of the function f(x) = ab^(x+p) + q?
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What is the domain of the function f(x) = ab^(x+p) + q?
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What is the purpose of breaking down periods in compound interest calculations?
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What is the formula for compound interest?
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What is the definition of dependent events?
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What is the formula for the effective interest rate?
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What is the purpose of the addition rule for mutually exclusive events?
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What is the formula for the conditional probability of event A given event B?
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What is the purpose of Venn diagrams in probability?
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What is the formula for the probability of two independent events occurring?
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What is the purpose of calculating the accumulated value at the end of each period in compound interest?
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What is the definition of mutually exclusive events?
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What is the formula for the probability of a union of three events A, B, and C?
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What is the probability of an event occurring given that another event has occurred, denoted by P(A|B)?
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What is the purpose of a contingency table?
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What is the formula for the probability of a path in a tree diagram?
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What is the characteristic of independent events?
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What is the formula for the probability of an event A, denoted by P(A)?
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What is the purpose of a tree diagram?
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What is the condition for two events A and B to be independent?
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What is the formula for calculating the probability of a desired outcome when there are multiple paths leading to it?
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