Questions and Answers
What is the value of r when r^n = a?
What is the value of a^(1/n)?
What is the value of a^(-1/n)?
What is the value of a^(m/n)?
Signup and view all the answers
What is the radical symbol √[n]{a} indicating?
Signup and view all the answers
What is a surd?
Signup and view all the answers
What is the formula for simplifying surds?
Signup and view all the answers
What is the purpose of rationalizing denominators?
Signup and view all the answers
What is the rule for raising a power to a power?
Signup and view all the answers
What is the definition of a surd?
Signup and view all the answers
What is the purpose of rationalizing denominators?
Signup and view all the answers
What is the first step in solving surd equations?
Signup and view all the answers
What is the formula for exponential growth or decay?
Signup and view all the answers
What is the purpose of checking solutions in surd equations?
Signup and view all the answers
What is the key concept in solving quadratic surd equations?
Signup and view all the answers
What is the difference between exponential growth and decay?
Signup and view all the answers
What is the formula for compound interest?
Signup and view all the answers
What is the formula to find the final amount in exponential growth or decay?
Signup and view all the answers
What is the set of natural numbers represented by?
Signup and view all the answers
What is the formula to solve any quadratic equation of the form ax² + bx + c = 0?
Signup and view all the answers
What is the purpose of completing the square method in quadratic equations?
Signup and view all the answers
What is the formula to find the nth root of a number a?
Signup and view all the answers
What is the formula to find a^(-m/n)?
Signup and view all the answers
What is the formula to find a^(m/n)?
Signup and view all the answers
What is the purpose of dividing by a in the quadratic equation ax² + bx + c = 0?
Signup and view all the answers
What is the formula to find the square root of a number a?
Signup and view all the answers
What is the set of real numbers represented by?
Signup and view all the answers
What is the formula for determining the roots of a quadratic equation?
Signup and view all the answers
What type of roots does a quadratic equation have when b^2 - 4ac > 0?
Signup and view all the answers
What is the purpose of making a substitution in solving quadratic equations?
Signup and view all the answers
What is the formula for the discriminant of a quadratic equation?
Signup and view all the answers
What is the result of multiplying the terms in the quadratic equation (x - r_1)(x - r_2) = 0?
Signup and view all the answers
What type of roots does a quadratic equation have when b^2 - 4ac < 0?
Signup and view all the answers
What is the purpose of identifying restrictions in solving quadratic equations?
Signup and view all the answers
What is the result of solving the quadratic equation in terms of k?
Signup and view all the answers
What is the purpose of verifying restrictions in solving quadratic equations?
Signup and view all the answers
What is the nature of the roots of a quadratic equation when Δ = 0?
Signup and view all the answers
What is the last step in solving a system of equations using the substitution or elimination method?
Signup and view all the answers
What is the purpose of solving word problems in mathematics?
Signup and view all the answers
What is the general form of a quadratic sequence?
Signup and view all the answers
What is the effect of q on the graph of y = ax^2 + q?
Signup and view all the answers
What is the purpose of solving systems of equations?
Signup and view all the answers
What is the first step in solving a word problem?
Signup and view all the answers
What is the effect of a on the shape of the graph of y = ax^2 + q?
Signup and view all the answers
What is the purpose of finding the general term of a quadratic sequence?
Signup and view all the answers
What is the result of solving a system of equations graphically?
Signup and view all the answers
What is the importance of problem-solving strategies in mathematics?
Signup and view all the answers
What does the discriminant Δ represent in a quadratic equation?
Signup and view all the answers
What is the purpose of determining the critical values when solving a quadratic inequality?
Signup and view all the answers
What is the formula for the discriminant Δ in a quadratic equation?
Signup and view all the answers
What is the method of solving a quadratic inequality by analyzing the sign of each factor on intervals defined by the critical values?
Signup and view all the answers
What is the purpose of creating a table of signs when solving a quadratic inequality?
Signup and view all the answers
What is the method of solving simultaneous equations by expressing one of the variables in terms of the other?
Signup and view all the answers
What is the purpose of solving simultaneous equations?
Signup and view all the answers
What is the number of independent equations required to solve for the values of n unknown variables?
Signup and view all the answers
What is the purpose of the graphical method in solving simultaneous equations?
Signup and view all the answers
What is the method of solving quadratic inequalities by sketching the graph and visually identifying the regions where the quadratic expression satisfies the inequality?
Signup and view all the answers
What is the average gradient of the curve at point P when h = 0?
Signup and view all the answers
What is the horizontal asymptote of a hyperbolic function of the form y = a/x + q?
Signup and view all the answers
What is the effect of a change in q on the graph of a hyperbolic function of the form y = a/(x + p) + q?
Signup and view all the answers
What is the domain of the hyperbolic function y = a/(x + p) + q?
Signup and view all the answers
What is the effect of a change in p on the graph of a hyperbolic function of the form y = a/(x + p) + q?
Signup and view all the answers
What is the range of the hyperbolic function y = a/(x + p) + q?
Signup and view all the answers
What is the point of intersection of the axes of symmetry of the hyperbola y = a/(x + p) + q?
Signup and view all the answers
What is the effect of a change in a on the shape of the exponential function y = ab^x + q?
Signup and view all the answers
What is the effect of a change in b on the direction of the exponential function y = ab^x + q?
Signup and view all the answers
What is the horizontal asymptote of the exponential function y = ab^x + q?
Signup and view all the answers
What is the effect of a change in parameter $p$ on the graph of $y = ab^{(x+p)} + q$?
Signup and view all the answers
What is the range of the function $y = ab^{(x+p)} + q$ when $a > 0$?
Signup and view all the answers
What is the formula for simple depreciation?
Signup and view all the answers
What is the characteristic of the graph of $y = ab^{(x+p)} + q$ when $a < 0$?
Signup and view all the answers
What is the purpose of a timeline in compounding interest?
Signup and view all the answers
What is the formula for compound depreciation?
Signup and view all the answers
What is the effect of a change in parameter $q$ on the graph of $y = ab^{(x+p)} + q$?
Signup and view all the answers
What is the domain of the function $y = ab^{(x+p)} + q$?
Signup and view all the answers
What is the difference between simple and compound depreciation?
Signup and view all the answers
What is the purpose of adjusting for compounding periods in timelines?
Signup and view all the answers
What is the effect of a horizontal shift on the graph of a quadratic function?
Signup and view all the answers
What is the effect of a negative value of a on the graph of a quadratic function?
Signup and view all the answers
What is the domain of a quadratic function?
Signup and view all the answers
What is the axis of symmetry of a quadratic function in the form f(x) = a(x + p)^2 + q?
Signup and view all the answers
What is the formula for calculating the average gradient of a curve between two points?
Signup and view all the answers
What is the turning point of a quadratic function in the form f(x) = a(x + p)^2 + q?
Signup and view all the answers
What is the effect of a vertical shift on the graph of a quadratic function?
Signup and view all the answers
What is the range of a quadratic function with a positive value of a?
Signup and view all the answers
What is the formula for finding the y-intercept of a quadratic function?
Signup and view all the answers
What is the effect of a negative value of q on the graph of a quadratic function?
Signup and view all the answers
What does each branch of a tree diagram represent?
Signup and view all the answers
What is the probability of a path in a tree diagram?
Signup and view all the answers
What is the purpose of a contingency table?
Signup and view all the answers
How do you calculate the probability of an event A?
Signup and view all the answers
What is the formula for conditional probability P(A|B)?
Signup and view all the answers
What is the condition for independence between two events A and B?
Signup and view all the answers
What is the purpose of drawing a tree diagram?
Signup and view all the answers
What is the formula for the probability of multiple independent events?
Signup and view all the answers
What is the formula for calculating the accumulated value of an investment using compound interest?
Signup and view all the answers
What is the formula for calculating the effective interest rate?
Signup and view all the answers
What is the formula for calculating the probability of two independent events?
Signup and view all the answers
What is the formula for calculating the probability of two mutually exclusive events?
Signup and view all the answers
What is the concept of conditional probability?
Signup and view all the answers
What is the formula for calculating the probability of three events using the general addition rule?
Signup and view all the answers
What is the purpose of using tree diagrams in probability?
Signup and view all the answers
What is the definition of dependent events in probability?
Signup and view all the answers
What is the formula for calculating the accumulated value using simple interest?
Signup and view all the answers
What is the value of $a^{rac{m}{n}}$?
Signup and view all the answers
What is the result of multiplying $a^{rac{m}{n}}$ by $a^{rac{p}{n}}$?
Signup and view all the answers
What is the result of dividing $\sqrt[n]{a}$ by $\sqrt[n]{b}$?
Signup and view all the answers
What is the purpose of rationalizing the denominator?
Signup and view all the answers
What is the value of $\left(\sqrt[n]{a} ight)^m$?
Signup and view all the answers
What is the condition for the radicand to have real roots?
Signup and view all the answers
What is the result of multiplying $\sqrt[n]{a}$ by $\sqrt[n]{a}$?
Signup and view all the answers
What is the purpose of simplifying surds?
Signup and view all the answers
What is the nature of the roots of a quadratic equation when Δ is greater than 0?
Signup and view all the answers
What is the purpose of determining the critical values when solving a quadratic inequality?
Signup and view all the answers
What is the formula to calculate the discriminant Δ of a quadratic equation in standard form ax^2 + bx + c = 0?
Signup and view all the answers
What is the next step after factorizing the quadratic expression when solving a quadratic inequality?
Signup and view all the answers
What is the purpose of solving quadratic inequalities?
Signup and view all the answers
What is the result of solving a quadratic equation when Δ is equal to 0?
Signup and view all the answers
What is the first step in solving a quadratic inequality?
Signup and view all the answers
What is the purpose of graphing a quadratic function when solving a quadratic inequality?
Signup and view all the answers
What is the result of solving a quadratic equation when Δ is less than 0?
Signup and view all the answers
What is the last step in solving a quadratic inequality?
Signup and view all the answers
What is the primary goal when solving surd equations?
Signup and view all the answers
What is the purpose of writing surds in exponential notation?
Signup and view all the answers
What is the condition for a quadratic equation to have real and distinct roots?
Signup and view all the answers
What is the formula for exponential growth or decay?
Signup and view all the answers
What is the purpose of identifying restrictions when solving quadratic equations by substitution?
Signup and view all the answers
What is the formula for finding the roots of a quadratic equation?
Signup and view all the answers
What is the purpose of checking solutions in surd equations?
Signup and view all the answers
What is the nature of the roots of a quadratic equation when Δ < 0?
Signup and view all the answers
What is the difference between exponential growth and decay?
Signup and view all the answers
What is the purpose of making a substitution when solving quadratic equations?
Signup and view all the answers
What is the formula for compound interest?
Signup and view all the answers
What is the value of x in the equation x^2 + 4x + 4 = 0?
Signup and view all the answers
What is the formula for the discriminant (Δ) of a quadratic equation?
Signup and view all the answers
Which of the following is a condition for exponential growth or decay?
Signup and view all the answers
What is the key concept in solving quadratic surd equations?
Signup and view all the answers
What is the purpose of rationalizing denominators?
Signup and view all the answers
What is the purpose of verifying restrictions when solving quadratic equations?
Signup and view all the answers
What is the purpose of the quadratic formula?
Signup and view all the answers
What is the importance of simplifying surds?
Signup and view all the answers
What is the result of taking half the coefficient of the x term and squaring it in the completing the square method?
Signup and view all the answers
What is the result of solving the quadratic equation in terms of k when using substitution?
Signup and view all the answers
What is the value of a in the equation a^0 = 1?
Signup and view all the answers
What is the condition for a quadratic equation to have real and equal roots?
Signup and view all the answers
What is the rule for raising a power to a power?
Signup and view all the answers
What is the purpose of dividing by a in the quadratic equation ax^2 + bx + c = 0?
Signup and view all the answers
What is the purpose of finding the quadratic equation given its roots?
Signup and view all the answers
What is the formula for the nth root of a number a?
Signup and view all the answers
What is the purpose of the completing the square method?
Signup and view all the answers
What is the result of taking the square root of both sides in the quadratic formula?
Signup and view all the answers
What is the set of real numbers represented by?
Signup and view all the answers
What is the final step in solving a system of equations using the substitution or elimination method?
Signup and view all the answers
What is the purpose of writing a set of equations to describe a word problem?
Signup and view all the answers
What is the result of solving a system of equations graphically?
Signup and view all the answers
What is the purpose of problem-solving strategies in mathematics?
Signup and view all the answers
What is the effect of q on the graph of y = ax^2 + q?
Signup and view all the answers
What is the purpose of finding the general term of a quadratic sequence?
Signup and view all the answers
What is the effect of a on the shape of the graph of y = ax^2 + q?
Signup and view all the answers
What is the purpose of solving systems of equations?
Signup and view all the answers
What does each branch of a tree diagram represent?
Signup and view all the answers
What is the first step in solving a word problem?
Signup and view all the answers
What is the importance of problem-solving strategies in mathematics?
Signup and view all the answers
What is the formula to calculate the probability of a specific path in a tree diagram?
Signup and view all the answers
What is the purpose of a two-way contingency table?
Signup and view all the answers
What is the formula to calculate the probability of an event A?
Signup and view all the answers
What is the condition for two events A and B to be independent?
Signup and view all the answers
What is the purpose of calculating the probability of a path in a tree diagram?
Signup and view all the answers
What is the structure of a two-way contingency table?
Signup and view all the answers
What is the formula to calculate the conditional probability of A given B?
Signup and view all the answers
What is the effect of a on the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What is the axis of symmetry for the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What is the turning point of the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What is the effect of p on the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What is the range of the graph of y = a(x + p)^2 + q if a > 0?
Signup and view all the answers
How do you find the y-intercept of the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What is the formula to calculate the average gradient of a curve between two points A and C?
Signup and view all the answers
What is the domain of the graph of y = a(x + p)^2 + q?
Signup and view all the answers
How do you shift the graph of y = a(x + p)^2 + q to the right by m units?
Signup and view all the answers
What is the effect of a change in p on the graph of y = ab^(x+p) + q?
Signup and view all the answers
Which of the following is true about the range of y = ab^(x+p) + q?
Signup and view all the answers
What is the purpose of determining the turning point of the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What is the formula for simple depreciation?
Signup and view all the answers
What is the main difference between simple and compound depreciation?
Signup and view all the answers
What is the purpose of using timelines in compounding interest problems?
Signup and view all the answers
How do you adjust the interest rate when compounding more than once a year?
Signup and view all the answers
What is the effect of q on the graph of y = ab^(x+p) + q?
Signup and view all the answers
Which of the following is a characteristic of the graph of y = ab^(x+p) + q?
Signup and view all the answers
What is the formula for compound depreciation?
Signup and view all the answers
What is the key point to note about compound depreciation?
Signup and view all the answers
What is the formula for calculating the accumulated value of an investment or loan using compound interest?
Signup and view all the answers
What is the difference between nominal and effective interest rates?
Signup and view all the answers
What is the formula for calculating the probability of two independent events?
Signup and view all the answers
What is the purpose of Venn diagrams in probability theory?
Signup and view all the answers
What is the formula for calculating the conditional probability of event A given event B?
Signup and view all the answers
What is the difference between mutually exclusive and independent events?
Signup and view all the answers
What is the purpose of tree diagrams in probability theory?
Signup and view all the answers
What is the formula for calculating the probability of the union of two events that are not mutually exclusive?
Signup and view all the answers
What is the key concept in solving dependent events problems?
Signup and view all the answers
What is the formula for calculating the effective interest rate from the nominal interest rate?
Signup and view all the answers
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))?
Signup and view all the answers
What is the effect of q on the graph of y = a/x + q?
Signup and view all the answers
What is the domain of the function y = a/(x + p) + q?
Signup and view all the answers
What is the horizontal asymptote of the function y = a/(x + p) + q?
Signup and view all the answers
What is the effect of a on the shape of the graph of y = a/x?
Signup and view all the answers
What is the axes of symmetry of the hyperbola y = a/(x + p) + q?
Signup and view all the answers
What is the effect of p on the graph of y = a/(x + p) + q?
Signup and view all the answers
What is the range of the function y = a/(x + p) + q?
Signup and view all the answers
What is the vertical asymptote of the function y = a/(x + p) + q?
Signup and view all the answers
What is the formula for the exponential function y = ab^x + q?
Signup and view all the answers
What is the value of a when a^(1/2) = 4?
Signup and view all the answers
What is the value of a when a^(1/3) = 2?
Signup and view all the answers
What is the value of a when a^(-1/2) = 1/2?
Signup and view all the answers
What is the value of a when a^(3/2) = 8?
Signup and view all the answers
What is the value of a when a^(2/3) = 2?
Signup and view all the answers
What is the value of a when a^(-3/2) = 1/4?
Signup and view all the answers
What is the value of a when a^(1/4) = 2?
Signup and view all the answers
What is the value of a when a^(-2/3) = 1/2?
Signup and view all the answers
What is the result of applying the power of a power rule to the expression $(a^m)^n$?
Signup and view all the answers
What is the purpose of rationalizing denominators?
Signup and view all the answers
What is the first step in solving a surd equation?
Signup and view all the answers
What is the formula for exponential growth or decay?
Signup and view all the answers
What is the formula to determine the roots of a quadratic equation ax^2 + bx + c = 0?
Signup and view all the answers
What is the purpose of checking solutions in surd equations?
Signup and view all the answers
What is the key concept in solving quadratic surd equations?
Signup and view all the answers
Under what condition does a quadratic equation have two distinct real roots?
Signup and view all the answers
What is the difference between exponential growth and decay?
Signup and view all the answers
What is the purpose of making a substitution in solving quadratic equations?
Signup and view all the answers
What is the nature of the roots of a quadratic equation when Δ < 0?
Signup and view all the answers
What is the purpose of applying the rule of indices in solving surd equations?
Signup and view all the answers
What is the result of applying the rule of indices to the expression a^(-m/n)?
Signup and view all the answers
What is the formula to find the quadratic equation given the roots r_1 and r_2?
Signup and view all the answers
What is the purpose of using exponentials in real-world applications?
Signup and view all the answers
Under what condition does a quadratic equation have exactly one real root?
Signup and view all the answers
What is the purpose of identifying restrictions in solving quadratic equations?
Signup and view all the answers
What is the result of solving the quadratic equation in terms of k?
Signup and view all the answers
What is the purpose of verifying restrictions in solving quadratic equations?
Signup and view all the answers
What is the nature of the roots of a quadratic equation when Δ = 0?
Signup and view all the answers
What is the value of x in the equation x^2 + 4x + 4 = 0?
Signup and view all the answers
Which of the following is a correct application of the rule of exponents a^m × a^n = a^(m+n)?
Signup and view all the answers
What is the final amount of money after 5 years if the initial amount is $100, the interest rate is 10% per annum, and the interest is compounded annually?
Signup and view all the answers
What is the equation in standard form that corresponds to the equation (x + 2)^2 = 16?
Signup and view all the answers
What is the value of x in the equation x^2 - 6x + 8 = 0?
Signup and view all the answers
Which of the following is a correct application of the rule of exponents a^(m+n) = a^m × a^n?
Signup and view all the answers
What is the equation in standard form that corresponds to the equation (x - 3)^2 = 9?
Signup and view all the answers
What is the value of x in the equation x^2 + 2x + 1 = 0?
Signup and view all the answers
Which of the following is a correct application of the rule of exponents a^(-n) = 1/a^n?
Signup and view all the answers
What is the final amount of money after 3 years if the initial amount is $50, the interest rate is 5% per annum, and the interest is compounded annually?
Signup and view all the answers
What is the nature of the roots of a quadratic equation when Δ is greater than 0?
Signup and view all the answers
What is the effect of a on the shape of the graph of y = ax^2 + q?
Signup and view all the answers
What is the first step in solving a quadratic inequality?
Signup and view all the answers
What is the purpose of determining the critical values when solving a quadratic inequality?
Signup and view all the answers
What is the effect of p on the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What is the formula for the discriminant Δ in a quadratic equation?
Signup and view all the answers
What is the axis of symmetry for the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What is the turning point of the graph of y = a(x + p)^2 + q?
Signup and view all the answers
How many independent equations are required to solve for the values of n unknown variables?
Signup and view all the answers
What is the domain of the function y = a(x + p)^2 + q?
Signup and view all the answers
What is the purpose of a table of signs when solving a quadratic inequality?
Signup and view all the answers
What is the nature of the roots of a quadratic equation when Δ is equal to 0?
Signup and view all the answers
What is the range of the function y = a(x + p)^2 + q when a > 0?
Signup and view all the answers
What is the last step in solving a quadratic inequality?
Signup and view all the answers
How do you find the y-intercept of the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What is the purpose of graphing a quadratic function when solving a quadratic inequality?
Signup and view all the answers
What is the formula to find the average gradient of a curve between two points?
Signup and view all the answers
What is the purpose of finding the average gradient of a curve?
Signup and view all the answers
What is the nature of the roots of a quadratic equation when Δ is less than 0?
Signup and view all the answers
How do you shift a parabola horizontally to the right by m units?
Signup and view all the answers
What is the main goal of solving systems of equations?
Signup and view all the answers
Which of the following is an example of a real-world application of quadratic sequences?
Signup and view all the answers
What is the main difference between the substitution and elimination methods for solving systems of equations?
Signup and view all the answers
What is the effect of a positive value of q on the graph of y = ax^2 + q?
Signup and view all the answers
What is the purpose of identifying the question and determining what needs to be solved in a word problem?
Signup and view all the answers
What is the result of solving a system of equations graphically?
Signup and view all the answers
What is the importance of problem-solving strategies in mathematics?
Signup and view all the answers
What is the general form of a quadratic sequence?
Signup and view all the answers
What is the effect of a negative value of q on the graph of y = ax^2 + q?
Signup and view all the answers
What is the purpose of finding the general term of a quadratic sequence?
Signup and view all the answers
What is the effect of a change in p on the graph of y = ab^(x+p) + q?
Signup and view all the answers
What is the range of the function y = ab^(x+p) + q when a > 0?
Signup and view all the answers
What is the formula for simple depreciation?
Signup and view all the answers
What is the result of compound depreciation?
Signup and view all the answers
How do you find the annual depreciation rate i?
Signup and view all the answers
What is the purpose of using timelines in compound interest?
Signup and view all the answers
What happens when you break down periods in a compound interest problem?
Signup and view all the answers
What is the effect of q on the graph of y = ab^(x+p) + q?
Signup and view all the answers
What is the domain of the function y = ab^(x+p) + q?
Signup and view all the answers
What is the characteristic of the graph of y = ab^(x+p) + q when a < 0?
Signup and view all the answers
What is the average gradient of a curve at a point P when h = 0?
Signup and view all the answers
What is the effect of q on the graph of y = a / x + q?
Signup and view all the answers
What is the domain of the function y = a / (x + p) + q?
Signup and view all the answers
What is the vertical asymptote of the function y = a / (x + p) + q?
Signup and view all the answers
What is the horizontal asymptote of the function y = a / (x + p) + q?
Signup and view all the answers
What is the effect of a on the shape of the graph of y = a / x?
Signup and view all the answers
What is the effect of p on the graph of y = a / (x + p) + q?
Signup and view all the answers
What is the axes of symmetry of the hyperbola y = a / (x + p) + q?
Signup and view all the answers
What is the formula for the average gradient of a curve?
Signup and view all the answers
What is the effect of a on the graph of y = ab^x + q?
Signup and view all the answers
What does each branch of a tree diagram represent?
Signup and view all the answers
What is the formula to calculate the probability of a specific sequence of events in a tree diagram?
Signup and view all the answers
What is the purpose of a two-way contingency table?
Signup and view all the answers
What is the formula to calculate the probability of an event A?
Signup and view all the answers
What is the formula to calculate the conditional probability of A given B?
Signup and view all the answers
What is the condition for two events A and B to be independent?
Signup and view all the answers
What is the purpose of calculating the probability of a path in a tree diagram?
Signup and view all the answers
What is the result of multiplying the probabilities along a path in a tree diagram?
Signup and view all the answers
What is the formula for calculating the accumulated value using the compound interest formula?
Signup and view all the answers
What is the difference between dependent and independent events?
Signup and view all the answers
What is the formula for calculating the effective interest rate?
Signup and view all the answers
What is the purpose of a Venn diagram in probability?
Signup and view all the answers
What is the formula for calculating the probability of two dependent events?
Signup and view all the answers
What is the purpose of calculating the nominal interest rate?
Signup and view all the answers
What is the formula for calculating the probability of two independent events?
Signup and view all the answers
What is the purpose of a tree diagram in probability?
Signup and view all the answers
What is the formula for calculating the probability of the union of two events?
Signup and view all the answers
What is the purpose of calculating the conditional probability?
Signup and view all the answers
What is the value of x in the exponential growth equation A = 2(1 + 0.1)^x, where A = 4.48?
Signup and view all the answers
Which of the following is a correct step in solving the quadratic equation x^2 + 4x + 3 = 0 using the completing the square method?
Signup and view all the answers
What is the value of x in the equation 2^(3x) = 16, where x is a real number?
Signup and view all the answers
Which of the following is a correct application of the quadratic formula to solve the equation x^2 - 5x + 2 = 0?
Signup and view all the answers
What is the value of x in the equation 3^(x-1) = 9, where x is a real number?
Signup and view all the answers
Which of the following is a correct step in solving the quadratic equation x^2 - 2x - 3 = 0 using the completing the square method?
Signup and view all the answers
What is the value of x in the equation 4^(2x) = 64, where x is a real number?
Signup and view all the answers
Which of the following is a correct application of the quadratic formula to solve the equation x^2 + 3x - 2 = 0?
Signup and view all the answers
What is the condition for a quadratic equation to have two complex conjugate roots?
Signup and view all the answers
What is the value of x in the equation 2^(x+2) = 32, where x is a real number?
Signup and view all the answers
Which of the following is a correct step in solving the quadratic equation x^2 + 2x + 1 = 0 using the completing the square method?
Signup and view all the answers
What is the purpose of making a substitution in solving quadratic equations by substitution?
Signup and view all the answers
What is the result of multiplying the terms in the quadratic equation (x - r_1)(x - r_2) = 0?
Signup and view all the answers
What is the nature of the roots of a quadratic equation when Δ = 0?
Signup and view all the answers
What is the purpose of identifying restrictions in solving quadratic equations?
Signup and view all the answers
What is the formula for the discriminant of a quadratic equation?
Signup and view all the answers
What is the condition for a quadratic equation to have two distinct real roots?
Signup and view all the answers
What is the purpose of solving quadratic equations by substitution?
Signup and view all the answers
What is the result of solving the quadratic equation in terms of k?
Signup and view all the answers
What is the purpose of verifying restrictions in solving quadratic equations?
Signup and view all the answers
What is the value of $a^{rac{m}{n}}$ in exponential form?
Signup and view all the answers
If $a^m = 27$ and $a^n = 9$, what is the value of $m$ in terms of $n$?
Signup and view all the answers
What is the formula to solve the equation $a^x = b^y$?
Signup and view all the answers
What is the value of $\sqrt{a^2}$ in terms of $a$?
Signup and view all the answers
What is the formula to solve the equation $a^x = a^y$?
Signup and view all the answers
What is the value of $a^0$?
Signup and view all the answers
What is the value of $a^{rac{m}{n}}$ in terms of radical notation?
Signup and view all the answers
What is the formula to solve the equation $a^x = b$?
Signup and view all the answers
What is the result of rationalizing the denominator of the expression $\frac{1}{\sqrt[3]{2}}$?
Signup and view all the answers
What is the value of $\left(a^{rac{1}{n}}\right)^m$ in terms of $a$?
Signup and view all the answers
What is the value of $a^{-m}$ in terms of $a$?
Signup and view all the answers
What is the result of multiplying $\sqrt[n]{a}$ and $\sqrt[n]{b}$?
Signup and view all the answers
What is the formula to solve the equation $a^x = a^{x + 1}$?
Signup and view all the answers
What is the value of $(a^m)^n$ in terms of $a$?
Signup and view all the answers
What is the value of $\left(\sqrt[n]{a}\right)^{-m}$ in terms of $a$?
Signup and view all the answers
What is the result of dividing $\sqrt[n]{a}$ by $\sqrt[n]{b}$?
Signup and view all the answers
What is the value of $a^{\frac{m}{n}}$ in terms of radical notation?
Signup and view all the answers
What is the result of rationalizing the denominator of the expression $\frac{1}{\sqrt[n]{a}}$?
Signup and view all the answers
What is the nature of the roots of a quadratic equation when the discriminant Δ is a perfect square?
Signup and view all the answers
What is the graphical method for solving a quadratic inequality?
Signup and view all the answers
What is the purpose of solving a system of simultaneous equations?
Signup and view all the answers
What is the formula for the discriminant Δ in a quadratic equation?
Signup and view all the answers
What is the purpose of creating a table of signs when solving a quadratic inequality?
Signup and view all the answers
What is the method for solving a quadratic inequality when the quadratic expression can be factorized?
Signup and view all the answers
What is the result of multiplying the terms in the quadratic equation (x - r_1)(x - r_2) = 0?
Signup and view all the answers
What is the purpose of determining the critical values when solving a quadratic inequality?
Signup and view all the answers
What is the method for solving a system of simultaneous equations with linear and non-linear equations?
Signup and view all the answers
What is the purpose of solving quadratic inequalities?
Signup and view all the answers
What is the main advantage of using the elimination method to solve systems of equations?
Signup and view all the answers
When solving a word problem, what is the purpose of assigning variables to unknown quantities?
Signup and view all the answers
What is the characteristic of a quadratic sequence?
Signup and view all the answers
What is the effect of 'q' on the graph of y = ax^2 + q?
Signup and view all the answers
What is the purpose of solving systems of equations?
Signup and view all the answers
What is the result of solving a system of equations graphically?
Signup and view all the answers
What is the importance of problem-solving strategies in mathematics?
Signup and view all the answers
What is the general form of a quadratic sequence?
Signup and view all the answers
What is the effect of 'a' on the shape of the graph of y = ax^2 + q?
Signup and view all the answers
What is the purpose of finding the general term of a quadratic sequence?
Signup and view all the answers
What is the effect of a negative value of a on the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What is the axis of symmetry for the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What is the effect of p on the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What is the range of the graph of y = a(x + p)^2 + q if a > 0?
Signup and view all the answers
What is the turning point of the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What is the effect of q on the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What is the domain of the graph of y = a(x + p)^2 + q?
Signup and view all the answers
How do you find the x-intercepts of the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What is the formula to find the average gradient of a curve between two points A and C?
Signup and view all the answers
What is the effect of a positive value of a on the graph of y = a(x + p)^2 + q?
Signup and view all the answers
What does each branch of a tree diagram represent?
Signup and view all the answers
What is the probability of a path in a tree diagram?
Signup and view all the answers
What is the purpose of a two-way contingency table?
Signup and view all the answers
What is the formula for the probability of an event A?
Signup and view all the answers
What is the formula for the conditional probability of A given B?
Signup and view all the answers
What is the condition for independence between two events A and B?
Signup and view all the answers
What is the purpose of calculating the probability of a specific path in a tree diagram?
Signup and view all the answers
What is the formula for calculating the probability of a desired outcome using multiple paths?
Signup and view all the answers
What is the accumulated value of an investment after 5 years, given an initial principal of $1000, an annual interest rate of 4%, and quarterly compounding?
Signup and view all the answers
If two events A and B are independent, what is the probability of both events occurring?
Signup and view all the answers
What is the effective interest rate if the nominal interest rate is 6% and the compounding is done quarterly?
Signup and view all the answers
If event A is dependent on event B, what is the formula for the probability of event A occurring given that event B has occurred?
Signup and view all the answers
What is the average gradient of the curve at point P when h = 0?
Signup and view all the answers
What is the effect of q on the graph of y = a/x + q?
Signup and view all the answers
What is the total accumulated value of an investment after 3 years, given an initial principal of $500, an annual interest rate of 5%, and monthly compounding, with a deposit of $100 at the end of the first year and a withdrawal of $200 at the end of the second year?
Signup and view all the answers
What is the domain of the function y = a/(x + p) + q?
Signup and view all the answers
If two events A and B are mutually exclusive, what is the probability of either event occurring?
Signup and view all the answers
What is the effect of a on the shape of the graph of y = a/(x + p) + q?
Signup and view all the answers
What is the effect of a change in parameter p on the graph of y = ab^(x+p) + q?
Signup and view all the answers
What is the nominal interest rate if the effective interest rate is 7.25% and the compounding is done quarterly?
Signup and view all the answers
What is the effect of p on the graph of y = a/(x + p) + q?
Signup and view all the answers
If event A is independent of event B, what is the probability of event A occurring given that event B has occurred?
Signup and view all the answers
What is the range of the function y = ab^(x+p) + q when a > 0?
Signup and view all the answers
What are the axes of symmetry of the graph of y = a/(x + p) + q?
Signup and view all the answers
What is the formula for compound depreciation?
Signup and view all the answers
What is the formula for the probability of three events A, B, and C occurring, given that they are independent?
Signup and view all the answers
What is the accumulated value of an investment after 10 years, given an initial principal of $2000, an annual interest rate of 3%, and monthly compounding?
Signup and view all the answers
What is the effect of a change in parameter q on the graph of y = ab^(x+p) + q?
Signup and view all the answers
What is the range of the function y = a/(x + p) + q?
Signup and view all the answers
What is the characteristic of the graph of y = ab^(x+p) + q when a < 0?
Signup and view all the answers
What is the effect of a on the graph of y = ab^x + q?
Signup and view all the answers
What is the formula for finding the depreciation rate i in compound depreciation?
Signup and view all the answers
What is the effect of b on the graph of y = ab^x + q?
Signup and view all the answers
What is the importance of timelines in compound interest and depreciation?
Signup and view all the answers
What is the effect of q on the graph of y = ab^x + q?
Signup and view all the answers
What is the characteristic of simple depreciation?
Signup and view all the answers
What is the effect of compounding more than once a year in compound interest and depreciation?
Signup and view all the answers
What is the formula for finding the book value A in simple depreciation?
Signup and view all the answers