Questions and Answers
Which set includes all positive integers starting from 1?
What is the definition of irrational numbers?
Which of the following is an example of a rational number?
What does the symbol Z represent in the real number system?
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Which of the following sets includes zero and all positive integers?
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Which statement accurately defines imaginary numbers?
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What is the result of applying the zero exponent law?
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Which of the following accurately represents the multiplication of exponents with the same base?
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How do you simplify the expression (ab)^{2}?
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Which operation will you use to solve the equation a^{x} = a^{3}?
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What is the effect of a negative exponent on a base?
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Which property applies if you have the expression rac{a^{1/2}}{a^{1/3}}?
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How can you convert a square root into a rational exponent?
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What is the correct way to factor the expression a^{2} - b^{2}?
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What should be done first when faced with a complex fraction?
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What is a binomial?
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What is the general formula for multiplying two linear binomials \( (ax + b)(cx + d) \)?
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How can a quadratic trinomial of the form ( ax^2 + bx + c ) be factorised?
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What is the result of multiplying a monomial by a binomial ( a(x + y) )?
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Which of the following identities is used for factorising a difference of two squares?
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When simplifying $rac{a}{b} imes rac{c}{d}$, which statement is correct?
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What is the first step in simplifying algebraic fractions?
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In the process of factorisation, what does factoring by grouping entail?
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Which expression represents the sum of two cubes?
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What is the solution to a system of simultaneous linear equations when solved graphically?
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Which step is NOT part of the problem-solving strategy for word problems?
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What is a literal equation?
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How does the value of 'm' affect the graph of the function $y = mx + c$?
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What must be done to solve an inequality if both sides involve division by a negative number?
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What happens to the graph of a linear function if the value of 'c' is less than 0?
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In solving literal equations, what should be done if the unknown variable is in two or more terms?
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When solving a linear inequality, what do you do if the inequality involves a multiplication by a negative number?
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What is needed to effectively tackle word problems involving simultaneous equations?
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If 'm' is greater than 0 in the function $y = mx + c$, how does the graph behave?
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What is the highest exponent of the variable in a linear equation?
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What is the purpose of checking for extraneous solutions?
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Which step comes first when solving linear equations?
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How many solutions can a linear equation have?
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What is a quadratic equation characterized by?
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In the factorization method for quadratic equations, what form must the equation take?
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How are simultaneous equations typically solved?
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What method can be used to reduce the number of equations in simultaneous equations?
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What is a necessary step after solving for a variable in quadratic equations?
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What should always be performed on both sides of an equation?
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Which of the following is true about irrational numbers?
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What is the first step in converting a recurring decimal into a rational number?
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Which of the following statements about rounding off is correct?
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How can you identify a surd?
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Which of the following correctly describes rational numbers?
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What is the characteristic of terminating decimals?
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What is a key step in estimating surds?
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Which of the following represents a rational number?
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What happens when you round 9.999 to one decimal place?
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Which expression is a term in mathematics?
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What happens to the graph of an exponential function when the value of q is positive?
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In the function of the form y = a sin θ + q, how does a affect the graph?
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Which of the following statements about the sine function is incorrect?
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For the function y = a cos θ + q, what does a < 0 indicate?
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What defines the asymptote of an exponential function in the form y = ab^x + q?
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What is the domain of the tangent function y = tan θ?
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When the value of b in the exponential function is between 0 and 1, what type of function does it represent?
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What is the range of the sine function y = a sin θ + q for a > 0?
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What is the standard form of a straight-line graph?
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How can the sine and cosine graphs be related?
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How can the y-intercept be calculated for the equation y = mx + c?
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What effect does a positive value of 'a' have on the parabola y = ax^2 + q?
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What happens to the graph of the cosine function with a positive q?
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Which statement about the range of the function f(x) = mx + c is true?
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What effect does 'q' have on the graph of a parabola in the equation y = ax^2 + q?
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For which condition will a parabola have a maximum turning point?
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What is the domain of the function f(x) = mx + c?
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If a parabola opens downwards, what can be inferred about the value of 'a'?
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When plotting a straight-line graph, which points are typically used?
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What indicates the steepness of a line in the equation y = mx + c?
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What is the range of the function when $a < 0$?
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Where is the turning point of the function $f(x) = ax^2 + q$ when $a > 0$?
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Which of the following is the horizontal asymptote for hyperbolic functions of the form $y = \frac{a}{x} + q$?
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What happens to a hyperbolic graph when $q > 0$?
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What is the domain of the function $y = \frac{a}{x} + q$?
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What is the axis of symmetry for the function $f(x) = ax^2 + q$?
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What describes the x-intercept calculation for functions of the form $y = \frac{a}{x} + q$?
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What effect does the parameter $a$ have in exponential functions $y = ab^x + q$?
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When sketching the graph of $y = b^x$, which characteristic is NOT considered?
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What effect does the value of 'a' have on the graph of a parabola?
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Which statement is true about the y-intercept of the tangent function?
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How are asymptotes for a hyperbola determined?
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What determines the domain of a tangent function?
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When determining the equation of a hyperbola, what should you look for in the graph?
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How is the vertical shift represented in the equation of a parabola?
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What is the significance of the value 'q' in the trigonometric functions?
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Which method is used to find 'a' in the equation of a hyperbola?
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What can be derived from the range of a function like a hyperbola?
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Which of the following statements is true about the intercepts of parabolic graphs?
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Which statement is true about whole numbers?
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What characterizes integers in the real number system?
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Which of the following is an example of an irrational number?
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What distinguishes rational numbers from irrational numbers?
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Which type of number includes negative values as well as zero?
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Which statement best describes real numbers?
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Which of the following decimal types is not considered a rational number?
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What is the first step in converting a recurring decimal into a rational number?
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Which of the following statements about surds is true?
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When rounding off a decimal number, what happens if the digit after the required place is 5 or greater?
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What represents the relationship between rational and irrational numbers in decimal form?
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Which of the following describes a key characteristic of irrational numbers?
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How can you estimate the square root of a number that is not a perfect square?
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Which of the following must be true about the coefficients in a term of an expression?
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What is the characteristic of products in mathematical expressions?
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What is the maximum number of solutions a linear equation can have?
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Which method is typically used to solve simultaneous equations?
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When solving quadratic equations, which of the following steps is NOT essential?
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What does it mean to check for extraneous solutions?
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What is the first step in solving a quadratic equation?
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How are the solutions of a quadratic equation generally found?
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What is a critical step when performing operations on equations?
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In order to solve simultaneous equations by elimination, what must be achieved first?
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Which of the following is true regarding the roots of a quadratic equation?
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What is required to solve for two unknown variables using simultaneous equations?
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What does the intersection of two linear equations represent when solved graphically?
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Which of the following is the first step in the problem-solving strategy for word problems?
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What is the main concept of a literal equation?
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When solving a linear inequality, what happens to the inequality sign when both sides are divided by a negative number?
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What effect does a positive value for 'c' have on the graph of the function $y = mx + c$?
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Which of the following steps is necessary when isolating an unknown variable in a literal equation?
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What must be taken into account when taking the square root of both sides of an equation?
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Which statement describes the effect of increasing the value of 'm' in the equation $y = mx + c$?
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When writing equations for word problems, what is the main goal?
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In the equation $y = mx + c$, what property is represented by the variable 'm'?
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What is the domain of the function defined by the equation $y = mx + c$?
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How does a negative value of $a$ in the parabola $y = ax^2 + q$ affect its graph?
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What determines the steepness of the line in the equation $y = mx + c$?
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What is the effect of $q > 0$ on the parabola defined by $y = ax^2 + q$?
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What points are essential to sketch a straight-line graph using the dual intercept method?
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For the equation $y = mx + c$, which condition leads to a horizontal line?
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How does the value of $c$ contribute to the graph of a linear function?
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When $a > 0$ in a parabola $y = ax^2 + q$, what is the behavior of the graph?
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In the equation $m = \frac{\text{change in } y}{\text{change in } x}$, what does $m$ represent?
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What happens to the graph of a parabola when $a$ approaches 0 from the positive side?
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What is the result of applying the law of exponents for dividing expressions with the same base?
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Which expression correctly demonstrates the negative exponent law?
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When simplifying $(ab)^{m/n}$, what is the correct application of the exponent laws?
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Which statement about simplifying rational exponents is NOT true?
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What is the first step in solving the exponential equation $a^x = a^2$?
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Which property defines the zero exponent law?
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What does the expression $a^{m/n}$ represent when $n$ is an integer?
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How should the expression $rac{a^{2/3}}{a^{1/3}}$ be simplified?
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What strategy is recommended for simplifying complex fractions?
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Which of the following correctly shows the application of the law of exponents for a product raised to a power?
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What type of asymptote does the function of the form $y = ab^x + q$ have?
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What effect does a positive value of $q$ have on the graph of $y = a an heta + q$?
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For the function $y = a an heta + q$, what happens when $a < 0$?
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Which of the following describes the domain of the sine function $y = ext{sin}( heta)$?
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What is the effect of the value of $b$ on the graph of an exponential function?
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How does the sign of $a$ affect the curvature of the graph for the exponential function $y = ab^x$?
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What defines the range of a sine function given by $y = a ext{sin}( heta) + q$ for $a > 0$?
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What is the vertical shift of the cosine function $y = a ext{cos}( heta) + q$ when $q < 0$?
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What characteristic do the sine and cosine functions share regarding their periodicity?
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How many x-intercepts does the sine function $y = ext{sin}( heta)$ have within its domain?
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What is the range of the function if the parameter $a$ is less than 0?
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What can be concluded about the graph of the function $f(x) = ax^2 + q$ if $a > 0$?
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What is the significance of the axes of symmetry for the function $f(x) = ax^2 + q$?
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For the function $y = rac{a}{x} + q$, what is the behavior of the graph when $x = 0$?
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What type of asymptote does the hyperbolic function $y = rac{a}{x} + q$ exhibit?
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How does the sign of parameter $a$ affect the quadrants in which the hyperbola $y = rac{a}{x} + q$ lies?
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What is the domain of the hyperbolic function $y = rac{a}{x} + q$?
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What characteristic does the exponential function $y = ab^x + q$ exhibit for all real values of $x$?
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For the exponential function where $a > 0$, what is the behavior of its range?
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What shifting effect does the constant $q$ have on a hyperbola $y = rac{a}{x} + q$?
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What is a monomial?
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Which expression represents the product of a binomial and a trinomial?
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What is the first step in the general procedure for factorising a trinomial?
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What is the result of applying the difference of squares identity?
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What is a trinomial?
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Which operation do you perform to simplify the expression ( \frac{a}{b} \div \frac{c}{d} )?
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Which of the following expressions is the correct identity for the sum of two cubes?
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What does factorising by grouping involve?
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In the multiplication of two linear binomials, what is the term that results from the product of the constants?
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When simplifying algebraic fractions, what is the second step after factorizing the numerator and denominator?
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What is the effect of increasing the value of 'a' in the equation of a parabola?
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How can the y-intercept of a trigonometric function in the form $y = a an heta + q$ be calculated?
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Which statement accurately describes how to find the vertical shift 'q' for a parabola?
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What is the significance of the asymptotes in the graph of a hyperbola?
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What is required to determine the equation of a hyperbola using given points?
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Which of the following best describes the domain of the tangent function?
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How does the vertical shift 'q' affect the graph of a trigonometric function?
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Which method is used to find points of intersection between two graphs?
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What characterizes the range of the function represented by a hyperbola?
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How is the steepness of the graph branches of a hyperbola influenced?
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Which of the following subsets of the real number system includes both positive and negative whole numbers along with zero?
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What distinguishes irrational numbers from rational numbers?
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Which symbol represents the set of all numbers that can be expressed as a fraction of two integers where the denominator is not zero?
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Which statement is true regarding the set of real numbers?
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What is the set of natural numbers represented by?
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Which of the following expressions is an irrational number?
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What is the maximum number of solutions a quadratic equation can have?
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Which step should come immediately after expanding all brackets when solving a linear equation?
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In solving quadratic equations, what form should the equation be in before attempting factorization?
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What is the primary purpose of checking your solution after solving an equation?
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When solving simultaneous equations by elimination, what is the first step typically taken?
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What is indicated when a quadratic equation has no real solutions?
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Which of the following is true about the solution set of a linear equation?
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What is the consequence of not balancing an equation after performing an operation?
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When solving by substitution, what is the ultimate goal of the process?
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What is the recommended approach if one of the factors in a quadratic equation is not easily factorable?
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Which of the following decimal representations is classified as a rational number?
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What type of number is represented by the expression ( \sqrt{5} )?
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Which statement correctly describes the rounding process of the number 4.786 to two decimal places?
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What is the primary challenge in estimating the value of the surd ( \sqrt{27} )?
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When converting the recurring decimal ( 0.6666... ) into a rational number, which of the following steps is necessary?
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Which of these sets represents only irrational numbers?
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Which of the following choices accurately places the set of rational numbers (Q) in relation to natural numbers (N)?
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What is the goal when solving a system of simultaneous equations graphically?
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How can the process of rounding affect the representation of an irrational number?
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What is a characteristic feature of a surd?
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What is the first step in the problem-solving strategy for word problems?
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What does isolating the unknown variable in a literal equation involve?
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How is the value of 'm' in the linear function $y = mx + c$ represented?
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When rearranging a literal equation, what should you do if the unknown variable is in the denominator?
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What occurs when dividing both sides of a linear inequality by a negative number?
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Which of the following statements is true about word problems?
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Which expression correctly demonstrates the power of a power law?
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What is the correct way to simplify the expression ( \frac{a^{1/2}}{a^{1/3}} )?
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What is the effect of 'c' in the linear function $y = mx + c$ when 'c' is greater than 0?
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Which statement correctly describes how to solve an exponential equation ( a^x = a^y )?
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What should be the result when solving a linear equation?
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What are simultaneous equations best solved through when only two graphs are involved?
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How can you express the square root of a number in terms of a rational exponent?
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Which method can be used when the bases in the equation ( 2^x = 8 ) are not the same?
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What is the result when applying the law of negative exponents to the expression a^{-3}?
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What is an essential step when simplifying an expression with complex fractions?
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Which of the following is a true statement about rational exponents?
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Which expression represents the multiplication of two exponents with the same base?
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When simplifying ( (ab)^{m/n} ), which of the following is true?
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What is the result of multiplying the binomials ((ax + b)(cx + d))?
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When simplifying the fraction (\frac{a}{b} \div \frac{c}{d}), which expression represents the correct operation?
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What is the correct formula for the difference of two cubes?
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Which statement accurately describes factorizing by grouping?
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To factor the quadratic trinomial (ax^2 + bx + c), what is typically the first step?
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What does the expression ((A + B)(C + D + E)) expand to?
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Which identity is used for factorizing the expression (a^2 - b^2)?
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What is the purpose of factorization in simplifying expressions?
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Which method can be applied to simplify the expression (\frac{x^2 - 1}{x - 1})?
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What happens to the graph of the function when the value of 'c' is greater than 0?
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What happens in the multiplication of two fractions (\frac{a}{b} \times \frac{c}{d})?
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In the equation $y = ax^2 + q$, how does the sign of 'a' affect the parabola?
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What is the range of the function $f(x) = ax^2 + q$ when 'a' is positive?
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Which statement about the y-intercept of the line $y = mx + c$ is accurate?
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When classifying the shape of a parabola, if 'a' is between 0 and 1, what happens to the graph?
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What is the effect of 'q' on the graph of $y = ax^2 + q$?
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Which two points are primarily used to sketch the graph of a linear equation?
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What defines the steepness of a line represented by the equation $y = mx + c$?
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What is the domain of the function $f(x) = mx + c$?
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What does the sign of the parameter $a$ in the function $y = ab^x + q$ determine?
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Which characteristic is affected by the value of $q$ in the functions $y = a an heta + q$?
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What is the period of the sine function represented by $y = ext{sin} heta$?
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In the context of exponential functions, what does $b > 1$ indicate?
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What is the range of the sine function $y = a ext{sin} heta + q$ when $a > 0$?
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Which point represents the y-intercept of the function $y = a ext{cos} heta + q$?
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What are the x-intercepts of the cosine function $y = ext{cos} heta$ within one period?
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Which of the following characteristics is NOT applicable to the tangent function $y = an heta$?
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What effect does a negative value of $a$ have in the function $y = a ext{sin} heta + q$?
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What is the range of the function if $a < 0$ in the form $f(x) = ax^2 + q$?
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What determines whether the graph of $f(x) = ax^2 + q$ has a minimum or maximum turning point?
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Which statement is true regarding hyperbolic functions of the form $y = \frac{a}{x} + q$?
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What do the vertical and horizontal asymptotes represent in hyperbolic functions?
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Given the function $y = ab^x + q$, which statement is true regarding the domain?
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What is the characteristic of the turning point in the function $y = ax^2 + q$?
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How does the value of $q$ affect the graph of a hyperbolic function?
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Which is true about the x-intercepts of the function $y = \frac{a}{x} + q$?
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What defines the axis of symmetry for functions in the form $f(x) = ax^2 + q$?
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What occurs when $a > 0$ in the function $f(x) = ax^2 + q$?
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What effect does increasing the value of 'a' have on the branches of the graph?
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What determines the vertical shift of a parabola in the equation form $y = ax^2 + q$?
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Which points would help you determine the parameters 'a' and 'q' in the hyperbola equation $y = \frac{a}{x} + q$?
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What is the range of the function for the tangent graph represented by $y = a \tan \theta + q$?
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Which of the following is a characteristic of the asymptotes in a hyperbola?
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In the equation $y = a \sin \theta + q$, what does 'q' represent?
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What identifies the smoothness of graph branches in a function based on the value of 'a'?
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What is the domain of the tangent function in the form $y = a \tan \theta + q$?
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Which calculation is necessary to find the y-intercept for the equation of a parabola?
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What determines the type of trigonometric graph when analyzing the equation $y = a \cos \theta + q$?
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What is the maximum number of solutions that a linear equation can have?
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During the process of solving a linear equation, which step follows after expanding all brackets?
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Why is it essential to check for extraneous solutions when solving equations?
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What unique characteristic distinguishes quadratic equations from linear equations?
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When solving simultaneous equations using the elimination method, what must be done first?
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What form must a quadratic equation be in before applying the factorisation method?
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How many independent equations are required to solve for 'n' unknown variables?
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Which method can effectively reduce the number of equations when solving simultaneous equations?
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What must be performed consistently on both sides of an equation when solving?
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What is the first action taken when solving quadratic equations?
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Which subset of real numbers includes negative integers and zero?
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Which statement about irrational numbers is true?
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Which of the following examples is not a rational number?
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Which of the following correctly represents the multiplication of rational exponents?
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What does the expression $a^{0}$ equal when $a eq 0$?
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What type of numbers does the set of real numbers include?
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When simplifying the expression $rac{(a^2b^3)^3}{a^3b^4}$, what is the first step?
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Which of the following statements best describes whole numbers?
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What differentiates rational numbers from irrational numbers?
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Which law of exponents would be used to simplify the expression $a^{-3}b^2$ before canceling?
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How is the equation $4^{x} = 64$ solved when finding $x$?
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What is the result of applying the power of a product rule to $(ab)^{2}$?
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Which of the following expressions represents the simplification process for $rac{a^{m/n}}{a^{p/q}}$?
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Which step should be taken first when faced with an exponential equation involving logarithms?
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What form does the expression $2^{x} = 8^{x-1}$ take when simplified?
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When applying the difference of squares formula, which expression must be factored?
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Which statement about irrational numbers is true?
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What method can be used to convert a terminating decimal into a rational number?
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How can one identify a surd?
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In rounding off 3.784 to two decimal places, what would be the result?
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Given the surd $ ewline rac{ ext{1}}{4}$, which operation best describes its relationship in terms of simplicity?
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What distinguishes rational numbers from irrational numbers?
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What is a key characteristic of decimal numbers classified as rational?
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When estimating the value of a surd such as $ ewline ext{between } ext{1}^2 ext{ and } ext{2}^2 ?$ Which is the best approximation?
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Which of the following correctly describes the process of converting a recurring decimal into a fraction?
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What is the correct expression for the product of a binomial and a trinomial?
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Which operation is used to simplify the fraction ( \frac{a}{b} \div \frac{c}{d} )?
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How is the difference of two cubes factorized?
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What is the result of using the identity ( a^2 - b^2 = (a + b)(a - b) ) on the expression ( 16 - x^2 )?
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Which statement describes the role of the coefficient in the term ( 7x^2 )?
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What do you obtain from the expansion of ( (ax + b)(cx + d) )?
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What are the initial steps in simplifying an algebraic fraction?
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Which process involves grouping terms to aid in factorization?
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Which expression correctly represents the multiplication of a monomial by a binomial?
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What is the solution to a system of simultaneous linear equations when solved graphically?
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Which step is crucial when translating a word problem into mathematical equations?
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When solving a literal equation, how should an unknown variable that is in multiple terms be handled?
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How does one manage the inequality sign when both sides of a linear inequality are divided by a negative number?
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In the equation $y = mx + c$, what does the constant 'c' specifically represent?
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Which general principle applies when solving a system of equations using substitution?
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What happens to the graph of a linear function if 'm' is less than 0?
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What is indicated if the inequality $2x + 2 < 1$ is solved?
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When manipulating literal equations, what must be done if the unknown variable is in the denominator?
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Which part of the problem-solving strategy emphasizes checking the solution for correctness?
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What describes the y-intercept of the hyperbolic function defined as $y = \frac{a}{x} + q$?
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What is the effect of increasing the value of $q$ in the hyperbolic function $y = \frac{a}{x} + q$ when $a > 0$?
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Which equations describe the asymptotes of the hyperbolic function $y = \frac{a}{x} + q$?
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What can be determined about the graph of the function $f(x) = ax^2 + q$ if $a < 0$?
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How does the sign of $a$ in the exponential function $y = ab^x + q$ affect its range?
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Which statement accurately describes the domain of hyperbolic functions of the form $y = \frac{a}{x} + q$?
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What can be inferred about the graph of the function $y = ax^2 + q$ if $a > 0$?
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Which of the following statements is true about the axes of symmetry for the hyperbolic function $y = \frac{a}{x} + q$?
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What is the primary factor affecting the shape of the graph for the function $y = \frac{a}{x} + q$?
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If the coefficient 'm' in the equation $y = mx + c$ is negative, which of the following must be true about the y-intercept?
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What effect does a positive value of 'a' have on the graph of the parabola defined by $y = ax^2 + q$?
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In the equation $y = mx + c$, which factor primarily affects the steepness of the line?
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What determines whether a parabola is a 'smile' or a 'frown'?
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If both 'm' and 'c' are zero in the equation $y = mx + c$, what is the nature of the resulting line?
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For the parabola defined by $y = ax^2 + q$, what happens if 'q' is negative?
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What is the range of the function defined by $y = ax^2 + q$ when 'a' is less than zero?
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When using the dual intercept method to sketch a line, which two values are essential to determine?
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What is the vertical shift of the graph when the value of q is -3?
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In relation to the function $f(x) = mx + c$, which statements about domain and range are accurate?
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Which of the following describes the effect of a negative value of a on the graph of the function y = a sin θ + q?
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What is the range of the function y = 2 sin θ - 1?
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If a parabolic function has a positive 'q' and a negative 'a', what is the nature of its vertex?
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If the function y = -3b^x + 2 has an asymptote, what is the equation of the asymptote?
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For an exponential function to experience growth, which of the following conditions must hold true?
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What is the domain of the function y = tan θ?
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When comparing the sine and cosine functions, what is the maximum turning point for y = cos θ?
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In what scenario does the value of b affect the graph of a sine function?
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What are the x-intercepts for the function y = a cos θ + q?
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How does a positive value of 'a' affect the shape of a parabola?
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What determines the vertical shift of a hyperbola?
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What do the asymptotes of a hyperbola indicate?
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In the function of a tangent graph, what happens when 'q' is negative?
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To find the y-intercept of a trigonometric function like $y = a an heta + q$, which angle should you use?
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What method is used to determine the equation of a hyperbola using given points?
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What is the significance of setting the denominator to zero in analyzing the graph of functions?
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For trigonometric functions, which factor significantly modifies the amplitude of the graph?
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What determines the domain of the tangent function?
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