Gr 11 Math Nov P1 (Easy)
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Questions and Answers

What is the value of r if r^n = a?

  • r = √(n/a)
  • r = ∛(a^n)
  • r = √(a/n)
  • r = √(a) (correct)

What is the value of a^(1/n)?

  • √(n/a)
  • n√(a)
  • √(a) (correct)
  • 1/√(n/a)

What is the value of a^(-1/n)?

  • n/√(a)
  • 1/√(a) (correct)
  • 1/√(n/a)
  • 1/√(n/a)

What is the purpose of rationalising the denominator?

<p>To eliminate the surd from the denominator (C)</p> Signup and view all the answers

What is the result of multiplying √(a) and √(b)?

<p>√(ab) (C)</p> Signup and view all the answers

What is the result of dividing √(a) by √(b)?

<p>√(a/b) (B)</p> Signup and view all the answers

What is the result of raising √(a) to the power of m?

<p>√(a^m) (B)</p> Signup and view all the answers

What is the power of a power rule in exponentiation?

<p>(a^m)^n = a^(mn) (B)</p> Signup and view all the answers

What is the definition of a negative exponent?

<p>a^(-m) = 1/a^m (D)</p> Signup and view all the answers

What is the purpose of rationalizing denominators?

<p>To eliminate radicals from the denominator (C)</p> Signup and view all the answers

What is the first step in solving a surd equation?

<p>Isolate the surd (B)</p> Signup and view all the answers

What is the purpose of checking solutions in surd equations?

<p>To eliminate extraneous solutions (A)</p> Signup and view all the answers

What is the formula for exponential growth and decay?

<p>P(t) = P_0 × (1 + r)^t (B)</p> Signup and view all the answers

What is the purpose of compound interest in finance?

<p>To calculate the amount of money accumulated over time (C)</p> Signup and view all the answers

What is the definition of a fractional exponent?

<p>a^(m/n) = √(a^m) (A)</p> Signup and view all the answers

What is the purpose of writing surds in exponential notation?

<p>To make manipulation easier (D)</p> Signup and view all the answers

What is the formula for solving quadratic surd equations?

<p>Isolate and simplify, then square both sides (C)</p> Signup and view all the answers

What is the first step in identifying the variables in an exponential growth or decay problem?

<p>Determine the initial amount, growth rate, and time period (C)</p> Signup and view all the answers

What is the nature of the roots of a quadratic equation if the discriminant Δ is less than 0?

<p>Imaginary (C)</p> Signup and view all the answers

What is the set of whole numbers represented by?

<p>ℕ₀ (D)</p> Signup and view all the answers

What is the formula for the discriminant Δ of a quadratic equation in standard form?

<p>b^2 - 4ac (C)</p> Signup and view all the answers

What is the formula for a⁻ⁿ?

<p>1/aⁿ (C)</p> Signup and view all the answers

What is the first step in solving a quadratic inequality?

<p>Write the quadratic in standard form (C)</p> Signup and view all the answers

What is the purpose of completing the square in solving quadratic equations?

<p>To transform the equation into a perfect square trinomial (A)</p> Signup and view all the answers

What is the formula for solving quadratic equations of the form ax² + bx + c = 0?

<p>x = -b ± √(b² - 4ac) / 2a (C)</p> Signup and view all the answers

What is the purpose of a table of signs in solving quadratic inequalities?

<p>To determine where the quadratic expression is positive or negative (A)</p> Signup and view all the answers

What is the graphical representation of a quadratic function used for in solving quadratic inequalities?

<p>To visually identify the regions where the quadratic expression satisfies the inequality (B)</p> Signup and view all the answers

What is the result of a⁰, where a ≠ 0?

<p>1 (B)</p> Signup and view all the answers

What is the restriction to consider when solving inequalities with fractions?

<p>Ensure the denominator is not zero (B)</p> Signup and view all the answers

What is the notation for the set of rational numbers?

<p>ℚ (C)</p> Signup and view all the answers

What is the number of independent equations required to solve for n unknown variables?

<p>n (A)</p> Signup and view all the answers

What is the purpose of converting percentages to decimal form in exponential growth or decay problems?

<p>To use the exponential growth or decay formula (C)</p> Signup and view all the answers

What is the first step in solving a quadratic equation using the method of completing the square?

<p>Write the equation in the standard form (A)</p> Signup and view all the answers

What method is mostly used for solving systems of simultaneous equations with linear and non-linear equations?

<p>Substitution (B)</p> Signup and view all the answers

What is the result of √(aⁿ), where n is a positive integer?

<p>a^(n⁄²) (A)</p> Signup and view all the answers

What is the purpose of the critical values in solving quadratic inequalities?

<p>To determine the intervals where the quadratic expression is positive or negative (B)</p> Signup and view all the answers

What is the general method for solving quadratic inequalities?

<p>Factorize, find critical values, create a table of signs, and graph the solution (D)</p> Signup and view all the answers

What is the formula to determine the roots of a quadratic equation?

<p>x = -b ± √(b^2 - 4ac) / 2a (A)</p> Signup and view all the answers

What type of roots does a quadratic equation have when b^2 - 4ac = 0?

<p>Real and equal roots (D)</p> Signup and view all the answers

What is the purpose of making a substitution in solving quadratic equations?

<p>To simplify the equation (B)</p> Signup and view all the answers

What is the first step in solving a quadratic equation by substitution?

<p>Identify restrictions (B)</p> Signup and view all the answers

How can you determine the original quadratic equation given its roots?

<p>By working backwards from the roots (C)</p> Signup and view all the answers

What is the discriminant of a quadratic equation?

<p>b^2 - 4ac (D)</p> Signup and view all the answers

What type of roots does a quadratic equation have when Δ < 0?

<p>Imaginary roots (B)</p> Signup and view all the answers

What type of roots does a quadratic equation have when Δ = 0?

<p>Real and equal roots (D)</p> Signup and view all the answers

What is the condition for a quadratic equation to have two distinct real roots?

<p>Δ &gt; 0 (B)</p> Signup and view all the answers

What happens when Δ is a perfect square in a quadratic equation?

<p>The roots are rational (A)</p> Signup and view all the answers

What is the first step in solving a system of equations using the substitution method?

<p>Express one of the variables in terms of the other (C)</p> Signup and view all the answers

What is the purpose of solving word problems?

<p>To describe real-life contexts using mathematical language (D)</p> Signup and view all the answers

What is the definition of a quadratic sequence?

<p>A sequence of numbers with a constant second difference (A)</p> Signup and view all the answers

What is the general form of the nth term of a quadratic sequence?

<p>Tn = an^2 + bn + c (C)</p> Signup and view all the answers

What is the effect of q > 0 on a parabolic function?

<p>The turning point of f(x) is above the x-axis (D)</p> Signup and view all the answers

What is the first step in solving a system of equations using the elimination method?

<p>Make one of the variables the subject of both equations (B)</p> Signup and view all the answers

What is the purpose of solving systems of equations graphically?

<p>To find the solution to the system of equations (A)</p> Signup and view all the answers

What is the role of problem-solving strategies in natural sciences and engineering disciplines?

<p>To solve real-life problems (D)</p> Signup and view all the answers

What is the final step in solving a word problem?

<p>Write the final answer (A)</p> Signup and view all the answers

What is the purpose of finding the general term of a quadratic sequence?

<p>To determine the values of a, b, and c (D)</p> Signup and view all the answers

What is the effect of a > 0 on the graph of f(x)?

<p>The graph is a 'smile' and has a minimum turning point. (D)</p> Signup and view all the answers

What is the effect of p on the graph of f(x)?

<p>A horizontal shift. (D)</p> Signup and view all the answers

What is the domain of the function f(x)?

<p>{x : x ∈ ℝ}. (D)</p> Signup and view all the answers

What is the axis of symmetry of the graph of f(x)?

<p>The vertical line x = -p. (D)</p> Signup and view all the answers

What is the formula to find the y-intercept of the graph of f(x)?

<p>Set x = 0. (B)</p> Signup and view all the answers

What is the turning point of the graph of f(x)?

<p>(-p, q). (A)</p> Signup and view all the answers

What is the range of the function f(x) when a > 0?

<p>{y : y ≥ q, y ∈ ℝ}. (D)</p> Signup and view all the answers

What is the formula to shift the graph of f(x) to the right by m units?

<p>Replace x with x + m. (B)</p> Signup and view all the answers

What is the formula to calculate the average gradient of a curve?

<p>Gradient = (y_A - y_C) / (x_A - x_C). (D)</p> Signup and view all the answers

What is the method to find the equation of a parabola from the graph?

<p>Use the equation y = a(x - x_1)(x - x_2). (B)</p> Signup and view all the answers

What is the formula for the average gradient of a curve?

<p>(y_2 - y_1) / (x_2 - x_1) (B)</p> Signup and view all the answers

What is the effect of q on the graph of y = a/x + q?

<p>Vertical shift (C)</p> Signup and view all the answers

What is the vertical asymptote of the graph of y = a/(x + p) + q?

<p>x = -p (B)</p> Signup and view all the answers

What is the domain of the function y = a/(x + p) + q?

<p>All real numbers except x = -p (A)</p> Signup and view all the answers

What is the effect of a on the shape of the graph of y = a/x + q?

<p>Changes the shape of the graph in quadrants (C)</p> Signup and view all the answers

What is the formula for the hyperbolic function of the form y = a/(x + p) + q?

<p>y = a/(x + p) + q (C)</p> Signup and view all the answers

What is the horizontal asymptote of the graph of y = a/(x + p) + q?

<p>y = q (C)</p> Signup and view all the answers

What is the effect of p on the graph of y = a/(x + p) + q?

<p>Horizontal shift (B)</p> Signup and view all the answers

What is the axes of symmetry of the graph of y = a/(x + p) + q?

<p>x = -p, y = q (B)</p> Signup and view all the answers

What is the effect of a on the shape of the graph of y = ab^x + q?

<p>Changes the shape of the graph to increasing or decreasing (C)</p> Signup and view all the answers

What happens to the graph of y = ab^(x+p) + q when p > 0?

<p>The graph is shifted to the left by p units. (A)</p> Signup and view all the answers

What is the range of the function y = ab^(x+p) + q when a > 0?

<p>All real numbers greater than q. (A)</p> Signup and view all the answers

What is the effect of a change in q on the graph of y = ab^(x+p) + q?

<p>The graph is shifted vertically. (D)</p> Signup and view all the answers

What is the formula for simple depreciation?

<p>A = P(1 - in) (C)</p> Signup and view all the answers

What is the characteristic of the depreciation amount in simple depreciation?

<p>It remains the same every year. (D)</p> Signup and view all the answers

What is the formula for compound depreciation?

<p>A = P(1 - i)^n (C)</p> Signup and view all the answers

What is the effect of compounding more than once a year on an investment?

<p>The interest rate is divided by p and the number of years is multiplied by p. (B)</p> Signup and view all the answers

What is the purpose of using timelines in finance?

<p>To visualize the periods and changes in compounding and interest rates. (B)</p> Signup and view all the answers

What happens to the depreciation amount in compound depreciation?

<p>It decreases each year. (C)</p> Signup and view all the answers

What is the key point about the book value in compound depreciation?

<p>The book value never reaches zero. (A)</p> Signup and view all the answers

What is the first step in calculating the accumulated value of an investment?

<p>Break down the timeline into segments and calculate each period separately (C)</p> Signup and view all the answers

What is the formula for calculating compound interest?

<p>A = P(1 + i)^n (A)</p> Signup and view all the answers

What is the formula for the probability of three events A, B, and C occurring?

<p>P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C) (B)</p> Signup and view all the answers

What is the purpose of calculating the accumulated value at the end of each segment?

<p>To adjust the principal for the next period (D)</p> Signup and view all the answers

What is the condition for two events to be independent?

<p>P(A ∩ B) = P(A) × P(B) (D)</p> Signup and view all the answers

What is the purpose of a tree diagram?

<p>To visualize the outcomes of a sequence of events (A)</p> Signup and view all the answers

What is the formula for calculating the effective interest rate?

<p>1 + i_effective = (1 + i_nominal/m)^m (C)</p> Signup and view all the answers

What is the definition of independent events?

<p>Two events that do not affect the probability of each other (B)</p> Signup and view all the answers

What is the formula for the probability of a path in a tree diagram?

<p>P(Event 1) × P(Event 2) × ... (A)</p> Signup and view all the answers

What is the formula for calculating the probability of two independent events?

<p>P(A and B) = P(A) * P(B) (D)</p> Signup and view all the answers

What is the purpose of a two-way contingency table?

<p>To compute the probability of two events and their complements (C)</p> Signup and view all the answers

What is the purpose of using Venn diagrams?

<p>To visualize the relationships between events (B)</p> Signup and view all the answers

What is the formula for the conditional probability of an event A given event B?

<p>P(A and B) / P(B) (A)</p> Signup and view all the answers

What is the condition for two events to be mutually exclusive?

<p>P(A ∩ B) = 0 (D)</p> Signup and view all the answers

What is the formula for calculating the probability of two mutually exclusive events?

<p>P(A or B) = P(A) + P(B) (A)</p> Signup and view all the answers

What is the definition of conditional probability?

<p>The probability of event A occurring given that event B has occurred (D)</p> Signup and view all the answers

What is the formula for the probability of an event A in a contingency table?

<p>n(A) / n(Total) (D)</p> Signup and view all the answers

What is the purpose of the independence test in a contingency table?

<p>To test if two events are independent (C)</p> Signup and view all the answers

What is the formula for calculating the conditional probability of event A given event B?

<p>P(A|B) = P(A and B) / P(B) (C)</p> Signup and view all the answers

What is the formula for the probability of two events A and B occurring in a contingency table?

<p>n(A and B) / n(Total) (C)</p> Signup and view all the answers

What is the definition of a rational number?

<p>A number that can be written as a fraction with an integer in the numerator and the denominator (B)</p> Signup and view all the answers

What is the value of a^(1/n) where a > 0 and n is a positive integer?

<p>√(a) (C)</p> Signup and view all the answers

What is the purpose of simplifying surds?

<p>To express the radicand as a product of factors (C)</p> Signup and view all the answers

What is the result of multiplying √(a) and √(b)?

<p>√(ab) (C)</p> Signup and view all the answers

What is the definition of a surd?

<p>A radical resulting in an irrational number (B)</p> Signup and view all the answers

What is the purpose of rationalizing the denominator?

<p>To eliminate the surd from the denominator (D)</p> Signup and view all the answers

What is the result of a^(m/n) where a > 0, m and n are integers, and n ≠ 0?

<p>√(a^m) (B)</p> Signup and view all the answers

What is the law of exponents that states a^m × a^n = a^(m+n)?

<p>Product of Powers (D)</p> Signup and view all the answers

What is the power of a power rule in exponentiation?

<p>a^(m*n) = (a^m)^n (B)</p> Signup and view all the answers

What is the purpose of rationalising the denominator in surd equations?

<p>To simplify the equation by removing the surd from the denominator (B)</p> Signup and view all the answers

What is the formula for solving exponential growth and decay problems?

<p>P(t) = P_0 * (1 + r)^t (A)</p> Signup and view all the answers

What is the purpose of writing surds in exponential notation?

<p>To make manipulation easier (D)</p> Signup and view all the answers

What is the first step in solving a surd equation?

<p>Isolate the surd term on one side of the equation (B)</p> Signup and view all the answers

What is the purpose of checking solutions in surd equations?

<p>To verify the solution is correct and there are no extraneous solutions (D)</p> Signup and view all the answers

What is the result of a^0, where a ≠ 0?

<p>1 (C)</p> Signup and view all the answers

What is the purpose of solving exponential problems?

<p>To model population growth and radioactive decay (D)</p> Signup and view all the answers

What is the definition of a fractional exponent?

<p>A power that is a fraction (B)</p> Signup and view all the answers

What is the purpose of applying exponent laws in solving surd equations?

<p>To simplify the equation by applying exponent laws (C)</p> 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))?

<p>$\frac{f(a + h) - f(a)}{h}$ (A)</p> Signup and view all the answers

What is the effect of q on the graph of a hyperbolic function y = a/x + q?

<p>A vertical shift (A)</p> Signup and view all the answers

What is the range of the function y = a/(x + p) + q?

<p>{y: y ∈ ℝ, y ≠ q} (D)</p> Signup and view all the answers

What is the effect of p on the graph of a hyperbolic function y = a/(x + p) + q?

<p>A horizontal shift (A)</p> Signup and view all the answers

What is the formula for the vertical asymptote of a hyperbolic function y = a/(x + p) + q?

<p>x = -p (C)</p> Signup and view all the answers

What is the axes of symmetry of a hyperbola in the form y = a/(x + p) + q?

<p>(p, q), (-p, q) (A)</p> Signup and view all the answers

What is the effect of a on the shape of a hyperbolic function y = a/x + q?

<p>A change in shape (A)</p> Signup and view all the answers

What is the effect of q on the graph of an exponential function y = ab^x + q?

<p>A vertical shift (D)</p> Signup and view all the answers

What is the horizontal asymptote of an exponential function y = ab^x + q?

<p>y = q (D)</p> Signup and view all the answers

What is the formula for determining the roots of a quadratic equation?

<p>x = -b / 2a ± √(b^2 - 4ac) / 2a (A)</p> Signup and view all the answers

What is the condition for a quadratic equation to have real and distinct roots?

<p>b^2 - 4ac &gt; 0 (A)</p> Signup and view all the answers

What is the purpose of making a substitution in solving quadratic equations?

<p>To identify the repeated expression (A)</p> Signup and view all the answers

What is the first step in identifying the variables in an exponential growth or decay problem?

<p>Determine the initial amount, growth rate, and time period (B)</p> Signup and view all the answers

What type of roots does a quadratic equation have when Δ = 0?

<p>Real and equal roots (B)</p> Signup and view all the answers

What is the purpose of completing the square in solving quadratic equations?

<p>To transform the equation into a perfect square trinomial (B)</p> Signup and view all the answers

What is the set of real numbers represented by?

<p>ℝ (D)</p> Signup and view all the answers

What is the step to find the original quadratic equation given its roots?

<p>Write the roots as two equations (A)</p> Signup and view all the answers

What is the formula for solving quadratic equations of the form ax² + bx + c = 0?

<p>x = -b ± √(b² - 4ac) / 2a (B)</p> Signup and view all the answers

What is the purpose of identifying restrictions in solving quadratic equations by substitution?

<p>To ensure the values do not make the denominator equal to zero (A)</p> Signup and view all the answers

What is the effect of the parameter b on the direction of the function f(x) if a > 0?

<p>f(x) is increasing if b &gt; 1, decreasing if 0 &lt; b &lt; 1, and not defined if b ≤ 0 (D)</p> Signup and view all the answers

What is the effect of a change in the parameter p on the graph of y = ab^(x+p) + q?

<p>A horizontal shift (B)</p> Signup and view all the answers

What happens when Δ is a perfect square in a quadratic equation?

<p>The roots are rational (B)</p> Signup and view all the answers

What is the result of a⁰, where a ≠ 0?

<p>1 (B)</p> Signup and view all the answers

What is the purpose of converting percentages to decimal form in exponential growth or decay problems?

<p>To convert the growth rate into a decimal form (D)</p> Signup and view all the answers

What is the range of the function y = ab^(x+p) + q if a > 0?

<p>All real numbers greater than q (B)</p> Signup and view all the answers

What type of roots does a quadratic equation have when Δ < 0?

<p>Imaginary roots (A)</p> Signup and view all the answers

What is the formula for simple depreciation?

<p>A = P(1 - in) (C)</p> Signup and view all the answers

What is the first step in solving a quadratic equation by substitution?

<p>Identify the restrictions (C)</p> Signup and view all the answers

What is the condition for a quadratic equation to have two distinct real roots?

<p>Δ &gt; 0 (A)</p> Signup and view all the answers

What is the formula for the discriminant Δ of a quadratic equation in standard form?

<p>Δ = b^2 - 4ac (A)</p> Signup and view all the answers

What is the characteristic of compound depreciation?

<p>The book value never reaches zero (C)</p> Signup and view all the answers

What is the notation for the set of irrational numbers?

<p>ℚᶜ (A)</p> Signup and view all the answers

What is the purpose of using timelines in finance?

<p>To visualize the periods and changes in compounding and interest rates (C)</p> Signup and view all the answers

What is the method used to solve quadratic equations by rewriting them in the form of a perfect square trinomial?

<p>Completing the square (A)</p> Signup and view all the answers

What is the purpose of the quadratic formula?

<p>To solve quadratic equations of the form ax² + bx + c = 0 (A)</p> Signup and view all the answers

How is the interest rate adjusted when compounding occurs more than once a year?

<p>The interest rate is divided by the number of compounding periods (A)</p> Signup and view all the answers

What is the horizontal asymptote of the function y = ab^(x+p) + q?

<p>y = q (D)</p> Signup and view all the answers

What is the difference between simple and compound depreciation?

<p>Simple depreciation calculates depreciation on the initial principal amount, compound depreciation calculates depreciation on the remaining value (A)</p> Signup and view all the answers

What is the formula for compound depreciation?

<p>A = P(1 - i)^n (C)</p> Signup and view all the answers

What is the nature of the roots of a quadratic equation if the discriminant Δ is greater than 0?

<p>Real and unequal roots (D)</p> Signup and view all the answers

What is the purpose of determining the critical values in solving quadratic inequalities?

<p>To determine the sign of the quadratic expression (B)</p> Signup and view all the answers

What is the formula for calculating the discriminant Δ of a quadratic equation in standard form?

<p>Δ = b^2 - 4ac (A)</p> Signup and view all the answers

What is the general method for solving quadratic inequalities?

<p>Graphing the quadratic function and using a table of signs (A)</p> Signup and view all the answers

What is the purpose of creating a table of signs in solving quadratic inequalities?

<p>To determine the sign of the quadratic expression on different intervals (A)</p> Signup and view all the answers

What is the result of solving a quadratic equation with a discriminant Δ equal to 0?

<p>One real root (D)</p> Signup and view all the answers

What is the method mostly used for solving systems of simultaneous equations with linear and non-linear equations?

<p>Substitution method (A)</p> Signup and view all the answers

What is the restriction to consider when solving inequalities with fractions?

<p>Ensuring the denominator is not zero (A)</p> Signup and view all the answers

What is the purpose of graphing the quadratic function in solving quadratic inequalities?

<p>To visualize the solution and identify the regions where the inequality holds true (B)</p> Signup and view all the answers

What is the number of independent equations required to solve for n unknown variables?

<p>n equations (A)</p> Signup and view all the answers

What is the purpose of making a substitution in solving quadratic equations?

<p>To make the equation simpler (A)</p> Signup and view all the answers

What is the result of the second difference between any two consecutive terms in a quadratic sequence?

<p>The difference is constant (B)</p> Signup and view all the answers

What is the purpose of solving systems of equations?

<p>To find the value of multiple variables (D)</p> Signup and view all the answers

What is the general form of a quadratic sequence?

<p>Tn = an^2 + bn + c (C)</p> 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?

<p>To identify the variables in the problem (D)</p> Signup and view all the answers

What is the effect of q on the graph of a parabolic function y = ax^2 + q?

<p>The graph is shifted vertically upwards (A)</p> Signup and view all the answers

What is the purpose of setting up a system of equations in a word problem?

<p>To solve for multiple variables (A)</p> Signup and view all the answers

What is the method of solving systems of equations that involves making one of the variables the subject of both equations?

<p>Solving by equating (C)</p> Signup and view all the answers

What is the purpose of solving systems of equations in real-life problems?

<p>To understand how the natural world works (B)</p> Signup and view all the answers

What is the step in problem-solving strategies that involves translating the words into algebraic expressions?

<p>Translate the words into algebraic expressions (B)</p> Signup and view all the answers

What is the effect of a on the shape of the graph of f(x) = a(x + p)^2 + q?

<p>The graph is a 'smile' if a &gt; 0 and a 'frown' if a &lt; 0 (B)</p> Signup and view all the answers

What is the effect of p on the graph of f(x) = a(x + p)^2 + q?

<p>A horizontal shift (D)</p> Signup and view all the answers

What is the range of the graph of f(x) = a(x + p)^2 + q if a > 0?

<p>All real numbers greater than or equal to q (A)</p> Signup and view all the answers

What is the turning point of the graph of f(x) = a(x + p)^2 + q?

<p>(-p, q) (A)</p> Signup and view all the answers

What is the axis of symmetry of the graph of f(x) = a(x + p)^2 + q?

<p>The line x = -p (B)</p> Signup and view all the answers

What is the formula for the average gradient of a curve between two points?

<p>Gradient = (y_A - y_C) / (x_A - x_C) (B)</p> Signup and view all the answers

What is the purpose of shifting the equation of a parabola?

<p>To change the position of the graph (C)</p> Signup and view all the answers

How do you find the equation of a parabola from the graph?

<p>Use the formula y = a(x - x_1)(x - x_2) (C)</p> Signup and view all the answers

What is the effect of a horizontal shift on the graph of f(x) = a(x + p)^2 + q?

<p>The graph is shifted to the left by p units (A)</p> Signup and view all the answers

What is the effect of a vertical shift on the graph of f(x) = a(x + p)^2 + q?

<p>The graph is shifted upwards by q units (A)</p> Signup and view all the answers

What is the formula for the probability of three events A, B, and C occurring?

<p>P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C) (B)</p> Signup and view all the answers

What are events that cannot occur simultaneously?

<p>Mutually exclusive events (C)</p> Signup and view all the answers

What is the purpose of a tree diagram?

<p>To visualize and organize the outcomes of a sequence of events (C)</p> Signup and view all the answers

What is the formula for the probability of two independent events A and B occurring?

<p>P(A) × P(B) (C)</p> Signup and view all the answers

What is the purpose of a contingency table?

<p>To compute probabilities and test for independence between events (C)</p> Signup and view all the answers

What is the formula for the probability of an event A given event B?

<p>P(A and B) / P(B) (C)</p> Signup and view all the answers

What is the condition for two events A and B to be independent?

<p>P(A) × P(B) = P(A and B) (D)</p> Signup and view all the answers

What is the purpose of determining a specific path in a tree diagram?

<p>To calculate the probability of a specific sequence of events (A)</p> Signup and view all the answers

What is the formula for the probability of an event A?

<p>P(A) = n(A) / n(Total) (A)</p> Signup and view all the answers

What is the purpose of calculating the sum of probabilities in a tree diagram?

<p>To calculate the probability of multiple paths leading to a desired outcome (B)</p> Signup and view all the answers

What is the formula for calculating the accumulated value in compound interest?

<p>A = P(1 + i)^n (A)</p> Signup and view all the answers

What is the purpose of breaking down periods in compound interest calculations?

<p>To calculate the accumulated value at the end of each segment (D)</p> Signup and view all the answers

What is the formula for calculating the effective interest rate?

<p>1 + i_effective = (1 + i_nominal/m)^m (C)</p> Signup and view all the answers

What is the difference between independent and dependent events?

<p>Independent events do not affect the probability of each other, while dependent events do affect the probability of each other (A)</p> Signup and view all the answers

What is the formula for the probability of two independent events?

<p>P(A and B) = P(A) × P(B) (A)</p> Signup and view all the answers

What is the purpose of Venn diagrams?

<p>To visualize the relationships between events (B)</p> Signup and view all the answers

What is the formula for the probability of two mutually exclusive events?

<p>P(A or B) = P(A) + P(B) (C)</p> Signup and view all the answers

What is the concept of conditional probability?

<p>The probability of an event occurring given that another event has occurred (A)</p> Signup and view all the answers

What is the formula for calculating the accumulated value in simple interest?

<p>A = P(1 + in) (D)</p> Signup and view all the answers

What is the difference between nominal and effective interest rates?

<p>Nominal interest rate is the interest rate per compounding period, while effective interest rate is the actual interest rate per year (C)</p> Signup and view all the answers

What is the value of a^(m/n) when a > 0 and m, n are integers?

<p>a^(m/n) (B)</p> Signup and view all the answers

What is the purpose of rationalising the denominator?

<p>To eliminate the surd from the denominator (D)</p> Signup and view all the answers

What is the result of (√a)^m when a > 0 and m is an integer?

<p>a^(m/2) (D)</p> Signup and view all the answers

What is the definition of a surd?

<p>A radical resulting in an irrational number (D)</p> Signup and view all the answers

What is the property of ∏(a) × ∏(b)?

<p>∏(ab) (A)</p> Signup and view all the answers

What is the radical symbol ∏(a) equivalent to?

<p>a^(1/n) (B)</p> Signup and view all the answers

What is the law of exponents for the quotient of powers?

<p>a^m ÷ a^n = a^(m-n) (B)</p> Signup and view all the answers

What is the result of ∏(a^m)?

<p>a^(m/n) (B)</p> Signup and view all the answers

What is the primary goal when solving equations involving surds?

<p>To eliminate the surd on one side of the equation (B)</p> Signup and view all the answers

What is the purpose of writing surds in exponential notation?

<p>To make manipulation easier (D)</p> Signup and view all the answers

What is the result of raising both sides of an equation to the power corresponding to the root?

<p>The surd is eliminated (C)</p> Signup and view all the answers

What is the formula for exponential growth and decay?

<p>P(t) = P_0 * (1 + r)^t (D)</p> Signup and view all the answers

What is the purpose of solving surd equations?

<p>To find the roots of the equation (B)</p> Signup and view all the answers

What is the result of applying the power of a power rule in exponentiation?

<p>a^(mn) = (a^m)^n (B)</p> Signup and view all the answers

What is the purpose of checking solutions in surd equations?

<p>To verify the solution is correct (A)</p> Signup and view all the answers

What is the result of applying the negative exponent rule in exponentiation?

<p>a^(-m) = 1 / a^m (D)</p> Signup and view all the answers

What is the purpose of rationalizing denominators?

<p>To eliminate radicals from the denominator (B)</p> Signup and view all the answers

What is the nature of exponential growth and decay models?

<p>Exponential (C)</p> Signup and view all the answers

What is the formula for determining the roots of a quadratic equation in the form ax^2 + bx + c = 0?

<p>x = -b / 2a ± √(b^2 - 4ac) / 2a (D)</p> Signup and view all the answers

What is the condition for a quadratic equation to have real and distinct roots?

<p>b^2 - 4ac &gt; 0 (C)</p> Signup and view all the answers

What is the purpose of making a substitution in solving quadratic equations?

<p>To simplify the equation (A)</p> Signup and view all the answers

How can you determine the original quadratic equation given its roots?

<p>By writing the roots as a product of two factors (D)</p> Signup and view all the answers

What is the nature of the roots of a quadratic equation when the discriminant Δ is less than 0?

<p>Imaginary (A)</p> Signup and view all the answers

What is the first step in solving a quadratic equation by substitution?

<p>Identify the restrictions (D)</p> Signup and view all the answers

What happens when the discriminant Δ is a perfect square in a quadratic equation?

<p>The roots are rational (B)</p> Signup and view all the answers

What is the purpose of finding the discriminant of a quadratic equation?

<p>To determine the nature of the roots (A)</p> Signup and view all the answers

What is the nature of the roots of a quadratic equation if the discriminant Δ is greater than 0?

<p>Real and unequal (C)</p> Signup and view all the answers

What is the formula to calculate the discriminant Δ of a quadratic equation in standard form?

<p>b^2 - 4ac (B)</p> Signup and view all the answers

What type of roots does a quadratic equation have when Δ = 0?

<p>Real and equal (B)</p> Signup and view all the answers

What is the purpose of factorizing the quadratic expression in solving quadratic inequalities?

<p>To identify the regions where the quadratic expression is positive or negative (A)</p> Signup and view all the answers

What is the condition for a quadratic equation to have real and equal roots?

<p>b^2 - 4ac = 0 (C)</p> Signup and view all the answers

What is the graphical representation of a quadratic function used for in solving quadratic inequalities?

<p>To identify the regions where the quadratic expression is positive or negative (A)</p> Signup and view all the answers

What is the purpose of creating a table of signs in solving quadratic inequalities?

<p>To identify the regions where the quadratic expression is positive or negative (C)</p> Signup and view all the answers

What is the restriction to consider when solving inequalities with fractions?

<p>To ensure the denominator is not zero (D)</p> Signup and view all the answers

What method is mostly used for solving systems of simultaneous equations with linear and non-linear equations?

<p>Substitution (C)</p> Signup and view all the answers

What is the number of independent equations required to solve for n unknown variables?

<p>n (C)</p> Signup and view all the answers

What is the purpose of completing the square in solving quadratic equations?

<p>To solve the quadratic equation in standard form (A)</p> Signup and view all the answers

What is the general method for solving quadratic inequalities?

<p>Factoring, solving for critical values, creating a table of signs, and graphing (A)</p> Signup and view all the answers

What is the first step in solving a system of linear equations using the substitution method?

<p>Solve for one of the variables in one of the equations (D)</p> Signup and view all the answers

What is the purpose of solving word problems?

<p>To apply mathematical language to describe real-life contexts (D)</p> Signup and view all the answers

What is the definition of a quadratic sequence?

<p>A sequence of numbers in which the second difference between any two consecutive terms is constant (B)</p> Signup and view all the answers

What is the effect of q on the graph of y = ax^2 + q?

<p>Vertical shift upwards by q units (A), Vertical shift downwards by q units (B)</p> Signup and view all the answers

What is the first step in solving a quadratic equation using the elimination method?

<p>Add or subtract the equations to eliminate one variable (B)</p> Signup and view all the answers

What is the purpose of assigning variables to the unknown quantities in a word problem?

<p>To translate the words into algebraic expressions (B)</p> Signup and view all the answers

What is the general form of a quadratic sequence?

<p>Tn = an^2 + bn + c (C)</p> Signup and view all the answers

What is the purpose of solving simultaneous equations?

<p>To find the values of the unknown variables (C)</p> Signup and view all the answers

What is the result of solving a system of linear equations using the substitution method?

<p>The values of the unknown variables (B)</p> Signup and view all the answers

What is the purpose of translating the words into algebraic expressions in a word problem?

<p>To set up a system of equations (A)</p> Signup and view all the answers

What is the effect of a parameter p on the graph of y = a(x + p)^2 + q?

<p>Horizontal shift (D)</p> Signup and view all the answers

What is the range of the graph of f(x) = a(x + p)^2 + q when a > 0?

<p>{y : y ≥ q, y ∈ ℝ} (B)</p> Signup and view all the answers

What is the turning point of the graph of f(x) = a(x - p)^2 + q?

<p>(p, q) (C)</p> Signup and view all the answers

What is the axis of symmetry of the graph of f(x) = a(x + p)^2 + q?

<p>x = -p (A)</p> Signup and view all the answers

What is the effect of a horizontal shift on the graph of y = a(x + p)^2 + q?

<p>The graph is shifted to the left (D)</p> Signup and view all the answers

What is the formula for calculating the average gradient between two points on a curve?

<p>Gradient = (y_A - y_C) / (x_A - x_C) (D)</p> Signup and view all the answers

What is the effect of a vertical shift on the graph of y = a(x + p)^2 + q?

<p>The graph is shifted upward (D)</p> Signup and view all the answers

What is the purpose of sketching the graph of a quadratic function?

<p>To determine the characteristics of the graph (A)</p> Signup and view all the answers

What is the domain of the graph of y = a(x + p)^2 + q?

<p>{x : x ∈ ℝ} (D)</p> Signup and view all the answers

What is the effect of a on the shape of the graph of y = a(x + p)^2 + q?

<p>The graph is narrower for larger values of a (A)</p> Signup and view all the answers

What is the purpose of completing the square in solving quadratic equations?

<p>To convert the equation into a perfect square trinomial (D)</p> Signup and view all the answers

What is the formula for solving quadratic equations of the form ax^2 + bx + c = 0?

<p>x = (-b ± √(b^2 - 4ac)) / 2a (A)</p> Signup and view all the answers

What is the result of a^0, where a ≠ 0?

<p>1 (A)</p> Signup and view all the answers

What is the set of rational numbers represented by?

<p>ℚ (D)</p> Signup and view all the answers

What is the purpose of converting percentages to decimal form in exponential growth or decay problems?

<p>To use the formula correctly (D)</p> Signup and view all the answers

What is the definition of a quadratic equation?

<p>An equation of the form ax^2 + bx + c = 0 (A)</p> Signup and view all the answers

What is the formula for the discriminant Δ of a quadratic equation in standard form?

<p>b^2 - 4ac (C)</p> Signup and view all the answers

What is the result of √(a^n), where n is a positive integer?

<p>a^(n/2) (C)</p> Signup and view all the answers

What is the nature of the roots of a quadratic equation if the discriminant Δ is less than 0?

<p>Complex and distinct (C)</p> Signup and view all the answers

What is the purpose of identifying the variables in an exponential growth or decay problem?

<p>To determine the initial amount, growth rate, and time period (D)</p> Signup and view all the answers

What is the average gradient of the curve at point P when h = 0?

<p>2a (B)</p> Signup and view all the answers

What is the horizontal asymptote of the hyperbolic function y = a/x + q?

<p>y = q (D)</p> Signup and view all the answers

What is the effect of a change in p on the graph of the hyperbolic function y = a/(x + p) + q?

<p>A horizontal shift (D)</p> Signup and view all the answers

What is the domain of the hyperbolic function y = a/(x + p) + q?

<p>{x : x ∈ ℝ, x ≠ -p} (A)</p> Signup and view all the answers

What is the range of the hyperbolic function y = a/(x + p) + q?

<p>{y : y ∈ ℝ, y ≠ q} (D)</p> Signup and view all the answers

What is the axes of symmetry of the hyperbolic function y = a/(x + p) + q?

<p>The lines x = -p and y = q (D)</p> Signup and view all the answers

If b > 1, what is the effect on the function f(x)?

<p>f(x) is an increasing function (D)</p> Signup and view all the answers

What is the effect of a on the shape of the exponential function y = ab^x + q?

<p>For a &gt; 0, the function is increasing, and for a &lt; 0, the function is decreasing (D)</p> Signup and view all the answers

What is the effect of a change in p on the graph of y = ab^(x+p) + q?

<p>A horizontal shift (C)</p> Signup and view all the answers

What is the range of y = ab^(x+p) + q when a > 0?

<p>{y: y &gt; q, y ∈ ℝ} (D)</p> Signup and view all the answers

What is the effect of q on the graph of the exponential function y = ab^x + q?

<p>A vertical shift (D)</p> Signup and view all the answers

What is the horizontal asymptote of the exponential function y = ab^x + q?

<p>y = q (D)</p> Signup and view all the answers

What is the formula for simple depreciation?

<p>A = P(1 - in) (A)</p> Signup and view all the answers

What is the purpose of finding the axes of symmetry of a hyperbolic function?

<p>To identify the axes of symmetry of the function (A)</p> Signup and view all the answers

What is the effect of compound depreciation on the depreciation amount?

<p>The depreciation amount decreases every year (B)</p> Signup and view all the answers

What is the purpose of using timelines in finance?

<p>To visualize the periods and changes in compounding and interest rates (C)</p> Signup and view all the answers

What is the effect of a change in q on the graph of y = ab^(x+p) + q?

<p>A vertical shift (B)</p> Signup and view all the answers

What is the horizontal asymptote of the graph of y = ab^(x+p) + q?

<p>y = q (A)</p> Signup and view all the answers

What is the formula to find the annual depreciation rate (i) for compound decay?

<p>A = P(1 - i)^n (B)</p> Signup and view all the answers

What is the effect of compounding more than once a year on the interest rate?

<p>The interest rate is divided by p (C)</p> Signup and view all the answers

What is the formula for calculating the accumulated value in compound interest?

<p>A = P(1 + i)^n (C)</p> Signup and view all the answers

What is the purpose of breaking down periods in compound interest calculations?

<p>To calculate the accumulated value at the end of each period (C)</p> Signup and view all the answers

What is the formula for calculating the effective interest rate?

<p>1 + i_effective = (1 + i_nominal/m)^m (A)</p> Signup and view all the answers

What is the definition of independent events in probability?

<p>Two events are independent if the occurrence of one does not affect the probability of the other (A)</p> Signup and view all the answers

What is the formula for calculating the probability of two independent events?

<p>P(A and B) = P(A) × P(B) (A)</p> Signup and view all the answers

What is the purpose of using Venn diagrams in probability?

<p>To visualize the sample space and events (A)</p> Signup and view all the answers

What is the formula for calculating the union of two events?

<p>P(A or B) = P(A) + P(B) - P(A and B) (C)</p> Signup and view all the answers

What is the formula for calculating the conditional probability of an event?

<p>P(A|B) = P(A and B) / P(B) (D)</p> Signup and view all the answers

What is the definition of mutually exclusive events in probability?

<p>Two events are mutually exclusive if they cannot occur at the same time (B)</p> Signup and view all the answers

What is the formula for calculating the probability of two mutually exclusive events?

<p>P(A or B) = P(A) + P(B) (A)</p> Signup and view all the answers

What is the formula for the general addition rule for three events?

<p>P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) (C)</p> Signup and view all the answers

What is the definition of mutually exclusive events?

<p>Events that cannot occur simultaneously (C)</p> Signup and view all the answers

What is the purpose of a tree diagram?

<p>To organise and visualise the different possible outcomes of a sequence of events (B)</p> Signup and view all the answers

What is the formula for the probability of a path in a tree diagram?

<p>P(A) × P(B) × ... (A)</p> Signup and view all the answers

What is the purpose of a contingency table?

<p>To test for independence between two events (C)</p> Signup and view all the answers

What is the formula for the conditional probability P(A|B) ?

<p>P(A and B) / P(B) (B)</p> Signup and view all the answers

What is the definition of independent events?

<p>The occurrence of one event does not affect the probability of the other (B)</p> Signup and view all the answers

What is the formula for the probability of two independent events A and B?

<p>P(A) × P(B) (D)</p> Signup and view all the answers

What is the purpose of calculating the probability of an event using a tree diagram?

<p>To calculate the probability of a specific sequence of events (C)</p> Signup and view all the answers

What is the definition of a dependent event?

<p>The occurrence of one event affects the probability of the other (A)</p> Signup and view all the answers

What is the value of $a^{rac{m}{n}}$?

<p>$\sqrt[n]{a^m}$ (D)</p> Signup and view all the answers

What is the purpose of rationalising the denominator?

<p>To eliminate the surd from the denominator (A)</p> Signup and view all the answers

What is the value of $a^{-rac{1}{n}}$?

<p>$\sqrt[n]{a^{-1}}$ (B)</p> Signup and view all the answers

What is the definition of a surd?

<p>A radical resulting in an irrational number (D)</p> Signup and view all the answers

What is the result of multiplying $\sqrt[n]{a}$ and $\sqrt[n]{b}$?

<p>$\sqrt[n]{ab}$ (D)</p> Signup and view all the answers

What is the value of $\sqrt[n]{a^m}$?

<p>$a^{rac{m}{n}}$ (B)</p> Signup and view all the answers

What is the purpose of the laws of exponents?

<p>To extend the rules of exponents to rational numbers (D)</p> Signup and view all the answers

What is the result of raising $\sqrt[n]{a}$ to the power of $m$?

<p>$a^{rac{m}{n}}$ (D)</p> Signup and view all the answers

What is the purpose of converting surds to exponential notation?

<p>To make it easier to manipulate expressions (A)</p> Signup and view all the answers

What is the main goal when solving surd equations?

<p>To isolate the surd (C)</p> Signup and view all the answers

What is the formula for exponential growth or decay?

<p>P(t) = P_0 × (1 + r)^t (C)</p> Signup and view all the answers

What should you do after eliminating the surd in a surd equation?

<p>Solve the resulting equation (D)</p> Signup and view all the answers

Why do you need to check the solution in a surd equation?

<p>To verify the solution is correct (C)</p> Signup and view all the answers

What is the purpose of rationalizing the denominator in a surd expression?

<p>To make the expression easier to manipulate (A)</p> Signup and view all the answers

What is the result of raising both sides of a surd equation to the power corresponding to the root?

<p>Eliminating the surd (C)</p> Signup and view all the answers

What is the purpose of applying the rules of exponents in surd equations?

<p>To make the equation easier to manipulate (B)</p> Signup and view all the answers

What is the result of substituting a solution back into the original surd equation?

<p>Verifying the solution is correct (A)</p> Signup and view all the answers

What is the purpose of factorizing in solving quadratic surd equations?

<p>To make the equation easier to solve (D)</p> Signup and view all the answers

What is the purpose of completing the square in solving quadratic equations?

<p>To find the roots of a quadratic equation (C)</p> Signup and view all the answers

What is the formula for exponential growth and decay?

<p>A = P(1 + r)^t (C)</p> Signup and view all the answers

What is the result of a^0, where a ≠ 0?

<p>1 (A)</p> Signup and view all the answers

What is the purpose of converting percentages to decimal form in exponential growth or decay problems?

<p>To simplify the equation (D)</p> Signup and view all the answers

What is the definition of a quadratic equation?

<p>An equation of the form ax^2 + bx + c = 0 (B)</p> Signup and view all the answers

What is the quadratic formula?

<p>x = (-b - √(b^2 - 4ac)) / 2a (A), x = (-b + √(b^2 - 4ac)) / 2a (B)</p> Signup and view all the answers

What is the purpose of the quadratic formula?

<p>To solve quadratic equations (C)</p> Signup and view all the answers

What is the definition of a rational exponent?

<p>A fractional exponent (D)</p> Signup and view all the answers

What is the purpose of simplifying surds?

<p>To simplify the equation (C)</p> Signup and view all the answers

What is the definition of a surd?

<p>A root of a number that is not a perfect square (C)</p> Signup and view all the answers

What is the quadratic formula used to determine?

<p>The roots of a quadratic equation (B)</p> Signup and view all the answers

What does the discriminant Δ represent in a quadratic equation?

<p>The type of roots of a quadratic equation (B)</p> Signup and view all the answers

What is the condition for a quadratic equation to have two distinct real roots?

<p>b^2 - 4ac &gt; 0 (B)</p> Signup and view all the answers

What is the purpose of making a substitution in solving quadratic equations?

<p>To simplify the equation (B)</p> Signup and view all the answers

What is the first step in solving a quadratic equation by substitution?

<p>Identify the repeated expression (D)</p> Signup and view all the answers

What happens when Δ is a perfect square in a quadratic equation?

<p>The equation has two rational roots (A)</p> Signup and view all the answers

What is the formula for the discriminant Δ of a quadratic equation in standard form?

<p>b^2 - 4ac (B)</p> Signup and view all the answers

What is the nature of the roots of a quadratic equation when Δ = 0?

<p>One real root (A)</p> Signup and view all the answers

What is the purpose of finding the quadratic equation given its roots?

<p>To work backwards and find the original equation (C)</p> Signup and view all the answers

What is the formula for the roots of a quadratic equation in standard form?

<p>x = (-b ± √(b^2 - 4ac)) / 2a (A)</p> Signup and view all the answers

What is the nature of the roots of a quadratic equation if the discriminant Δ is equal to 0?

<p>Real and equal (one root) (C)</p> Signup and view all the answers

What is the formula for the discriminant Δ of a quadratic equation in standard form?

<p>b^2 - 4ac (C)</p> Signup and view all the answers

What is the purpose of completing a table of signs in solving quadratic inequalities?

<p>To identify the regions where the quadratic expression is positive or negative (D)</p> Signup and view all the answers

What is the method mostly used for solving systems of simultaneous equations with linear and non-linear equations?

<p>Substitution method (B)</p> Signup and view all the answers

What is the general method for solving quadratic inequalities?

<p>All of the above (D)</p> Signup and view all the answers

What is the condition for a quadratic equation to have two distinct real roots?

<p>Δ &gt; 0 (D)</p> Signup and view all the answers

What happens when Δ is a perfect square in a quadratic equation?

<p>The roots are rational (B)</p> Signup and view all the answers

What is the purpose of the critical values in solving quadratic inequalities?

<p>To determine the regions where the quadratic expression is positive or negative (B)</p> Signup and view all the answers

What is the first step in solving a quadratic inequality?

<p>Write the quadratic inequality in standard form (A)</p> Signup and view all the answers

What is the purpose of considering restrictions when solving inequalities with fractions?

<p>To avoid undefined expressions (D)</p> Signup and view all the answers

What happens to the graph of f(x) = a(x + p)^2 + q when a > 0?

<p>The graph becomes a 'smile' and has a minimum turning point. (D)</p> Signup and view all the answers

What is the first step in solving a system of linear equations using the substitution method?

<p>Solve for one variable in one of the equations. (A)</p> Signup and view all the answers

What is the effect of p on the graph of f(x) = a(x + p)^2 + q?

<p>A horizontal shift. (B)</p> Signup and view all the answers

What is the domain of the function f(x) = a(x + p)^2 + q?

<p>{x : x ∈ ℝ} (C)</p> Signup and view all the answers

What is the main purpose of using mathematical models to solve real-world problems?

<p>To describe real-life contexts and make predictions. (A)</p> Signup and view all the answers

What is the definition of a quadratic sequence?

<p>A sequence of numbers in which the second difference between any two consecutive terms is constant. (A)</p> Signup and view all the answers

What is the axis of symmetry for the function f(x) = a(x + p)^2 + q?

<p>The vertical line x = -p. (D)</p> Signup and view all the answers

What is the purpose of setting up a system of equations to solve a word problem?

<p>To translate the words into algebraic expressions. (D)</p> Signup and view all the answers

What is the range of the function f(x) = a(x + p)^2 + q when a > 0?

<p>{y : y ≥ q, y ∈ ℝ} (A)</p> Signup and view all the answers

What is the result of shifting the graph of y = ax^2 vertically upwards by q units?

<p>The turning point of the graph is above the x-axis. (D)</p> Signup and view all the answers

How do you find the y-intercept of the function f(x) = a(x + p)^2 + q?

<p>Set x = 0 and solve for y. (D)</p> Signup and view all the answers

What is the turning point of the function f(x) = a(x + p)^2 + q?

<p>(-p, q) (A)</p> Signup and view all the answers

What is the purpose of solving systems of linear equations?

<p>To find the solution to a real-world problem. (B)</p> Signup and view all the answers

What is the formula for the average gradient of a curve?

<p>Average gradient = (f(a + h) - f(a)) / h (C)</p> Signup and view all the answers

What is the formula for the average gradient of a curve between two points A and C?

<p>Gradient = (yA - yC) / (xA - xC) (C)</p> Signup and view all the answers

What is the effect of a change in q on the graph of y = a/x + q?

<p>A vertical shift (D)</p> Signup and view all the answers

What is the general form of a quadratic sequence?

<p>Tn = an^2 + bn + c. (D)</p> Signup and view all the answers

What is the first step in solving a word problem using mathematical models?

<p>Read the problem carefully and identify the question. (A)</p> Signup and view all the answers

What is the vertical asymptote of the graph of y = a/(x + p) + q?

<p>x = -p (B)</p> Signup and view all the answers

What is the purpose of shifting the equation of a parabola?

<p>To change the position of the parabola. (B)</p> Signup and view all the answers

What is the purpose of solving systems of linear equations graphically?

<p>To find the solution to a system of equations. (D)</p> Signup and view all the answers

What is the domain of the function y = a/(x + p) + q?

<p>{x : x ∈ ℝ, x ≠ -p} (C)</p> Signup and view all the answers

What is the formula for finding the equation of a parabola from the graph?

<p>y = a(x - x1)(x - x2) (A)</p> Signup and view all the answers

What is the condition for a quadratic equation to have two distinct real roots?

<p>b^2 - 4ac &gt; 0. (B)</p> Signup and view all the answers

What is the effect of a change in a on the shape of the graph of y = a/x + q?

<p>The graph moves closer to or further away from the axes (B)</p> Signup and view all the answers

What is the effect of a change in p on the graph of y = a/(x + p) + q?

<p>A horizontal shift (D)</p> Signup and view all the answers

What is the range of the function y = ab^x + q?

<p>{y : y ∈ ℝ, y ≠ q} (D)</p> Signup and view all the answers

What is the effect of a change in q on the graph of y = ab^x + q?

<p>A vertical shift (D)</p> Signup and view all the answers

What is the effect of a change in a on the shape of the graph of y = ab^x + q?

<p>The graph becomes increasing or decreasing (B)</p> Signup and view all the answers

What are the axes of symmetry of the graph of y = a/(x + p) + q?

<p>The lines x = -p and y = q (A)</p> Signup and view all the answers

What is the effect of b on the direction of the graph of f(x) = ab^x when a > 0?

<p>If b &gt; 1, the graph is increasing; if 0 &lt; b &lt; 1, the graph is decreasing. (B)</p> Signup and view all the answers

What happens to the graph of f(x) = ab^(x+p) + q when p > 0?

<p>The graph is shifted to the left by p units. (B)</p> Signup and view all the answers

What is the range of the graph of f(x) = ab^x + q when a > 0?

<p>All real numbers greater than q (D)</p> Signup and view all the answers

What type of depreciation reduces the value of an asset by a constant amount each year?

<p>Simple depreciation (B)</p> Signup and view all the answers

What is the formula for compound depreciation?

<p>A = P(1 - i)^n (B)</p> Signup and view all the answers

What is the purpose of using timelines in finance?

<p>To visualize the periods and changes in compounding and interest rates over time (A)</p> Signup and view all the answers

What happens when an investment is compounded more than once a year?

<p>The number of years is multiplied by the compounding frequency (D)</p> Signup and view all the answers

What is the horizontal asymptote of the graph of f(x) = ab^x + q?

<p>y = q (B)</p> Signup and view all the answers

What is the domain of the graph of f(x) = ab^x + q?

<p>All real numbers (D)</p> Signup and view all the answers

What is the formula for simple depreciation?

<p>A = P(1 - in) (A)</p> Signup and view all the answers

What is the purpose of breaking down periods in compound interest calculations?

<p>To account for changes in interest rates or additional deposits/withdrawals (D)</p> Signup and view all the answers

What is the formula for compound interest?

<p>A = P(1 + i)^n (A)</p> Signup and view all the answers

What is the difference between nominal and effective interest rates?

<p>Nominal interest rate is the interest rate per year, while effective interest rate is the interest rate per compounding period (D)</p> Signup and view all the answers

What is the formula for independent events?

<p>P(A and B) = P(A) × P(B) (D)</p> Signup and view all the answers

What is the purpose of the addition rule for mutually exclusive events?

<p>To find the probability of the union of two mutually exclusive events (B)</p> Signup and view all the answers

What is the definition of conditional probability?

<p>The probability of event A occurring given that event B has occurred (D)</p> Signup and view all the answers

What is the formula for the effective interest rate?

<p>1 + i_effective = (1 + i_nominal/m)^m (A)</p> Signup and view all the answers

What is the purpose of Venn diagrams in probability?

<p>To visualize the sample space and events (C)</p> Signup and view all the answers

What is the definition of dependent events?

<p>Two events that affect the probability of each other (D)</p> Signup and view all the answers

What is the addition rule for non-mutually exclusive events?

<p>P(A ∪ B) = P(A) + P(B) - P(A ∩ B) (D)</p> Signup and view all the answers

What is the formula for the probability of the union of three events A, B, and C?

<p>P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C) (A)</p> Signup and view all the answers

What is the definition of mutually exclusive events?

<p>Events that cannot occur simultaneously (C)</p> Signup and view all the answers

What is the purpose of a tree diagram?

<p>To organize and visualize the different possible outcomes of a sequence of events (B)</p> Signup and view all the answers

What is the formula for the probability of two independent events A and B?

<p>P(A) × P(B) (C)</p> Signup and view all the answers

What is the structure of a two-way contingency table?

<p>Rows represent one event and its complement, columns represent another event (B)</p> Signup and view all the answers

What is the formula for the probability of an event A given event B?

<p>P(A and B) / P(B) (A)</p> Signup and view all the answers

What is the purpose of a contingency table?

<p>To test for independence between events (B)</p> Signup and view all the answers

What is the formula for the probability of a specific path in a tree diagram?

<p>P(Event 1) × P(Event 2) × ... (D)</p> Signup and view all the answers

What is the purpose of calculating the probability of a desired outcome in a tree diagram?

<p>To find the probability of a specific sequence of events (A)</p> Signup and view all the answers

What is the condition for two events A and B to be independent?

<p>P(A and B) = P(A) × P(B) (A)</p> Signup and view all the answers

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