Gr 11 Math Nov P1 (Mix)
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Questions and Answers

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

  • r = √[a^(1/n)] (correct)
  • r = √(n/a)
  • r = a^n
  • r = √(a/n)

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

  • n√a
  • √(a/n) (correct)
  • √[a^n]
  • √a^n

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

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

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

<p>√[a^m]^(1/n) (C)</p> Signup and view all the answers

What is the radical symbol √[n]{a} indicating?

<p>n-th root of a (B)</p> Signup and view all the answers

What is a surd?

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

What is the formula for simplifying surds?

<p>√a × √b = √ab (D)</p> Signup and view all the answers

What is the purpose of rationalizing denominators?

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

What is the rule for raising a power to a power?

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

What is the definition of a surd?

<p>A radical that results in an irrational number (C)</p> Signup and view all the answers

What is the purpose of rationalizing denominators?

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

What is the first step in solving surd equations?

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

What is the formula for exponential growth or decay?

<p>P(t) = P₀ × (1 + r)^t (D)</p> Signup and view all the answers

What is the purpose of checking solutions in surd equations?

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

What is the key concept in solving quadratic surd equations?

<p>Squaring both sides of the equation (D)</p> Signup and view all the answers

What is the difference between exponential growth and decay?

<p>Growth has a positive growth rate, while decay has a negative growth rate (B)</p> Signup and view all the answers

What is the formula for compound interest?

<p>P(t) = P₀ × (1 + r)^t (B)</p> Signup and view all the answers

What is the formula to find the final amount in exponential growth or decay?

<p>A × (1 + r)^n (D)</p> Signup and view all the answers

What is the set of natural numbers represented by?

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

What is the formula to solve any quadratic equation 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 completing the square method in quadratic equations?

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

What is the formula to find the nth root of a number a?

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

What is the formula to find a^(-m/n)?

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

What is the formula to find a^(m/n)?

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

What is the purpose of dividing by a in the quadratic equation ax² + bx + c = 0?

<p>To make the coefficient of x² equal to 1 (B)</p> Signup and view all the answers

What is the formula to find the square root of a number a?

<p>a^(1/2) (D)</p> Signup and view all the answers

What is the set of real numbers represented by?

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

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

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

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

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

What is the formula for the discriminant of a quadratic equation?

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

What is the result of multiplying the terms in the quadratic equation (x - r_1)(x - r_2) = 0?

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

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

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

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

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

What is the result of solving the quadratic equation in terms of k?

<p>The values of k are obtained (C)</p> Signup and view all the answers

What is the purpose of verifying restrictions in solving quadratic equations?

<p>To check the solutions against any restrictions identified (C)</p> Signup and view all the answers

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

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

What is the last step in solving a system of equations using the substitution or elimination method?

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

What is the purpose of solving word problems in mathematics?

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

What is the general form of a quadratic sequence?

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

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

<p>It shifts the graph vertically (B)</p> Signup and view all the answers

What is the purpose of solving systems of equations?

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

What is the first step in solving a word problem?

<p>Read the problem carefully (C)</p> Signup and view all the answers

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

<p>It makes the graph narrower (D)</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 (A)</p> Signup and view all the answers

What is the result of solving a system of equations graphically?

<p>The solution is the coordinates of the points where the two graphs intersect (C)</p> Signup and view all the answers

What is the importance of problem-solving strategies in mathematics?

<p>They are used in various fields to understand real-life situations (B)</p> Signup and view all the answers

What does the discriminant Δ represent in a quadratic equation?

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

What is the purpose of determining the critical values when solving a quadratic inequality?

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

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

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

What is the method of solving a quadratic inequality by analyzing the sign of each factor on intervals defined by the critical values?

<p>Table of signs (B)</p> Signup and view all the answers

What is the purpose of creating a table of signs when solving a quadratic inequality?

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

What is the method of solving simultaneous equations by expressing one of the variables in terms of the other?

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

What is the purpose of solving simultaneous equations?

<p>To find the intersection point of two lines (D)</p> Signup and view all the answers

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

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

What is the purpose of the graphical method in solving simultaneous equations?

<p>To determine the intersection point of two lines (B)</p> Signup and view all the answers

What is the method of solving quadratic inequalities by sketching the graph and visually identifying the regions where the quadratic expression satisfies the inequality?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<p>A change in the direction of the graph (A)</p> Signup and view all the answers

What is the effect of a change in b on the direction of the exponential function y = ab^x + q?

<p>The direction of the graph changes (A)</p> Signup and view all the answers

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

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

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

<p>A horizontal shift to the left (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 $q$ (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 characteristic of the graph of $y = ab^{(x+p)} + q$ when $a < 0$?

<p>The graph lies below the horizontal asymptote (D)</p> Signup and view all the answers

What is the purpose of a timeline in compounding interest?

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

What is the formula for compound depreciation?

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

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

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

What is the domain of the function $y = ab^{(x+p)} + q$?

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

What is the difference between simple and compound depreciation?

<p>Simple depreciation has a constant depreciation amount, while compound depreciation has a decreasing depreciation amount (C)</p> Signup and view all the answers

What is the purpose of adjusting for compounding periods in timelines?

<p>To modify the interest rate and the number of compounding periods according to the frequency of compounding (D)</p> Signup and view all the answers

What is the effect of a horizontal shift on the graph of a quadratic function?

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

What is the effect of a negative value of a on the graph of a quadratic function?

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

What is the domain of a quadratic function?

<p>The domain is all real numbers (C)</p> Signup and view all the answers

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

<p>The axis of symmetry is the vertical line x = -p (A)</p> Signup and view all the answers

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

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

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

<p>The turning point is (-p, q) (D)</p> Signup and view all the answers

What is the effect of a vertical shift on the graph of a quadratic function?

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

What is the range of a quadratic function with a positive value of a?

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

What is the formula for finding the y-intercept of a quadratic function?

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

What is the effect of a negative value of q on the graph of a quadratic function?

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

What does each branch of a tree diagram represent?

<p>A possible outcome of an event (B)</p> Signup and view all the answers

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

<p>The product of the probabilities along the path (B)</p> Signup and view all the answers

What is the purpose of a contingency table?

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

How do you calculate the probability of an event A?

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

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

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

What is the condition for independence between two events A and B?

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

What is the purpose of drawing a tree diagram?

<p>To show the outcomes of multiple events (A)</p> Signup and view all the answers

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

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

What is the formula for calculating the accumulated value of an investment using compound interest?

<p>A = P(1 + \frac{i}{p})^{np} (B)</p> Signup and view all the answers

What is the formula for calculating the effective interest rate?

<p>1 + i-effective = (1 + \frac{i-nominal}{m})^m (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) (C)</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 concept 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 calculating the probability of three events using the general addition rule?

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

What is the purpose of using tree diagrams in probability?

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

What is the definition of dependent events in probability?

<p>Events that are affected by the occurrence of each other (D)</p> Signup and view all the answers

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

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

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

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

What is the result of multiplying $a^{rac{m}{n}}$ by $a^{rac{p}{n}}$?

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

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

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

What is the purpose of rationalizing the denominator?

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

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

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

What is the condition for the radicand to have real roots?

<p>The radicand must be positive (B)</p> Signup and view all the answers

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

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

What is the purpose of simplifying surds?

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

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

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

What is the purpose of determining the critical values when solving a quadratic inequality?

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

What is the formula to calculate the discriminant Δ of a quadratic equation in standard form ax^2 + bx + c = 0?

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

What is the next step after factorizing the quadratic expression when solving a quadratic inequality?

<p>Determine the sign of each factor on intervals defined by the critical values (C)</p> Signup and view all the answers

What is the purpose of solving quadratic inequalities?

<p>To determine which part of the graph of a quadratic function lies above or below the x-axis (A)</p> Signup and view all the answers

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

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

What is the purpose of graphing a quadratic function when solving a quadratic inequality?

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

What is the result of solving a quadratic equation when Δ is less than 0?

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

What is the last step in solving a quadratic inequality?

<p>Write the final solution and represent it on a number line (C)</p> Signup and view all the answers

What is the primary goal when solving surd equations?

<p>To eliminate the surd term from 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 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 formula for exponential growth or decay?

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

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

<p>To eliminate possible values that would make the expression undefined (B)</p> Signup and view all the answers

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

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

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

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

What is the difference between exponential growth and decay?

<p>Growth is when the rate is positive, decay is when the rate is negative (A)</p> Signup and view all the answers

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

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

What is the formula for compound interest?

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

What is the value of x in the equation x^2 + 4x + 4 = 0?

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

What is the formula for the discriminant (Δ) of a quadratic equation?

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

Which of the following is a condition for exponential growth or decay?

<p>The percentage rate must be converted to decimal form. (A)</p> Signup and view all the answers

What is the key concept in solving quadratic surd equations?

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

What is the purpose of rationalizing denominators?

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

What is the purpose of verifying restrictions when solving quadratic equations?

<p>To check the validity of the solutions obtained (D)</p> Signup and view all the answers

What is the purpose of the quadratic formula?

<p>To solve any quadratic equation in the form ax^2 + bx + c = 0. (B)</p> Signup and view all the answers

What is the importance of simplifying surds?

<p>It simplifies the equation (A)</p> Signup and view all the answers

What is the result of taking half the coefficient of the x term and squaring it in the completing the square method?

<p>Addition and subtraction of the value to the equation. (C)</p> Signup and view all the answers

What is the result of solving the quadratic equation in terms of k when using substitution?

<p>The value of k (C)</p> Signup and view all the answers

What is the value of a in the equation a^0 = 1?

<p>Any non-zero real number. (D)</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 (A)</p> Signup and view all the answers

What is the rule for raising a power to a power?

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

What is the purpose of dividing by a in the quadratic equation ax^2 + bx + c = 0?

<p>To make the coefficient of x^2 equal to 1. (D)</p> Signup and view all the answers

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

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

What is the formula for the nth root of a number a?

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

What is the purpose of the completing the square method?

<p>To solve quadratic equations in the form ax^2 + bx + c = 0. (D)</p> Signup and view all the answers

What is the result of taking the square root of both sides in the quadratic formula?

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

What is the set of real numbers represented by?

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

What is the final step in solving a system of equations using the substitution or elimination method?

<p>Substitute the solution into the original equation to find the value of the other unknown variable. (B)</p> Signup and view all the answers

What is the purpose of writing a set of equations to describe a word problem?

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

What is the result of solving a system of equations graphically?

<p>The solution to the system of equations is a single point. (B)</p> Signup and view all the answers

What is the purpose of problem-solving strategies in mathematics?

<p>To understand how to approach a problem in a logical and methodical way. (A)</p> Signup and view all the answers

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

<p>It shifts the graph vertically. (D)</p> Signup and view all the answers

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

<p>To describe the sequence in a general form. (D)</p> Signup and view all the answers

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

<p>It changes the shape of the graph. (C)</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 does each branch of a tree diagram represent?

<p>A possible outcome of an event (D)</p> Signup and view all the answers

What is the first step in solving a word problem?

<p>Identify the question and determine what needs to be solved. (C)</p> Signup and view all the answers

What is the importance of problem-solving strategies in mathematics?

<p>It helps to understand how to approach a problem in a logical and methodical way. (C)</p> Signup and view all the answers

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

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

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

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

What is the formula to calculate the probability of an event A?

<p>n(A) / n(Total) (B)</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 calculating the probability of a path in a tree diagram?

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

What is the formula to calculate the conditional probability of A given B?

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

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

<p>The graph is narrower for a &gt; 0 and wider for a &lt; 0. (A)</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

<p>Gradient = (y_A - y_C) / (x_A - x_C) (C)</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

How do you shift the graph of y = a(x + p)^2 + q to the right by m units?

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

Which of the following is true about the range of y = ab^(x+p) + q?

<p>The range depends on the sign of a (B)</p> Signup and view all the answers

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

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

What is the formula for simple depreciation?

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

What is the main difference between simple and compound depreciation?

<p>The method of calculating the depreciation amount (D)</p> Signup and view all the answers

What is the purpose of using timelines in compounding interest problems?

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

How do you adjust the interest rate when compounding more than once a year?

<p>Divide the interest rate by the number of compounding periods (D)</p> Signup and view all the answers

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

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

Which of the following is a characteristic of the graph of y = ab^(x+p) + q?

<p>The graph has a horizontal asymptote (C)</p> Signup and view all the answers

What is the formula for compound depreciation?

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

What is the key point to note about compound depreciation?

<p>The depreciation amount changes each year, decreasing as the asset's value decreases (B)</p> Signup and view all the answers

What is the formula for calculating the accumulated value of an investment or loan using compound interest?

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

What is the difference between nominal and effective interest rates?

<p>Nominal interest rate is the rate before compounding, while effective interest rate is the rate after compounding (B)</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) (C)</p> Signup and view all the answers

What is the purpose of Venn diagrams in probability theory?

<p>To visualize the relationships between different events (A)</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 ∩ B) / P(B) (D)</p> Signup and view all the answers

What is the difference between mutually exclusive and independent events?

<p>Mutually exclusive events cannot occur simultaneously, while independent events are not affected by each other (B)</p> Signup and view all the answers

What is the purpose of tree diagrams in probability theory?

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

What is the formula for calculating the probability of the union of two events that are not mutually exclusive?

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

What is the key concept in solving dependent events problems?

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

What is the formula for calculating the effective interest rate from the nominal interest rate?

<p>i_effective = (1 + i_nominal / m) ^ m (D)</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>$\frac{f(a + h) - f(a)}{h}$ (D)</p> Signup and view all the answers

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

<p>It causes a vertical shift. (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} (B)</p> Signup and view all the answers

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

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

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

<p>It changes the shape of the graph, moving it closer to or further from the axes. (A)</p> Signup and view all the answers

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

<p>The lines x = -p and 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>It causes a horizontal shift. (D)</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} (B)</p> Signup and view all the answers

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

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

What is the formula for the exponential function y = ab^x + q?

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

What is the value of a when a^(1/2) = 4?

<p>16 (B)</p> Signup and view all the answers

What is the value of a when a^(1/3) = 2?

<p>8 (D)</p> Signup and view all the answers

What is the value of a when a^(-1/2) = 1/2?

<p>4 (B)</p> Signup and view all the answers

What is the value of a when a^(3/2) = 8?

<p>16 (A)</p> Signup and view all the answers

What is the value of a when a^(2/3) = 2?

<p>6 (D)</p> Signup and view all the answers

What is the value of a when a^(-3/2) = 1/4?

<p>16 (B)</p> Signup and view all the answers

What is the value of a when a^(1/4) = 2?

<p>16 (B)</p> Signup and view all the answers

What is the value of a when a^(-2/3) = 1/2?

<p>8 (B)</p> Signup and view all the answers

What is the result of applying the power of a power rule to the expression $(a^m)^n$?

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

What is the purpose of rationalizing denominators?

<p>To simplify the expression by eliminating radicals from the denominator (B)</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 (A)</p> Signup and view all the answers

What is the formula for exponential growth or decay?

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

What is the formula to determine the roots of a quadratic equation ax^2 + bx + c = 0?

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

What is the purpose of checking solutions in surd equations?

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

What is the key concept in solving quadratic surd equations?

<p>Raising both sides to the power corresponding to the root (D)</p> Signup and view all the answers

Under what condition does a quadratic equation have two distinct real roots?

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

What is the difference between exponential growth and decay?

<p>Growth occurs with a positive growth rate, while decay occurs with a negative growth rate (D)</p> Signup and view all the answers

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

<p>To simplify the process by identifying a repeated expression (C)</p> Signup and view all the answers

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

<p>The equation has no real roots, only imaginary ones (C)</p> Signup and view all the answers

What is the purpose of applying the rule of indices in solving surd equations?

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

What is the result of applying the rule of indices to the expression a^(-m/n)?

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

What is the formula to find the quadratic equation given the roots r_1 and r_2?

<p>(x - r_1)(x - r_2) = 0 (A)</p> Signup and view all the answers

What is the purpose of using exponentials in real-world applications?

<p>To model exponential growth or decay (B)</p> Signup and view all the answers

Under what condition does a quadratic equation have exactly one real root?

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

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

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

What is the result of solving the quadratic equation in terms of k?

<p>The value of k is obtained (A)</p> Signup and view all the answers

What is the purpose of verifying restrictions in solving quadratic equations?

<p>To ensure that the solutions are valid (A)</p> Signup and view all the answers

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

<p>The equation has one real root (D)</p> Signup and view all the answers

What is the value of x in the equation x^2 + 4x + 4 = 0?

<p>x = -2 (C)</p> Signup and view all the answers

Which of the following is a correct application of the rule of exponents a^m × a^n = a^(m+n)?

<p>2^3 × 2^4 = 2^7 (C)</p> Signup and view all the answers

What is the final amount of money after 5 years if the initial amount is $100, the interest rate is 10% per annum, and the interest is compounded annually?

<p>$161.05 (B)</p> Signup and view all the answers

What is the equation in standard form that corresponds to the equation (x + 2)^2 = 16?

<p>x^2 + 4x + 4 = 0 (A)</p> Signup and view all the answers

What is the value of x in the equation x^2 - 6x + 8 = 0?

<p>x = 4 (C), x = 2 (D)</p> Signup and view all the answers

Which of the following is a correct application of the rule of exponents a^(m+n) = a^m × a^n?

<p>2^(3+4) = 2^3 × 2^4 (B)</p> Signup and view all the answers

What is the equation in standard form that corresponds to the equation (x - 3)^2 = 9?

<p>x^2 - 6x + 9 = 0 (B)</p> Signup and view all the answers

What is the value of x in the equation x^2 + 2x + 1 = 0?

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

Which of the following is a correct application of the rule of exponents a^(-n) = 1/a^n?

<p>2^(-3) = 1/2^3 (C)</p> Signup and view all the answers

What is the final amount of money after 3 years if the initial amount is $50, the interest rate is 5% per annum, and the interest is compounded annually?

<p>$63.77 (D)</p> Signup and view all the answers

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

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

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

<p>The graph becomes wider as a gets closer to 0. (B)</p> Signup and view all the answers

What is the first step in solving a quadratic inequality?

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

What is the purpose of determining the critical values when solving a quadratic inequality?

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

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

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

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

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

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

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

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

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

How many independent equations are required to solve for the values of n unknown variables?

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

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

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

What is the purpose of a table of signs when solving a quadratic inequality?

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

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

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

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

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

What is the last step in solving a quadratic inequality?

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

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

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

What is the purpose of graphing a quadratic function when solving a quadratic inequality?

<p>To visualize the solution (A)</p> Signup and view all the answers

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

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

What is the purpose of finding the average gradient of a curve?

<p>To understand the shape of the curve. (C)</p> Signup and view all the answers

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

<p>Non-real (D)</p> Signup and view all the answers

How do you shift a parabola horizontally to the right by m units?

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

What is the main goal of solving systems of equations?

<p>To find the point of intersection of two graphs. (C)</p> Signup and view all the answers

Which of the following is an example of a real-world application of quadratic sequences?

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

What is the main difference between the substitution and elimination methods for solving systems of equations?

<p>The way the equations are manipulated. (B)</p> Signup and view all the answers

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

<p>The graph is shifted vertically upwards. (A)</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 understand the problem and identify the key elements. (D)</p> Signup and view all the answers

What is the result of solving a system of equations graphically?

<p>The coordinates of the point of intersection. (A)</p> Signup and view all the answers

What is the importance of problem-solving strategies in mathematics?

<p>They are used in various disciplines, including physics, biology, and economics. (B)</p> Signup and view all the answers

What is the general form of a quadratic sequence?

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

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

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

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

<p>To find the nth term of the sequence. (A)</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>It causes a horizontal shift. (B)</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. (B)</p> Signup and view all the answers

What is the formula for simple depreciation?

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

What is the result of compound depreciation?

<p>The book value decreases exponentially. (B)</p> Signup and view all the answers

How do you find the annual depreciation rate i?

<p>Rearrange the formula to solve for i. (D)</p> Signup and view all the answers

What is the purpose of using timelines in compound interest?

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

What happens when you break down periods in a compound interest problem?

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

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

<p>It changes the horizontal asymptote. (A)</p> Signup and view all the answers

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

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

What is the characteristic of the graph of y = ab^(x+p) + q when a < 0?

<p>The graph lies below the horizontal asymptote. (D)</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

<p>It changes the shape of the graph (C)</p> Signup and view all the answers

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

<p>It causes a horizontal shift (B)</p> Signup and view all the answers

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

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

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

<p>(f(a + h) - f(a)) / h (D)</p> Signup and view all the answers

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

<p>It affects the direction of the graph (D)</p> Signup and view all the answers

What does each branch of a tree diagram represent?

<p>A possible outcome of an event (D)</p> Signup and view all the answers

What is the formula to calculate the probability of a specific sequence of events in a tree diagram?

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

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

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

What is the formula to calculate the probability of an event A?

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

What is the formula to calculate the conditional probability of A given B?

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

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

<p>To calculate the probability of multiple events occurring (C)</p> Signup and view all the answers

What is the result of multiplying the probabilities along a path in a tree diagram?

<p>The product of the probabilities (C)</p> Signup and view all the answers

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

<p>A = P(1 + rac{i}{p})^{np} (D)</p> Signup and view all the answers

What is the difference between dependent and independent events?

<p>Dependent events are affected by the occurrence of one another, while independent events are not. (B)</p> Signup and view all the answers

What is the formula for calculating the effective interest rate?

<p>1 + i_effective = (1 + rac{i_nominal}{m})^m (D)</p> Signup and view all the answers

What is the purpose of a Venn diagram in probability?

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

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

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

What is the purpose of calculating the nominal interest rate?

<p>To determine the effective interest rate. (C)</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) (B)</p> Signup and view all the answers

What is the purpose of a tree diagram in probability?

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

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

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

What is the purpose of calculating the conditional probability?

<p>To determine the probability of an event occurring given that another event has occurred. (D)</p> Signup and view all the answers

What is the value of x in the exponential growth equation A = 2(1 + 0.1)^x, where A = 4.48?

<p>15 (C)</p> Signup and view all the answers

Which of the following is a correct step in solving the quadratic equation x^2 + 4x + 3 = 0 using the completing the square method?

<p>Take half the coefficient of the x term and square it (D)</p> Signup and view all the answers

What is the value of x in the equation 2^(3x) = 16, where x is a real number?

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

Which of the following is a correct application of the quadratic formula to solve the equation x^2 - 5x + 2 = 0?

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

What is the value of x in the equation 3^(x-1) = 9, where x is a real number?

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

Which of the following is a correct step in solving the quadratic equation x^2 - 2x - 3 = 0 using the completing the square method?

<p>Take half the coefficient of the x term and square it (B)</p> Signup and view all the answers

What is the value of x in the equation 4^(2x) = 64, where x is a real number?

<p>1/2 (B)</p> Signup and view all the answers

Which of the following is a correct application of the quadratic formula to solve the equation x^2 + 3x - 2 = 0?

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

What is the condition for a quadratic equation to have two complex conjugate roots?

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

What is the value of x in the equation 2^(x+2) = 32, where x is a real number?

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

Which of the following is a correct step in solving the quadratic equation x^2 + 2x + 1 = 0 using the completing the square method?

<p>Take half the coefficient of the x term and square it (D)</p> Signup and view all the answers

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

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

What is the result of multiplying the terms in the quadratic equation (x - r_1)(x - r_2) = 0?

<p>x^2 + (r_1 + r_2)x + r_1r_2 = 0 (A)</p> Signup and view all the answers

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

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

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

<p>To ensure that the expressions are not undefined (C)</p> Signup and view all the answers

What is the formula for the discriminant of a quadratic equation?

<p>b^2 - 4ac (D)</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 solving quadratic equations by substitution?

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

What is the result of solving the quadratic equation in terms of k?

<p>The roots of the original equation are obtained (B)</p> Signup and view all the answers

What is the purpose of verifying restrictions in solving quadratic equations?

<p>To ensure that the solutions are valid (D)</p> Signup and view all the answers

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

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

If $a^m = 27$ and $a^n = 9$, what is the value of $m$ in terms of $n$?

<p>$m = 3n$ (A)</p> Signup and view all the answers

What is the formula to solve the equation $a^x = b^y$?

<p>$x = rac{y \log b}{\log a}$ (C)</p> Signup and view all the answers

What is the value of $\sqrt{a^2}$ in terms of $a$?

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

What is the formula to solve the equation $a^x = a^y$?

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

What is the value of $a^0$?

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

What is the value of $a^{rac{m}{n}}$ in terms of radical notation?

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

What is the formula to solve the equation $a^x = b$?

<p>$x = \log_a b$ (B)</p> Signup and view all the answers

What is the result of rationalizing the denominator of the expression $\frac{1}{\sqrt[3]{2}}$?

<p>$\frac{\sqrt[3]{4}}{2}$ (C)</p> Signup and view all the answers

What is the value of $\left(a^{rac{1}{n}}\right)^m$ in terms of $a$?

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

What is the value of $a^{-m}$ in terms of $a$?

<p>$rac{1}{a^m}$ (B)</p> Signup and view all the answers

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

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

What is the formula to solve the equation $a^x = a^{x + 1}$?

<p>$x = 0$ (D)</p> Signup and view all the answers

What is the value of $(a^m)^n$ in terms of $a$?

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

What is the value of $\left(\sqrt[n]{a}\right)^{-m}$ in terms of $a$?

<p>$a^{-\frac{m}{n}}$ (A)</p> Signup and view all the answers

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

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

What is the value of $a^{\frac{m}{n}}$ in terms of radical notation?

<p>$\left(a^m\right)^{\frac{1}{n}}$ (A)</p> Signup and view all the answers

What is the result of rationalizing the denominator of the expression $\frac{1}{\sqrt[n]{a}}$?

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

What is the nature of the roots of a quadratic equation when the discriminant Δ is a perfect square?

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

What is the graphical method for solving a quadratic inequality?

<p>Sketch the graph to determine the regions where the quadratic expression is positive or negative (D)</p> Signup and view all the answers

What is the purpose of solving a system of simultaneous equations?

<p>To find the point of intersection of two or more lines (C)</p> Signup and view all the answers

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

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

What is the purpose of creating a table of signs when solving a quadratic inequality?

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

What is the method for solving a quadratic inequality when the quadratic expression can be factorized?

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

What is the result of multiplying the terms in the quadratic equation (x - r_1)(x - r_2) = 0?

<p>x^2 + (r_1 + r_2)x + r_1r_2 = 0 (B)</p> Signup and view all the answers

What is the purpose of determining the critical values when solving a quadratic inequality?

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

What is the method for solving a system of simultaneous equations with linear and non-linear equations?

<p>Substitution method or graphical method (D)</p> Signup and view all the answers

What is the purpose of solving quadratic inequalities?

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

What is the main advantage of using the elimination method to solve systems of equations?

<p>It reduces the number of variables by one. (D)</p> Signup and view all the answers

When solving a word problem, what is the purpose of assigning variables to unknown quantities?

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

What is the characteristic of a quadratic sequence?

<p>The second difference between any two consecutive terms is constant. (C)</p> Signup and view all the answers

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

<p>It shifts the graph vertically upwards or downwards. (A)</p> Signup and view all the answers

What is the purpose of solving systems of equations?

<p>To find the values of multiple variables that satisfy multiple equations. (D)</p> Signup and view all the answers

What is the result of solving a system of equations graphically?

<p>The coordinates of the points where the two graphs intersect. (D)</p> Signup and view all the answers

What is the importance of problem-solving strategies in mathematics?

<p>They are used to solve complex word problems in various fields. (C)</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 effect of 'a' on the shape of the graph of y = ax^2 + q?

<p>It changes the width of the graph. (D)</p> Signup and view all the answers

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

<p>To find the nth term of the sequence. (C)</p> Signup and view all the answers

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

<p>The graph is a concave downwards parabola. (D)</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

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

How do you find the x-intercepts of the graph of y = a(x + p)^2 + q?

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

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

<p>Average gradient = (y_A - y_C) / (x_A - x_C). (A)</p> Signup and view all the answers

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

<p>The graph is a concave upwards parabola. (D)</p> Signup and view all the answers

What does each branch of a tree diagram represent?

<p>A possible outcome of an event (C)</p> Signup and view all the answers

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

<p>The product of the probabilities along the path (C)</p> Signup and view all the answers

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

<p>To calculate probabilities and test for independence between events (B)</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 formula for the conditional probability of A given B?

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

What is the condition for independence between two events A and B?

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

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

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

What is the formula for calculating the probability of a desired outcome using multiple paths?

<p>P(Desired Outcome) = P(Path 1) + P(Path 2) + … (C)</p> Signup and view all the answers

What is the accumulated value of an investment after 5 years, given an initial principal of $1000, an annual interest rate of 4%, and quarterly compounding?

<p>$1219.39 (A)</p> Signup and view all the answers

If two events A and B are independent, what is the probability of both events occurring?

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

What is the effective interest rate if the nominal interest rate is 6% and the compounding is done quarterly?

<p>6.09% (C)</p> Signup and view all the answers

If event A is dependent on event B, what is the formula for the probability of event A occurring given that event B has occurred?

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

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

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

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

<p>A vertical shift by q units (C)</p> Signup and view all the answers

What is the total accumulated value of an investment after 3 years, given an initial principal of $500, an annual interest rate of 5%, and monthly compounding, with a deposit of $100 at the end of the first year and a withdrawal of $200 at the end of the second year?

<p>$645.19 (C)</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} (A)</p> Signup and view all the answers

If two events A and B are mutually exclusive, what is the probability of either event occurring?

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

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

<p>It determines the shape of the graph in the first and third quadrants (C)</p> Signup and view all the answers

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

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

What is the nominal interest rate if the effective interest rate is 7.25% and the compounding is done quarterly?

<p>6.95% (D)</p> Signup and view all the answers

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

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

If event A is independent of event B, what is the probability of event A occurring given that event B has occurred?

<p>P(A) (B)</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. (D)</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 formula for compound depreciation?

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

What is the formula for the probability of three events A, B, and C occurring, given that they are independent?

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

What is the accumulated value of an investment after 10 years, given an initial principal of $2000, an annual interest rate of 3%, and monthly compounding?

<p>$2619.49 (D)</p> Signup and view all the answers

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

<p>A vertical shift upwards by q units. (B)</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} (C)</p> Signup and view all the answers

What is the characteristic of the graph of y = ab^(x+p) + q when a < 0?

<p>The graph lies below the horizontal asymptote. (C)</p> Signup and view all the answers

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

<p>It determines the shape of the graph (A)</p> Signup and view all the answers

What is the formula for finding the depreciation rate i in compound depreciation?

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

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

<p>It determines the direction of the graph (C)</p> Signup and view all the answers

What is the importance of timelines in compound interest and depreciation?

<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 q on the graph of y = ab^x + q?

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

What is the characteristic of simple depreciation?

<p>The depreciation amount remains the same each year. (B)</p> Signup and view all the answers

What is the effect of compounding more than once a year in compound interest and depreciation?

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

What is the formula for finding the book value A in simple depreciation?

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

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