Gr 11 Math Term 3 Test
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Questions and Answers

What is the formula for the area of a triangle using the area rule?

  • 1/2 bc sin A (correct)
  • 1/2 ac sin B
  • bc sin A
  • 1/2 ab sin C (correct)

    • When would you use the sine rule in a triangle?

  • When two angles and a side are given. (correct)
  • When a right angle is given.
  • When two sides and the included angle are given.
  • When three sides are given.

    • What is the formula for the cosine rule in a triangle?

  • a^2 = b^2 + c^2 - 2bc cos A (correct)
  • a^2 = b^2 + c^2 + 2bc cos A
  • a^2 = b^2 - c^2 + 2bc cos A
  • a^2 = b^2 + c^2 - 2bc sin A

    • In which quadrant is the sine function positive?

    <p>Quadrant II</p> Signup and view all the answers

    What is the main purpose of the area rule?

    <p>To find the area of a triangle.</p> Signup and view all the answers

    When would you use the cosine rule in a triangle?

    <p>When three sides are given.</p> Signup and view all the answers

    What is the main difference between the sine rule and the cosine rule?

    <p>The sine rule is used for two sides and an angle, while the cosine rule is used for three sides or two sides and the included angle.</p> Signup and view all the answers

    What is the purpose of the CAST diagram?

    <p>To determine the signs of trigonometric functions in different quadrants.</p> Signup and view all the answers

    What is the formula for calculating the total accumulated value at the end of an investment or loan term?

    <p>Sum the values from each period</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</p> Signup and view all the answers

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

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

    What is the formula for calculating the probability of event A occurring given that event B has occurred?

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

    What is the concept of mutually exclusive events in probability?

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

    What is the purpose of a Venn diagram in probability?

    <p>To visualize and organize the possible outcomes of events</p> Signup and view all the answers

    What is the concept of the intersection of two events in a Venn diagram?

    <p>The set of outcomes that are in both events A and B</p> Signup and view all the answers

    What is the purpose of a tree diagram in probability?

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

    What is the concept of a branch in a tree diagram?

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

    What is the concept of a level in a tree diagram?

    <p>A level in the tree representing a stage in the sequence of events</p> Signup and view all the answers

    What is the formula for simple depreciation?

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

    What is the main difference between simple and compound depreciation?

    <p>Simple depreciation calculates depreciation on the initial principal amount, while compound depreciation calculates it on the remaining value.</p> Signup and view all the answers

    What is the purpose of a timeline in calculating compound interest?

    <p>To visualize the periods and changes in compounding and interest rates over the term of the investment or loan.</p> Signup and view all the answers

    What is the formula for compound interest when interest is compounded more than once a year?

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

    What is the relationship between the initial value, final value, and depreciation rate in simple decay?

    <p>Linear</p> Signup and view all the answers

    How is the depreciation rate calculated in simple decay?

    <p>Rearranging the formula to solve for i.</p> Signup and view all the answers

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

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

    What happens to the depreciation amount in compound depreciation?

    <p>It decreases as the asset's value decreases.</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 and adjust the principal for the next period accordingly.</p> Signup and view all the answers

    What is the formula for finding the angle θ in trigonometry when sin(θ) = x?

    <p>θ = sin^(-1)(x) + k · 360°</p> Signup and view all the answers

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

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

    In a tree diagram, what is represented on the first level?

    <p>Outcomes of the first event</p> Signup and view all the answers

    What is the purpose of a contingency table?

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

    What is the characteristic of a histogram that distinguishes it from a bar graph?

    <p>No gaps between the bars unless a class interval has a frequency of zero</p> Signup and view all the answers

    What is the purpose of a frequency polygon?

    <p>To visualize the frequency distribution of continuous data</p> Signup and view all the answers

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

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

    What is the purpose of a tree diagram?

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

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

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

    What is the characteristic of a histogram that represents the frequency of data in a class interval?

    <p>The height of each bar</p> Signup and view all the answers

    What does a large standard deviation indicate about a dataset?

    <p>The data points are spread out over a wide range of values.</p> Signup and view all the answers

    What is the purpose of calculating the variance in a dataset?

    <p>To measure the spread of the data.</p> Signup and view all the answers

    Which of the following is a characteristic of a symmetric distribution?

    <p>The left and right tails are balanced.</p> Signup and view all the answers

    What is the formula for calculating the standard deviation of a dataset?

    <p>$\sqrt{rac{\sum_{i=1}^{n} (x_i - ar{x})^2}{n}}$</p> Signup and view all the answers

    What is the purpose of a box-and-whisker diagram?

    <p>To visualize the distribution of a dataset.</p> Signup and view all the answers

    How do you calculate the interquartile range (IQR) of a dataset?

    <p>By subtracting the first quartile (Q1) from the third quartile (Q3).</p> Signup and view all the answers

    What is an outlier in a dataset?

    <p>A data value that is significantly deviates from the other values in a dataset.</p> Signup and view all the answers

    What is the formula for calculating the upper boundary for identifying outliers?

    <p>$Q3 + 1.5 imes IQR$</p> Signup and view all the answers

    What is the purpose of a scatter plot?

    <p>To show relationships between two variables.</p> Signup and view all the answers

    Which of the following is a characteristic of a right-skewed distribution?

    <p>The mean is greater than the median.</p> Signup and view all the answers

    What is the purpose of plotting points at the midpoint of each class interval in a frequency polygon?

    <p>To represent the data in a more visual format</p> Signup and view all the answers

    What is the formula for calculating the cumulative frequency?

    <p>CF_i = Σf_j</p> Signup and view all the answers

    What is the purpose of an ogive?

    <p>To find the median, quartiles, and percentiles of a data set</p> Signup and view all the answers

    What is the definition of variance?

    <p>The average of the squared differences from the mean</p> Signup and view all the answers

    What is the property of standard deviation that makes it directly comparable with the mean or the data themselves?

    <p>It has the same units as the original data</p> Signup and view all the answers

    What is the formula for calculating the standard deviation?

    <p>σ = √(Σ(x_i - x̄)² / n)</p> Signup and view all the answers

    What is the purpose of finding the median class?

    <p>To find the median of a data set</p> Signup and view all the answers

    What is the definition of relative frequency?

    <p>The ratio of the frequency of an event to the total number of observations</p> Signup and view all the answers

    What is the purpose of finding the cumulative frequency?

    <p>To construct an ogive</p> Signup and view all the answers

    What is the definition of a class interval?

    <p>A range of values in a data set divided into intervals of equal length</p> Signup and view all the answers

    What is the main difference between the Area Rule and the Sine Rule?

    <p>The Area Rule is used for solving triangles when we know two sides and the included angle, while the Sine Rule is used for solving triangles when we know two sides and a non-included angle.</p> Signup and view all the answers

    In which quadrant is cosine positive?

    <p>Quadrant IV (270° to 360°)</p> Signup and view all the answers

    What is the formula for finding the length of a side in a triangle using the Cosine Rule?

    <p>a^2 = b^2 + c^2 - 2bc cos A</p> Signup and view all the answers

    When would you use the Area Rule to solve a triangle?

    <p>When no perpendicular height is given.</p> Signup and view all the answers

    What is the main purpose of the CAST diagram?

    <p>To show the signs of trigonometric functions in different quadrants.</p> Signup and view all the answers

    Why is the Sine Rule useful for solving triangles?

    <p>Because it can be used to find the length of a side when we know two sides and a non-included angle.</p> Signup and view all the answers

    What is the formula for finding the area of a triangle using the Area Rule?

    <p>Area = 1/2 ab sin C</p> Signup and view all the answers

    When would you use the Cosine Rule to solve a triangle?

    <p>When we know two sides and the included angle.</p> Signup and view all the answers

    What is the purpose of rearranging the formula to solve for i in simple and compound depreciation?

    <p>To find the annual depreciation rate</p> Signup and view all the answers

    What happens to the depreciation amount in compound depreciation over time?

    <p>It decreases over time</p> Signup and view all the answers

    What is the purpose of using a timeline in compound interest calculations?

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

    What is the formula for calculating the accumulated value in compound interest when interest is compounded more than once a year?

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

    What is the relationship between the initial value, final value, and depreciation rate in compound decay?

    <p>The relationship involves solving an exponential equation</p> Signup and view all the answers

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

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

    What is the formula for finding the angle θ in trigonometry when sin(θ) = x?

    <p>θ = sin^(-1)(x) + k ⋅ 360°</p> Signup and view all the answers

    What is the purpose of using a timeline in calculating compound depreciation?

    <p>To visualize the periods and changes in depreciation rates</p> Signup and view all the answers

    What is the formula for calculating the book value or depreciated value in simple depreciation?

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

    What is the purpose of using a timeline in calculating compound interest?

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

    What is the formula for calculating the total accumulated value at the end of an investment or loan term?

    <p>Sum the values from each period</p> Signup and view all the answers

    What is the formula for simple interest?

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

    What is the concept of mutually exclusive events in probability?

    <p>Two events that cannot occur simultaneously</p> Signup and view all the answers

    What is the purpose of a Venn diagram in probability?

    <p>To visualize the probability of two or more events</p> Signup and view all the answers

    What is the formula for compound interest when interest is compounded more than once a year?

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

    What is the concept of the intersection of two events in a Venn diagram?

    <p>The set of outcomes that are in both events</p> Signup and view all the answers

    What is the purpose of a tree diagram in probability?

    <p>To visualize the probability of multiple events</p> Signup and view all the answers

    What is the concept of a branch in a tree diagram?

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

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

    <p>The product of the probabilities of each event</p> Signup and view all the answers

    What is the purpose of a contingency table?

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

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

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

    What is the characteristic of a histogram that distinguishes it from a bar graph?

    <p>There are no gaps between the bars</p> Signup and view all the answers

    What is the formula for the conditional probability of A given B in a contingency table?

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

    What is the purpose of a frequency polygon?

    <p>To show the frequency distribution of a dataset</p> Signup and view all the answers

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

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

    What is the purpose of a tree diagram?

    <p>To show the probability of multiple dependent events</p> Signup and view all the answers

    What is the characteristic of a histogram that represents the frequency of data in a class interval?

    <p>The height of the bar</p> Signup and view all the answers

    What is the formula for the probability of multiple dependent events occurring?

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

    What represents the ratio of the frequency of an event to the total number of observations?

    <p>Relative Frequency</p> Signup and view all the answers

    What is the purpose of plotting points at the midpoint of each class interval in a frequency polygon?

    <p>To represent the frequency of each class interval</p> Signup and view all the answers

    What is the formula for calculating the cumulative frequency?

    <p>CF_i = ∑_(j=1)^i f_j</p> Signup and view all the answers

    What does a large standard deviation indicate about a dataset?

    <p>The data points are spread out from the mean</p> Signup and view all the answers

    What is the purpose of calculating the variance in a dataset?

    <p>To measure the spread of the data around the mean</p> Signup and view all the answers

    What is the formula for the standard deviation of a dataset?

    <p>σ = √(∑_(i=1)^n (x_i - x̄)^2 / n)</p> Signup and view all the answers

    What is the purpose of an ogive?

    <p>To plot the cumulative frequency of a dataset</p> Signup and view all the answers

    What is the formula for finding the median of a dataset using an ogive?

    <p>Locate the 50th percentile on the cumulative frequency axis</p> Signup and view all the answers

    What is the purpose of a frequency polygon?

    <p>To visualize the distribution of a dataset</p> Signup and view all the answers

    What is the characteristic of a histogram that distinguishes it from a bar graph?

    <p>The bars are of equal width</p> Signup and view all the answers

    What is the main purpose of calculating the variance in a dataset?

    <p>To measure the spread of the dataset from the mean</p> Signup and view all the answers

    In a symmetric distribution, what is the relationship between the mean and the median?

    <p>The mean is approximately equal to the median</p> Signup and view all the answers

    What is the formula for calculating the standard deviation of a dataset?

    <p>σ = √(Σ(x_i - x̄)^2 / n)</p> Signup and view all the answers

    What is the purpose of a box-and-whisker diagram?

    <p>To visualize the distribution of a dataset</p> Signup and view all the answers

    What is the characteristic of a right-skewed distribution?

    <p>The mean is greater than the median</p> Signup and view all the answers

    How do you calculate the interquartile range (IQR) of a dataset?

    <p>IQR = Q3 - Q1</p> Signup and view all the answers

    What is the formula for calculating the upper boundary for identifying outliers?

    <p>Upper Boundary = Q3 + 1.5 × IQR</p> Signup and view all the answers

    What is the purpose of a scatter plot?

    <p>To show the relationship between two variables</p> Signup and view all the answers

    What is an outlier in a dataset?

    <p>A data value that is significantly deviates from the other values in the dataset</p> Signup and view all the answers

    What is the purpose of calculating the variance in a dataset?

    <p>To measure the spread of the dataset from the mean</p> Signup and view all the answers

    What is the main difference between the Area Rule and the Sine Rule?

    <p>The Area Rule is used when the height of the triangle is known, while the Sine Rule is used when the height is unknown.</p> Signup and view all the answers

    What is the purpose of the CAST diagram in trigonometry?

    <p>To determine the signs of trigonometric functions in different quadrants.</p> Signup and view all the answers

    What is the condition for using the Cosine Rule to solve a triangle?

    <p>Two sides and the included angle are given.</p> Signup and view all the answers

    What is the significance of the periodic nature of trigonometric functions in solving trigonometric equations?

    <p>It allows us to find multiple solutions to the equation.</p> Signup and view all the answers

    What is the inverse operation of the sine function in the context of trigonometry?

    <p>arcsin</p> Signup and view all the answers

    When would you use the Sine Rule to solve a triangle?

    <p>When two angles and a side are given.</p> Signup and view all the answers

    What is the correct formula for calculating the depreciated value of an asset using the compound depreciation method?

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

    What is the condition for using the Area Rule to solve a triangle?

    <p>No perpendicular height is given.</p> Signup and view all the answers

    What is the purpose of using a timeline in calculating compound interest?

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

    What is the relationship between the Area Rule and the Sine Rule formulas?

    <p>The Area Rule formula is a rearrangement of the Sine Rule formula.</p> Signup and view all the answers

    What is the purpose of the sine, cosine, and tangent functions in trigonometry?

    <p>To determine the relationships between the sides and angles of a triangle.</p> Signup and view all the answers

    What is the relationship between the initial value, final value, and depreciation rate in compound decay?

    <p>The relationship involves solving an exponential equation</p> Signup and view all the answers

    What is the formula for finding the accumulated value in compound interest when interest is compounded more than once a year?

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

    What happens to the depreciation amount in compound depreciation?

    <p>It decreases as the asset's value decreases</p> Signup and view all the answers

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

    <p>To adjust the principal for changes in interest rates or additional transactions</p> Signup and view all the answers

    What is the formula for finding the angle θ in trigonometry when tan(θ) = x?

    <p>θ = tan^(-1)x + k ⋅ 180°</p> Signup and view all the answers

    What is the main difference between simple and compound depreciation?

    <p>Simple depreciation reduces the value of an asset by a constant amount each year, while compound depreciation calculates depreciation on the remaining value of the asset each year</p> Signup and view all the answers

    What is the purpose of using a timeline in calculating compound interest when interest is compounded more than once a year?

    <p>To visualize the periods and changes in compounding and interest rates over the term of the investment or loan</p> Signup and view all the answers

    What is the primary difference between independent and dependent events in probability?

    <p>Independent events have no effect on each other, while dependent events do</p> Signup and view all the answers

    When drawing a tree diagram, what is represented on the second level?

    <p>The outcomes of the second event, given the outcomes of the first event</p> Signup and view all the answers

    What is the purpose of a contingency table in probability?

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

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

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

    What is the characteristic of a histogram that distinguishes it from a bar graph?

    <p>Bars are not separated by gaps, unless a class interval has a frequency of zero</p> Signup and view all the answers

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

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

    What is the purpose of a frequency polygon?

    <p>To display the frequency distribution of a dataset</p> Signup and view all the answers

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

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

    What is the key concept in calculating the probability of multiple dependent events?

    <p>The probability of each event is dependent on the previous events</p> Signup and view all the answers

    What is the purpose of a contingency table in calculating the probability of an event?

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

    What is the total accumulated value at the end of an investment or loan term if the initial value is $100, the interest rate is 5%, and the investment is compounded annually for 5 years?

    <p>$141.75</p> Signup and view all the answers

    Two events A and B are dependent. If P(A) = 0.4 and P(B|A) = 0.7, what is the probability of both events occurring?

    <p>0.28</p> Signup and view all the answers

    A company has a nominal interest rate of 6% per annum, compounded quarterly. What is the effective interest rate?

    <p>6.14%</p> Signup and view all the answers

    In a Venn diagram, what is the representation of the set of outcomes that are not in event A?

    <p>A'</p> Signup and view all the answers

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

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

    What is the purpose of a tree diagram in probability?

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

    What is the formula for simple depreciation if the initial value is $100, the depreciation rate is 10%, and the depreciation is calculated for 5 years?

    <p>A = P(1 - 0.10)^5</p> Signup and view all the answers

    What is the probability of event A occurring given that event B has occurred, if P(A) = 0.3, P(B) = 0.5, and P(A and B) = 0.2?

    <p>0.67</p> Signup and view all the answers

    What is the formula for the total accumulated value at the end of an investment or loan term if the interest is compounded more than once a year?

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

    In a Venn diagram, what is the representation of the set of outcomes that are in both events A and B?

    <p>A ∩ B</p> Signup and view all the answers

    What is the main purpose of calculating the variance in a dataset?

    <p>To quantify the amount of variation in the data</p> Signup and view all the answers

    Which of the following distributions is characterized by a longer right tail?

    <p>Right-skewed distribution</p> Signup and view all the answers

    What is the formula for calculating the lower boundary for identifying outliers?

    <p>Q1 - 1.5 × IQR</p> Signup and view all the answers

    What is the purpose of a scatter plot in identifying outliers?

    <p>To show the relationship between two variables</p> Signup and view all the answers

    What is the main characteristic of a symmetric distribution?

    <p>Mean is approximately equal to the median</p> Signup and view all the answers

    What is the formula for calculating the standard deviation of a dataset?

    <p>√(Σ(xi - x̄)^2 / n)</p> Signup and view all the answers

    What is the purpose of a box-and-whisker diagram?

    <p>To compare the distribution of two or more variables</p> Signup and view all the answers

    What is the formula for calculating the interquartile range (IQR) of a dataset?

    <p>Q3 - Q1</p> Signup and view all the answers

    What is the characteristic of a left-skewed distribution?

    <p>Mean is less than the median</p> Signup and view all the answers

    What is the purpose of calculating the five-number summary of a dataset?

    <p>To summarize the distribution of the dataset</p> Signup and view all the answers

    What is the main purpose of plotting points at the midpoint of each class interval in a frequency polygon?

    <p>To create a visual representation of the frequency distribution</p> Signup and view all the answers

    What is the relationship between the variance and the standard deviation of a dataset?

    <p>The standard deviation is the square of the variance</p> Signup and view all the answers

    What is the main difference between the relative frequency and the cumulative frequency?

    <p>The relative frequency is the ratio of the frequency to the total number of observations, while the cumulative frequency is the sum of the relative frequencies</p> Signup and view all the answers

    What is the purpose of finding the median class in a dataset?

    <p>To identify the middle value of the data</p> Signup and view all the answers

    What is the formula for calculating the variance of a dataset?

    <p>σ^2 = (Σ(x_i - x̄)^2) / n</p> Signup and view all the answers

    What is the main purpose of drawing an ogive?

    <p>To visualize the cumulative frequency distribution</p> Signup and view all the answers

    What is the characteristic of a dataset with a small standard deviation?

    <p>The data points are close to the mean</p> Signup and view all the answers

    What is the formula for calculating the cumulative frequency up to the i-th interval?

    <p>CF_i = f_i + CF_(i-1)</p> Signup and view all the answers

    What is the purpose of calculating the quartiles of a dataset?

    <p>To understand the distribution of the data</p> Signup and view all the answers

    What is the main difference between a histogram and a frequency polygon?

    <p>A histogram is a bar graph, while a frequency polygon is a line graph</p> Signup and view all the answers

    What is the general form of the angle θ in trigonometry when cos(θ) = x?

    <p>θ = 180^° - cos^(-1) x + k · 360^°</p> Signup and view all the answers

    An asset is depreciated using the compound depreciation method. If the principal amount is $1000 and the depreciation rate is 10% per year, what is the book value after 2 years?

    <p>$729</p> Signup and view all the answers

    What is the main difference between the formulas for simple and compound depreciation?

    <p>One formula is linear and the other is exponential.</p> Signup and view all the answers

    An investment is compounded quarterly with an annual interest rate of 8%. If the principal amount is $5000, what is the accumulated value after 5 years?

    <p>$7948.72</p> Signup and view all the answers

    What is the purpose of creating a timeline when calculating compound interest?

    <p>To visualize the compounding periods and interest rates.</p> Signup and view all the answers

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

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

    What is the relationship between the initial value, final value, and depreciation rate in compound decay?

    <p>The relationship involves solving an exponential equation.</p> Signup and view all the answers

    What happens to the depreciation amount in compound depreciation over time?

    <p>It decreases exponentially.</p> Signup and view all the answers

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

    <p>To adjust for changes in interest rates or additional transactions.</p> Signup and view all the answers

    What is the formula for finding the angle θ in trigonometry when tan(θ) = x?

    <p>θ = tan^(-1) x + k · 180^°</p> Signup and view all the answers

    Which of the following formulas is used to calculate the total accumulated value at the end of an investment or loan term?

    <p>The sum of the values from each period</p> Signup and view all the answers

    What is the main difference between the Area Rule and the Sine Rule?

    <p>One is used for finding the area of a triangle and the other is used for finding the lengths of sides</p> Signup and view all the answers

    What is the relationship between the nominal interest rate and the effective interest rate?

    <p>The nominal interest rate is equal to the effective interest rate when compounded annually</p> Signup and view all the answers

    When would you use the Cosine Rule to find the length of a side of a triangle?

    <p>When three sides are given</p> Signup and view all the answers

    Which of the following events is an example of dependent events?

    <p>Drawing a card from a deck and drawing another card from the same deck</p> Signup and view all the answers

    What is the formula for calculating the probability of event A given that event B has occurred?

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

    In what quadrant is the cosine function positive?

    <p>Quadrant IV</p> Signup and view all the answers

    What is the purpose of the CAST diagram in trigonometry?

    <p>To determine the sign of a trigonometric function in a quadrant</p> Signup and view all the answers

    Which of the following is an example of mutually exclusive events?

    <p>Heads and tails on a coin flip</p> Signup and view all the answers

    What is the purpose of a Venn diagram in probability?

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

    When would you use the Sine Rule to find the length of a side of a triangle?

    <p>When two angles and a side are given</p> Signup and view all the answers

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

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

    What is the main difference between the Sine Rule and the Cosine Rule?

    <p>One is used when two sides and the included angle are given, and the other is used when two sides and a non-included angle are given</p> Signup and view all the answers

    What is the purpose of the Area Rule in trigonometry?

    <p>To find the area of a triangle</p> Signup and view all the answers

    What is the concept of a level in a tree diagram?

    <p>A stage in the sequence of events</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</p> Signup and view all the answers

    In what quadrant is the tangent function positive?

    <p>Quadrant III</p> Signup and view all the answers

    What is the purpose of a tree diagram in probability?

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

    What is the main difference between independent and dependent events?

    <p>The probability of one event is affected by the occurrence of the other</p> Signup and view all the answers

    What is the purpose of a contingency table?

    <p>To visualize the relationship between two categorical variables</p> Signup and view all the answers

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

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

    What is the main difference between a histogram and a bar graph?

    <p>A histogram does not have gaps between the bars, while a bar graph does</p> Signup and view all the answers

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

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

    What is the purpose of a frequency polygon?

    <p>To show the distribution of a set of continuous data</p> Signup and view all the answers

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

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

    What is the purpose of a tree diagram?

    <p>To visualize the probability of different outcomes in a multi-stage experiment</p> Signup and view all the answers

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

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

    What is the characteristic of a histogram that represents the frequency of data in a class interval?

    <p>The height of the bar</p> Signup and view all the answers

    What is the primary purpose of plotting points at the midpoint of each class interval in a frequency polygon?

    <p>To visualize the distribution of data</p> Signup and view all the answers

    What is the relationship between the variance and standard deviation of a dataset?

    <p>Standard deviation is the square root of the variance</p> Signup and view all the answers

    What is the purpose of calculating the cumulative frequency in an ogive?

    <p>To determine the percentile of a specific data value</p> Signup and view all the answers

    What is the characteristic of a dataset with a small standard deviation?

    <p>The data points are close to the mean</p> Signup and view all the answers

    What is the purpose of drawing a histogram?

    <p>To visualize the distribution of data</p> Signup and view all the answers

    What is the formula for calculating the variance of a dataset?

    <p>$\sigma^2 = rac{\sum_{i=1}^{n} (x_i - ar{x})^2}{n}$</p> Signup and view all the answers

    What is the purpose of calculating the relative frequency of a dataset?

    <p>To compare the frequency of different classes</p> Signup and view all the answers

    What is the characteristic of a dataset with a large standard deviation?

    <p>The data points are highly spread out</p> Signup and view all the answers

    What is the purpose of drawing a frequency polygon?

    <p>To visualize the distribution of data</p> Signup and view all the answers

    What is the formula for calculating the cumulative frequency of a dataset?

    <p>$CF_i = \sum_{j=1}^{i} f_j + CF_{i-1}$</p> Signup and view all the answers

    What is the primary reason for calculating the variance of a dataset?

    <p>To quantify the spread or dispersion of the dataset</p> Signup and view all the answers

    A dataset has a mean of 10 and a standard deviation of 2. Which of the following values is most likely to be an outlier?

    <p>18</p> Signup and view all the answers

    What is the main difference between a symmetric distribution and a right-skewed distribution?

    <p>The median is closer to the first quartile in a right-skewed distribution</p> Signup and view all the answers

    What is the purpose of calculating the interquartile range (IQR) in a dataset?

    <p>To identify the presence of outliers in the dataset</p> Signup and view all the answers

    What is the main advantage of using a box-and-whisker diagram to display a dataset?

    <p>It provides a visual representation of the dataset's distribution</p> Signup and view all the answers

    Which of the following is a characteristic of a left-skewed distribution?

    <p>The left tail is longer than the right tail</p> Signup and view all the answers

    What is the primary purpose of using a scatter plot to display bivariate data?

    <p>To show the relationship between the two variables</p> Signup and view all the answers

    What is the formula for calculating the variance of a dataset?

    <p>σ^2 = (∑(x_i - μ)^2) / n</p> Signup and view all the answers

    Which of the following is a characteristic of a symmetric distribution?

    <p>The left and right tails are balanced</p> Signup and view all the answers

    What is the purpose of calculating the standard deviation of a dataset?

    <p>To quantify the spread or dispersion of the dataset</p> Signup and view all the answers

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