Gr 11 Math Nov P2 (Hard)
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Questions and Answers

What is the purpose of the two-point form of the straight line equation?

  • To determine the midpoint of a line when two points are known.
  • To determine the y-intercept of a line when two points are known.
  • To determine the gradient of a line when two points are known.
  • To find the equation of a line when two points are known. (correct)

What is the general formula for the gradient–point form of the straight line equation?

  • y = y_1 + mx_1
  • y = mx + c
  • y = mx_1 - m
  • y - y_1 = m(x - x_1) (correct)

What is the value of c in the gradient–intercept form of the straight line equation?

  • mx_1 - y_1
  • y_1 - mx_1 (correct)
  • y_1 + mx_1
  • mx_1 + y_1

What is the significance of the y-intercept c in the gradient–intercept form?

<p>It is the point where the line intersects the y-axis. (C)</p> Signup and view all the answers

What is the condition for the two-point form to be used?

<p>Two points on the line are known. (A)</p> Signup and view all the answers

What is the condition for the gradient–point form to be used?

<p>The gradient of the line is known and one point on the line is known. (D)</p> Signup and view all the answers

What is the condition for the gradient–intercept form to be used?

<p>The gradient of the line is known and the y-intercept is known. (D)</p> Signup and view all the answers

What is the relationship between the gradient–point form and the gradient–intercept form?

<p>They are equivalent forms of the equation of a line. (D)</p> Signup and view all the answers

What is the relationship between the gradient of a line and the inclination of the line?

<p>m = tan(θ) (A)</p> Signup and view all the answers

What is the value of the gradient of a vertical line?

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

What is the equation of a line that passes through the point (2, 3) and is parallel to the line y = 2x + 1?

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

What is the inclination of a line with a gradient of -3?

<p>180° + tan^-1(-3) (D)</p> Signup and view all the answers

What is the condition for two lines to be parallel?

<p>m1 = m2 (A)</p> Signup and view all the answers

What is the value of the gradient of a horizontal line?

<p>0 (C)</p> Signup and view all the answers

What is the relationship between the tangent function and the angle of inclination?

<p>tan(θ) = m for 0° ≤ θ &lt; 180° (B)</p> Signup and view all the answers

What is the point-slope form of the equation of a line?

<p>y - y1 = m(x - x1) (A)</p> Signup and view all the answers

What is the equation of a line that is parallel to the line y = 3x - 2 and passes through the point (1, 4)?

<p>y = 3x + 1 (A)</p> Signup and view all the answers

What is the inclination of a line with a gradient of 2?

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

What is the condition for two lines to be perpendicular?

<p>Their gradients multiply to -1. (D)</p> Signup and view all the answers

What is the amplitude of the function y = sin(θ) for 0° ≤ θ ≤ 360°?

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

What is the effect of q on the graph of y = a sin(θ) + q?

<p>q causes a vertical shift of the graph. (A)</p> Signup and view all the answers

What is the period of the function y = sin(kθ)?

<p>360°|k| (B)</p> Signup and view all the answers

What is the effect of a on the graph of y = a sin(θ)?

<p>a changes the amplitude of the function. (A)</p> Signup and view all the answers

What is the equation of a line that is perpendicular to y = 2x + 3 and passes through the point (1, 4)?

<p>y = -1/2x + 5 (C)</p> Signup and view all the answers

What is the x-intercept of the function y = sin(θ)?

<p>(180°, 0) (A)</p> Signup and view all the answers

What is the effect of p on the graph of y = sin(θ + p)?

<p>p causes a horizontal shift of the graph. (D)</p> Signup and view all the answers

What is the range of the function y = sin(kθ)?

<p>[-1, 1] (A)</p> Signup and view all the answers

What is the equation of a line that is perpendicular to y = 3x - 2 and passes through the point (2, 5)?

<p>y = -1/3x + 7 (C)</p> Signup and view all the answers

What is the effect of q on the graph of y = a cos θ + q?

<p>The graph shifts vertically by q units. (D)</p> Signup and view all the answers

What is the period of the function y = cos kθ?

<p>360° / k (A)</p> Signup and view all the answers

What is the effect of a on the graph of y = a tan θ + q?

<p>The graph is stretched by a factor of a. (C)</p> Signup and view all the answers

What is the range of the function y = cos θ?

<p>[-1, 1] (B)</p> Signup and view all the answers

What is the effect of k on the period of the function y = tan kθ?

<p>The period decreases by a factor of k. (C)</p> Signup and view all the answers

What is the domain of the function y = cos θ?

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

What is the y-intercept of the function y = cos θ?

<p>(0, 1) (C)</p> Signup and view all the answers

What is the effect of p on the graph of y = cos(θ + p)?

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

What is the amplitude of the function y = a cos θ?

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

What is the period of the function y = tan θ?

<p>180° (A)</p> Signup and view all the answers

What is the domain of the function y = tan(kθ) in degrees?

<p>θ ∈ ℝ, -90°/k &lt; θ &lt; 90°/k (C)</p> Signup and view all the answers

What is the effect of p on the graph of y = tan(θ + p) when p > 0?

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

What is the formula for the area of a trapezium?

<p>A = (1/2) × (a + b) × h (B)</p> Signup and view all the answers

What is the formula for the volume of a cylinder?

<p>V = πr² × h (D)</p> Signup and view all the answers

What is the surface area of a rectangular prism?

<p>SA = 2(lb + bh + lh) (C)</p> Signup and view all the answers

What is the volume of a triangular prism?

<p>V = (1/2)b × h × H (D)</p> Signup and view all the answers

What is the circumference of a circle with radius r?

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

What is the characteristic of a right pyramid?

<p>The line from the apex to the center of the base is perpendicular to the base (B)</p> Signup and view all the answers

What is the formula for the area of a circle?

<p>A = πr² (D)</p> Signup and view all the answers

What is the shape of the net of a cylinder?

<p>Two identical circles and a rectangle (D)</p> Signup and view all the answers

What is the primary purpose of calculating the interquartile range (IQR) in identifying outliers?

<p>To calculate the boundaries for outliers (C)</p> Signup and view all the answers

What is the term for the data points that lie far from the general trend or pattern of the rest of the data in a scatter plot?

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

What is the formula for calculating the lower boundary for outliers in a box-and-whisker diagram?

<p>Q1 - 1.5*IQR (B)</p> Signup and view all the answers

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

<p>To identify outliers in a dataset (D)</p> Signup and view all the answers

What is the term for the summary of a dataset that includes the minimum, first quartile, median, third quartile, and maximum values?

<p>Five number summary (B)</p> Signup and view all the answers

If a circle is scaled by a factor of 2, what will be the ratio of the new surface area to the original surface area?

<p>4:1 (B)</p> Signup and view all the answers

What is the name of the theorem that states that the angle at the center of a circle is twice the angle at the circumference?

<p>Angle at the Center (C)</p> Signup and view all the answers

What is the formula for the surface area of a triangular pyramid?

<p>$rac{1}{2} b (h_b + 3h_s)$ (A)</p> Signup and view all the answers

What is the formula for the volume of a right cone?

<p>$rac{1}{3} \pi r^2 imes H$ (A)</p> Signup and view all the answers

What is the name of the line that touches the circle at only one point on the circumference?

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

If two tangents are drawn from the same point outside a circle, what can be said about their lengths?

<p>They are equal in length (A)</p> Signup and view all the answers

What is the formula for the surface area of a sphere?

<p>$4\pi r^2$ (C)</p> Signup and view all the answers

What is the name of the part of the circle that is cut off by a chord?

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

If a rectangular prism has dimensions $l, b, h$ and one dimension is multiplied by a constant factor $k$, what is the new volume?

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

What is the formula for the surface area of a right cone?

<p>$\pi r (r + h_s)$ (D)</p> Signup and view all the answers

If a line segment from the center of a circle is perpendicular to a chord, what can be said about the line segment?

<p>It bisects the chord (A)</p> Signup and view all the answers

If a rectangular prism has dimensions $l, b, h$ and all three dimensions are multiplied by a constant factor $k$, what is the new volume?

<p>$k^3(lbh)$ (B)</p> Signup and view all the answers

What is the name of the theorem that states that the angle between a tangent and a chord is equal to the angle in the alternate segment?

<p>Tangent-Chord Theorem (C)</p> Signup and view all the answers

What is the formula for the volume of a triangular prism?

<p>$rac{1}{2} b imes h imes H$ (A)</p> Signup and view all the answers

If the opposite angles of a cyclic quadrilateral are supplementary, what can be said about the quadrilateral?

<p>It is a cyclic quadrilateral (C)</p> Signup and view all the answers

What is the name of the part of the circle that is a straight line joining the ends of an arc?

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

What is the formula for the surface area of a square pyramid?

<p>$b (b + 2h_s)$ (C)</p> Signup and view all the answers

What is the formula for the volume of a sphere?

<p>$rac{4}{3} \pi r^3$ (C)</p> Signup and view all the answers

If an angle at the center of a circle is twice the angle at the circumference, what can be said about the angles?

<p>The angle at the center is twice the angle at the circumference (B)</p> Signup and view all the answers

If a rectangular prism has dimensions $l, b, h$ and two dimensions are multiplied by a constant factor $k$, what is the new surface area?

<p>$2k [klh + lb + kbh]$ (B)</p> Signup and view all the answers

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

<p>A histogram uses bars, while a frequency polygon uses points connected by lines. (C)</p> Signup and view all the answers

What is the formula for calculating the relative frequency of an event?

<p>Relative Frequency = Frequency / Total number of observations (A)</p> Signup and view all the answers

What is the purpose of finding the midpoint of a class interval in a histogram?

<p>To determine the class mark. (B)</p> Signup and view all the answers

What is the formula for calculating the cumulative frequency of a class interval?

<p>Cumulative Frequency = Sum of all previous frequencies + Current frequency (D)</p> Signup and view all the answers

What is the purpose of plotting points on an ogive?

<p>To determine the median and quartiles of a set of data. (A)</p> Signup and view all the answers

What is the significance of the 50th percentile on an ogive?

<p>It represents the median. (C)</p> Signup and view all the answers

What is the difference between a class interval and a class mark?

<p>A class interval is a range of values, while a class mark is the midpoint of the interval. (D)</p> Signup and view all the answers

What is the formula for the k-th percentile?

<p>Pk = (k/100) × N (A)</p> Signup and view all the answers

What is the definition of variance in a dataset?

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

What is the purpose of drawing a histogram?

<p>To display the frequency distribution of a set of data. (B)</p> Signup and view all the answers

What is the significance of the modal class in a histogram?

<p>It represents the class interval with the highest frequency. (B)</p> Signup and view all the answers

What is the relationship between the mean and median in a right-skewed distribution?

<p>Mean is greater than the median (C)</p> Signup and view all the answers

What is the definition of an outlier in a dataset?

<p>A data value that is significantly different from the other values (C)</p> Signup and view all the answers

What is the purpose of drawing a frequency polygon?

<p>To display the frequency distribution of a set of data. (D)</p> Signup and view all the answers

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

<p>To measure the spread of the dataset (B)</p> Signup and view all the answers

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

<p>σ = (∑(xi - x̄)^2)/n (B)</p> Signup and view all the answers

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

<p>The data values are close to the mean (C)</p> Signup and view all the answers

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

<p>To measure the spread of the dataset (B)</p> Signup and view all the answers

What is the characteristic of a right-skewed distribution?

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

What is the purpose of identifying outliers in a dataset?

<p>To determine if the data values are significantly different from the rest of the dataset (D)</p> Signup and view all the answers

What is the primary equation used to derive the gradient–point form of the straight line equation?

<p>frac{y - y_1}{x - x_1} = frac{y_2 - y_1}{x_2 - x_1} (B)</p> Signup and view all the answers

Given the gradient–intercept form of the straight line equation y = mx + c, what is the value of y when x = 1 and m = 2 and c = 3?

<p>7 (C)</p> Signup and view all the answers

Which of the following forms of the straight line equation can be used to find the equation of a line that passes through two points?

<p>Two-point form (C)</p> Signup and view all the answers

What is the value of the gradient of a line that passes through the points (2, 3) and (4, 5)?

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

If a line has a gradient of -3 and passes through the point (1, 2), what is the equation of the line in gradient–point form?

<p>y - 2 = -3(x - 1) (A)</p> Signup and view all the answers

What is the value of c in the gradient–intercept form of the straight line equation y = mx + c when the line passes through the point (2, 5) and has a gradient of 2?

<p>3 (B)</p> Signup and view all the answers

Which of the following forms of the straight line equation can be used to find the equation of a line that has a gradient of 3 and passes through the point (1, 2)?

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

What is the value of y when x = 0 in the equation y = mx + c, given that the line passes through the point (2, 3) and has a gradient of 1?

<p>3 (D)</p> Signup and view all the answers

What is the relationship between the gradients of two perpendicular lines?

<p>Their product is -1 (C)</p> Signup and view all the answers

If a line has a gradient of 3, what is the gradient of a line that is perpendicular to it?

<p>-1/3 (B)</p> Signup and view all the answers

What is the effect of the value of k on the period of the function y = sin(kθ)?

<p>The period decreases as k increases (D)</p> Signup and view all the answers

What is the effect of the value of a on the shape of the function y = a sin(θ)?

<p>The amplitude increases as a increases (A)</p> Signup and view all the answers

What is the effect of the value of p on the graph of the function y = sin(θ + p)?

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

What is the equation of a line that is perpendicular to the line y = 2x + 3 and passes through the point (1, 4)?

<p>y = -1/2x + 5 (D)</p> Signup and view all the answers

What is the domain of the function y = sin(kθ)?

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

What is the range of the function y = a sin(θ)?

<p>[-a, a] (B)</p> Signup and view all the answers

What is the equation of a line that is parallel to the line y = 3x - 2 and passes through the point (2, 5)?

<p>y = 3x + 1 (C)</p> Signup and view all the answers

What is the x-intercept of the function y = sin(θ)?

<p>180° (A), 360° (B), 0° (D)</p> Signup and view all the answers

What is the relationship between the gradient of a line and its inclination?

<p>The gradient of a line is equal to the tangent of its inclination. (D)</p> Signup and view all the answers

What is the inclination of a line with a gradient of 1/2?

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

What is the equation of a line that is parallel to the line y = 2x + 3 and passes through the point (4, 5)?

<p>y = 2x + 7 (A)</p> Signup and view all the answers

What is the domain of the function y = tan kθ in degrees?

<p>The domain of the function is {θ: -90°/k &lt; θ &lt; 90°/k, θ ∈ ℝ} (D)</p> Signup and view all the answers

What is the condition for two lines to be parallel?

<p>They have the same gradient but different y-intercepts. (D)</p> Signup and view all the answers

What is the range of the function y = tan kθ?

<p>The range of the function is (-∞, ∞) (C)</p> Signup and view all the answers

What is the gradient of a line that is perpendicular to the line y = 3x - 2?

<p>-1/3 (B)</p> Signup and view all the answers

What is the effect of a negative gradient on the inclination of a line?

<p>The inclination is obtuse. (D)</p> Signup and view all the answers

What is the effect of p on the graph of y = tan(θ + p) when p > 0?

<p>The graph shifts to the right by p (A)</p> Signup and view all the answers

What is the formula for the area of a triangle?

<p>Area = 1/2 bh (A)</p> Signup and view all the answers

What is the point-slope form of the equation of a line?

<p>y - y1 = m(x - x1) (C)</p> Signup and view all the answers

What is the surface area of a rectangular prism?

<p>2(lw + lh + wh) (A)</p> Signup and view all the answers

What is the gradient of a horizontal line?

<p>0 (A)</p> Signup and view all the answers

What is the relationship between the tangent function and the angle of inclination?

<p>The tangent function is equal to the ratio of the sine to the cosine of the angle of inclination. (D)</p> Signup and view all the answers

What is the volume of a triangular prism?

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

What is the circumference of a circle with radius r?

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

What is the inclination of a vertical line?

<p>90° (A)</p> Signup and view all the answers

What is the shape of the net of a cylinder?

<p>A rectangle with two identical circles (B)</p> Signup and view all the answers

What is the characteristic of a right pyramid?

<p>The line from the apex to the center of the base is perpendicular to the base (D)</p> Signup and view all the answers

What is the formula for the area of a circle?

<p>πr^2 (A)</p> Signup and view all the answers

What is the effect of q on the graph of y = a cos θ + q?

<p>The graph shifts vertically upwards by q units. (B)</p> Signup and view all the answers

What is the period of the function y = tan kθ?

<p>180°/|k| (C)</p> Signup and view all the answers

What is the effect of a on the graph of y = a tan θ + q?

<p>The amplitude of the graph increases. (C)</p> Signup and view all the answers

What is the domain of the function y = cos(kθ)?

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

What is the range of the function y = cos(kθ)?

<p>[-1, 1] (B)</p> Signup and view all the answers

What is the effect of p on the graph of y = cos(θ + p)?

<p>The graph shifts horizontally to the left by p units. (D)</p> Signup and view all the answers

What is the period of the function y = cos θ?

<p>360° (B)</p> Signup and view all the answers

What is the effect of k on the period of the function y = cos kθ?

<p>The period decreases. (A)</p> Signup and view all the answers

What is the x-intercept of the function y = cos θ?

<p>(90, 0) (D)</p> Signup and view all the answers

What is the amplitude of the function y = a cos θ?

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

What is the scale factor of the surface area when the dimensions of an object are multiplied by a factor of k?

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

What is the relationship between the radius and diameter of a circle?

<p>The radius is half the length of the diameter. (C)</p> Signup and view all the answers

What is the angle at the center of a circle subtended by an arc, if the angle at the circumference is 30 degrees?

<p>60 degrees (B)</p> Signup and view all the answers

What is the property of a tangent to a circle?

<p>It is perpendicular to the radius drawn to the point of contact. (D)</p> Signup and view all the answers

What is the consequence of the perpendicular bisector of a chord passing through the center of a circle?

<p>The chord is bisected. (B)</p> Signup and view all the answers

What is the relationship between the angles subtended by the same arc in a circle?

<p>They are equal. (A)</p> Signup and view all the answers

What is the consequence of two tangents being drawn from the same point outside a circle?

<p>They are equal in length. (D)</p> Signup and view all the answers

What is the property of a cyclic quadrilateral?

<p>The opposite angles are supplementary. (B)</p> Signup and view all the answers

What is the relationship between the segment and the chord of a circle?

<p>The segment is a part of the chord. (D)</p> Signup and view all the answers

What is the consequence of the angle at the center of a circle being 60 degrees?

<p>The angle at the circumference is 30 degrees. (A)</p> Signup and view all the answers

What is the formula for the surface area of a right cone?

<p>πr(r + h) (C)</p> Signup and view all the answers

What is the primary purpose of calculating the Five Number Summary in identifying outliers?

<p>To calculate the IQR and determine the boundaries for outliers (C)</p> Signup and view all the answers

What is the formula for the volume of a sphere?

<p>4/3πr^3 (C)</p> Signup and view all the answers

What happens to the surface area and volume of a rectangular prism when one dimension is multiplied by a constant factor k?

<p>Surface area increases by a factor of k, volume increases by a factor of k^2 (D)</p> Signup and view all the answers

What is the formula for the Upper Boundary of outliers in a box-and-whisker diagram?

<p>Q3 + 1.5 × IQR (D)</p> Signup and view all the answers

What is the formula for the volume of a right cone?

<p>1/3πr^2H (B)</p> Signup and view all the answers

What is the term for the data points that are outside the boundaries of Q1 - 1.5 × IQR and Q3 + 1.5 × IQR in a box-and-whisker diagram?

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

What is the formula for the surface area of a triangular pyramid?

<p>1/2b(h_b + 3h_s) (B)</p> Signup and view all the answers

What type of plot is used to show the relationship between two variables?

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

What happens to the surface area and volume of a rectangular prism when all three dimensions are multiplied by a constant factor k?

<p>Surface area increases by a factor of k^2, volume increases by a factor of k^3 (C)</p> Signup and view all the answers

What is the formula for the Interquartile Range (IQR) in a box-and-whisker diagram?

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

What is the formula for the volume of a triangular prism?

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

What is the formula for the surface area of a square pyramid?

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

What is the formula for the volume of a right cylinder?

<p>πr^2h (A)</p> Signup and view all the answers

What happens to the surface area and volume of a rectangular prism when two dimensions are multiplied by a constant factor k?

<p>Surface area increases by a factor of k^2, volume increases by a factor of k^2 (A)</p> Signup and view all the answers

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

<p>There are gaps between the bars. (A)</p> Signup and view all the answers

What is the formula for calculating the relative frequency of an event?

<p>Relative Frequency = Frequency / Total number of observations (C)</p> Signup and view all the answers

What is the term for the midpoint of a class interval?

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

What is the purpose of a frequency polygon?

<p>To display the frequencies of different class intervals (D)</p> Signup and view all the answers

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

<p>CFi = ∑j=1i fj (D)</p> Signup and view all the answers

What is the purpose of an ogive?

<p>To display the cumulative frequencies of a dataset (A)</p> Signup and view all the answers

How do you find the median using an ogive?

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

What is the first quartile (Q1) of a dataset?

<p>The 25th percentile (B)</p> Signup and view all the answers

What is the purpose of dividing a dataset into equal-length intervals in a histogram?

<p>To facilitate the counting of frequencies in each interval (B)</p> Signup and view all the answers

What is the relationship between the points on a frequency polygon and the class intervals?

<p>Each point represents the midpoint of a class interval (A)</p> Signup and view all the answers

What is the purpose of calculating the k-th percentile in a dataset?

<p>To locate the value that k percent of the data points are below (A)</p> Signup and view all the answers

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

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

What is the property of a small standard deviation in a dataset?

<p>The data values are close to the mean (B)</p> Signup and view all the answers

What is the characteristic of a right skewed distribution?

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

What is the purpose of identifying outliers in a dataset?

<p>To identify data points that significantly deviate from the rest of the data (B)</p> Signup and view all the answers

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

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

What is the characteristic of a symmetric distribution?

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

What is the purpose of calculating the variance and standard deviation in a dataset?

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

What is the property of a large standard deviation in a dataset?

<p>The data values are spread out over a large range (D)</p> Signup and view all the answers

What is the characteristic of a left skewed distribution?

<p>The mean is less than the median (B)</p> Signup and view all the answers

What is the main advantage of using the two-point form of the straight line equation?

<p>It requires only two points on the line. (C)</p> Signup and view all the answers

If a line has a gradient of 2 and passes through the point (3, 4), what is the equation of the line in gradient-intercept form?

<p>y = 2x + 10 (C)</p> Signup and view all the answers

What is the relationship between the gradient of a line and the inclination of the line?

<p>The inclination is the tangent of the angle between the line and the x-axis. (D)</p> Signup and view all the answers

What is the condition for two lines to be parallel?

<p>They have the same gradient but different y-intercepts. (C)</p> Signup and view all the answers

What is the equation of a line that is perpendicular to y = 2x + 3 and passes through the point (1, 4)?

<p>y = -1/2x + 5 (B)</p> Signup and view all the answers

What is the significance of the y-intercept in the gradient-intercept form of the straight line equation?

<p>It is the point where the line crosses the y-axis. (B)</p> Signup and view all the answers

What is the value of tanθ when θ is 60°?

<p>√3 (C)</p> Signup and view all the answers

What is the relationship between the gradient-point form and the gradient-intercept form of the straight line equation?

<p>They are equivalent forms. (A)</p> Signup and view all the answers

What is the main difference between the two-point form and the gradient-point form of the straight line equation?

<p>The two-point form requires two points, while the gradient-point form requires the gradient and one point. (B)</p> Signup and view all the answers

If two lines are perpendicular, what is the relationship between their gradients?

<p>The product of their gradients is -1 (D)</p> Signup and view all the answers

What is the equation of a line that passes through the point (3, 4) and is parallel to the line y = 2x + 1?

<p>y = 2x + 3 (B)</p> Signup and view all the answers

What is the angle of inclination of a line with a gradient of -1/2?

<p>135° (C)</p> Signup and view all the answers

What is the gradient of a line that passes through the points (2, 3) and (4, 5)?

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

What is the inclination of a horizontal line?

<p>0° (A)</p> Signup and view all the answers

What is the equation of a line that is parallel to the line y = 3x - 2 and passes through the point (1, 4)?

<p>y = 3x + 2 (D)</p> Signup and view all the answers

What is the value of tanθ when θ is 135°?

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

What is the gradient of a line that passes through the points (1, 2) and (3, 4)?

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

What is the equation of a line that is perpendicular to the line y = 2x + 1 and passes through the point (2, 3)?

<p>y = -1/2x + 4 (D)</p> Signup and view all the answers

What is the gradient of a line that is perpendicular to a line with a gradient of 3?

<p>-1/3 (D)</p> Signup and view all the answers

What is the amplitude of the function y = 2sin(θ) for 0° ≤ θ ≤ 360°?

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

What is the period of the function y = sin(2θ)?

<p>180° (D)</p> Signup and view all the answers

What is the equation of a line that is perpendicular to y = 2x - 3 and passes through the point (1, 4)?

<p>y = -1/2x + 5 (D)</p> Signup and view all the answers

What is the horizontal shift of the graph of y = sin(θ + 30°)?

<p>30° to the left (D)</p> Signup and view all the answers

What is the range of the function y = 2sin(θ)?

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

What is the effect of q on the graph of y = sin(θ) + q?

<p>Vertical shift upwards by q units (D)</p> Signup and view all the answers

What is the equation of a line that is parallel to y = 3x - 2 and passes through the point (2, 5)?

<p>y = 3x + 1 (D)</p> Signup and view all the answers

What is the x-intercept of the function y = sin(θ)?

<p>(180°, 0) (A)</p> Signup and view all the answers

What is the domain of the function y = sin(kθ)?

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

What is the period of the function y = cos(kθ)?

<p>360°/|k| (C)</p> Signup and view all the answers

What is the domain of the function y = tan(kθ) in degrees?

<p>θ ∈ (-90°/k, 90°/k) (A)</p> Signup and view all the answers

What is the effect of a on the graph of y = a cos(θ)?

<p>The amplitude of the graph increases if a &gt; 1. (C)</p> Signup and view all the answers

What is the range of the function y = tan(kθ)?

<p>(-∞, ∞) (D)</p> Signup and view all the answers

What is the effect of k on the graph of y = tan(kθ)?

<p>The graph is stretched horizontally by a factor of 1/k. (C)</p> Signup and view all the answers

What is the effect of p on the graph of y = cos(θ + p)?

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

What is the formula for the area of a rectangle?

<p>A = bh (D)</p> Signup and view all the answers

What is the formula for the volume of a triangular prism?

<p>V = (1/2) × b × h × H (C)</p> Signup and view all the answers

What is the domain of the function y = tan(kθ)?

<p>(-∞, ∞) except θ = 90° + 180°n, n ∈ ℤ (A)</p> Signup and view all the answers

What is the y-intercept of the function y = cos(θ)?

<p>(0, 1) (C)</p> Signup and view all the answers

What is the shape of the net of a cylinder?

<p>A rectangle with two identical circles (A)</p> Signup and view all the answers

What is the period of the function y = tan(kθ)?

<p>180°/|k| (B)</p> Signup and view all the answers

What is the effect of p on the graph of y = tan(θ + p) when p > 0?

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

What is the effect of q on the graph of y = a tan(θ) + q?

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

What is the formula for the surface area of a rectangular prism?

<p>SA = 2(l × b + b × h + h × l) (B)</p> Signup and view all the answers

What is the domain of the function y = tan(θ) in degrees?

<p>θ ∈ (-90°, 90°) (A)</p> Signup and view all the answers

What is the amplitude of the function y = a cos(kθ)?

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

What is the formula for the area of a circle?

<p>A = πr^2 (B)</p> Signup and view all the answers

What is the characteristic of a right pyramid?

<p>The line from the apex to the center of the base is perpendicular to the base. (C)</p> Signup and view all the answers

What does the interquartile range (IQR) represent in a box-and-whisker diagram?

<p>The range of the middle 50% of the data (B)</p> Signup and view all the answers

What is the formula for calculating the upper boundary for identifying outliers in a box-and-whisker diagram?

<p>Q3 + 1.5 × IQR (D)</p> Signup and view all the answers

What is the purpose of a scatter plot in relation to outliers?

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

What is the term for data points that are outside the boundaries of Q1 - 1.5 × IQR and Q3 + 1.5 × IQR in a box-and-whisker diagram?

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

What is the first step in identifying outliers in a box-and-whisker diagram?

<p>Determine the five-number summary (A)</p> Signup and view all the answers

If a circle is scaled up by a factor of 2, what will be the ratio of the new surface area to the original surface area?

<p>4:1 (A)</p> Signup and view all the answers

What is the angle at the center of a circle subtended by an arc of length 60°?

<p>90° (B)</p> Signup and view all the answers

If two chords of a circle are equal, what can be said about the angles subtended by these chords at the center of the circle?

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

What is the result of bisecting a chord by a line drawn from the center of a circle?

<p>The chord is divided into two equal segments (C)</p> Signup and view all the answers

What is the characteristic of a cyclic quadrilateral?

<p>The opposite angles are supplementary (B)</p> Signup and view all the answers

If two tangents are drawn from an external point to a circle, what can be said about the lengths of these tangents?

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

What is the relationship between the radius and the diameter of a circle?

<p>The radius is half the diameter (A)</p> Signup and view all the answers

What is the angle between a tangent and a chord drawn from the point of contact?

<p>The angle subtended by the chord in the alternate segment (A)</p> Signup and view all the answers

If an angle at the center of a circle is 60°, what is the corresponding angle at the circumference?

<p>30° (B)</p> Signup and view all the answers

What is the result of drawing a perpendicular bisector of a chord of a circle?

<p>The bisector passes through the center of the circle (C)</p> Signup and view all the answers

What is the surface area of a right cone with a radius of 4 cm and a height of 6 cm?

<p>48π cm^2 (D)</p> Signup and view all the answers

If a rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 4 cm, what is the volume of the prism?

<p>40 cm^3 (D)</p> Signup and view all the answers

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

<p>The height of each bar corresponds to the frequency of data in that class interval. (C)</p> Signup and view all the answers

What is the formula for calculating the relative frequency of an event?

<p>Relative Frequency = Frequency / Total number of observations (A)</p> Signup and view all the answers

What is the volume of a sphere with a radius of 3 cm?

<p>36π cm^3 (D)</p> Signup and view all the answers

What is the formula to calculate the k-th percentile?

<p>Pk = (k/100 × N) (D)</p> Signup and view all the answers

What is the purpose of finding the midpoint of a class interval in drawing a frequency polygon?

<p>To plot the point at the midpoint of the class interval (C)</p> Signup and view all the answers

What is the purpose of calculating the variance?

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

If a square pyramid has a base length of 4 cm and a height of 6 cm, what is the surface area of the pyramid?

<p>48 cm^2 (C)</p> Signup and view all the answers

What is the effect on the surface area and volume of a rectangular prism if the length, width, and height are each multiplied by a factor of 2?

<p>The surface area is multiplied by 4, and the volume is multiplied by 8. (B)</p> Signup and view all the answers

What is the effect of a large standard deviation on the data?

<p>It indicates that the data points are spread out over a wide range of values (B)</p> Signup and view all the answers

What is the formula for calculating the cumulative frequency up to the ith interval?

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

What is the characteristic of a right-skewed distribution?

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

What is the purpose of drawing an ogive?

<p>To find the median and quartiles of a dataset (A)</p> Signup and view all the answers

What is the formula for the surface area of a triangular pyramid with a base length of b and a slant height of hs?

<p>b(hb + 3hs) (A)</p> Signup and view all the answers

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

<p>To show the distribution of the data (A)</p> Signup and view all the answers

What is the volume of a right cone with a radius of 3 cm and a height of 5 cm?

<p>20π cm^3 (D)</p> Signup and view all the answers

What is the term for the midpoint of a class interval?

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

What is the purpose of finding the median class?

<p>To find the median of a dataset (A)</p> Signup and view all the answers

What is the definition of an outlier?

<p>A data point that is far away from the central cluster of data points (B)</p> Signup and view all the answers

What is the effect on the surface area and volume of a sphere if the radius is multiplied by a factor of 3?

<p>The surface area is multiplied by 9, and the volume is multiplied by 27. (A)</p> Signup and view all the answers

What is the term for the class interval with the highest frequency?

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

What is the purpose of calculating the standard deviation?

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

What is the formula for the volume of a triangular prism with a base length of b, a base width of h, and a height of H?

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

What is the purpose of drawing a frequency polygon?

<p>To display the distribution of continuous data (C)</p> Signup and view all the answers

What is the characteristic of a symmetric distribution?

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

What is the surface area of a rectangular prism with a length of 6 cm, a width of 4 cm, and a height of 3 cm?

<p>52 cm^2 (A)</p> Signup and view all the answers

What is the effect of a small standard deviation on the data?

<p>It indicates that the data points are close to the mean (C)</p> Signup and view all the answers

What is the formula for calculating the cumulative frequency up to the ith interval?

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

What is the purpose of identifying outliers in a dataset?

<p>To understand the distribution of the data and identify unusual patterns (B)</p> Signup and view all the answers

What is the form of the straight line equation that can be used when the gradient and the y-intercept of the line are known?

<p>Gradient–intercept form (B)</p> Signup and view all the answers

A line passes through the points (2, 3) and (4, 5). Which of the following forms can be used to find the equation of the line?

<p>Two-point form (C)</p> Signup and view all the answers

What is the value of y when x = 0 in the equation y = mx + c?

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

A line has a gradient of 2 and passes through the point (3, 4). Which of the following forms can be used to find the equation of the line?

<p>Gradient–point form (B)</p> Signup and view all the answers

What is the relationship between the gradient of a line and the inclination of the line?

<p>The gradient is the tangent of the inclination (B)</p> Signup and view all the answers

A line has a y-intercept of 3 and a gradient of 1. What is the equation of the line?

<p>y = x + 3 (C)</p> Signup and view all the answers

What is the purpose of the gradient–point form of the straight line equation?

<p>To find the equation of a line when the gradient and one point on the line are known (A)</p> Signup and view all the answers

What is the difference between the gradient–intercept form and the slope–intercept form of the straight line equation?

<p>There is no difference between the two forms (A)</p> Signup and view all the answers

What is the relationship between the gradient of a line and the inclination of the line?

<p>m = tan(θ) (C)</p> Signup and view all the answers

What is the angle of inclination of a line with a gradient of 1/2?

<p>26.6° (B)</p> Signup and view all the answers

What is the equation of a line that is parallel to the line y = 2x + 3 and passes through the point (4, 5)?

<p>y = 2x + 1 (B)</p> Signup and view all the answers

What is the inclination of a vertical line?

<p>90° (D)</p> Signup and view all the answers

What is the relationship between the gradients of two parallel lines?

<p>m1 = m2 (A)</p> Signup and view all the answers

What is the equation of a line that passes through the point (3, 4) and is parallel to the line y = x + 2?

<p>y = x + 1 (D)</p> Signup and view all the answers

What is the inclination of a line with a gradient of -1/3?

<p>161.6° (A)</p> Signup and view all the answers

What is the gradient of a line that is perpendicular to the line y = 2x + 3?

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

What is the equation of a line that passes through the point (2, 3) and is parallel to the line y = 3x - 2?

<p>y = 3x + 1 (A)</p> Signup and view all the answers

What is the inclination of a line with a gradient of 3/4?

<p>53.1° (D)</p> Signup and view all the answers

What is the condition for two lines to be perpendicular?

<p>m1 × m2 = -1 (C)</p> Signup and view all the answers

What is the effect of k on the period of the function y = sin(kθ)?

<p>The period is calculated as 360°/k (D)</p> Signup and view all the answers

What is the equation of a line that is perpendicular to y = 2x + 3 and passes through the point (1, 4)?

<p>y = -0.5x + 4.5 (D)</p> Signup and view all the answers

What is the effect of a on the graph of y = a sin(θ)?

<p>The amplitude increases by a factor of a (D)</p> Signup and view all the answers

What is the equation of a line that is parallel to the line y = 3x - 2 and passes through the point (2, 5)?

<p>y = 3x + 1 (D)</p> Signup and view all the answers

What is the effect of q on the graph of y = a cos(θ) + q?

<p>The graph shifts vertically by q units (B)</p> Signup and view all the answers

What is the condition for two lines to be parallel?

<p>m1 = m2 (B)</p> Signup and view all the answers

What is the effect of p on the graph of y = sin(θ + p)?

<p>The graph shifts horizontally by p units (B)</p> Signup and view all the answers

What is the range of the function y = cos(θ)?

<p>[-1, 1] (A)</p> Signup and view all the answers

What is the period of the function y = cos(kθ)?

<p>360°/k (B)</p> Signup and view all the answers

What is the formula for the area of a triangle?

<p>1/2 × base × height (D)</p> Signup and view all the answers

What is the shape of the net of a triangular prism?

<p>Two triangles and three rectangles (A)</p> Signup and view all the answers

What is the formula for the volume of a right prism?

<p>area of base × height (B)</p> Signup and view all the answers

What is the formula for the circumference of a circle?

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

What is the effect of a on the amplitude of the function y = a cos θ?

<p>The amplitude increases for a &gt; 1 and decreases for a &lt; 1. (B)</p> Signup and view all the answers

What is the characteristic of a right pyramid?

<p>The line from the apex to the center of the base is perpendicular to the base (C)</p> Signup and view all the answers

What is the surface area of a square pyramid with a base of side length b and slant height hs?

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

What is the formula for the area of a parallelogram?

<p>base × height (C)</p> Signup and view all the answers

What is the period of the function y = cos(kθ) when k = 2?

<p>90° (B)</p> Signup and view all the answers

What is the effect of p on the graph of y = cos(θ + p) when p > 0?

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

If the dimensions of a rectangular prism are multiplied by a constant factor k, what is the effect on the volume?

<p>The volume is multiplied by k^3 (B)</p> Signup and view all the answers

What is the shape of the net of a cylinder?

<p>Two identical circles and a rectangle (B)</p> Signup and view all the answers

What is the formula for the volume of a right cone with a base radius r and height H?

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

What is the domain of the function y = tan(kθ) when k = 2?

<p>{θ: 0° ≤ θ ≤ 360°, θ ≠ 45°, 135°, 225°, 315°} (C)</p> Signup and view all the answers

What is the formula for the volume of a cylinder?

<p>π × radius^2 × height (B)</p> Signup and view all the answers

What is the range of the function y = tan(kθ) when k = 2?

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

What is the formula for the area of a square?

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

If the dimensions of a sphere are multiplied by a constant factor k, what is the effect on the surface area?

<p>The surface area is multiplied by k^2 (C)</p> Signup and view all the answers

What is the formula for the surface area of a triangular pyramid with a base of side length b and height hb?

<p>1/2 b(hb + 3hs) (B)</p> Signup and view all the answers

What is the effect of k on the period of the function y = tan(kθ) when k > 1?

<p>The period decreases. (A)</p> Signup and view all the answers

What is the formula for the surface area of a rectangular prism?

<p>2 × (length × width + width × height + length × height) (D)</p> Signup and view all the answers

If the dimensions of a cylinder are multiplied by a constant factor k, what is the effect on the volume?

<p>The volume is multiplied by k^3 (D)</p> Signup and view all the answers

What is the effect of a on the shape of the graph of y = a tan(θ) when a > 1?

<p>The branches of the graph become steeper. (C)</p> Signup and view all the answers

What is the formula for the volume of a triangular prism with a base of side length b and height H?

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

What is the y-intercept of the function y = tan(θ) when θ = 0°?

<p>(0°, 0) (A)</p> Signup and view all the answers

What is the effect of p on the graph of y = tan(θ + p) when p > 0?

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

What is the effect on the surface area of a rectangular prism if one of its dimensions is multiplied by a constant factor k?

<p>The surface area is multiplied by k (A)</p> Signup and view all the answers

What is the asymptote of the function y = tan(kθ) when k = 2?

<p>θ = 45°, 135°, 225°, 315° (C)</p> Signup and view all the answers

What is the formula for the surface area of a sphere with radius r?

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

What is the effect on the volume of a pyramid if its dimensions are multiplied by a constant factor k?

<p>The volume is multiplied by k^3 (C)</p> Signup and view all the answers

What is the characteristic of a tangent to a circle?

<p>It is a straight line that touches the circle at only one point on the circumference. (D)</p> Signup and view all the answers

What is the relationship between the angle at the center of a circle and the angle at the circumference subtended by the same arc?

<p>The angle at the center is twice the angle at the circumference. (B)</p> Signup and view all the answers

What is the characteristic of a cyclic quadrilateral?

<p>All vertices lie on the circumference of a circle. (D)</p> Signup and view all the answers

What is the theorem that states that the angle between a tangent to a circle and a chord drawn from the point of contact is equal to the angle which the chord subtends in the alternate segment?

<p>Tangent-Chord Theorem (A)</p> Signup and view all the answers

What is the characteristic of a histogram?

<p>It is a graphical representation of the frequency distribution of a set of continuous data. (D)</p> Signup and view all the answers

What is the relationship between the length of two tangents drawn from the same point outside a circle?

<p>The lengths are equal. (C)</p> Signup and view all the answers

What is the characteristic of a segment of a circle?

<p>It is a part of the circle cut off by a chord. (D)</p> Signup and view all the answers

What is the corollary that states that equal chords subtend equal angles at the center of the circle?

<p>Equal chords of a circle subtend equal angles at the center of the circle. (B)</p> Signup and view all the answers

What is the theorem that states that a line segment from the center of a circle perpendicular to a chord will bisect the chord?

<p>Perpendicular Line from Circle Center Bisects Chord (C)</p> Signup and view all the answers

What is the characteristic of the angle subtended by a chord at the center of a circle?

<p>It is twice the angle subtended by the chord on the circumference. (B)</p> Signup and view all the answers

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

<p>The use of lines to connect the points (A)</p> Signup and view all the answers

What is the formula for calculating the cumulative frequency of a class interval?

<p>CF_i = ∑(f_j) + f_i (C)</p> Signup and view all the answers

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

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

What is the characteristic of the modal class in a dataset?

<p>It has the highest frequency (B)</p> Signup and view all the answers

What is the use of the relative frequency in a dataset?

<p>To compare the frequencies of different class intervals (D)</p> Signup and view all the answers

What is the difference between an ogive and a frequency polygon?

<p>An ogive is used for cumulative frequencies, while a frequency polygon is used for individual frequencies (B)</p> Signup and view all the answers

What is the formula for calculating the relative frequency of a class interval?

<p>Relative Frequency = Frequency / Total number of observations (D)</p> Signup and view all the answers

What is the purpose of finding the quartiles in a dataset?

<p>To calculate the interquartile range (C)</p> Signup and view all the answers

What is the use of the class mark in a histogram?

<p>To plot the points on the frequency polygon (B)</p> Signup and view all the answers

What is the difference between the frequency polygon and the ogive?

<p>The frequency polygon is used for individual frequencies, while the ogive is used for cumulative frequencies (B)</p> Signup and view all the answers

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

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

What is the primary characteristic of a symmetric distribution?

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

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

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

What is the term for the data points that lie far from the general trend or pattern of the rest of the data in a dataset?

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

What is the purpose of calculating the interquartile range (IQR) in identifying outliers?

<p>To identify the outliers in the data (C)</p> Signup and view all the answers

What is the characteristic of a right-skewed distribution?

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

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

<p>Minimum, Q1, Median, Q3, Maximum (D)</p> Signup and view all the answers

What is the purpose of the box-and-whisker plot in identifying outliers?

<p>To identify the outliers in the data (B)</p> Signup and view all the answers

What is the characteristic of a left-skewed distribution?

<p>The mean is less than the median. (A)</p> Signup and view all the answers

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

<p>To measure the spread of the data (D)</p> Signup and view all the answers

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