Gr 11 Math Nov P2 (Mix)
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Questions and Answers

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

  • $y = mx + c$
  • $m = (y_2 - y_1) / (x_2 - x_1)$
  • $y - y_1 = m(x - x_1)$
  • $(y - y_1) / (x - x_1) = (y_2 - y_1) / (x_2 - x_1)$ (correct)

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

  • y - y_1 = m(x - x_1) (correct)
  • (y - y_1) / (x - x_1) = (y_2 - y_1) / (x_2 - x_1)
  • m = (y_2 - y_1) / (x_2 - x_1)
  • y = mx + c

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

  • y - y_1 = m(x - x_1)
  • (y - y_1) / (x - x_1) = (y_2 - y_1) / (x_2 - x_1)
  • m = (y_2 - y_1) / (x_2 - x_1)
  • y = mx + c (correct)

What is the value of y when x = 0 in the gradient–intercept form?

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

What is the definition of the constant c in the gradient–intercept form?

<p>The y-intercept of the line (A)</p> Signup and view all the answers

Which form of the straight line equation is used when the gradient and the y-intercept are known?

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

Which form of the straight line equation is used when two points on the line are known?

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

Which of the following is not a form of the straight line equation?

<p>Slope–intercept form (D)</p> Signup and view all the answers

What is the measure of the steepness of a line?

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

What is the value of y when the line crosses the y-axis?

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

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

<p>m = tan(θ) (A)</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 gradient of a horizontal line?

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

If the gradient of a line is negative, what can be said about its inclination?

<p>It is obtuse (D)</p> Signup and view all the answers

What is the condition for two lines to be parallel?

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

What is the equation form used to find the equation of a parallel line?

<p>Point-Slope Form (B)</p> Signup and view all the answers

What is the importance of ensuring the given line's equation is in gradient-intercept form?

<p>To find the gradient (C)</p> Signup and view all the answers

What is the relationship between the tangent function and the inclination of a line?

<p>tan(θ) is positive for acute angles and negative for obtuse angles (D)</p> Signup and view all the answers

What is the formula to calculate the area of a square?

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

What is the formula to calculate the area of a triangle?

<p>0.5bh (D)</p> Signup and view all the answers

What is the formula to calculate the surface area of a cylinder?

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

What is the formula to calculate the volume of a rectangular prism?

<p>l × b × h (D)</p> Signup and view all the answers

What is the formula to calculate the circumference of a circle?

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

What is the formula to calculate the area of a trapezium?

<p>0.5(a + b)h (D)</p> Signup and view all the answers

What is the formula to calculate the volume of a cylinder?

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

What is the formula to calculate the area of a parallelogram?

<p>b × h (A)</p> Signup and view all the answers

What is the formula to calculate the volume of a triangular prism?

<p>0.5b × h × H (C)</p> Signup and view all the answers

What shifts the graph of the tangent function to the right?

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

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

<p>It increases the amplitude of the graph for a &gt; 1 (A)</p> Signup and view all the answers

What is the period of the graph y = coskθ?

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

What is a 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 range of the function y = cosθ?

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

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

<p>m_1 × m_2 = -1 (C)</p> Signup and view all the answers

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

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

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

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

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

<p>q shifts the graph vertically (A)</p> Signup and view all the answers

What is the domain of the function y = tanθ?

<p>{θ: 0° ≤ θ ≤ 360°, θ ≠ 90°, 270°} (A)</p> Signup and view all the answers

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

<p>It increases the steepness of the branches for a &gt; 1 (D)</p> Signup and view all the answers

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

<p>a increases or decreases the amplitude of the graph (B)</p> Signup and view all the answers

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

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

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

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

What is the range of the function y = tanθ?

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

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

<p>p shifts the graph horizontally (D)</p> Signup and view all the answers

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

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

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

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

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

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

What is the y-intercept of the graph y = tanθ?

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

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

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

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

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

If one dimension of a rectangular prism is multiplied by a constant factor k, how does the volume change?

<p>The volume increases by a factor of k (A)</p> Signup and view all the answers

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

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

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

<p>1/3 × b × h × H (B)</p> Signup and view all the answers

If all three dimensions of a rectangular prism are multiplied by a constant factor k, how does the surface area change?

<p>The surface area increases by a factor of k^2 (C)</p> Signup and view all the answers

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

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

What is the formula for the volume of a sphere?

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

If two dimensions of a rectangular prism are multiplied by a constant factor k, how does the volume change?

<p>The volume increases by a factor of k^2 (B)</p> Signup and view all the answers

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

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

What is the main purpose of a histogram?

<p>To display the distribution of a single variable (A)</p> Signup and view all the answers

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

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

What is the relative frequency of an event?

<p>The frequency of an event divided by the total number of observations (C)</p> Signup and view all the answers

What is the class mark of a class interval?

<p>The midpoint of the class interval (C)</p> Signup and view all the answers

What is the modal class of a dataset?

<p>The class interval with the highest frequency (D)</p> Signup and view all the answers

What is the cumulative frequency of a class interval?

<p>The sum of all previous frequencies plus the current frequency (C)</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 (C)</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 an ogive?

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

What is the first step in constructing a histogram?

<p>Determine the class intervals for the data (B)</p> Signup and view all the answers

What is the definition of a radius in a circle?

<p>A straight line from the center of the circle to a point on the circumference. (C)</p> Signup and view all the answers

What is the definition of a diameter in a circle?

<p>A special chord that passes through the center of the circle. (B)</p> Signup and view all the answers

What is the definition of a segment in a circle?

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

What is the definition of a tangent in a circle?

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

What is the theorem that states that a tangent to a circle is perpendicular to the radius drawn to the point of contact?

<p>Tangent Perpendicular to Radius (B)</p> Signup and view all the answers

What is the definition of a histogram?

<p>A graphical representation of the frequency distribution of a set of continuous or discrete data. (C)</p> Signup and view all the answers

What is the characteristic of a histogram where each bar represents a class interval?

<p>Each bar represents a class interval. (A)</p> Signup and view all the answers

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

<p>Angle at the Center is Twice the Angle at the Circumference (D)</p> Signup and view all the answers

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

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

What is the characteristic of a histogram where the height of the bar corresponds to the frequency of data within that interval?

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

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

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

What is the standard deviation of a dataset?

<p>The square root of the variance (C)</p> Signup and view all the answers

What is a characteristic of a symmetric distribution?

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

What is the purpose of calculating the variance and standard deviation?

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

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

<p>$IQR = Q3 - Q1$ (B)</p> Signup and view all the answers

What is the purpose of the five-number summary?

<p>To summarize the main features of a dataset (B)</p> Signup and view all the answers

What is a 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 a box-and-whisker plot?

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

What does a small standard deviation indicate about a dataset?

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

Which form of the straight line equation is used when the gradient and one point on the line are known?

<p>Gradient–Point Form (A)</p> Signup and view all the answers

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

<p>The y-intercept of the straight line (A)</p> Signup and view all the answers

Which of the following is a characteristic of the gradient–intercept form of the straight line equation?

<p>It is used when the gradient and the y-intercept are known (B)</p> Signup and view all the answers

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

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

What is the relationship between the gradient of a line and its inclination in the range 0° ≤ θ < 180°?

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

What is the inclination of a horizontal line?

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

Why is the gradient–intercept form of the straight line equation also called the standard form?

<p>Because it can be used to find the equation of any line (C)</p> Signup and view all the answers

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

<p>To find the equation of a line when two points are known (D)</p> Signup and view all the answers

If a line has a negative gradient, what can be said about its inclination?

<p>It is an obtuse angle (A)</p> Signup and view all the answers

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

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

What is the condition for two lines to be parallel?

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

How do you find the equation of a line that is parallel to a given line and passes through a specific point?

<p>Use the point-slope form (B)</p> Signup and view all the answers

What is the advantage of using the gradient–intercept form of the straight line equation?

<p>It can be used to find the equation of any line (C)</p> Signup and view all the answers

What is the importance of ensuring the given line's equation is in gradient-intercept form?

<p>To easily identify the gradient (B)</p> Signup and view all the answers

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

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

What is the period of the graph y = coskθ?

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

What is the relationship between the tangent function and the inclination of a line?

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

What is the adjustment needed for the angle of inclination θ when the gradient of a line is negative?

<p>θ = 180° + θ (C)</p> Signup and view all the answers

What is the range of the function y = cosθ?

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

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

<p>Horizontal shift to the left by p units. (B)</p> Signup and view all the answers

What is the definition of the inclination of a line?

<p>The angle a line makes with the positive x-axis (C)</p> Signup and view all the answers

What is the relationship between the gradient of a line and the angle of inclination θ in the range 0° ≤ θ < 90°?

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

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

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

What is the range of the function y = tanθ?

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

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

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

What is the domain of the function y = tanθ?

<p>{θ: θ ∈ ℝ, θ ≠ 90°, 270°} (D)</p> Signup and view all the answers

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

<p>Horizontal shift to the left by p units. (B)</p> Signup and view all the answers

What is the y-intercept of the function y = cosθ?

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

What is the condition for two lines to be perpendicular?

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

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

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

What is the period of the graph y = sin kθ?

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

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

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

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

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

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

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

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

<p>A vertical shift (A)</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 a on the graph of y = a cos θ?

<p>An increase in amplitude (C)</p> Signup and view all the answers

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

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

What is the surface area of a triangular pyramid with base area bh/2 and height of triangular sides hs?

<p>bh/2 + 3(bhs/2) (B)</p> Signup and view all the answers

What is the formula for the volume of a square pyramid with base length b and height H?

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

What happens to the surface area of a rectangular prism when one of its dimensions is multiplied by a constant factor k?

<p>It increases by a factor of k^2 (C)</p> Signup and view all the answers

What is the formula to calculate the area of a rectangle?

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

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

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

What is the formula to calculate the volume of a triangular prism?

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

What is the surface area of a right cone with radius r and height hs?

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

What is the formula to calculate the surface area of a rectangular prism?

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

What happens to the volume of a rectangular prism when all its dimensions are multiplied by a constant factor k?

<p>It increases by a factor of k^3 (B)</p> Signup and view all the answers

What is the formula to calculate the area of a circle?

<p>A = π × r² (A)</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 formula to calculate the volume of a cylinder?

<p>V = π × r² × h (C)</p> Signup and view all the answers

What is the volume of a rectangular prism with length l, width b, and height h?

<p>l × b × h (A)</p> Signup and view all the answers

What is the formula to calculate the surface area of a cylinder?

<p>SA = 2 × π × r × (r + h) (D)</p> Signup and view all the answers

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

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

What is the formula for the volume of a triangular prism with base area bh/2 and height H?

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

What is the shape of a right prism's base?

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

What is the formula to calculate the area of a trapezium?

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

What is the formula to calculate the circumference of a circle?

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

What is the definition of a right pyramid?

<p>A pyramid with a polygon as its base and the line from the vertex to the center of the base is perpendicular to the base (A)</p> Signup and view all the answers

What is the definition of a radius in a circle?

<p>A line from the center of the circle to a point on the circumference (B)</p> Signup and view all the answers

What is the tangent-chord theorem?

<p>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 (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?

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

What is a histogram?

<p>A graphical representation of the frequency distribution of a set of continuous or discrete data (A)</p> Signup and view all the answers

What is the perpendicular bisector of a chord?

<p>A line that passes through the midpoint of the chord and is perpendicular to the chord (A)</p> Signup and view all the answers

What is the exterior angle of a cyclic quadrilateral?

<p>Equal to the interior opposite angle (A)</p> Signup and view all the answers

What is the angle subtended by a chord of a circle on the same side of the chord?

<p>Equal to the angle subtended by the chord on the opposite side (C)</p> Signup and view all the answers

What is the segment of a circle?

<p>A part of the circle cut off by a chord (B)</p> Signup and view all the answers

What is the diameter of a circle?

<p>A special chord that passes through the center of the circle (A)</p> Signup and view all the answers

What is the tangent to a circle?

<p>A line that touches the circle at one point (B)</p> Signup and view all the answers

What is the purpose of a histogram in data analysis?

<p>To display the frequency of data in different class intervals (C)</p> Signup and view all the answers

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

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

What is the purpose of an ogive in data analysis?

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

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

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

What is the class mark of a class interval?

<p>The midpoint of the class interval (B)</p> Signup and view all the answers

What is the modal class of a dataset?

<p>The class interval with the highest frequency (C)</p> Signup and view all the answers

What is the formula for calculating the k-th percentile of a dataset?

<p>P_k = (k/100) * N (B)</p> Signup and view all the answers

What is the purpose of constructing a frequency polygon from a histogram?

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

What is the variance of a data set?

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

What is the standard deviation of a data set?

<p>The square root of the variance (C)</p> Signup and view all the answers

What is a characteristic of a symmetric distribution?

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

What is a characteristic of a right skewed distribution?

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

What is the purpose of the five number summary?

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

What is the formula for the interquartile range (IQR)?

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

What does a small standard deviation indicate?

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

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

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

What is a characteristic of a left skewed distribution?

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

What is an outlier in a data set?

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

What is the key condition to use the two-point form of the straight line equation?

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

What is the main advantage of using the gradient-intercept form of the straight line equation?

<p>It is easy to find the y-intercept and gradient from this form. (B)</p> Signup and view all the answers

Which form of the straight line equation is most useful when we know the gradient and the y-intercept of the line?

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

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

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

How can we derive the gradient-point form of the straight line equation?

<p>Using the definition of gradient and the two-point form (A)</p> Signup and view all the answers

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

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

When do we use the gradient-point form of the straight line equation?

<p>When we know the gradient and one point on the line. (A)</p> Signup and view all the answers

What is the benefit of using different forms of the straight line equation?

<p>It helps us to choose the most suitable form for a particular problem. (B)</p> Signup and view all the answers

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

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

What is the inclination of a horizontal line?

<p>0° (D)</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 formula to adjust the angle of inclination for a line with a negative gradient?

<p>θ = 180° + tan⁻¹(m) (B)</p> Signup and view all the answers

What is the equation form used to find the equation of a parallel line?

<p>Point-slope form (C)</p> Signup and view all the answers

What is the importance of ensuring the given line's equation is in gradient-intercept form?

<p>To easily read off the gradient (B)</p> Signup and view all the answers

What is the relationship between the tangent function and the inclination of a line?

<p>tan(θ) = m (D)</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 gradient of a line with an inclination of 45°?

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

What is the formula to find the inclination of a line with a negative gradient?

<p>θ = 180° + tan⁻¹(m) (B)</p> Signup and view all the answers

What is the condition for two lines to be perpendicular?

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

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

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

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

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

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

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

What is the range of the function y = tanθ?

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

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

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

What is the equation form used to find the equation of a perpendicular line?

<p>Point-slope form (D)</p> Signup and view all the answers

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

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

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

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

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

<p>For a &gt; 1, the branches of the graph are steeper. (C)</p> Signup and view all the answers

What is the importance of ensuring the given line's equation is in gradient-intercept form?

<p>To find the gradient (A)</p> Signup and view all the answers

What is the range of the function y = tanθ?

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

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

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

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

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

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

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

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

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

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

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

What is the period of the graph y = cosθ?

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

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

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

What is the formula for the area of a circle?

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

What is the shape of the base of a right pyramid?

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

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

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

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

<p>$2\pi r imes h + 2\pi r^2$ (A)</p> Signup and view all the answers

What is the shape of a right cone's base?

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

What is the formula for the area of a rectangle?

<p>$l imes w$ (B)</p> Signup and view all the answers

What is the formula for the volume of a cylinder?

<p>$\pi r^2 imes h$ (A)</p> Signup and view all the answers

What is the shape of the base of a right prism?

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

What is the formula for the circumference of a circle?

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

What is the formula for the area of a trapezium?

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

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

<p>$rac{1}{2} b (h_b + 3h_s)$ (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 its volume?

<p>60 cm (A)</p> Signup and view all the answers

What is the formula for the volume of a sphere?

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

If a cone has a radius of 3 cm and a height of 5 cm, what is its surface area?

<p>$20 \pi cm^2$ (C)</p> Signup and view all the answers

What happens to the volume of a rectangular prism if its length, width, and height are all multiplied by 2?

<p>The volume is multiplied by 8 (D)</p> Signup and view all the answers

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

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

If a cylinder has a radius of 2 cm and a height of 5 cm, what is its volume?

<p>$20 \pi cm^3$ (C)</p> Signup and view all the answers

What is the purpose of a histogram?

<p>To display the frequency of data in each class interval (A)</p> Signup and view all the answers

What happens to the surface area of a rectangular prism if its length, width, and height are all multiplied by 3?

<p>The surface area is multiplied by 9 (D)</p> Signup and view all the answers

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

<p>$rac{1}{2} bhH$ (A)</p> Signup and view all the answers

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

<p>A histogram uses bars, while a frequency polygon uses lines (B)</p> Signup and view all the answers

What is the formula for calculating the relative frequency?

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

If a cone has a radius of 2 cm and a height of 4 cm, what is its volume?

<p>$rac{16}{3} \pi cm^3$ (B)</p> Signup and view all the answers

What is the purpose of an ogive?

<p>To find the median and quartiles of a dataset (C)</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 formula for calculating the cumulative frequency?

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

What is the class mark of a class interval?

<p>The midpoint of the class interval (B)</p> Signup and view all the answers

What is the modal class?

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

What is the purpose of the steps to draw a histogram?

<p>To display the frequency of each class interval (A)</p> Signup and view all the answers

What is the definition of a radius in a circle?

<p>A line from the center of the circle to a point on the circumference (C)</p> Signup and view all the answers

What is the theorem that states that a tangent to a circle is perpendicular to the radius drawn to the point of contact?

<p>Tangent Perpendicular to Radius (A)</p> Signup and view all the answers

What is 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 is Twice the Angle at the Circumference (D)</p> Signup and view all the answers

What is the definition of a segment in a circle?

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

What is the theorem that states that opposite angles of a cyclic quadrilateral are supplementary?

<p>Opposite Angles of a Cyclic Quadrilateral are Supplementary (B)</p> Signup and view all the answers

What is the definition of a histogram?

<p>A graphical representation of the frequency distribution of a set of continuous or discrete data (B)</p> Signup and view all the answers

What is the key characteristic of a histogram?

<p>Each bar represents a class interval (D)</p> Signup and view all the answers

What is the theorem that states that the perpendicular bisector of a chord passes through the center of the circle?

<p>Perpendicular Bisector of Chord Passes Through Circle Center (C)</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 (D)</p> Signup and view all the answers

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

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

What is the variance of a data set?

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

What is the standard deviation of a data set?

<p>The square root of the variance. (D)</p> Signup and view all the answers

What is a characteristic of a symmetric distribution?

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

What is a characteristic of a right skewed distribution?

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

What is the purpose of the interquartile range (IQR)?

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

What is a characteristic of a data point that is an outlier?

<p>It is far away from the central cluster of data points. (D)</p> Signup and view all the answers

What is the formula for calculating the variance of a data set?

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

What is the formula for calculating the standard deviation of a data set?

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

What is the purpose of calculating the standard deviation of a data set?

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

What is the unit of the standard deviation of a data set?

<p>The same unit as the data points. (C)</p> Signup and view all the answers

What is the most suitable form of the straight line equation to use when given the gradient and a point on the line?

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

What is the value of y when x = 1 in the equation y = 2x + 3?

<p>5 (C)</p> Signup and view all the answers

What is the relationship between the gradient of a line and the y-intercept in the gradient-intercept form?

<p>The gradient is not related to the y-intercept (D)</p> Signup and view all the answers

Which of the following is a common application of the straight line equation?

<p>Modeling real-world linear relationships (D)</p> Signup and view all the answers

What is the advantage of using the gradient-intercept form over the other forms of the straight line equation?

<p>It is easier to find the y-intercept (A)</p> Signup and view all the answers

What is the difference between the gradient-point form and the gradient-intercept form?

<p>The gradient-point form has a point, while the gradient-intercept form has a y-intercept (C)</p> Signup and view all the answers

What is the purpose of the constant c in the gradient-intercept form?

<p>To represent the y-intercept of the line (A)</p> Signup and view all the answers

Which of the following is a benefit of using the two-point form of the straight line equation?

<p>It is easier to find the equation of a line when two points are known (B)</p> Signup and view all the answers

What is the relationship between the gradient of a line and its inclination, given that the angle of inclination θ is between 0° and 180°?

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

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

<p>150° (C)</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 (1, 4)?

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

What is the 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 = x - 2 and passes through the point (2, 3)?

<p>y = x + 1 (D)</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>2/3 (B)</p> Signup and view all the answers

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

<p>143.1° (C)</p> Signup and view all the answers

What is the equation of a line that is parallel to the line y = 2x + 1 and passes through the point (3, 5)?

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

What is the relationship between the gradients of two lines that are perpendicular to each other?

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

What is the graph of y = sin(kθ) shifted by when k is negative?

<p>Reflected about the y-axis. (A)</p> Signup and view all the answers

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

<p>The amplitude is increased by a. (B)</p> Signup and view all the answers

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

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

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

<p>The graph is shifted vertically upwards by q. (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 equation of a line that is perpendicular to the line y = mx + c and passes through the point (x1, y1)?

<p>y - y1 = -1/m(x - x1) (D)</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 to the left by p. (B)</p> Signup and view all the answers

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

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

What is the condition for two lines to be perpendicular?

<p>They have gradients that multiply to -1. (A)</p> Signup and view all the answers

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

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

What is the formula for the volume of a cylinder?

<p>$V = \pi r^2 h$ (B)</p> Signup and view all the answers

What is the shape of a right pyramid when its base is a circle?

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

What is the formula for the area of a parallelogram?

<p>$A = b h$ (C)</p> Signup and view all the answers

What is the shape of a geometric solid with a polygon as its base and sides that converge at a point?

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

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

<p>$A = 2b h + l h + b l$ (D)</p> Signup and view all the answers

What is the formula for the area of a circle?

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

What is the shape of a geometric solid that is perfectly round and looks the same from any direction?

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

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

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

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

<p>$A = 2 \pi r h + 2 \pi r^2$ (D)</p> Signup and view all the answers

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

<p>For a &gt; 1, the branches of the graph are steeper. (B)</p> Signup and view all the answers

What is the period of the graph y = coskθ?

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

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

<p>For p &gt; 0, the graph shifts to the left by p units. (A)</p> Signup and view all the answers

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

<p>{θ: θ ∈ ℝ, θ ≠ 90°/|k|, 270°/|k|} (C)</p> Signup and view all the answers

What is the range of the function y = cosθ?

<p>{f(θ): f(θ) ∈ [-1, 1]} (C)</p> Signup and view all the answers

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

<p>For q &gt; 0, the graph shifts vertically upwards by q units. (A)</p> Signup and view all the answers

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

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

What is the y-intercept of the function y = tanθ?

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

What is the effect of a on the graph of y = a cosθ?

<p>For a &gt; 1, the amplitude increases. (B)</p> Signup and view all the answers

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

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

If the dimensions of a rectangular prism are tripled, what is the resulting change in its surface area?

<p>The surface area will increase by a factor of 9. (D)</p> Signup and view all the answers

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

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

What is the effect of multiplying one dimension of a rectangular prism by a constant factor k on its volume?

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

What is the formula for the volume of a sphere?

<p>frac{4}{3} π r^3 (C)</p> Signup and view all the answers

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

<p>π r (r + h) (B)</p> Signup and view all the answers

If the dimensions of a rectangular prism are doubled, what is the resulting change in its volume?

<p>The volume will increase by a factor of 8. (A)</p> Signup and view all the answers

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

<p>frac{1}{3} b h H (D)</p> Signup and view all the answers

What is the effect of multiplying all dimensions of a rectangular prism by a constant factor k on its surface area?

<p>The surface area will increase by a factor of k^2. (D)</p> Signup and view all the answers

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

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

What is the effect of multiplying one dimension of a rectangular prism by a constant factor k on its surface area?

<p>The surface area will increase by a factor of k. (A)</p> Signup and view all the answers

What is the relationship between the perpendicular bisector of a chord and the center of the circle?

<p>The perpendicular bisector of a chord passes through the center of the circle. (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>The two tangents are equal in length. (A)</p> Signup and view all the answers

What is the purpose of the tangent-chord theorem in circles?

<p>To find the angle between a tangent and a chord. (A)</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?

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

What is the definition of a segment in a circle?

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

What is the characteristic of the angle subtended by a chord on the same side of the chord?

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

What is the consequence of the perpendicular line from the center of a circle to a chord?

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

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

<p>It is used to find the properties of equal chords. (D)</p> Signup and view all the answers

What is the characteristic of a histogram in statistical graphs?

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

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

<p>Histograms use bars to represent the data, while frequency polygons use points connected by lines. (D)</p> Signup and view all the answers

What is the formula for calculating the cumulative frequency?

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

What is the purpose of a histogram in statistical analysis?

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

What is the purpose of an ogive?

<p>To visualize the cumulative frequency of a dataset (B)</p> Signup and view all the answers

What is the formula for finding the k-th percentile?

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

What is the class mark?

<p>The midpoint of a class interval (C)</p> Signup and view all the answers

What is the modal class?

<p>The class interval with the highest frequency (D)</p> Signup and view all the answers

What is the purpose of dividing the data into class intervals?

<p>To create a histogram or frequency polygon (B)</p> Signup and view all the answers

What is the relationship between the relative frequency and the frequency of an event?

<p>Relative frequency is the frequency of an event divided by the total number of observations (A)</p> Signup and view all the answers

What is the purpose of plotting the points on the ogive?

<p>To visualize the cumulative frequency of the data (C)</p> Signup and view all the answers

What is the difference between a histogram and an ogive?

<p>A histogram shows the frequency of each class interval, while an ogive shows the cumulative frequency (A)</p> Signup and view all the answers

What is the main difference between variance and standard deviation?

<p>Variance is the average of the squared differences from the mean, while standard deviation is the square root of the variance. (C)</p> Signup and view all the answers

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

<p>The mean is approximately equal to the median, and the left and right tails are balanced. (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. (C)</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 purpose of the interquartile range (IQR) in identifying outliers?

<p>To identify outliers by comparing them to the IQR. (B)</p> Signup and view all the answers

What is the difference between a small standard deviation and a large standard deviation?

<p>A small standard deviation indicates low variability, while a large standard deviation indicates high variability. (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. (B)</p> Signup and view all the answers

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

<p>To summarize the main features of the data distribution. (A)</p> Signup and view all the answers

What is the relationship between the mean and median in a symmetric distribution?

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

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

<p>To visualize the distribution of the data and identify outliers. (B)</p> Signup and view all the answers

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