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

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

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

    What is the measure of the steepness of a line?

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

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

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

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

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

    What is the inclination of a vertical line?

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

    What is the gradient of a horizontal line?

    <p>0</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</p> Signup and view all the answers

    What is the condition for two lines to be parallel?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    What is the period of the graph y = coskθ?

    <p>360°/k</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.</p> Signup and view all the answers

    What is the range of the function y = cosθ?

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

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

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

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

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

    What is the domain of the function y = tanθ?

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

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

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

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

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

    What is the range of the function y = tanθ?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    What is the formula for the volume of a sphere?

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

    What is the main purpose of a histogram?

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

    What is the class mark of a class interval?

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

    What is the modal class of a dataset?

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

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

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

    What is the first step in constructing a histogram?

    <p>Determine the class intervals for the data</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.</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.</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.</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.</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</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.</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.</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</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.</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.</p> Signup and view all the answers

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

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

    What is the standard deviation of a dataset?

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

    What is a characteristic of a symmetric distribution?

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

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

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

    What is a characteristic of a right-skewed distribution?

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

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

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

    What is the inclination of a horizontal line?

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

    What is the condition for two lines to be parallel?

    <p>m1 = m2</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</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</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</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.</p> Signup and view all the answers

    What is the period of the graph y = coskθ?

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

    What is the range of the function y = cosθ?

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

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

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

    What is the range of the function y = tanθ?

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

    What is the domain of the function y = tanθ?

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

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

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

    What is the condition for two lines to be perpendicular?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    <p>A = π × r²</p> Signup and view all the answers

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

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

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

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

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

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

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

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

    What is the exterior angle of a cyclic quadrilateral?

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

    What is the tangent to a circle?

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

    What is the class mark of a class interval?

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

    What is the modal class of a dataset?

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

    What is the standard deviation of a data set?

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

    What is a characteristic of a symmetric distribution?

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

    What is a characteristic of a right skewed distribution?

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

    What is the purpose of the five number summary?

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

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

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

    What does a small standard deviation indicate?

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

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

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

    What is a characteristic of a left skewed distribution?

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

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

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

    What is the inclination of a horizontal line?

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

    What is the condition for two lines to be parallel?

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

    What is the inclination of a vertical line?

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

    What is the gradient of a line with an inclination of 45°?

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

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

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

    What is the range of the function y = tanθ?

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

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

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

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

    <p>360°</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.</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</p> Signup and view all the answers

    What is the range of the function y = tanθ?

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

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

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

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

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

    What is the period of the graph y = cosθ?

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

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

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

    What is the formula for the area of a circle?

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

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

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

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

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

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

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

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

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

    What is the formula for the area of a rectangle?

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

    What is the formula for the volume of a cylinder?

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

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

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

    What is the formula for the circumference of a circle?

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

    What is the formula for the area of a trapezium?

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

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

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

    What is the formula for the volume of a sphere?

    <p>$rac{4}{3} \pi r^3$</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>$20 \pi cm^2$</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</p> Signup and view all the answers

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

    <p>$b (b + 2h_s)$</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>$20 \pi cm^3$</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</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</p> Signup and view all the answers

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

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

    What is the formula for calculating the relative frequency?

    <p>Relative Frequency = Frequency / Total number of observations</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>$rac{16}{3} \pi cm^3$</p> Signup and view all the answers

    What is the purpose of an ogive?

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

    What is the class mark of a class interval?

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

    What is the modal class?

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

    What is the key characteristic of a histogram?

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

    What is the standard deviation of a data set?

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

    What is a characteristic of a symmetric distribution?

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

    What is a characteristic of a right skewed distribution?

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

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

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

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

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

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

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

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

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

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

    <p>150°</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</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</p> Signup and view all the answers

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

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

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

    <p>143.1°</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</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</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.</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.</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.</p> Signup and view all the answers

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

    <p>360°/|k|</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.</p> Signup and view all the answers

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

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

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

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

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

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

    What is the formula for the volume of a cylinder?

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

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

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

    What is the formula for the area of a parallelogram?

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

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

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

    What is the formula for the area of a circle?

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

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

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

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

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

    What is the period of the graph y = coskθ?

    <p>360°/|k|</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.</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|}</p> Signup and view all the answers

    What is the range of the function y = cosθ?

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

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

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

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

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

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

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

    What is the formula for the volume of a sphere?

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

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

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

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

    <p>4π r^2</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.</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.</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.</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.</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.</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.</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.</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.</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.</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.</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.</p> Signup and view all the answers

    What is the formula for calculating the cumulative frequency?

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

    What is the purpose of a histogram in statistical analysis?

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

    What is the purpose of an ogive?

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

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

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

    What is the class mark?

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

    What is the modal class?

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

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

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

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

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

    What is the characteristic of a right-skewed distribution?

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

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

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

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