Gr 11 Math Nov P2 (Medium)
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Questions and Answers

What is the equation of the straight line that passes through two points (x_1, y_1) and (x_2, y_2)?

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

    • What is the gradient of the line that passes through two points (x_1, y_1) and (x_2, y_2)?

  • m = (x_2 - x_1) / (y_2 - y_1)
  • m = (y_1 + y_2) / (x_1 + x_2)
  • m = (y_1 - y_2) / (x_1 - x_2)
  • m = (y_2 - y_1) / (x_2 - x_1) (correct)

    • What is the y-intercept of the line with equation y = mx + c?

  • m
  • c (correct)
  • mx
  • x

    • What is the form of the equation of a straight line that 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 equation of the straight line that passes through the point (x_1, y_1) with gradient m?

    <p>y - y_1 = m(x - x_1)</p> Signup and view all the answers

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

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

    What is the equation of the straight line that passes through the point (x_1, y_1) and (x_2, y_2)?

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

    What is the definition of the gradient of a line?

    <p>The ratio of the change in y to the change in x</p> Signup and view all the answers

    What is the value of the y-intercept for a line in the gradient-intercept form?

    <p>The value of y where the line crosses the y-axis</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 gradient of a vertical line?

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

    What is the condition for two lines to be perpendicular?

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

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

    <p>y = -2x + 6</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 inclination of a line with a negative gradient?

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

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

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

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

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

    What is the equation of a line that is parallel to a given line with gradient m and passes through a point (x1, y1)?

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

    What is the value of θ for a horizontal line?

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

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

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

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

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

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

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

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

    <p>y = -3x + 11</p> Signup and view all the answers

    What is the gradient of a line with an inclination of 90°?

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

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

    <p>Amplitude increases if a &gt; 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 y-intercept of the function y = sin(θ) + 2?

    <p>(0, 2)</p> Signup and view all the answers

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

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

    What is the period of the function y = cosθ?

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

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

    <p>Vertical shift</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 k on the period of the function y = coskθ?

    <p>The period decreases</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 period of the function y = tanθ?

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

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

    <p>Steeper branches</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 k on the period of the function y = tan kθ?

    <p>The period decreases</p> Signup and view all the answers

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

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

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

    <p>$\pi r (r + h)$</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 dimension of a rectangular prism is multiplied by a constant factor k, what happens to the volume?

    <p>It is multiplied by k</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

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

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

    If two dimensions of a rectangular prism are multiplied by a constant factor k, what happens to the volume?

    <p>It is multiplied by k^2</p> Signup and view all the answers

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

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

    If all three dimensions of a rectangular prism are multiplied by a constant factor k, what happens to the surface area?

    <p>It is multiplied by k^2 and then multiplied by 2</p> Signup and view all the answers

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

    <p>$rac{1}{3} imes rac{1}{2} b h imes H$</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 main purpose of a scatter plot?

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

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

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

    What type of data is used to create a scatter plot?

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

    What is the term for the values that are either below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR in a box-and-whisker diagram?

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

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

    <p>Q2 - Q1</p> Signup and view all the answers

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

    <p>All real numbers except for θ = -90°/k and θ = 90°/k</p> Signup and view all the answers

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

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

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

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

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

    <p>A horizontal shift to the left by p</p> Signup and view all the answers

    What is the area of a triangle with a base of 5 units and a height of 6 units?

    <p>30 square units</p> Signup and view all the answers

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

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

    What is the effect of multiplying dimensions by a factor k on the volume?

    <p>It scales by k^3</p> Signup and view all the answers

    What is the surface area of a rectangular prism with a length of 5 units, a width of 4 units, and a height of 3 units?

    <p>74 square units</p> Signup and view all the answers

    What is the definition of a chord in a circle?

    <p>A straight line joining the ends of an arc</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 volume of a cylinder with a radius of 3 units and a height of 4 units?

    <p>36π cubic units</p> Signup and view all the answers

    What is the name of the line segment that joins the center of a circle and the midpoint of a chord?

    <p>Segment through center and midpoint</p> Signup and view all the answers

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

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

    What is the definition of a right pyramid?

    <p>A pyramid with a polygon base and a perpendicular line from the apex to the center of the base</p> Signup and view all the answers

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

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

    What is the angle at the center of a circle subtended by an arc, relative to the angle at the circumference?

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

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

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

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

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

    What is the corollary that states that equal chords subtend equal angles on the circle in corresponding segments?

    <p>Equal chords subtend equal angles on the circle in corresponding segments</p> Signup and view all the answers

    What is the name of the quadrilateral where all vertices lie on the circumference of a circle?

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

    What is the primary purpose of a histogram in data analysis?

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

    What is the key characteristic of a frequency polygon compared to a histogram?

    <p>The use of points connected by straight lines to represent class intervals</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 term for the midpoint of a class interval in a histogram?

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

    What is the purpose of an ogive in data analysis?

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

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

    <p>CF_i = Sum of all previous frequencies + Frequency_i</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 difference between a histogram and a frequency polygon?

    <p>A histogram uses bars, while a frequency polygon uses points</p> Signup and view all the answers

    What is the purpose of the class intervals in a histogram?

    <p>To divide the data into equal length intervals</p> Signup and view all the answers

    What is the term for the class interval with the highest frequency in a histogram?

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

    What is the k-th percentile in a data set?

    <p>The value below which k% of the data points fall</p> Signup and view all the answers

    What is the formula to calculate the variance of a data set?

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

    What is the main difference between variance and standard deviation?

    <p>Variance is in squared units, while standard deviation is in the same units as the data</p> Signup and view all the answers

    What does a small standard deviation indicate about the data?

    <p>The data values are close to the mean, indicating low variability</p> Signup and view all the answers

    What is the characteristic of a symmetric distribution?

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

    What is a right-skewed distribution characterized by?

    <p>The mean is greater 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 different from the other values in the dataset</p> Signup and view all the answers

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

    <p>To measure the spread or variability of the data set</p> Signup and view all the answers

    What is the formula to calculate the standard deviation of a data set?

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

    What does a large standard deviation indicate about the data?

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

    When is the two-point form of the equation of a straight line used?

    <p>When two points on the line are known</p> Signup and view all the answers

    What is the value of y when x = 0 in the gradient-intercept form of the equation of a straight line?

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

    Which of the following forms of the equation of a straight line is also known as the standard form?

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

    What is the gradient of a line that passes through the points (x1, y1) and (x2, y2)?

    <p>m = (y2 - y1) / (x2 - x1)</p> Signup and view all the answers

    What is the main purpose of using the gradient-point form of the equation of a straight line?

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

    Which of the following equations is in the gradient-intercept form?

    <p>y = mx + c</p> Signup and view all the answers

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

    <p>The gradient of a line is proportional to its inclination</p> Signup and view all the answers

    What is the equation of the line that passes through the point (x1, y1) with gradient m?

    <p>y - y1 = m(x - x1)</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

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

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

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

    <p>120°</p> Signup and view all the answers

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

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

    What is the gradient of a horizontal line?

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

    What is the equation of a line that is parallel to y = mx + c and passes through the point (x1, y1)?

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

    What is the relationship between the gradient of a line and the change in the y-direction and the change in the x-direction?

    <p>m = Δy/Δx</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 form of the equation of a straight line that is used when the gradient and y-intercept are known?

    <p>y = mx + c</p> Signup and view all the answers

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

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

    What is the period of the function y = cosθ?

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

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

    <p>The period changes by a factor of |k|.</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 q on the graph of y = acosθ + q?

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

    What is the period of the function y = tanθ?

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

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

    <p>The period changes by a factor of |k|.</p> Signup and view all the answers

    What is the domain of the function y = tanθ?

    <p>[0, 360], θ ≠ 90°, 270°</p> Signup and view all the answers

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

    <p>The graph is stretched vertically by a factor of a.</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 effect of p on the graph of y = cos(θ + p)?

    <p>The graph is shifted horizontally by p units.</p> Signup and view all the answers

    What is the purpose of a scatter plot?

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

    What is the formula to calculate the Interquartile Range (IQR)?

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

    How are outliers identified in a box-and-whisker diagram?

    <p>Any data point greater than Q3 + 1.5 × IQR or less than Q1 - 1.5 × IQR</p> Signup and view all the answers

    What is the purpose of calculating the Five Number Summary?

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

    What is the term for the extreme values of the data in a box-and-whisker diagram?

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

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

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

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

    <p>The period is divided by k</p> Signup and view all the answers

    What is the formula for the area of a trapezium?

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

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

    <p>1/2b × h × H</p> Signup and view all the answers

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

    <p>The graph is shifted to the left by p</p> Signup and view all the answers

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

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

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

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

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

    <p>l × b × h</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 effect of a on the graph of y = a sin(θ)?

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

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

    <p>The graph is stretched horizontally by k</p> Signup and view all the answers

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

    <p>1/2b × h</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 equation of a line that is perpendicular to y = 2x + 3 and passes through the point (1, 4)?

    <p>y = -0.5x + 5</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 by p units.</p> Signup and view all the answers

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

    <p>y = 2x + 5</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 range of the function y = sin(θ)?

    <p>{y: y ∈ [-1, 1]}</p> Signup and view all the answers

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

    <p>It decreases the period by a factor of 1/k.</p> Signup and view all the answers

    What is the equation of a line that is perpendicular to y = mx + c and passes through the point (x1, y1)?

    <p>y = -1/mx + y1</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

    If one dimension of a rectangular prism is multiplied by a constant factor k, what happens to the volume?

    <p>It increases by a factor of k</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

    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

    If two dimensions of a rectangular prism are multiplied by a constant factor k, what happens to the volume?

    <p>It increases by a factor of k^2</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 all three dimensions of a rectangular prism are multiplied by a constant factor k, what happens to the surface area?

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

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

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

    What is the purpose of a histogram?

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

    What is the key characteristic of a frequency polygon?

    <p>It uses points connected by straight lines to represent the frequency of each class interval</p> Signup and view all the answers

    What is the formula for calculating the relative frequency?

    <p>Frequency / Total number of observations</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 an ogive?

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

    What is the formula for calculating the cumulative frequency?

    <p>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 first quartile (Q1) in an ogive?

    <p>25th percentile</p> Signup and view all the answers

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

    <p>To divide the data into equal length intervals</p> Signup and view all the answers

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

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

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

    <p>The surface area increases by k^2 and the volume increases by k^3</p> Signup and view all the answers

    What is the definition of a chord in a circle?

    <p>A straight line joining the ends of an arc</p> Signup and view all the answers

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

    <p>Twice the angle at the circumference subtended by the same arc</p> Signup and view all the answers

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

    <p>It passes through the center of the circle</p> Signup and view all the answers

    What is the relationship between the angles subtended by the same arc on the same side of the chord?

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

    What is the result of drawing a line segment from the center of a circle to the midpoint of a chord?

    <p>It is perpendicular to the chord</p> Signup and view all the answers

    What is the definition of a tangent to a circle?

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

    What is the result of drawing two tangents from the same point outside a circle?

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

    What is the definition of a segment in a circle?

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

    What is the result of drawing a line segment from the center of a circle perpendicular to a chord?

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

    What is the formula for the k-th percentile?

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

    What is the main 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 characteristic of a right-skewed distribution?

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

    What is the definition of an outlier?

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

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

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

    What is the characteristic of a symmetric distribution?

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

    What is the property of the standard deviation?

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

    What is the interpretation of a small standard deviation?

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

    What is the interpretation of a large standard deviation?

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

    What is the characteristic of a left-skewed distribution?

    <p>The mean is less than the median</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 y when x = 0 in the equation y = mx + c?

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

    What is the constant c in the equation y = mx + c?

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

    What is the equation of the straight line that passes through two points (x1, y1) and (x2, y2)?

    <p>y - y1 = (y2 - y1)/(x2 - x1)(x - x1)</p> Signup and view all the answers

    What is the relationship between the gradient m and the y-intercept c in the equation y = mx + c?

    <p>c is the y-intercept when m = 0</p> Signup and view all the answers

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

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

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

    <p>The gradient-point form is used when the gradient and one point are known, while the gradient-intercept form is used when the gradient and y-intercept are known</p> Signup and view all the answers

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

    <p>It is easier to find the y-intercept of the line</p> Signup and view all the answers

    What is the condition for two lines to be perpendicular?

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

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

    <p>Amplitude change</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 equation of a line that is perpendicular to y = 2x + 3 and passes through the point (1, 4)?

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

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

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

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

    <p>y = 2x + 6</p> Signup and view all the answers

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

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

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

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

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

    <p>y = -1/3x + 7</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 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 line with a gradient of -1?

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

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

    <p>y = 2x + 2</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 gradient of a horizontal line?

    <p>0</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 relationship between the inclination of a line and the tangent function?

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

    What is the equation of a line that is parallel to a given line with gradient m and passes through a point (x1, y1)?

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

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

    <p>45°</p> Signup and view all the answers

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

    <p>-1/m</p> Signup and view all the answers

    What is the period of the function y = cosθ?

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

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

    <p>Vertical shift by q units</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 k on the period of the function y = cos kθ?

    <p>The period decreases</p> Signup and view all the answers

    What is the period of the function y = tanθ?

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

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

    <p>The branches of the graph are steeper</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 k on the period of the function y = tan kθ?

    <p>The period decreases</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 effect of p on the graph of y = cos(θ + p)?

    <p>Horizontal shift by p units</p> Signup and view all the answers

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

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

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

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

    What is the formula for the area of a trapezium?

    <p>½(a + b)h</p> Signup and view all the answers

    What is the surface area of a right prism?

    <p>The sum of the areas of the lateral faces and the base</p> Signup and view all the answers

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

    <p>½bhH</p> Signup and view all the answers

    What is the formula for the volume of a cylinder?

    <p>πr²h</p> Signup and view all the answers

    What is the surface area of a right pyramid?

    <p>The sum of the areas of the lateral faces and the base</p> Signup and view all the answers

    What is the formula for the volume of a sphere?

    <p>πr³</p> Signup and view all the answers

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

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

    What is the formula for the circumference of a circle?

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

    What is the purpose of a scatter plot?

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

    What is the formula for calculating the IQR?

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

    What is the definition of an outlier in a box-and-whisker diagram?

    <p>Any data point greater than Q3 + 1.5 × IQR or less than Q1 - 1.5 × IQR</p> Signup and view all the answers

    What is the purpose of calculating the five number summary?

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

    What is the purpose of calculating the upper and lower boundaries in a box-and-whisker diagram?

    <p>To identify outliers in a dataset</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

    If one dimension of a rectangular prism is multiplied by a constant factor k, what happens to the volume?

    <p>It is multiplied by k.</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

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

    <p>It is multiplied by k^2.</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 sphere?

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

    If two dimensions of a rectangular prism are multiplied by a constant factor k, what happens to the volume?

    <p>It is multiplied by k^2.</p> Signup and view all the answers

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

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

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

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

    What happens to the volume of a rectangular prism if two dimensions are multiplied by a constant factor k?

    <p>It is multiplied by k^2.</p> Signup and view all the answers

    If the radius of a circle is increased by a factor of 2, what happens to the circumference?

    <p>It increases by a factor of 2</p> Signup and view all the answers

    What is the angle at the center of a circle subtended by an arc, if the angle at the circumference is 40 degrees?

    <p>80 degrees</p> Signup and view all the answers

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

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

    What is the name of the line segment that joins the center of a circle to a point on the circumference?

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

    What can be said about the opposite angles of a cyclic quadrilateral?

    <p>They are supplementary</p> Signup and view all the answers

    If a line segment is drawn from the center of a circle perpendicular to a chord, what happens to the chord?

    <p>It is bisected</p> Signup and view all the answers

    What is the name of 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 relationship between the surface area and volume of a rectangular prism when its dimensions are multiplied by a factor of k?

    <p>The surface area increases by a factor of k^2, and the volume increases by a factor of k^3</p> Signup and view all the answers

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

    <p>There are no gaps between the bars in a histogram unless a class interval has a frequency of zero.</p> Signup and view all the answers

    What is the name of the line segment that joins two points on a circle?

    <p>Chord</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

    What is the angle subtended by a diameter at the circumference of a circle?

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

    What is the purpose of marking the midpoints of each class interval when drawing a frequency polygon?

    <p>To plot the points at the height corresponding to the frequency at each midpoint</p> Signup and view all the answers

    What is the cumulative frequency?

    <p>The sum of all previous frequencies plus the current frequency</p> Signup and view all the answers

    What is the purpose of an ogive plot?

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

    How do you find the median from an ogive plot?

    <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 data set?

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

    What is the purpose of dividing the data into equal length intervals when drawing a histogram?

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

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

    <p>A histogram uses bars to represent the frequency distribution, while a frequency polygon uses points connected by lines</p> Signup and view all the answers

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

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

    What is the definition of variance?

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

    What is the formula for calculating the standard deviation?

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

    What is the characteristic of a symmetric distribution?

    <p>The mean is approximately equal to the median.</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 standard deviation?

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

    What is an outlier in a dataset?

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

    What is the formula for calculating the variance?

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

    What is the characteristic of a left-skewed distribution?

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

    What is the purpose of calculating the third quartile (Q3)?

    <p>To locate the 75th percentile.</p> Signup and view all the answers

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

    <p>It is derived from the definition of gradient and the two-point form.</p> Signup and view all the answers

    What is the relationship between the y-intercept and the equation y = mx + c?

    <p>The y-intercept is the value of c in the equation.</p> Signup and view all the answers

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

    <p>The two-point form is used when two points on the line are known, while the gradient-point form is used when the gradient and one point on the line are known.</p> Signup and view all the answers

    What is the purpose of defining the constant c in the gradient-intercept form of the straight line equation?

    <p>To define the y-intercept of the line</p> Signup and view all the answers

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

    <p>It is easy to graph and find the y-intercept</p> Signup and view all the answers

    What is the result of expanding the brackets in the gradient-point form of the straight line equation?

    <p>y = mx - mx_1 + y_1</p> Signup and view all the answers

    What is the relationship between the coordinates of a point on the line and the gradient-point form of the straight line equation?

    <p>The coordinates of the point are used to derive the gradient-point form.</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

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

    <p>The gradient is equal to the tangent of the inclination.</p> Signup and view all the answers

    What is the inclination of a line with a gradient of 0?

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

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

    <p>They are equal.</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 of a line with the given gradient and point.</p> Signup and view all the answers

    What is the gradient of a line with an inclination of 180°?

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

    What is the formula for the gradient of a line in terms of the inclination?

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

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

    <p>The inclination is equal to the arctangent of the gradient.</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

    <p>The chord is bisected into two equal parts</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 relationship between the angles subtended by the same arc in a circle?

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

    What is the result of drawing a tangent to a circle and a chord from the point of contact?

    <p>The angle between the tangent and the chord is equal to the angle subtended by the chord in the alternate segment</p> Signup and view all the answers

    What happens to the volume of a rectangular prism if one dimension is multiplied by a constant factor k?

    <p>The volume is multiplied by k</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

    What is the characteristic of a cyclic quadrilateral?

    <p>The opposite angles are supplementary</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 result of drawing two tangents from the same point outside a circle?

    <p>The tangents are equal in length</p> Signup and view all the answers

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

    <p>Twice the angle subtended by the arc at the circumference</p> Signup and view all the answers

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

    <p>The surface area is multiplied by k^2</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

    What is the result of bisecting a chord of a circle with a perpendicular line?

    <p>The chord is bisected into two equal parts</p> Signup and view all the answers

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

    <p>The diameter is twice the radius</p> Signup and view all the answers

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

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

    If two dimensions of a rectangular prism are multiplied by a constant factor k, what happens to the volume?

    <p>The volume is multiplied by 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 + 3h_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

    What is the 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 formula for the gradient of a perpendicular line?

    <p>m1 = -1/m2</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 a on the graph of y = a sin(θ)?

    <p>The amplitude increases if a &gt; 1, and decreases if 0 &lt; a &lt; 1.</p> Signup and view all the answers

    What is the main characteristic of a histogram?

    <p>The height of each bar represents the frequency of data in that class interval</p> Signup and view all the answers

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

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

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

    <p>To plot the points at the height corresponding to the frequency</p> Signup and view all the answers

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

    <p>y = -1/2x + 3</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 amplitude of the function y = 2sin(θ)?

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

    What is the purpose of drawing a cumulative frequency table when constructing an ogive?

    <p>To calculate the cumulative frequency up to each interval</p> Signup and view all the answers

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

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

    What is the method to 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 method to find the first quartile (Q1) using an ogive?

    <p>Locate the 25th percentile on the cumulative frequency axis</p> Signup and view all the answers

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

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

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

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

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

    <p>A histogram uses bars, while a frequency polygon uses points</p> Signup and view all the answers

    What is the term for the range of values in a data set divided into intervals of equal length?

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

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

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

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

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

    What is the purpose of calculating the interquartile range (IQR) in a box-and-whisker diagram?

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

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

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

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

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

    What type of data is represented in a scatter plot?

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

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

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

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

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

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

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

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

    <p>The amplitude increases for a &gt; 1 and decreases for 0 &lt; a &lt; 1.</p> Signup and view all the answers

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

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

    What is the formula for the area of a trapezium?

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

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

    <p>To identify extreme values in the data</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 units.</p> Signup and view all the answers

    What is the formula for the volume of a cylinder?

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

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

    <p>SA = lw + 2lh + 2wh</p> Signup and view all the answers

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

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

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

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

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

    <p>The period decreases for k &gt; 1.</p> Signup and view all the answers

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

    <p>The period is decreased by a factor of k</p> Signup and view all the answers

    What is the amplitude of the function y = 2cos(θ)?

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

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

    <p>SA = 2πr(h + r)</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 effect of a on the shape of the graph of y = a tan(θ)?

    <p>The branches of the graph are steeper for a &gt; 1.</p> Signup and view all the answers

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

    <p>V = (1/3) × bh</p> Signup and view all the answers

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

    <p>720°</p> Signup and view all the answers

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

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

    What is the definition of variance?

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

    What is the main property of a standard deviation?

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

    What is the interpretation of a small standard deviation?

    <p>Data values are close to the mean.</p> Signup and view all the answers

    What is the characteristic of a symmetric distribution?

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

    What is the definition of an outlier?

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

    What is the 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 the formula for calculating the standard deviation?

    <p>σ = √(Σ(xi - x̄)² / n)</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 identifying outliers in a dataset?

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

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