Gr 11 Math Nov P2 (Easy)
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Questions and Answers

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

  • πr(r + h) (correct)
  • 2πr(h + r)
  • πr(h + r/2)
  • πr(h - r)

    • If a rectangular prism's dimensions are multiplied by a constant factor k, what happens to its volume?

  • It increases by a factor of k
  • It increases by a factor of k^2
  • It decreases by a factor of k
  • It increases by a factor of k^3 (correct)

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

  • 3πr^2
  • 2πr^2
  • πr(r + h)
  • 4πr^2 (correct)

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

    <p>1/3 bh 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

    If a rectangular prism's dimensions are multiplied by a constant factor k, what happens to its 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^2 H</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 formula for the volume of a sphere?

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

    If a rectangular prism's dimensions are multiplied by a constant factor k, what happens to its surface area if all three dimensions are multiplied?

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

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

    <p>{θ : -90°/k &lt; θ &lt; 90°/k, θ ∈ ℝ}</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 a positive 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 formula for the area of a square?

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

    What is the formula for the area of a circle?

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

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

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

    What is the formula for the volume of a cylinder?

    <p>V = π × r^2 × h</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 definition of a right prism?

    <p>A geometric solid with a polygon as its base and vertical sides perpendicular to the base.</p> Signup and view all the answers

    What is the definition of a cylinder?

    <p>A geometric solid with a circular base and vertical sides perpendicular to the base.</p> Signup and view all the answers

    What is the gradient of a line that is parallel to a line with a gradient of 2?

    <p>2</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 relationship between the gradient and inclination of a line?

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

    What is the equation form useful when given a gradient and a point?

    <p>Gradient-Point Form</p> Signup and view all the answers

    What is the y-intercept of a line with a gradient of 0?

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

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

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

    What is the formula to find the equation of a line parallel to a given line?

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

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

    <p>135°</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 amplitude of the function y = a cosθ + q?

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

    What is the equation form useful when given two points?

    <p>Two-Point Form</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 effect of q on the graph of y = cosθ + q?

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

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

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

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

    <p>$\frac{y_2 - y_1}{x_2 - x_1}$</p> Signup and view all the answers

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

    <p>360°|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 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 standard form of the straight line equation?

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

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

    <p>$y_1 - mx_1$</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 formula to find the gradient of a perpendicular line?

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

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

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

    What is the period of the sine function y = sinθ?

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

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

    <p>Change in steepness</p> Signup and view all the answers

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

    <p>It shifts the graph vertically by q units.</p> Signup and view all the answers

    What is the name of the form of the straight line equation that is used when the gradient and a point on the line are known?

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

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

    <p>180°|k|</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 value of $y$ when $x = 0$ in the gradient-intercept form of the straight line equation?

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

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

    <p>It changes the amplitude of the graph by a units.</p> Signup and view all the answers

    What is the name of the form of the straight line equation that is also known as the standard form?

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

    What is the period of the function y = sinkθ?

    <p>360°/|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 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 domain of the function y = sinθ?

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

    What is the range of the function y = sinθ?

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

    What is the maximum turning point of the function y = sinθ?

    <p>(90°, 1)</p> Signup and view all the answers

    What is the purpose of calculating the Interquartile Range (IQR) in identifying outliers?

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

    What is the term for the values 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 formula to calculate the Lower Boundary for outliers in a box-and-whisker diagram?

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

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

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

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

    <p>Five-number summary</p> Signup and view all the answers

    If a circle's dimensions are multiplied by a factor k, what happens to its surface area?

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

    What is the term for a straight line joining the ends of an arc in a circle?

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

    What is the theorem that states 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 happens to the volume of a shape when its dimensions are multiplied by a factor k?

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

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

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

    What is the theorem that states 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 term for a line that touches the circle at only one point on the circumference?

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

    What is the corollary that states 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 theorem that states if a line is drawn from the center of a circle perpendicular to a chord, it bisects the chord?

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

    What is the theorem that states angles on a circle that are subtended by the same arc are equal?

    <p>Angles Subtended by Same Arc</p> Signup and view all the answers

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

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

    What is the relative frequency of an event?

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

    What is the purpose of 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 up to the i-th interval?

    <p>CF_i = Sigma (j=1 to i) f_j</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

    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 modal class?

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

    What is the first step in drawing a histogram?

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

    What is the purpose of drawing a frequency polygon?

    <p>To show the distribution of data.</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 formula for calculating the k-th percentile?

    <p>Pk = (k/100) × N</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 does a small standard deviation indicate?

    <p>Low variability</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 definition of an outlier?

    <p>A data value that is significantly deviates from the other values</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 = √((∑(xi - x̄)^2)/n)</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 the formula for the two-point form of the straight line equation?

    <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 name of the form of the straight line equation that is used when the gradient and a 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 gradient-intercept form of the straight line equation?

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

    What is the definition of c in the gradient-intercept form of the straight line equation?

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

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

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

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

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

    What is the standard form of the straight line equation?

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

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

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

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

    <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 equation form useful when given a gradient and the y-intercept?

    <p>Gradient-Intercept Form</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 equation form useful when given two points?

    <p>Two-Point Form</p> Signup and view all the answers

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

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

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

    <p>The angle of inclination is obtuse</p> Signup and view all the answers

    What is the formula to find the equation of a line parallel to a given line?

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

    What is the name of the form of the straight line equation that is used when the gradient and a point on the line are known?

    <p>Gradient-Point Form</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 = a sinθ?

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

    What is the equation form useful when given a gradient and a point?

    <p>Point-slope form</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 p on the graph of y = sin(θ + p)?

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

    What is the range of the function y = sinθ?

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

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

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

    What is the amplitude of the function y = a sinθ + q?

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

    What is the equation form useful when given two points?

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

    What is the condition for two lines to be parallel?

    <p>They have the same gradient</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 a > 1 on the graph of y = a cosθ + q?

    <p>The amplitude increases</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 q > 0 on the graph of y = tanθ + q?

    <p>The graph shifts vertically upwards</p> Signup and view all the answers

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

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

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

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

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

    <p>(270°, 0)</p> Signup and view all the answers

    What is the effect of a < 0 on the graph of y = a cosθ + q?

    <p>The graph is reflected about the x-axis</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 p > 0 on the graph of y = cos(θ + p)?

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

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

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

    What is the surface area of a cylinder?

    <p>πr² + 2πrh</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 formula for the area of a trapezium?

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

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

    <p>½b × h × H</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 definition of a right prism?

    <p>A geometric solid with a polygon as its base and vertical sides perpendicular to the base.</p> Signup and view all the answers

    What is the formula for the area of a parallelogram?

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

    What is the formula for the volume of a cylinder?

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

    What is the formula for the area of a rectangle?

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

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

    <p>The way the data is displayed</p> Signup and view all the answers

    What is the formula for relative frequency?

    <p>Frequency / Total number of observations</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 purpose of drawing a frequency polygon?

    <p>To show the frequency distribution of a set of data</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 formula for cumulative frequency?

    <p>Sum of all previous frequencies + Current frequency</p> Signup and view all the answers

    What is the purpose of drawing an ogive?

    <p>To find the median and quartiles of a data set</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 term for the upper boundary of a class interval?

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

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

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

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

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

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

    <p>1/3b^2H</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 the dimensions of a rectangular prism are multiplied by a constant factor k, what happens to its surface area if all three dimensions are multiplied?

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

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

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

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

    <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 prism?

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

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

    <p>lwh</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

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

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

    What is an outlier in a Box-and-Whisker Diagram?

    <p>A 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 angle formed by a tangent to a circle and a radius drawn to the point of contact?

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

    What is the Lower Boundary for outliers in a Box-and-Whisker Diagram?

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

    What is the definition of a segment of 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 purpose of the Five Number Summary in a Box-and-Whisker Diagram?

    <p>To provide a summary of the minimum, maximum, and quartiles of the data</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 definition of a chord of a circle?

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

    What is the definition of a diameter of a circle?

    <p>The longest chord that passes through the center of the circle</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</p> Signup and view all the answers

    What is the definition of a tangent to 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 two tangents drawn from the same point outside a circle are equal in length?

    <p>Two Tangents from the Same Point</p> Signup and view all the answers

    What is the definition of a circle?

    <p>The set of points equidistant from a central point</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 definition of variance?

    <p>Variance is the average of the squared differences from the mean.</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 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 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 a dataset.</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 relationship between the mean and median in a skewed distribution?

    <p>The mean is greater than the median in a right skewed distribution, and less than the median in a left skewed distribution.</p> Signup and view all the answers

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

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

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

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

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

    <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 gradient of a horizontal line?

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

    What is the equation form useful when given a gradient and the y-intercept?

    <p>Gradient-Intercept Form</p> Signup and view all the answers

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

    <p>c</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 tangent of the angle of inclination of a line with a negative gradient?

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

    How do you derive the gradient–point form from the two-point form?

    <p>Substitute m = (y_2 - y_1)/(x_2 - x_1) into the two-point form.</p> Signup and view all the answers

    What is the standard form of the straight line equation?

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

    What is the name of the form of the straight line equation that is used when the gradient and a point on the line are known?

    <p>Gradient-Point Form</p> Signup and view all the answers

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

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

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

    <p>The angle of inclination is obtuse</p> Signup and view all the answers

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

    <p>y_1 - mx_1</p> Signup and view all the answers

    What is the formula to find the equation of a line parallel to a given line?

    <p>y - y1 = m(x - x1)</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 condition for the gradient–point form and the gradient–intercept form to represent the same line?

    <p>They have the same gradient and a point on the line.</p> Signup and view all the answers

    What is the standard form of the straight line equation?

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

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

    <p>Their product is -1</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 period of the function y = sin(kθ)?

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

    What is the effect of q in the function y = a cosθ + q?

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

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

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

    What is the domain of the function y = sinθ?

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

    What is the amplitude of the function y = a cosθ?

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

    What is the range of the function y = a sinθ + q?

    <p>[q - a, q + a]</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 in the function y = tan kθ?

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

    What is the formula to find the equation of a line perpendicular to a given line and passing through a point?

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

    What is the effect of a on the graph of the function y = a sinθ?

    <p>The amplitude increases</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 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 effect of a in the function y = a tanθ + q?

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

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

    <p>(270°, 0)</p> Signup and view all the answers

    What is the x-intercept of the function y = sinθ?

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

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

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

    What is the effect of p in the function y = cos(θ + p)?

    <p>Horizontal shift</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 name of the geometric solid with a polygon as its base and vertical sides perpendicular to the base?

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

    What is the formula for the area of a trapezium?

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

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

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

    What is the formula for the volume of a cylinder?

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

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

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

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

    <p>2(l × w) + 2(l × h) + 2(w × h)</p> Signup and view all the answers

    What is the name of the shape with a polygon as its base and a circular cross section?

    <p>Cylinder</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 effect of a positive p on the graph of the function y = tan(θ + p)?

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

    What is the formula for the area of a circle?

    <p>πr²</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 the interquartile range (IQR)?

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

    How do you calculate the upper boundary for outliers?

    <p>Q3 + 1.5 × IQR</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 purpose of a box-and-whisker diagram?

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

    If the dimensions of a shape are multiplied by a factor k, how does the volume scale?

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

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

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

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

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

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

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

    What is the name of the line that joins the ends of an arc?

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

    If a line 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 name of the line that passes through the center of a circle and connects two points on the circumference?

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

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

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

    What is the name of the perimeter or boundary line of a circle?

    <p>Circumference</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 happens to the volume of a rectangular prism if all its dimensions are multiplied by a constant factor k?

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

    What is the formula for the k-th percentile?

    <p>P_k = \left( \frac{k}{100} \times N \right)</p> Signup and view all the answers

    What is the formula for the volume of a sphere?

    <p>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

    What is the definition of variance?

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

    What happens to the surface area of a rectangular prism if all its 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 standard deviation of a dataset?

    <p>The square root of the variance.</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 formula for the volume of a square pyramid?

    <p>1/3 b^2 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 characteristic of a right-skewed distribution?

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

    If a rectangular prism's dimensions are multiplied by a constant factor k, what happens to its volume if two dimensions are multiplied?

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

    What is the definition of an outlier?

    <p>A data value that is far away from the central cluster of data points.</p> Signup and view all the answers

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

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

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

    <p>2(lh + lb + bh)</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>It is multiplied by k</p> Signup and view all the answers

    What is the purpose of the standard deviation?

    <p>All of the above.</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 use of the box-and-whisker plot?

    <p>All of the above.</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 height of each bar in a histogram?

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

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

    <p>The way the frequencies are displayed</p> Signup and view all the answers

    What is the formula for relative frequency?

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

    What is the cumulative frequency in an ogive?

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

    How is the median found using an ogive?

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

    What is the purpose of an ogive?

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

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

    <p>A class interval is a range of values, while a class mark is the midpoint of the interval</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 equation of the line passing through two points (x1, y1) and (x2, y2)?

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

    What is the name of the form of the straight line equation used when the gradient and a 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 gradient-intercept form of the straight line equation?

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

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

    <p>To find the equation of a line given the gradient and a point</p> Signup and view all the answers

    What is the standard form of the straight line equation?

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

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

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

    What is the definition of c in the gradient-intercept form of the straight line equation?

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

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

    <p>It is easier to find the equation of a line given the gradient and a point</p> Signup and view all the answers

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

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

    What is the equation form useful when given a gradient and the y-intercept?

    <p>Gradient-Intercept Form</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

    What is the condition for two lines to be parallel?

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

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

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

    What is the y-intercept of a line with a gradient of 0?

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

    What is the equation form useful when given two points?

    <p>Two-Point Form</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 formula to find the equation of a line parallel to a given line?

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

    What is the inclination of a horizontal line?

    <p>0° or 180°</p> Signup and view all the answers

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

    <p>Their product is -1.</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 negative value of k on the graph of y = sin(kθ)?

    <p>It reflects the graph about the y-axis.</p> Signup and view all the answers

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

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

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

    <p>It shifts the graph vertically upwards.</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 equation of a line that is perpendicular to a line with a gradient of m and passes through the point (x1, y1)?

    <p>y = -1/m(x - x1) + y1</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 equation form useful when given a gradient and a point?

    <p>y - y1 = m(x - x1)</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.</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 = cosθ + q?

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

    What is the amplitude of the function y = a cosθ + q?

    <p>a</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 graph of y = a tanθ + q?

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

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

    <p>Decreases the period</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 range of the function y = cosθ?

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

    What is the domain of the function y = tanθ?

    <p>[0, 360°) except 90° and 270°</p> Signup and view all the answers

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

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

    What is the primary purpose of a scatter plot?

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

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

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

    What is the term for the difference between the third quartile and the first quartile?

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

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

    <p>To create a box-and-whisker diagram</p> Signup and view all the answers

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

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

    If a shape's dimensions are multiplied by a factor k, what happens to its volume?

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

    What is the definition of a chord in circle geometry?

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

    What is the effect on the volume of a prism when 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 tangent to 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 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 the dimensions of a rectangular prism are multiplied by a constant factor k, what is the effect on its surface area?

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

    If a line 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 relationship between the angle at the center and the angle at the circumference of a circle?

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

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

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

    What is the definition of a segment in circle geometry?

    <p>A part of the circle that is cut off by a chord</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 theorem of perpendicular line from circle center?

    <p>A line segment from the center of a circle perpendicular to a chord will bisect the chord</p> Signup and view all the answers

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

    <p>The graph of the tangent function shifts to the right by p.</p> Signup and view all the answers

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

    <p>The volume 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 definition of a radius in circle geometry?

    <p>Any straight line from the center of the circle to a point on the circumference</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 theorem of angles subtended by the same arc?

    <p>Angles subtended by the same arc are equal</p> Signup and view all the answers

    What is the effect on the surface area of a triangular prism when one dimension is multiplied by a constant factor k?

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

    What is the name of the 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 area of a trapezium?

    <p>1/2 (a + b) × h</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 definition of a diameter in circle geometry?

    <p>A special chord that passes through the center of the circle, connecting two points on the circumference</p> Signup and view all the answers

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

    <p>2πr × h + 2πr²</p> Signup and view all the answers

    What is the effect on the volume of a rectangular prism when all three dimensions are multiplied by a constant factor k?

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

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

    <p>The graph of the tangent function is compressed horizontally.</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 formula for the circumference of a circle?

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

    What is the name of the geometric solid with a polygon as its base and vertical sides perpendicular to the base?

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

    What is the formula for the area of a triangle?

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

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

    <p>A histogram uses bars, while a frequency polygon uses points connected by straight 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

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

    <p>To plot the points at the correct heights</p> Signup and view all the answers

    What is the cumulative frequency of a class interval?

    <p>The sum of all previous frequencies and the current frequency</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 an ogive?

    <p>To find the cumulative frequency of a class interval</p> Signup and view all the answers

    How is the median found using an ogive?

    <p>By finding the 50th percentile</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 standard deviation?

    <p>σ = √(Σ(x_i - x̄)^2 / n)</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 main difference between a histogram and a bar graph?

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

    What is 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 drawing the axes when drawing a histogram?

    <p>To create a frame for the histogram</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 main purpose of a frequency polygon?

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

    What is the definition of an outlier?

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

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

    <p>The data values are close to the mean</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 a 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 identifying outliers in a dataset?

    <p>To identify data values that significantly deviate from the other values</p> Signup and view all the answers

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