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

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

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

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

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

What is the formula for the volume of a sphere?

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

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

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

What is the formula for the area of a square?

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

What is the formula for the area of a circle?

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

What is the formula for the volume of a cylinder?

<p>V = π × r^2 × h (C)</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 (B)</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. (B)</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. (A)</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 (A)</p> Signup and view all the answers

What is the inclination of a vertical line?

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

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

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

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

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

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

<p>Any value (A)</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 (B)</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) (D)</p> Signup and view all the answers

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

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

What is the period of the function y = cosθ?

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

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

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

What is the equation form useful when given two points?

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

What is the gradient of a horizontal line?

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

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

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

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

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

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

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

What is the range of the function y = cosθ?

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

What is the condition for two lines to be parallel?

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

What is the standard form of the straight line equation?

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

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

<p>$y_1 - mx_1$ (A)</p> Signup and view all the answers

What is the period of the function y = tanθ?

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

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

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

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

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

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

<p>Horizontal shift (D)</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>$c$ (A)</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. (C)</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 (C)</p> Signup and view all the answers

What is the period of the function y = sinkθ?

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

What is the domain of the function y = tanθ?

<p>[0, 360), θ ≠ 90°, 270° (A)</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. (C)</p> Signup and view all the answers

What is the domain of the function y = sinθ?

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

What is the range of the function y = sinθ?

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

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

<p>(90°, 1) (B)</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 (B)</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 (B)</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 (B)</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 (B)</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 (B)</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 (B)</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 (B)</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 (A)</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 (B)</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 (C)</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 (D)</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 (B)</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 (A)</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 (D)</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 (A)</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. (D)</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. (B)</p> Signup and view all the answers

What is the purpose of an ogive?

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

What is the class mark?

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

What is the modal class?

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

What is the first step in drawing a histogram?

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

What is the purpose of drawing a frequency polygon?

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

What is the formula for calculating the relative frequency?

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

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

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

What is the variance of a data set?

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

What is the standard deviation of a data set?

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

What does a small standard deviation indicate?

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

What is a characteristic of a symmetric distribution?

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

What is a characteristic of a right-skewed distribution?

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

What is the formula for calculating the standard deviation?

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

What is a characteristic of a left-skewed distribution?

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

What is 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) (D)</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 (B)</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 (B)</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 (B)</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 (D)</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) (C)</p> Signup and view all the answers

What is the standard form of the straight line equation?

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

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

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

What is the gradient of a vertical line?

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

What is the inclination of a horizontal line?

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

What is the condition for two lines to be parallel?

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

What is the equation form useful when given two points?

<p>Two-Point Form (A)</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 (C)</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 (C)</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) (D)</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 (C)</p> Signup and view all the answers

What is the condition for two lines to be perpendicular?

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

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

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

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

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

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

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

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

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

What is the range of the function y = sinθ?

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

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

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

What is the equation form useful when given two points?

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

What is the condition for two lines to be parallel?

<p>They have the same gradient (B)</p> Signup and view all the answers

What is the period of the function y = cosθ?

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

What is the range of the function y = tanθ?

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

What is the effect of q > 0 on the graph of y = tanθ + q?

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

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

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

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

<p>(270°, 0) (A), (90°, 0) (B)</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 (C)</p> Signup and view all the answers

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

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

What is the surface area of a cylinder?

<p>πr² + 2πrh (C)</p> Signup and view all the answers

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

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

What is the formula for the area of a trapezium?

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

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

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

What is the formula for the circumference of a circle?

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

What is the formula for the area of a parallelogram?

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

What is the formula for the volume of a cylinder?

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

What is the formula for the area of a rectangle?

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

What is the formula for relative frequency?

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

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

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

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

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

What is the formula for cumulative frequency?

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

How do you find the median using an ogive?

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

What is the term for the upper boundary of a class interval?

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

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

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

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

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

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

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

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

What is the formula for the volume of a sphere?

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

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

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

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

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

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

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

What is the purpose of a Scatter Plot?

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

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

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

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

<p>Perpendicular Bisector of Chord (A)</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 (B)</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 (A)</p> Signup and view all the answers

What is the definition of a circle?

<p>The set of points equidistant from a central point (A)</p> Signup and view all the answers

What is the formula for the k-th percentile?

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

What is the standard deviation of a dataset?

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

What is a characteristic of a symmetric distribution?

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

What is a characteristic of a right skewed distribution?

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

What is the definition of an outlier?

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

What is the gradient of a horizontal line?

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

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

<p>Gradient-Intercept Form (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 (D)</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 (A)</p> Signup and view all the answers

What is the condition for two lines to be parallel?

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

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

<p>Negative (B)</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. (C)</p> Signup and view all the answers

What is the standard form of the straight line equation?

<p>y = mx + c (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 (B)</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. (C)</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 (D)</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 (A)</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) (C)</p> Signup and view all the answers

What is the inclination of a vertical line?

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

What is the standard form of the straight line equation?

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

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

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

What is the period of the function y = cosθ?

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

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

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

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

<p>Vertical shift (A)</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 (D)</p> Signup and view all the answers

What is the domain of the function y = sinθ?

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

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

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

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

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

What is the period of the function y = tanθ?

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

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

<p>Period decrease (D)</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) (D)</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 (B)</p> Signup and view all the answers

What is the range of the function y = cosθ?

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

What is the condition for two lines to be parallel?

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

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

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

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

<p>(270°, 0) (C), (180°, 0) (D)</p> Signup and view all the answers

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

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

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

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

What is the domain of the function y = tanθ?

<p>[0°, 360°), θ ≠ 90°, 270° (D)</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 (A)</p> Signup and view all the answers

What is the formula for the area of a trapezium?

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

What is the formula for the volume of a cylinder?

<p>πr² × h (B)</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 (C)</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) (A)</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 (D)</p> Signup and view all the answers

What is the formula for the circumference of a circle?

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

What is the formula for the area of a circle?

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

What is the purpose of a scatter plot?

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

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

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

How do you calculate the upper boundary for outliers?

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

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

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

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

<p>Chord (D)</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 (D)</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 (C)</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 (A)</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 (A)</p> Signup and view all the answers

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

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

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

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

What is the formula for the volume of a sphere?

<p>4/3 π r^3 (A)</p> Signup and view all the answers

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

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

What is the definition of variance?

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

What is the standard deviation of a dataset?

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

What is the characteristic of a symmetric distribution?

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

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

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

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

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

What is the characteristic of a right-skewed distribution?

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

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 (C)</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. (D)</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. (B)</p> Signup and view all the answers

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

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

What is the purpose of the standard deviation?

<p>All of the above. (D)</p> Signup and view all the answers

What is the characteristic of a left-skewed distribution?

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

What is the use of the box-and-whisker plot?

<p>All of the above. (D)</p> Signup and view all the answers

What is a histogram?

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

What is the height of each bar in a histogram?

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

What is the formula for relative frequency?

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

What is the first quartile (Q1) in an ogive?

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

What is the modal class?

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

What is the standard form of the straight line equation?

<p>y = mx + c (D)</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 (A)</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 (B)</p> Signup and view all the answers

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

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

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

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

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

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

What is the condition for two lines to be parallel?

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

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

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

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

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

What is the equation form useful when given two points?

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

What is the gradient of a vertical line?

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

What is the inclination of a horizontal line?

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

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

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

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

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

What is the effect of a negative value of k on the graph of y = sin(kθ)?

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

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

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

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

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

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

What is the condition for two lines to be parallel?

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

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

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

What is the period of the function y = cosθ?

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

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

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

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

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

What is the period of the function y = tanθ?

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

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

<p>Steeper branches (B)</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 (A)</p> Signup and view all the answers

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

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

What is the range of the function y = cosθ?

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

What is the domain of the function y = tanθ?

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

What is the primary purpose of a scatter plot?

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

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

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

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

<p>Interquartile Range (B)</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 (A)</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 (D)</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 (D)</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 (D)</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 (A)</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 (B)</p> Signup and view all the answers

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

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

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

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

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

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

What is the formula for the volume of a sphere?

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

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

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

What is the formula for the area of a trapezium?

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

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

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

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

<p>2πr × h + 2πr² (A)</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 (D)</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. (C)</p> Signup and view all the answers

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

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

What is the formula for the circumference of a circle?

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

What is the formula for the area of a triangle?

<p>1/2b × h (A)</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. (C)</p> Signup and view all the answers

What is the formula for calculating the relative frequency?

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

What is the formula for the k-th percentile?

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

How is the median found using an ogive?

<p>By finding the 50th percentile (D)</p> Signup and view all the answers

What is the definition of variance?

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

What is the formula for standard deviation?

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

What is the class mark of a class interval?

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

What is the main difference between a histogram and a bar graph?

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

What is a characteristic of a symmetric distribution?

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

What is a characteristic of a right skewed distribution?

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

What is the main purpose of a frequency polygon?

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

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

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

What is a characteristic of a left skewed distribution?

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

What is the purpose of identifying outliers in a dataset?

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

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