Gr 11 Math Nov P2 (Mix)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<p>A vertical shift</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<p>The angle between a tangent to a circle and a chord drawn from the point of contact is equal to the angle which the chord subtends in the alternate segment</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<p>2/3</p> Signup and view all the answers

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

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

<p>2/3</p> Signup and view all the answers

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

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

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

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

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

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

<p>y - y1 = -1/m(x - x1)</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<p>The perpendicular bisector of a chord passes through the center of the circle.</p> Signup and view all the answers

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

<p>To find the angle between a tangent and a chord.</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<p>The mean is approximately equal to the median, and the left and right tails are balanced.</p> Signup and view all the answers

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

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

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

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

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

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

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

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