Gr 11 Math Nov P2 (Medium)

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

y = mx + c

y - y_1 = m(x - x_1)

(y - y_1) / (x - x_1) = (y_2 - y_1) / (x_2 - x_1) (correct)

x - x_1 = (y - y_1) / (y_2 - y_1)

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

m = (x_2 - x_1) / (y_2 - y_1)

m = (y_1 + y_2) / (x_1 + x_2)

m = (y_1 - y_2) / (x_1 - x_2)

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

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

m

c (correct)

mx

x

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

Gradient-point form Signup and view all the answers

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

y - y_1 = m(x - x_1) Signup and view all the answers

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

Gradient-intercept form Signup and view all the answers

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

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

What is the definition of the gradient of a line?

The ratio of the change in y to the change in x Signup and view all the answers

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

The value of y where the line crosses the y-axis Signup and view all the answers

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

m = tan(θ) Signup and view all the answers

What is the gradient of a vertical line?

undefined Signup and view all the answers

What is the condition for two lines to be perpendicular?

Their gradients multiply to -1. Signup and view all the answers

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

y = -2x + 6 Signup and view all the answers

How do you find the equation of a line that is parallel to a given line and passes through a specific point?

Use the point-slope form Signup and view all the answers

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

obtuse Signup and view all the answers

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

180° Signup and view all the answers

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

Vertical shift upwards by q units Signup and view all the answers

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

y - y1 = m(x - x1) Signup and view all the answers

What is the value of θ for a horizontal line?

0° Signup and view all the answers

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

2 Signup and view all the answers

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

(-∞, ∞) Signup and view all the answers

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

m1 = m2 Signup and view all the answers

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

y = -3x + 11 Signup and view all the answers

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

undefined Signup and view all the answers

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

Amplitude increases if a > 1 Signup and view all the answers

What is the formula to find the inclination of a line with a negative gradient?

θ = 180° + tan^-1(m) Signup and view all the answers

What is the y-intercept of the function y = sin(θ) + 2?

(0, 2) Signup and view all the answers

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

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

What is the period of the function y = cosθ?

360° Signup and view all the answers

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

Vertical shift Signup and view all the answers

What is the range of the function y = cosθ?

(-1, 1) Signup and view all the answers

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

The period decreases Signup and view all the answers

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

(0°, 1) Signup and view all the answers

What is the period of the function y = tanθ?

180° Signup and view all the answers

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

Steeper branches Signup and view all the answers

What is the domain of the function y = tanθ?

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

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

The period decreases Signup and view all the answers

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

Horizontal shift Signup and view all the answers

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

$\pi r (r + h)$ Signup and view all the answers

What is the formula for the volume of a sphere?

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

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

It is multiplied by k Signup and view all the answers

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

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

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

$4\pi r^2$ Signup and view all the answers

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

It is multiplied by k^2 Signup and view all the answers

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

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

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

It is multiplied by k^2 and then multiplied by 2 Signup and view all the answers

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

$rac{1}{3} imes rac{1}{2} b h imes H$ Signup and view all the answers

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

$b (b + 2h_s)$ Signup and view all the answers

What is the main purpose of a scatter plot?

To show the relationships between two variables Signup and view all the answers

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

Q1 - 1.5 × IQR Signup and view all the answers

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

Bivariate data Signup and view all the answers

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

Outliers Signup and view all the answers

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

Q2 - Q1 Signup and view all the answers

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

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

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

All real numbers Signup and view all the answers

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

(0, 0) Signup and view all the answers

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

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

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

30 square units Signup and view all the answers

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

πr^2 Signup and view all the answers

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

It scales by k^3 Signup and view all the answers

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

74 square units Signup and view all the answers

What is the definition of a chord in a circle?

A straight line joining the ends of an arc Signup and view all the answers

What is the theorem that states that a tangent to a circle is perpendicular to the radius drawn to the point of contact?

Tangent Perpendicular to Radius Signup and view all the answers

What is the volume of a cylinder with a radius of 3 units and a height of 4 units?

36π cubic units Signup and view all the answers

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

Segment through center and midpoint Signup and view all the answers

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

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

What is the definition of a right pyramid?

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

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

They are equal in length Signup and view all the answers

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

Twice the size Signup and view all the answers

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

It bisects the chord Signup and view all the answers

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

Tangent-Chord Theorem Signup and view all the answers

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

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

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

Cyclic Quadrilateral Signup and view all the answers

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

To display the distribution of a continuous or discrete variable Signup and view all the answers

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

The use of points connected by straight lines to represent class intervals Signup and view all the answers

What is the formula for calculating the relative frequency of an event?

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

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

Class mark Signup and view all the answers

What is the purpose of an ogive in data analysis?

To calculate the cumulative frequency of a dataset Signup and view all the answers

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

CF_i = Sum of all previous frequencies + Frequency_i Signup and view all the answers

How do you find the median using an ogive?

Locate the 50th percentile on the cumulative frequency axis Signup and view all the answers

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

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

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

To divide the data into equal length intervals Signup and view all the answers

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

Modal class Signup and view all the answers

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

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

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

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

What is the main difference between variance and standard deviation?

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

What does a small standard deviation indicate about the data?

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

What is the characteristic of a symmetric distribution?

The mean is approximately equal to the median Signup and view all the answers

What is a right-skewed distribution characterized by?

The mean is greater than the median Signup and view all the answers

What is an outlier in a data set?

A data value that is significantly different from the other values in the dataset Signup and view all the answers

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

To measure the spread or variability of the data set Signup and view all the answers

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

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

What does a large standard deviation indicate about the data?

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

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

When two points on the line are known Signup and view all the answers

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

c Signup and view all the answers

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

Gradient-intercept form Signup and view all the answers

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

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

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

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

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

y = mx + c Signup and view all the answers

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

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

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

y - y1 = m(x - x1) Signup and view all the answers

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

m = tan(θ) Signup and view all the answers

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

m1 = m2 Signup and view all the answers

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

120° Signup and view all the answers

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

y = 2x + 1 Signup and view all the answers

What is the gradient of a horizontal line?

0 Signup and view all the answers

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

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

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

m = Δy/Δx Signup and view all the answers

What is the inclination of a vertical line?

90° Signup and view all the answers

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

y = mx + c Signup and view all the answers

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

tan(θ) = m Signup and view all the answers

What is the period of the function y = cosθ?

360° Signup and view all the answers

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

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

What is the range of the function y = cosθ?

[-1, 1] Signup and view all the answers

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

The graph is shifted vertically by q units. Signup and view all the answers

What is the period of the function y = tanθ?

180° Signup and view all the answers

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

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

What is the domain of the function y = tanθ?

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

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

The graph is stretched vertically by a factor of a. Signup and view all the answers

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

(0, 1) Signup and view all the answers

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

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

What is the purpose of a scatter plot?

To show relationships between two variables Signup and view all the answers

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

IQR = Q3 - Q1 Signup and view all the answers

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

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

What is the purpose of calculating the Five Number Summary?

To identify the boundaries for outliers Signup and view all the answers

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

Whiskers Signup and view all the answers

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

(-∞, ∞) Signup and view all the answers

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

The period is divided by k Signup and view all the answers

What is the formula for the area of a trapezium?

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

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

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

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

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

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

2πr × h Signup and view all the answers

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

(-∞, ∞) Signup and view all the answers

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

l × b × h Signup and view all the answers

What is the condition for two lines to be perpendicular?

They have gradients that multiply to -1. Signup and view all the answers

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

It increases the amplitude of the graph if a > 1. Signup and view all the answers

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

The graph is stretched horizontally by k Signup and view all the answers

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

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

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

360°/|k| Signup and view all the answers

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

y = -0.5x + 5 Signup and view all the answers

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

It shifts the graph horizontally by p units. Signup and view all the answers

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

y = 2x + 5 Signup and view all the answers

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

{θ: θ ∈ ℝ} Signup and view all the answers

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

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

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

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

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

y = -1/mx + y1 Signup and view all the answers

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

πr(r + h) Signup and view all the answers

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

It increases by a factor of k Signup and view all the answers

What is the formula for the volume of a sphere?

4/3 πr^3 Signup and view all the answers

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

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

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

It increases by a factor of k^2 Signup and view all the answers

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

b(b + 2h_s) Signup and view all the answers

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

It increases by a factor of k^2 Signup and view all the answers

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

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

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

4πr^2 Signup and view all the answers

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

1/3 × (1/2 bh) × H Signup and view all the answers

What is the purpose of a histogram?

To display the frequency distribution of a set of data Signup and view all the answers

What is the key characteristic of a frequency polygon?

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

What is the formula for calculating the relative frequency?

Frequency / Total number of observations Signup and view all the answers

What is the modal class?

The class interval with the highest frequency Signup and view all the answers

What is the purpose of an ogive?

To find the median and quartiles of a dataset Signup and view all the answers

What is the formula for calculating the cumulative frequency?

Sum of all previous frequencies + Current frequency Signup and view all the answers

How do you find the median using an ogive?

Locate the 50th percentile on the cumulative frequency axis Signup and view all the answers

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

25th percentile Signup and view all the answers

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

To divide the data into equal length intervals Signup and view all the answers

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

The midpoint of a class interval Signup and view all the answers

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

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

What is the definition of a chord in a circle?

A straight line joining the ends of an arc Signup and view all the answers

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

Twice the angle at the circumference subtended by the same arc Signup and view all the answers

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

It passes through the center of the circle Signup and view all the answers

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

They are equal Signup and view all the answers

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

It is perpendicular to the chord Signup and view all the answers

What is the definition of a tangent to a circle?

A line that touches the circle at only one point Signup and view all the answers

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

They are equal in length Signup and view all the answers

What is the definition of a segment in a circle?

A part of the circle cut off by a chord Signup and view all the answers

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

It bisects the chord Signup and view all the answers

What is the formula for the k-th percentile?

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

What is the main purpose of calculating the standard deviation?

To measure the spread of data around the mean Signup and view all the answers

What is the characteristic of a right-skewed distribution?

The right tail is longer than the left tail Signup and view all the answers

What is the definition of an outlier?

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

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

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

What is the characteristic of a symmetric distribution?

The mean is equal to the median Signup and view all the answers

What is the property of the standard deviation?

It has the same units as the original data Signup and view all the answers

What is the interpretation of a small standard deviation?

The data values are close to the mean Signup and view all the answers

What is the interpretation of a large standard deviation?

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

What is the characteristic of a left-skewed distribution?

The mean is less than the median Signup and view all the answers

Which form of the straight line equation is used when the gradient and one point on the line are known?

Gradient-Point Form Signup and view all the answers

What is the value of y when x = 0 in the equation y = mx + c?

c Signup and view all the answers

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

The y-intercept of the line Signup and view all the answers

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

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

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

c is the y-intercept when m = 0 Signup and view all the answers

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

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

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

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

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

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

What is the condition for two lines to be perpendicular?

Their gradients multiply to -1 Signup and view all the answers

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

Amplitude change Signup and view all the answers

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

360°/k Signup and view all the answers

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

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

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

Vertical shift Signup and view all the answers

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

y = 2x + 6 Signup and view all the answers

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

[-1, 1] Signup and view all the answers

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

Decreases the period Signup and view all the answers

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

y = -1/3x + 7 Signup and view all the answers

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

{θ: θ ∈ ℝ} Signup and view all the answers

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

m = tan(θ) Signup and view all the answers

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

135° Signup and view all the answers

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

y = 2x + 2 Signup and view all the answers

What is the condition for two lines to be parallel?

m1 = m2 Signup and view all the answers

What is the gradient of a horizontal line?

0 Signup and view all the answers

What is the formula to find the inclination of a line with a negative gradient?

θ = 180° + tan^(-1)(m) Signup and view all the answers

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

tan(θ) = m Signup and view all the answers

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

y - y1 = m(x - x1) Signup and view all the answers

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

45° Signup and view all the answers

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

-1/m Signup and view all the answers

What is the period of the function y = cosθ?

360° Signup and view all the answers

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

Vertical shift by q units Signup and view all the answers

What is the range of the function y = cosθ?

(-1, 1) Signup and view all the answers

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

The period decreases Signup and view all the answers

What is the period of the function y = tanθ?

180° Signup and view all the answers

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

The branches of the graph are steeper Signup and view all the answers

What is the domain of the function y = tanθ?

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

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

The period decreases Signup and view all the answers

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

(0, 1) Signup and view all the answers

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

Horizontal shift by p units Signup and view all the answers

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

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

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

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

What is the formula for the area of a trapezium?

½(a + b)h Signup and view all the answers

What is the surface area of a right prism?

The sum of the areas of the lateral faces and the base Signup and view all the answers

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

½bhH Signup and view all the answers

What is the formula for the volume of a cylinder?

πr²h Signup and view all the answers

What is the surface area of a right pyramid?

The sum of the areas of the lateral faces and the base Signup and view all the answers

What is the formula for the volume of a sphere?

πr³ Signup and view all the answers

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

The period decreases by a factor of k Signup and view all the answers

What is the formula for the circumference of a circle?

2πr Signup and view all the answers

What is the purpose of a scatter plot?

To show the relationships between two variables Signup and view all the answers

What is the formula for calculating the IQR?

IQR = Q3 - Q1 Signup and view all the answers

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

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

What is the purpose of calculating the five number summary?

To describe the distribution of a dataset Signup and view all the answers

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

To identify outliers in a dataset Signup and view all the answers

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

πr(r+h) Signup and view all the answers

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

It is multiplied by k. Signup and view all the answers

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

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

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

It is multiplied by k^2. Signup and view all the answers

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

b(b+2h_s) Signup and view all the answers

What is the formula for the volume of a sphere?

4/3πr^3 Signup and view all the answers

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

It is multiplied by k^2. Signup and view all the answers

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

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

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

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

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

It is multiplied by k^2. Signup and view all the answers

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

It increases by a factor of 2 Signup and view all the answers

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

80 degrees Signup and view all the answers

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

They are equal Signup and view all the answers

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

Radius Signup and view all the answers

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

They are supplementary Signup and view all the answers

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

It is bisected 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?

Tangent-Chord Theorem Signup and view all the answers

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

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

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

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

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

Chord Signup and view all the answers

What is the formula for calculating the relative frequency?

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

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

90 degrees Signup and view all the answers

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

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

What is the cumulative frequency?

The sum of all previous frequencies plus the current frequency Signup and view all the answers

What is the purpose of an ogive plot?

To visualize the cumulative frequency distribution of a data set Signup and view all the answers

How do you find the median from an ogive plot?

Locate the 50th percentile on the cumulative frequency axis Signup and view all the answers

What is the class mark of a class interval?

The midpoint of the class interval Signup and view all the answers

What is the modal class of a data set?

The class interval with the highest frequency Signup and view all the answers

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

To visualize the frequency distribution of the data Signup and view all the answers

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

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

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

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

What is the definition of variance?

The average of the squared differences from the mean. Signup and view all the answers

What is the formula for calculating the standard deviation?

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

What is the characteristic of a symmetric distribution?

The mean is approximately equal to the median. Signup and view all the answers

What is the characteristic of a right-skewed distribution?

The mean is greater than the median. Signup and view all the answers

What is the purpose of calculating the standard deviation?

To measure the variability of the data. Signup and view all the answers

What is an outlier in a dataset?

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

What is the formula for calculating the variance?

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

What is the characteristic of a left-skewed distribution?

The mean is less than the median. Signup and view all the answers

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

To locate the 75th percentile. Signup and view all the answers

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

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

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

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

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

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

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

To define the y-intercept of the line Signup and view all the answers

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

It is easy to graph and find the y-intercept Signup and view all the answers

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

y = mx - mx_1 + y_1 Signup and view all the answers

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

The coordinates of the point are used to derive the gradient-point form. Signup and view all the answers

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

To find the equation of a line when two points are known. Signup and view all the answers

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

The gradient is equal to the tangent of the inclination. Signup and view all the answers

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

0° Signup and view all the answers

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

They are equal. Signup and view all the answers

How do you find the equation of a line that is parallel to a given line and passes through a specific point?

Use the point-slope form of a line with the given gradient and point. Signup and view all the answers

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

Undefined Signup and view all the answers

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

m = tan(θ) Signup and view all the answers

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

The inclination is equal to the arctangent of the gradient. Signup and view all the answers

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

Obtuse angle Signup and view all the answers

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

θ = 180° + tan^(-1)(m) Signup and view all the answers

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

They are equal. Signup and view all the answers

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

It increases by a factor of k^3 Signup and view all the answers

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

The angle subtended by the chord in the alternate segment Signup and view all the answers

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

The chord is bisected into two equal parts Signup and view all the answers

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

πr(r + h) Signup and view all the answers

What is the relationship between the angles subtended by the same arc in a circle?

They are equal Signup and view all the answers

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

The angle between the tangent and the chord is equal to the angle subtended by the chord in the alternate segment 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?

The volume is multiplied by k Signup and view all the answers

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

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

What is the characteristic of a cyclic quadrilateral?

The opposite angles are supplementary Signup and view all the answers

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

4πr^2 Signup and view all the answers

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

The tangents are equal in length Signup and view all the answers

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

Twice the angle subtended by the arc at the circumference Signup and view all the answers

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

The surface area is multiplied by k^2 Signup and view all the answers

What is the formula for the volume of a sphere?

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

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

The chord is bisected into two equal parts Signup and view all the answers

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

The diameter is twice the radius Signup and view all the answers

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

b(b + 2h) Signup and view all the answers

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

The volume is multiplied by k^2 Signup and view all the answers

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

1/2 × b(h + 3h_s) Signup and view all the answers

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

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

What is the condition for two lines to be parallel?

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

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

m1 = -1/m2 Signup and view all the answers

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

360°/|k| Signup and view all the answers

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

The amplitude increases if a > 1, and decreases if 0 < a < 1. Signup and view all the answers

What is the main characteristic of a histogram?

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

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

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

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

To plot the points at the height corresponding to the frequency Signup and view all the answers

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

y = -1/2x + 3 Signup and view all the answers

What is the formula for calculating the relative frequency of an event?

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

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

2 Signup and view all the answers

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

To calculate the cumulative frequency up to each interval Signup and view all the answers

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

All real numbers Signup and view all the answers

What is the method to find the median using an ogive?

Locate the 50th percentile on the cumulative frequency axis Signup and view all the answers

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

Locate the 25th percentile on the cumulative frequency axis Signup and view all the answers

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

[-1, 1] Signup and view all the answers

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

y = 2x + 4 Signup and view all the answers

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

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

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

Class interval Signup and view all the answers

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

Class mark Signup and view all the answers

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

Modal class Signup and view all the answers

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

To calculate the boundaries for outliers Signup and view all the answers

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

Q3 + 1.5 × IQR Signup and view all the answers

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

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

What type of data is represented in a scatter plot?

Bivariate data Signup and view all the answers

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

(−∞, ∞) Signup and view all the answers

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

90° 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?

Outliers Signup and view all the answers

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

The amplitude increases for a > 1 and decreases for 0 < a < 1. Signup and view all the answers

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

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

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

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

What is the formula for the area of a trapezium?

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

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

To identify extreme values in the data Signup and view all the answers

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

The graph is shifted to the left by p units. Signup and view all the answers

What is the formula for the volume of a cylinder?

V = πr² × h Signup and view all the answers

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

SA = lw + 2lh + 2wh Signup and view all the answers

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

(-∞, ∞) Signup and view all the answers

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

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

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

The period decreases for k > 1. Signup and view all the answers

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

The period is decreased by a factor of k Signup and view all the answers

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

2 Signup and view all the answers

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

SA = 2πr(h + r) Signup and view all the answers

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

(0°, 1) Signup and view all the answers

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

The branches of the graph are steeper for a > 1. Signup and view all the answers

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

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

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

720° Signup and view all the answers

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

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

What is the definition of variance?

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

What is the main property of a standard deviation?

It has the same units as the original data. Signup and view all the answers

What is the interpretation of a small standard deviation?

Data values are close to the mean. Signup and view all the answers

What is the characteristic of a symmetric distribution?

The mean is approximately equal to the median. Signup and view all the answers

What is the definition of an outlier?

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

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

To measure the spread of data around the mean. Signup and view all the answers

What is the formula for calculating the standard deviation?

σ = √(Σ(xi - x̄)² / n) Signup and view all the answers

What is the characteristic of a right-skewed distribution?

The mean is greater than the median. Signup and view all the answers

What is the purpose of identifying outliers in a dataset?

To understand the variability of the data. Signup and view all the answers

Gr 11 Math Nov P2 (Medium)

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Questions and Answers

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

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

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

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

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

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

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

What is the definition of the gradient of a line?

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

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

What is the gradient of a vertical line?

What is the condition for two lines to be perpendicular?

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

How do you find the equation of a line that is parallel to a given line and passes through a specific point?

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

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

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

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

What is the value of θ for a horizontal line?

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

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

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

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

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

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

What is the formula to find the inclination of a line with a negative gradient?

What is the y-intercept of the function y = sin(θ) + 2?

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

What is the period of the function y = cosθ?

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

What is the range of the function y = cosθ?

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

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

What is the period of the function y = tanθ?

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

What is the domain of the function y = tanθ?

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

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

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

What is the formula for the volume of a sphere?

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

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

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

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

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

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

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

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

What is the main purpose of a scatter plot?

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

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

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

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

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

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

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

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

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

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

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

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

What is the definition of a chord in a circle?

What is the theorem that states that a tangent to a circle is perpendicular to the radius drawn to the point of contact?

What is the volume of a cylinder with a radius of 3 units and a height of 4 units?

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

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

What is the definition of a right pyramid?

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

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

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

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

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

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

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

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

What is the formula for calculating the relative frequency of an event?