Gr 11 Math Nov P2 (Hard)

Play an AI-generated podcast conversation about this lesson

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

To determine the midpoint of a line when two points are known.

To determine the y-intercept of a line when two points are known.

To determine the gradient of a line when two points are known.

To find the equation of a line when two points are known. (correct)

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

y = y_1 + mx_1

y = mx + c

y = mx_1 - m

y - y_1 = m(x - x_1) (correct)

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

mx_1 - y_1

y_1 - mx_1 (correct)

y_1 + mx_1

mx_1 + y_1

What is the significance of the y-intercept c in the gradient–intercept form?

It is the point where the line intersects the y-axis. Signup and view all the answers

What is the condition for the two-point form to be used?

Two points on the line are known. Signup and view all the answers

What is the condition for the gradient–point form to be used?

The gradient of the line is known and one point on the line is known. Signup and view all the answers

What is the condition for the gradient–intercept form to be used?

The gradient of the line is known and the y-intercept is known. Signup and view all the answers

What is the relationship between the gradient–point form and the gradient–intercept form?

They are equivalent forms of the equation of a line. Signup and view all the answers

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

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

What is the value of the gradient of a vertical line?

undefined Signup and view all the answers

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

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

What is the inclination of a line with a gradient of -3?

180° + tan^-1(-3) 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 value of the gradient of a horizontal line?

0 Signup and view all the answers

What is the relationship between the tangent function and the angle of inclination?

tan(θ) = m for 0° ≤ θ < 180° Signup and view all the answers

What is the point-slope form of the equation of a line?

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

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

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

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

tan^-1(2) 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 amplitude of the function y = sin(θ) for 0° ≤ θ ≤ 360°?

1 Signup and view all the answers

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

q causes a vertical shift of the graph. 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)?

a changes the amplitude of the function. 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 x-intercept of the function y = sin(θ)?

(180°, 0) Signup and view all the answers

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

p causes a horizontal shift of the graph. Signup and view all the answers

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

[-1, 1] 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 effect of q on the graph of y = a cos θ + q?

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

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

360° / k Signup and view all the answers

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

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

What is the range of the function y = cos θ?

[-1, 1] 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 domain of the function y = cos θ?

All real numbers 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 p on the graph of y = cos(θ + p)?

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

What is the amplitude of the function y = a cos θ?

|a| Signup and view all the answers

What is the period of the function y = tan θ?

180° Signup and view all the answers

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

θ ∈ ℝ, -90°/k < θ < 90°/k Signup and view all the answers

What is the effect of p on the graph of y = tan(θ + p) when p > 0?

The graph shifts to the left by p 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 formula for the volume of a cylinder?

V = πr² × h Signup and view all the answers

What is the surface area of a rectangular prism?

SA = 2(lb + bh + lh) Signup and view all the answers

What is the volume of a triangular prism?

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

What is the circumference of a circle with radius r?

C = 2πr Signup and view all the answers

What is the characteristic of a right pyramid?

The line from the apex to the center of the base is perpendicular to the base Signup and view all the answers

What is the formula for the area of a circle?

A = πr² Signup and view all the answers

What is the shape of the net of a cylinder?

Two identical circles and a rectangle Signup and view all the answers

What is the primary purpose of calculating the interquartile range (IQR) in identifying outliers?

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

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

Q1 - 1.5*IQR Signup and view all the answers

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

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

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

Five number summary Signup and view all the answers

If a circle is scaled by a factor of 2, what will be the ratio of the new surface area to the original surface area?

4:1 Signup and view all the answers

What is the name of the theorem that states that the angle at the center of a circle is twice the angle at the circumference?

Angle at the Center 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 volume of a right cone?

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

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

Tangent 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 in length 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

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

Segment Signup and view all the answers

If a rectangular prism has dimensions $l, b, h$ and one dimension is multiplied by a constant factor $k$, what is the new volume?

$k(lbh)$ Signup and view all the answers

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

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

If a line segment from the center of a circle is perpendicular to a chord, what can be said about the line segment?

It bisects the chord Signup and view all the answers

If a rectangular prism has dimensions $l, b, h$ and all three dimensions are multiplied by a constant factor $k$, what is the new volume?

$k^3(lbh)$ 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 formula for the volume of a triangular prism?

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

If the opposite angles of a cyclic quadrilateral are supplementary, what can be said about the quadrilateral?

It is a cyclic quadrilateral Signup and view all the answers

What is the name of the part of the circle that is a straight line joining the ends of an arc?

Chord 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?

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

If an angle at the center of a circle is twice the angle at the circumference, what can be said about the angles?

The angle at the center is twice the angle at the circumference Signup and view all the answers

If a rectangular prism has dimensions $l, b, h$ and two dimensions are multiplied by a constant factor $k$, what is the new surface area?

$2k [klh + lb + kbh]$ 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 connected by lines. 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 purpose of finding the midpoint of a class interval in a histogram?

To determine the class mark. Signup and view all the answers

What is the formula for calculating the cumulative frequency of a class interval?

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

What is the purpose of plotting points on an ogive?

To determine the median and quartiles of a set of data. Signup and view all the answers

What is the significance of the 50th percentile on an ogive?

It represents the median. Signup and view all the answers

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

A class interval is a range of values, while a class mark is the midpoint of the interval. Signup and view all the answers

What is the formula for the k-th percentile?

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

What is the definition of variance in a dataset?

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

What is the purpose of drawing a histogram?

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

What is the significance of the modal class in a histogram?

It represents the class interval with the highest frequency. Signup and view all the answers

What is the relationship between the mean and median in a right-skewed distribution?

Mean is greater than the median Signup and view all the answers

What is the definition of an outlier in a dataset?

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

What is the purpose of drawing a frequency polygon?

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

What is the purpose of calculating the standard deviation of a dataset?

To measure the spread of the dataset Signup and view all the answers

What is the formula for the standard deviation of a dataset?

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

What is the characteristic of a dataset with a small standard deviation?

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

What is the purpose of calculating the variance of a dataset?

To measure the spread of the dataset 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 determine if the data values are significantly different from the rest of the dataset Signup and view all the answers

What is the primary equation used to derive the gradient–point form of the straight line equation?

frac{y - y_1}{x - x_1} = frac{y_2 - y_1}{x_2 - x_1} Signup and view all the answers

Given the gradient–intercept form of the straight line equation y = mx + c, what is the value of y when x = 1 and m = 2 and c = 3?

7 Signup and view all the answers

Which of the following forms of the straight line equation can be used to find the equation of a line that passes through two points?

Two-point form Signup and view all the answers

What is the value of the gradient of a line that passes through the points (2, 3) and (4, 5)?

1 Signup and view all the answers

If a line has a gradient of -3 and passes through the point (1, 2), what is the equation of the line in gradient–point form?

y - 2 = -3(x - 1) Signup and view all the answers

What is the value of c in the gradient–intercept form of the straight line equation y = mx + c when the line passes through the point (2, 5) and has a gradient of 2?

3 Signup and view all the answers

Which of the following forms of the straight line equation can be used to find the equation of a line that has a gradient of 3 and passes through the point (1, 2)?

Both A and B Signup and view all the answers

What is the value of y when x = 0 in the equation y = mx + c, given that the line passes through the point (2, 3) and has a gradient of 1?

3 Signup and view all the answers

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

Their product is -1 Signup and view all the answers

If a line has a gradient of 3, what is the gradient of a line that is perpendicular to it?

-1/3 Signup and view all the answers

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

The period decreases as k increases Signup and view all the answers

What is the effect of the value of a on the shape of the function y = a sin(θ)?

The amplitude increases as a increases Signup and view all the answers

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

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

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

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

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

θ ∈ ℝ Signup and view all the answers

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

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

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

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

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

180° 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 equal to the tangent of its inclination. Signup and view all the answers

What is the inclination of a line with a gradient of 1/2?

tan^(-1)(1/2) Signup and view all the answers

What is the equation of a line that is parallel to the line y = 2x + 3 and passes through the point (4, 5)?

y = 2x + 7 Signup and view all the answers

What is the domain of the function y = tan kθ in degrees?

The domain of the function is {θ: -90°/k < θ < 90°/k, θ ∈ ℝ} 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 range of the function y = tan kθ?

The range of the function is (-∞, ∞) Signup and view all the answers

What is the gradient of a line that is perpendicular to the line y = 3x - 2?

-1/3 Signup and view all the answers

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

The inclination is obtuse. Signup and view all the answers

What is the effect of p on the graph of y = tan(θ + p) when p > 0?

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

What is the formula for the area of a triangle?

Area = 1/2 bh Signup and view all the answers

What is the point-slope form of the equation of a line?

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

What is the surface area of a rectangular prism?

2(lw + lh + wh) Signup and view all the answers

What is the gradient of a horizontal line?

0 Signup and view all the answers

What is the relationship between the tangent function and the angle of inclination?

The tangent function is equal to the ratio of the sine to the cosine of the angle of inclination. Signup and view all the answers

What is the volume of a triangular prism?

1/2 bhH Signup and view all the answers

What is the circumference of a circle with radius r?

2πr Signup and view all the answers

What is the inclination of a vertical line?

90° Signup and view all the answers

What is the shape of the net of a cylinder?

A rectangle with two identical circles Signup and view all the answers

What is the characteristic of a right pyramid?

The line from the apex to the center of the base is perpendicular to the base Signup and view all the answers

What is the formula for the area of a circle?

πr^2 Signup and view all the answers

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

The graph shifts vertically upwards by q units. Signup and view all the answers

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

180°/|k| Signup and view all the answers

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

The amplitude of the graph increases. Signup and view all the answers

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

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

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

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

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

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

What is the period of the function y = cos θ?

360° 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 x-intercept of the function y = cos θ?

(90, 0) Signup and view all the answers

What is the amplitude of the function y = a cos θ?

a Signup and view all the answers

What is the scale factor of the surface area when the dimensions of an object are multiplied by a factor of k?

$k^2$ Signup and view all the answers

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

The radius is half the length of the diameter. 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 30 degrees?

60 degrees Signup and view all the answers

What is the property of a tangent to a circle?

It is perpendicular to the radius drawn to the point of contact. Signup and view all the answers

What is the consequence of the perpendicular bisector of a chord passing through the center of a circle?

The chord is bisected. 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 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 property of a cyclic quadrilateral?

The opposite angles are supplementary. Signup and view all the answers

What is the relationship between the segment and the chord of a circle?

The segment is a part of the chord. Signup and view all the answers

What is the consequence of the angle at the center of a circle being 60 degrees?

The angle at the circumference is 30 degrees. 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 primary purpose of calculating the Five Number Summary in identifying outliers?

To calculate the IQR and determine the boundaries for outliers 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

What happens to the surface area and volume of a rectangular prism when one dimension is multiplied by a constant factor k?

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

What is the formula for the Upper Boundary of outliers in a box-and-whisker diagram?

Q3 + 1.5 × IQR 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 is the term for the data points that are outside the boundaries of Q1 - 1.5 × IQR and Q3 + 1.5 × IQR in a box-and-whisker diagram?

Outliers 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 type of plot is used to show the relationship between two variables?

Scatter plot Signup and view all the answers

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

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

What is the formula for the Interquartile Range (IQR) in a box-and-whisker diagram?

Q3 - Q1 Signup and view all the answers

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

1/2bhH 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 right cylinder?

πr^2h Signup and view all the answers

What happens to the surface area and volume of a rectangular prism when two dimensions are multiplied by a constant factor k?

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

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

There are gaps between the bars. 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?

Class mark Signup and view all the answers

What is the purpose of a frequency polygon?

To display the frequencies of different class intervals Signup and view all the answers

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

CFi = ∑j=1i fj Signup and view all the answers

What is the purpose of an ogive?

To display the cumulative frequencies of a dataset 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) of a dataset?

The 25th percentile Signup and view all the answers

What is the purpose of dividing a dataset into equal-length intervals in a histogram?

To facilitate the counting of frequencies in each interval Signup and view all the answers

What is the relationship between the points on a frequency polygon and the class intervals?

Each point represents the midpoint of a class interval Signup and view all the answers

What is the purpose of calculating the k-th percentile in a dataset?

To locate the value that k percent of the data points are below Signup and view all the answers

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

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

What is the property of a small standard deviation in a dataset?

The data values are close to the mean 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 identify data points that significantly deviate from the rest of the data Signup and view all the answers

What is the formula for calculating the standard deviation of a dataset?

σ = √(Σ(x - 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 purpose of calculating the variance and standard deviation in a dataset?

To determine the spread of the data Signup and view all the answers

What is the property of a large standard deviation in a dataset?

The data values are spread out over a large 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

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

It requires only two points on the line. Signup and view all the answers

If a line has a gradient of 2 and passes through the point (3, 4), what is the equation of the line in gradient-intercept form?

y = 2x + 10 Signup and view all the answers

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

The inclination is the tangent of the angle between the line and the x-axis. 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 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 significance of the y-intercept in the gradient-intercept form of the straight line equation?

It is the point where the line crosses the y-axis. Signup and view all the answers

What is the value of tanθ when θ is 60°?

√3 Signup and view all the answers

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

They are equivalent forms. 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 requires two points, while the gradient-point form requires the gradient and one point. Signup and view all the answers

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

The product of their gradients is -1 Signup and view all the answers

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

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

What is the angle of inclination of a line with a gradient of -1/2?

135° Signup and view all the answers

What is the gradient of a line that passes through the points (2, 3) and (4, 5)?

1 Signup and view all the answers

What is the inclination of a horizontal line?

0° Signup and view all the answers

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

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

What is the value of tanθ when θ is 135°?

-1 Signup and view all the answers

What is the gradient of a line that passes through the points (1, 2) and (3, 4)?

1 Signup and view all the answers

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

y = -1/2x + 4 Signup and view all the answers

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

-1/3 Signup and view all the answers

What is the amplitude of the function y = 2sin(θ) for 0° ≤ θ ≤ 360°?

2 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 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 horizontal shift of the graph of y = sin(θ + 30°)?

30° to the left Signup and view all the answers

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

[-2, 2] Signup and view all the answers

What is the effect of q on the graph of y = sin(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 y = 3x - 2 and passes through the point (2, 5)?

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

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

(180°, 0) Signup and view all the answers

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

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

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

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

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

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

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

The amplitude of the graph increases if a > 1. 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 graph of y = tan(kθ)?

The graph is stretched horizontally by a factor of 1/k. 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 to the right by p units. Signup and view all the answers

What is the formula for the area of a rectangle?

A = bh 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 domain of the function y = tan(kθ)?

(-∞, ∞) except θ = 90° + 180°n, n ∈ ℤ 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 shape of the net of a cylinder?

A rectangle with two identical circles Signup and view all the answers

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

180°/|k| Signup and view all the answers

What is the effect of p on the graph of y = tan(θ + p) when p > 0?

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

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

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

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

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

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

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

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

|a| Signup and view all the answers

What is the formula for the area of a circle?

A = πr^2 Signup and view all the answers

What is the characteristic of a right pyramid?

The line from the apex to the center of the base is perpendicular to the base. Signup and view all the answers

What does the interquartile range (IQR) represent in a box-and-whisker diagram?

The range of the middle 50% of the data Signup and view all the answers

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

Q3 + 1.5 × IQR Signup and view all the answers

What is the purpose of a scatter plot in relation to outliers?

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

What is the term for data points that are outside the boundaries of Q1 - 1.5 × IQR and Q3 + 1.5 × IQR in a box-and-whisker diagram?

Outliers Signup and view all the answers

What is the first step in identifying outliers in a box-and-whisker diagram?

Determine the five-number summary Signup and view all the answers

If a circle is scaled up by a factor of 2, what will be the ratio of the new surface area to the original surface area?

4:1 Signup and view all the answers

What is the angle at the center of a circle subtended by an arc of length 60°?

90° Signup and view all the answers

If two chords of a circle are equal, what can be said about the angles subtended by these chords at the center of the circle?

They are equal Signup and view all the answers

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

The chord is divided into two equal segments 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

If two tangents are drawn from an external point to a circle, what can be said about the lengths of these tangents?

They are equal Signup and view all the answers

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

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

What is the angle between a tangent 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

If an angle at the center of a circle is 60°, what is the corresponding angle at the circumference?

30° Signup and view all the answers

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

The bisector passes through the center of the circle Signup and view all the answers

What is the surface area of a right cone with a radius of 4 cm and a height of 6 cm?

48π cm^2 Signup and view all the answers

If a rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 4 cm, what is the volume of the prism?

40 cm^3 Signup and view all the answers

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

The height of each bar corresponds to the frequency of data in that class interval. 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 volume of a sphere with a radius of 3 cm?

36π cm^3 Signup and view all the answers

What is the formula to calculate the k-th percentile?

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

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

To plot the point at the midpoint of the class interval Signup and view all the answers

What is the purpose of calculating the variance?

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

If a square pyramid has a base length of 4 cm and a height of 6 cm, what is the surface area of the pyramid?

48 cm^2 Signup and view all the answers

What is the effect on the surface area and volume of a rectangular prism if the length, width, and height are each multiplied by a factor of 2?

The surface area is multiplied by 4, and the volume is multiplied by 8. Signup and view all the answers

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

It indicates that the data points are spread out over a wide range of values Signup and view all the answers

What is the formula for calculating the cumulative frequency up to the ith interval?

CF_i = ∑(j=1 to i) f_j 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 drawing an ogive?

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

What is the formula for the surface area of a triangular pyramid with a base length of b and a slant height of hs?

b(hb + 3hs) Signup and view all the answers

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

To show the distribution of the data Signup and view all the answers

What is the volume of a right cone with a radius of 3 cm and a height of 5 cm?

20π cm^3 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 purpose of finding the median class?

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

What is the definition of an outlier?

A data point that is far away from the central cluster of data points Signup and view all the answers

What is the effect on the surface area and volume of a sphere if the radius is multiplied by a factor of 3?

The surface area is multiplied by 9, and the volume is multiplied by 27. 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 standard deviation?

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

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

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

What is the purpose of drawing a frequency polygon?

To display the distribution of continuous data 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 surface area of a rectangular prism with a length of 6 cm, a width of 4 cm, and a height of 3 cm?

52 cm^2 Signup and view all the answers

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

It indicates that the data points are close to the mean Signup and view all the answers

What is the formula for calculating the cumulative frequency up to the ith interval?

CF_i = ∑(j=1 to i) f_j Signup and view all the answers

What is the purpose of identifying outliers in a dataset?

To understand the distribution of the data and identify unusual patterns Signup and view all the answers

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

Gradient–intercept form Signup and view all the answers

A line passes through the points (2, 3) and (4, 5). Which of the following forms can be used to find the equation of the line?

Two-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

A line has a gradient of 2 and passes through the point (3, 4). Which of the following forms can be used to find the equation of the line?

Gradient–point form Signup and view all the answers

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

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

A line has a y-intercept of 3 and a gradient of 1. What is the equation of the line?

y = x + 3 Signup and view all the answers

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

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

What is the difference between the gradient–intercept form and the slope–intercept form of the straight line equation?

There is no difference between the two forms Signup and view all the answers

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

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

What is the angle of inclination of a line with a gradient of 1/2?

26.6° Signup and view all the answers

What is the equation of a line that is parallel to the line y = 2x + 3 and passes through the point (4, 5)?

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

What is the inclination of a vertical line?

90° Signup and view all the answers

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

m1 = m2 Signup and view all the answers

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

y = x + 1 Signup and view all the answers

What is the inclination of a line with a gradient of -1/3?

161.6° Signup and view all the answers

What is the gradient of a line that is perpendicular to the line y = 2x + 3?

-1/2 Signup and view all the answers

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

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

What is the inclination of a line with a gradient of 3/4?

53.1° Signup and view all the answers

What is the condition for two lines to be perpendicular?

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

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

The period is calculated as 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 + 4.5 Signup and view all the answers

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

The amplitude increases by a factor of a Signup and view all the answers

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

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

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

The graph shifts vertically by q units 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 effect of p on the graph of y = sin(θ + p)?

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

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

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

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

360°/k Signup and view all the answers

What is the formula for the area of a triangle?

1/2 × base × height Signup and view all the answers

What is the shape of the net of a triangular prism?

Two triangles and three rectangles Signup and view all the answers

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

area of base × height Signup and view all the answers

What is the formula for the circumference of a circle?

2 × π × radius Signup and view all the answers

What is the effect of a on the amplitude of the function y = a cos θ?

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

What is the characteristic of a right pyramid?

The line from the apex to the center of the base is perpendicular to the base Signup and view all the answers

What is the surface area of a square pyramid with a base of side length b and slant height hs?

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

What is the formula for the area of a parallelogram?

base × height Signup and view all the answers

What is the period of the function y = cos(kθ) when k = 2?

90° Signup and view all the answers

What is the effect of p on the graph of y = cos(θ + p) when p > 0?

The graph shifts to the left by p units. 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 the volume?

The volume is multiplied by k^3 Signup and view all the answers

What is the shape of the net of a cylinder?

Two identical circles and a rectangle Signup and view all the answers

What is the formula for the volume of a right cone with a base radius r and height H?

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

What is the domain of the function y = tan(kθ) when k = 2?

{θ: 0° ≤ θ ≤ 360°, θ ≠ 45°, 135°, 225°, 315°} Signup and view all the answers

What is the formula for the volume of a cylinder?

π × radius^2 × height Signup and view all the answers

What is the range of the function y = tan(kθ) when k = 2?

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

What is the formula for the area of a square?

side^2 Signup and view all the answers

If the dimensions of a sphere are multiplied by a constant factor k, what is the effect on the surface area?

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

What is the formula for the surface area of a triangular pyramid with a base of side length b and height hb?

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

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

The period decreases. Signup and view all the answers

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

2 × (length × width + width × height + length × height) Signup and view all the answers

If the dimensions of a cylinder are multiplied by a constant factor k, what is the effect on the volume?

The volume is multiplied by k^3 Signup and view all the answers

What is the effect of a on the shape of the graph of y = a tan(θ) when a > 1?

The branches of the graph become steeper. Signup and view all the answers

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

1/2 bhH Signup and view all the answers

What is the y-intercept of the function y = tan(θ) when θ = 0°?

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

What is the effect of p on the graph of y = tan(θ + p) when p > 0?

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

What is the effect on the surface area of a rectangular prism if one of its dimensions is multiplied by a constant factor k?

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

What is the asymptote of the function y = tan(kθ) when k = 2?

θ = 45°, 135°, 225°, 315° Signup and view all the answers

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

4πr^2 Signup and view all the answers

What is the effect on the volume of a pyramid if its dimensions are multiplied by a constant factor k?

The volume is multiplied by k^3 Signup and view all the answers

What is the characteristic of a tangent to a circle?

It is a straight line that touches the circle at only one point on the circumference. 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?

The angle at the center is twice the angle at the circumference. Signup and view all the answers

What is the characteristic of a cyclic quadrilateral?

All vertices lie on the circumference of a circle. Signup and view all the answers

What is 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 characteristic of a histogram?

It is a graphical representation of the frequency distribution of a set of continuous data. Signup and view all the answers

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

The lengths are equal. Signup and view all the answers

What is the characteristic of a segment of a circle?

It is a part of the circle cut off by a chord. Signup and view all the answers

What is the corollary that states that equal chords subtend equal angles at the center of the circle?

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

What is the theorem that states that a line segment from the center of a circle perpendicular to a chord will bisect the chord?

Perpendicular Line from Circle Center Bisects Chord Signup and view all the answers

What is the characteristic of the angle subtended by a chord at the center of a circle?

It is twice the angle subtended by the chord on the circumference. Signup and view all the answers

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

The use of lines to connect the points Signup and view all the answers

What is the formula for calculating the cumulative frequency of a class interval?

CF_i = ∑(f_j) + f_i Signup and view all the answers

What is the purpose of finding the median class in a dataset?

To find the median of the data Signup and view all the answers

What is the characteristic of the modal class in a dataset?

It has the highest frequency Signup and view all the answers

What is the use of the relative frequency in a dataset?

To compare the frequencies of different class intervals Signup and view all the answers

What is the difference between an ogive and a frequency polygon?

An ogive is used for cumulative frequencies, while a frequency polygon is used for individual frequencies Signup and view all the answers

What is the formula for calculating the relative frequency of a class interval?

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

What is the purpose of finding the quartiles in a dataset?

To calculate the interquartile range Signup and view all the answers

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

To plot the points on the frequency polygon Signup and view all the answers

What is the difference between the frequency polygon and the ogive?

The frequency polygon is used for individual frequencies, while the ogive is used for cumulative frequencies Signup and view all the answers

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

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

What is the primary characteristic of a symmetric distribution?

The left and right tails are balanced. Signup and view all the answers

What is the formula for calculating the standard deviation of a dataset?

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

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

Outliers Signup and view all the answers

Gr 11 Math Nov P2 (Hard)

Choose a study mode

Podcast

Questions and Answers

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

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

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

What is the significance of the y-intercept c in the gradient–intercept form?

What is the condition for the two-point form to be used?

What is the condition for the gradient–point form to be used?

What is the condition for the gradient–intercept form to be used?

What is the relationship between the gradient–point form and the gradient–intercept form?

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

What is the value of the gradient of a vertical line?

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

What is the inclination of a line with a gradient of -3?

What is the condition for two lines to be parallel?

What is the value of the gradient of a horizontal line?

What is the relationship between the tangent function and the angle of inclination?

What is the point-slope form of the equation of a line?

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

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

What is the condition for two lines to be perpendicular?

What is the amplitude of the function y = sin(θ) for 0° ≤ θ ≤ 360°?

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

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

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

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

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

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

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

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

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

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

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

What is the range of the function y = cos θ?

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

What is the domain of the function y = cos θ?

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

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

What is the amplitude of the function y = a cos θ?

What is the period of the function y = tan θ?

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

What is the effect of p on the graph of y = tan(θ + p) when p > 0?

What is the formula for the area of a trapezium?

What is the formula for the volume of a cylinder?

What is the surface area of a rectangular prism?

What is the volume of a triangular prism?

What is the circumference of a circle with radius r?

What is the characteristic of a right pyramid?

What is the formula for the area of a circle?

What is the shape of the net of a cylinder?

What is the primary purpose of calculating the interquartile range (IQR) in identifying outliers?

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

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

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

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

If a circle is scaled by a factor of 2, what will be the ratio of the new surface area to the original surface area?

What is the name of the theorem that states that the angle at the center of a circle is twice the angle at the circumference?

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

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

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

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

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

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

If a rectangular prism has dimensions $l, b, h$ and one dimension is multiplied by a constant factor $k$, what is the new volume?

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

If a line segment from the center of a circle is perpendicular to a chord, what can be said about the line segment?

If a rectangular prism has dimensions $l, b, h$ and all three dimensions are multiplied by a constant factor $k$, what is the new volume?

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 formula for the volume of a triangular prism?

If the opposite angles of a cyclic quadrilateral are supplementary, what can be said about the quadrilateral?

What is the name of the part of the circle that is a straight line joining the ends of an arc?

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

What is the formula for the volume of a sphere?

If an angle at the center of a circle is twice the angle at the circumference, what can be said about the angles?

If a rectangular prism has dimensions $l, b, h$ and two dimensions are multiplied by a constant factor $k$, what is the new surface area?

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

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

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