Gr 11 Math June P2 (Mix)

What is the quotient identity of trigonometry?

tan θ = sin θ + cos θ
tan θ = cos θ / sin θ
tan θ = sin θ / cos θ (correct)
tan θ = sin θ * cos θ

What is the square identity of trigonometry?

sin² θ + cos² θ = 2
sin² θ - cos² θ = 1
sin² θ + cos² θ = 1 (correct)
sin² θ + cos² θ = 0

What is the value of sin(180˚ - θ) in terms of θ?

sin θ (correct)
-cos θ
-sin θ
cos θ

What is the value of cos(180˚ - θ) in terms of θ?

-cos θ (A) Signup and view all the answers

What is the value of tan(180˚ - θ) in terms of θ?

-tan θ (C) Signup and view all the answers

What is the value of sin(180˚ + θ) in terms of θ?

-sin θ (A) Signup and view all the answers

What is the value of cos(180˚ + θ) in terms of θ?

-cos θ (C) Signup and view all the answers

What is the value of tan(180˚ + θ) in terms of θ?

-tan θ (D) Signup and view all the answers

What is the condition for two lines to be parallel?

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

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

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

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

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

What is the inclination of a vertical line?

90° (C) Signup and view all the answers

What is the first step in finding the equation of a perpendicular line?

Identify the gradient of the given line. (D) Signup and view all the answers

What is the equation form used when the gradient and the y-intercept are known?

Gradient-Intercept Form (B) Signup and view all the answers

What is the quotient identity for tangent in terms of sine and cosine?

tan θ = sin θ / cos θ (A) Signup and view all the answers

What is the condition for two lines to be parallel?

m1 = m2 (B) Signup and view all the answers

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

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

What is the square identity, also known as the Pythagorean identity?

sin^2 θ + cos^2 θ = 1 (A) Signup and view all the answers

What is the trigonometric relationship for acute angles?

tan(θ) is positive (D) 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 (C) Signup and view all the answers

What is a useful tip for proving trigonometric identities?

Change all trigonometric ratios to sine and cosine. (D) Signup and view all the answers

What is the equation form used to find the equation of a parallel line?

Point-Slope Form (A) Signup and view all the answers

What is the condition for a line to be perpendicular to another line?

The gradients of the two lines must multiply to -1. (B) Signup and view all the answers

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

c (B) Signup and view all the answers

What is the inclination of a horizontal line?

0° (D) Signup and view all the answers

What is the definition of the constant c in the gradient-intercept form of the straight line equation y = mx + c?

c = y_1 - mx_1 (A) Signup and view all the answers

What is the purpose of trigonometric identities?

To simplify expressions and solve equations. (B) Signup and view all the answers

What is the formula to derive the gradient-point form of the straight line equation from the two-point form?

m = (y_2 - y_1) / (x_2 - x_1) (B) Signup and view all the answers

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

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

What is the measurement of the steepness of a line?

Gradient (m) (C) Signup and view all the answers

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

Gradient-Intercept Form (D) Signup and view all the answers

What is the importance of ensuring the equation of a given line is in gradient-intercept form?

To directly read off the gradient. (D) Signup and view all the answers

What is the importance of identifying the gradient of the given line in finding the equation of a parallel line?

To directly read off the gradient (A) Signup and view all the answers

What is the formula to derive the gradient-intercept form of the straight line equation from the gradient-point form?

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

What are the three forms of the straight line equation mentioned in the content?

Two-Point Form, Gradient-Point Form, and Gradient-Intercept Form (A) Signup and view all the answers

What is the value of sin(180° + θ) in terms of sin(θ)?

-sin(θ) (B) Signup and view all the answers

What is the value of cos(360° - θ) in terms of cos(θ)?

cos(θ) (D) Signup and view all the answers

What is the value of tan(-θ) in terms of tan(θ)?

-tan(θ) (B) Signup and view all the answers

What is the value of sin(90° + θ) in terms of cos(θ)?

cos(θ) (D) Signup and view all the answers

What is the value of cos(90° - θ) in terms of sin(θ)?

sin(θ) (C) Signup and view all the answers

If points P and P' are symmetrical about the origin, what are the coordinates of P' if P is (x, y)?

(-x, -y) (D) Signup and view all the answers

If points P and P' are symmetrical about the x-axis, what are the coordinates of P' if P is (x, y)?

(x, -y) (D) Signup and view all the answers

What is the value of sin(360° + θ) in terms of sin(θ)?

sin(θ) (B) Signup and view all the answers

What is the value of cos(180° + θ) in terms of cos(θ)?

-cos(θ) (A) Signup and view all the answers

What is the value of tan(90° - θ) in terms of tan(θ)?

-tan(θ) (D) Signup and view all the answers

What is the formula for the area of a triangle?

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

What is the formula to calculate the volume of a rectangular prism?

l × b × h (C) Signup and view all the answers

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

4 × π × r^2 (A) Signup and view all the answers

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

l × b × h (C) Signup and view all the answers

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

4πr^2 (C) Signup and view all the answers

What is the formula for the area of a circle?

π × r^2 (D) Signup and view all the answers

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

360°/|k| (A) Signup and view all the answers

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

It is multiplied by k^3 (C) Signup and view all the answers

What is the effect of scaling on the volume of a shape?

Volume scales by k^3 (B) Signup and view all the answers

What is the formula to calculate the volume of a right cone?

1/3πr^2h (D) Signup and view all the answers

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

The period decreases (B) Signup and view all the answers

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

[-1, 1] (B) 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 (D) Signup and view all the answers

What is the formula to calculate the surface area of a triangular pyramid?

1/2bh + 3bh_s (D) Signup and view all the answers

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

Angle at the Center is Twice the Angle at the Circumference (C) Signup and view all the answers

What is the volume of a cylinder with radius r and height h?

πr^2h (A) Signup and view all the answers

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

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

What happens to the surface area of a prism if one of its dimensions is multiplied by a constant factor k?

It is multiplied by k (B) Signup and view all the answers

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

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

What is the definition of a segment in a circle?

A part of the circle that is cut off by a chord (C) Signup and view all the answers

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

180° (C) Signup and view all the answers

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

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

What is the formula to calculate the volume of a triangular pyramid?

1/3bhH (A) Signup and view all the answers

What is the formula to calculate the surface area of a right cone?

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

What is the effect of a > 1 on the graph of the function y = a*tan(θ) + q?

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

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

1/3 × π × r^2 × h (A) Signup and view all the answers

What is the volume of a sphere with radius r?

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

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

The period decreases (B) Signup and view all the answers

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

All real numbers except θ = 90°/k and θ = 270°/k (C) Signup and view all the answers

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

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

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

Twice the angle on the circle subtended by the same chord (C) Signup and view all the answers

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

A vertical shift upwards by q units (B) Signup and view all the answers

What is the period of y = sin(kθ)?

360°/|k| (A) Signup and view all the answers

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

A reflection about the y-axis (D) Signup and view all the answers

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

|a| (A) Signup and view all the answers

What is the domain of y = sin(θ)?

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

What is the range of y = sin(θ)?

[-1, 1] (D) Signup and view all the answers

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

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

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

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

What is the maximum turning point of y = cos(θ)?

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

What is the purpose of reduction formulae and co-function rules in trigonometry?

To evaluate trigonometric functions without using a calculator (B) Signup and view all the answers

What is the first step in solving trigonometric equations?

Use a calculator to find the reference angle (C) Signup and view all the answers

What is the formula for the area of a triangle?

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

What is the formula for the circumference of a circle?

C = 2π r (A) Signup and view all the answers

What is the purpose of the CAST diagram in trigonometry?

To determine the quadrants where the trigonometric function is positive or negative (A) Signup and view all the answers

What is the formula for the area of a trapezium?

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

What is the general solution to a trigonometric equation?

The solution in the interval [0°; 360°] and adding multiples of the period (D) Signup and view all the answers

What is a right prism?

A geometric solid with a polygon as its base and vertical sides perpendicular to the base (A) Signup and view all the answers

What is the purpose of unfolding a prism into a net?

To calculate the surface area (B) Signup and view all the answers

What is the formula for the area of a square?

A = s^2 (C) Signup and view all the answers

What is the form of the straight line equation used when two points on the line are known?

Two-Point Form (A) Signup and view all the answers

What is the definition of the constant c in the gradient-intercept form of the straight line equation y = mx + c?

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

What is the purpose of rearranging the equation y - y1 = m(x - x1) to make y the subject of the formula?

To derive the gradient-intercept form of the straight line equation (D) Signup and view all the answers

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

It is used when the gradient and one point on the line are known (B) Signup and view all the answers

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

m and c are independent (A) Signup and view all the answers

Why is the gradient-intercept form of the straight line equation y = mx + c also known as the standard form?

Because it is the simplest form of the straight line equation (B) Signup and view all the answers

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

It is used when two points on the line are known (A) Signup and view all the answers

What is the formula to derive the gradient-point form of the straight line equation from the two-point form?

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

What is the purpose of trigonometric identities?

To simplify trigonometric expressions (B) Signup and view all the answers

If $P(x, y)$ and $P'$ are symmetrical about the y-axis, what are the coordinates of $P'$?

($-x, y$) (D) Signup and view all the answers

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

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

What is the value of $\sin (360^\circ - heta)$ in terms of $ heta$?

$\sin heta$ (C) Signup and view all the answers

What is the inclination of a line with a gradient of -0.5?

150° (A) Signup and view all the answers

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

Their product is -1 (D) Signup and view all the answers

What is the equation form used to find the equation of a line that is parallel to a given line and passes through a specific point?

Point-Slope Form (D) Signup and view all the answers

What is the value of $ an (180^\circ + heta)$ in terms of $ heta$?

$- an heta$ (A) Signup and view all the answers

What is the condition for two lines to be parallel?

m1 = m2 (D) Signup and view all the answers

What is the condition for two lines to be perpendicular?

Their gradients are negative reciprocals of each other (D) Signup and view all the answers

What is the importance of ensuring the equation of a given line is in gradient-intercept form?

To directly read off the gradient (A) Signup and view all the answers

What is the value of $\cos (90^\circ - heta)$ in terms of $ heta$?

$\sin heta$ (C) Signup and view all the answers

What is the inclination of a vertical line?

90° (A) Signup and view all the answers

What is the value of $ an ( heta)$ in terms of $\sin heta$ and $\cos heta$?

$rac{\sin heta}{\cos heta}$ (D) Signup and view all the answers

What is the equation form used when the gradient and the y-intercept are known?

Gradient-Intercept Form (A) Signup and view all the answers

What is the trigonometric relationship for obtuse angles?

tan(θ) is negative (A) Signup and view all the answers

What is the measurement of the steepness of a line?

Gradient (C) Signup and view all the answers

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

Their product is -1 (D) Signup and view all the answers

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

Gradient-Intercept Form (C) Signup and view all the answers

What is the purpose of trigonometric identities?

All of the above (D) Signup and view all the answers

What is the first step in finding the equation of a perpendicular line?

Identify the gradient of the given line (D) Signup and view all the answers

What is the condition for two lines to be parallel?

They have the same gradient (B) Signup and view all the answers

What is the trigonometric identity derived from the Pythagorean theorem?

sin^2(θ) + cos^2(θ) = 1 (D) Signup and view all the answers

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

Point-slope form (B) Signup and view all the answers

What is the quotient identity of tangent in terms of sine and cosine?

tan(θ) = sin(θ) / cos(θ) (A) Signup and view all the answers

What is the importance of ensuring the equation of a given line is in gradient-intercept form?

To identify the gradient (A) Signup and view all the answers

What is the formula to find the equation of a perpendicular line that passes through a specific point?

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

What is the measurement of the steepness of a line?

Gradient (C) Signup and view all the answers

If points P and P' are symmetrical about the line y = x, what are the coordinates of P' if P is (x, y)?

(y, x) (B) Signup and view all the answers

What is the value of sin(360° - θ) in terms of sin(θ)?

-sin(θ) (C) Signup and view all the answers

What is the value of cos(90° + θ) in terms of θ?

-sin(θ) (B) Signup and view all the answers

What is the value of tan(180° + θ) in terms of θ?

tan(θ) (A) Signup and view all the answers

What is the value of sin(-θ) in terms of θ?

-sin(θ) (C) Signup and view all the answers

What is the value of cos(360° + θ) in terms of θ?

cos(θ) (D) Signup and view all the answers

If points P and P' are symmetrical about the origin, what are the coordinates of P' if P is (x, y)?

(-x, -y) (C) Signup and view all the answers

What is the value of tan(90° - θ) in terms of θ?

tan(θ) (C) Signup and view all the answers

What is the value of sin(180° - θ) in terms of θ?

sin(θ) (C) Signup and view all the answers

What is the value of cos(90° - θ) in terms of θ?

sin(θ) (C) Signup and view all the answers

What is the first step in solving a trigonometric equation?

Use a calculator to find the reference angle. (B) Signup and view all the answers

What is the formula for the area of a trapezium?

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

What is the general solution for a trigonometric equation when no interval is given?

The solution is found by adding multiples of the period to each answer. (C) Signup and view all the answers

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

Surface Area = 2(lw + lh + wh) (B) Signup and view all the answers

What is the formula for the area of a circle?

Area = πr^2 (B) Signup and view all the answers

What is the purpose of using the CAST diagram when solving trigonometric equations?

To determine the quadrants where the trigonometric function is positive or negative. (D) Signup and view all the answers

What is the formula for the circumference of a circle?

Circumference = 2πr (D) Signup and view all the answers

What is the definition of a right prism?

A geometric solid with a polygon as its base and vertical sides perpendicular to the base. (D) Signup and view all the answers

What is the formula for the area of a triangle?

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

What is the purpose of unfolding a prism or cylinder into a net?

To find the surface area. (D) Signup and view all the answers

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

It shifts the graph vertically upwards by q units. (B) Signup and view all the answers

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

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

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

It changes the amplitude of the graph by a factor of a. (C) Signup and view all the answers

What is the maximum turning point of the function y = sin θ?

(90°, 1) (C) Signup and view all the answers

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

[-1, 1] (A) 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 to the right by p units. (B) Signup and view all the answers

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

(90°, 0) (A) Signup and view all the answers

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

a (A) Signup and view all the answers

What is the formula for the volume of a cylinder?

πr^2h (C) Signup and view all the answers

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

360° (D) Signup and view all the answers

What is the minimum turning point of the function y = cos θ?

(180°, -1) (C) Signup and view all the answers

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

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

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

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

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

The surface area increases by k and the volume increases by k^2 (C) Signup and view all the answers

What is the formula for the volume of a sphere?

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

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

1/2bh + 3bh_s (C) Signup and view all the answers

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

1/3bhH (C) Signup and view all the answers

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

b^2 + 4bh_s (A) Signup and view all the answers

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

The volume increases by k^3 (A) Signup and view all the answers

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

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

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

360°/|k| (A) Signup and view all the answers

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

The period decreases (A) Signup and view all the answers

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

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

What is the formula for the area of a square?

$s^2$ (D) Signup and view all the answers

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

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

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

The sum of the areas of all faces (C) Signup and view all the answers

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

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

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

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

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

180°/|k| (D) Signup and view all the answers

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

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

What happens to the surface area of a sphere when its radius is tripled?

It increases by a factor of 27 (C) Signup and view all the answers

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

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

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

{θ : -90°/k < θ < 90°/k, θ ∈ ℝ} (C) Signup and view all the answers

What is the formula for the area of a trapezium?

$rac{1}{2} (a + b) imes h$ (A) Signup and view all the answers

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

The graph is shifted vertically by q units (D) Signup and view all the answers

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

Determined by setting f(θ) = 0 and solving for θ (D) 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 (A) Signup and view all the answers

What is the angle at the center of a circle when an arc subtends an angle of 30 at the circumference?

60 (B) Signup and view all the answers

What is the definition of a segment in circle geometry?

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

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

$2 \pi r (r + h)$ (B) Signup and view all the answers

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

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

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

c (C) Signup and view all the answers

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

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

What is the definition of the constant c in the gradient-intercept form of the straight line equation y = mx + c?

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

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

Gradient-intercept form (A) Signup and view all the answers

What is the formula to derive the gradient-intercept form of the straight line equation from the gradient-point form?

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

What are the three forms of the straight line equation mentioned in the content?

Two-point form, gradient-point form, gradient-intercept form (B) Signup and view all the answers

What is the purpose of deriving the different forms of the straight line equation?

To use depending on the information provided in the problem (B) Signup and view all the answers

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

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

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

210° (C) Signup and view all the answers

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

Gradient-Point Form (C) Signup and view all the answers

What is the condition for two lines to be parallel?

m1 = m2 (B) Signup and view all the answers

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

To find the equation of a line when given the gradient and one point on the line (B) Signup and view all the answers

What is the importance of ensuring the equation of a given line is in gradient-intercept form?

To easily identify the gradient (C) Signup and view all the answers

What is the trigonometric relationship for obtuse angles?

tan(θ) is negative (D) 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 (1, 4)?

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

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

36.9° (B) Signup and view all the answers

What is the importance of identifying the gradient of the given line in finding the equation of a parallel line?

To ensure the lines are parallel (C) Signup and view all the answers

What is the condition for the quotient identity of trigonometry to be defined?

cos(θ) ≠ 0 (A) Signup and view all the answers

What is the expression for sin^2(θ) + cos^2(θ) in terms of x and y?

x^2 / r^2 + y^2 / r^2 (D) Signup and view all the answers

What is the value of tan(θ) in terms of x and y?

y/x (A) Signup and view all the answers

What is the relationship between the coordinates of P and P' if they are symmetrical about the y-axis?

P' = (-x, y) (A) Signup and view all the answers

What is the value of sin(180° - θ) in terms of sin(θ) and cos(θ)?

sin(θ) (C) Signup and view all the answers

What is the value of cos(180° + θ) in terms of cos(θ)?

-cos(θ) (A) Signup and view all the answers

What is the purpose of reduction formulae in trigonometry?

To simplify trigonometric expressions (A) Signup and view all the answers

What is the relationship between the coordinates of P and P' if they are symmetrical about the origin?

P' = (-x, -y) (A) Signup and view all the answers

What is the condition for two lines to be perpendicular?

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

What is the first step in determining the equation of a perpendicular line?

Identify the gradient of the given line. (B) Signup and view all the answers

What is the purpose of trigonometric identities?

All of the above. (D) Signup and view all the answers

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

Point-slope form. (A) Signup and view all the answers

What is the importance of ensuring the equation of a given line is in gradient-intercept form?

To easily identify the gradient. (D) Signup and view all the answers

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

The y-intercept. (D) Signup and view all the answers

What is the formula for the tangent function in terms of sine and cosine?

tan(θ) = sin(θ) / cos(θ). (A) Signup and view all the answers

What is the square identity, also known as the Pythagorean identity?

sin²(θ) + cos²(θ) = 1. (B) Signup and view all the answers

What is a useful tip for proving trigonometric identities?

All of the above. (D) Signup and view all the answers

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

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

What is the value of sin(180° - θ) in terms of θ?

sin(θ) (C) Signup and view all the answers

If points P and P' are symmetrical about the y-axis, what are the coordinates of P' if P is (x, y)?

(-x, y) (B) Signup and view all the answers

What is the value of cos(90° + θ) in terms of θ?

-sin(θ) (A) Signup and view all the answers

What is the value of tan(360° + θ) in terms of θ?

tan(θ) (D) Signup and view all the answers

If points P and P' are symmetrical about the line y = x, what are the coordinates of P' if P is (x, y)?

(y, x) (B) Signup and view all the answers

What is the value of sin(360° - θ) in terms of θ?

-sin(θ) (D) Signup and view all the answers

What is the value of cos(90° - θ) in terms of θ?

sin(θ) (B), sin(θ) (C) Signup and view all the answers

What is the value of tan(180° - θ) in terms of θ?

-tan(θ) (C) Signup and view all the answers

What is the value of sin(90° - θ) in terms of θ?

cos(θ) (A) Signup and view all the answers

What is the value of cos(360° + θ) in terms of θ?

cos(θ) (A) Signup and view all the answers

What is the first step in solving a trigonometric equation?

Use a calculator to find the reference angle. (D) Signup and view all the answers

What is the formula for the area of a triangle?

Area = 1/2 b × h (D) Signup and view all the answers

What is the purpose of the CAST diagram in solving trigonometric equations?

To determine the quadrants where the trigonometric function is positive or negative. (B) Signup and view all the answers

What is the formula for the area of a parallelogram?

Area = b × h (A) Signup and view all the answers

What is the general solution for trigonometric equations when no interval is given?

Find the values of the angle in the interval [0°; 360°] and add multiples of the period to each answer. (B) Signup and view all the answers

What is the formula for the area of a circle?

Area = πr^2 (C) Signup and view all the answers

What is the purpose of finding the reference angle in solving trigonometric equations?

To find the values of the angle. (D) Signup and view all the answers

What is the surface area of a prism or cylinder?

The total area of the exposed or outer surfaces. (C) Signup and view all the answers

What is the formula for the circumference of a circle?

Circumference = 2πr (C) Signup and view all the answers

What is the purpose of unfolding a prism or cylinder into a net?

To find the surface area of the prism or cylinder. (C) Signup and view all the answers

What is the formula for the area of a square?

$s^2$ (D) Signup and view all the answers

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

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

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

$2(lb + lh + bh)$ (B) Signup and view all the answers

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

The period decreases (D) Signup and view all the answers

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

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

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

$rac{1}{3} \pi r^2 h$ (A) Signup and view all the answers

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

It is multiplied by $k^2$ (B) Signup and view all the answers

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

The graph shifts to the left (B) Signup and view all the answers

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

180°/k (B) Signup and view all the answers

What is the formula for the area of a trapezium?

$rac{1}{2} (a + b) h$ (C) 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 (D) Signup and view all the answers

What is the tangent to a circle?

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

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

{θ: θ ∈ ℝ, θ ≠ 90°/k} (B) Signup and view all the answers

What is the formula for the volume of a sphere?

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

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

$2 \pi r^2 + 2 \pi r h$ (D) Signup and view all the answers

What is the effect of q on the graph of the function y = a tan θ + q when q > 0?

The graph shifts upwards (D) Signup and view all the answers

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

The graph becomes steeper (A) Signup and view all the answers

What is the formula for the area of a circle?

$\pi r^2$ (D) Signup and view all the answers

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

$rac{1}{2} b h H$ (C) Signup and view all the answers

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

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

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

90° (D) Signup and view all the answers

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

It shifts the graph vertically. (C) Signup and view all the answers

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

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

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

2 (D) Signup and view all the answers

What is the effect of a on the function y = a sin(θ) when a < 0?

It reflects the graph about the y-axis. (C) Signup and view all the answers

What is the maximum turning point of the function y = cos(θ) for 0° ≤ θ ≤ 360°?

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

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

It decreases the period of the function. (D) Signup and view all the answers

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

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

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

(360°, 0) (A), (180°, 0) (B) Signup and view all the answers

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

It shifts the graph to the left. (B) Signup and view all the answers

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

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

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

[0°, 360°] (B) Signup and view all the answers

What is the formula for the volume of a cylinder?

$\pi r^2 imes h$ (B) 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 increases by a factor of k^3 (B) Signup and view all the answers

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

$b (b + 2h_s)$ (A) 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 surface area?

The surface area increases by a factor of k^2 (D) Signup and view all the answers

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

$rac{1}{3}b^2 imes H$ (D) Signup and view all the answers

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

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

What is the formula for the volume of a sphere?

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

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

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

What is the variable 'c' in the gradient-intercept form of a straight line equation?

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

Which of the following forms of the straight line equation requires knowledge of the gradient and one point on the line?

Gradient-point form (B) Signup and view all the answers

What is the purpose of rearranging the equation y - y1 = m(x - x1) to get y = mx + (y1 - mx1)?

To derive the gradient-intercept form of the straight line equation (A) Signup and view all the answers

Which of the following statements is true about the gradient-intercept form of a straight line equation?

It is used to find the y-intercept of a line when the gradient is given. (A) 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. (D) Signup and view all the answers

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

Gradient-intercept form (B) Signup and view all the answers

What is the formula used to derive the gradient-point form of the straight line equation from the two-point form?

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

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

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

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

150° (D) Signup and view all the answers

Which of the following is true about two parallel lines?

They have the same gradient (A) 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 (C) Signup and view all the answers

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

Gradient-Point Form (D) Signup and view all the answers

What is the tangent of the angle formed between a line and the positive x-axis?

The gradient of the line (D) Signup and view all the answers

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

0° (A) Signup and view all the answers

What is the equation form used when the gradient and the y-intercept are known?

Gradient-Intercept Form (C) Signup and view all the answers

What is the relationship between the gradients of two lines that are perpendicular to each other?

They are negative reciprocals of each other (C) Signup and view all the answers

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

90° (B) Signup and view all the answers

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

To find the equation of a parallel line (C) Signup and view all the answers

If two lines have gradients 2 and -1/2, what can be concluded about the lines?

The lines are perpendicular. (D) Signup and view all the answers

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

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

What is the value of sin^2(θ) + cos^2(θ) for any angle θ?

1 (D) Signup and view all the answers

What is the first step in finding the equation of a perpendicular line to a given line?

Determine the gradient of the given line. (C) Signup and view all the answers

What is the purpose of trigonometric identities?

All of the above. (D) Signup and view all the answers

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

y = -3/4x + 5 (D) Signup and view all the answers

What is the quotient identity of tangent in terms of sine and cosine?

tan(θ) = sin(θ)/cos(θ) (B) Signup and view all the answers

If $ an heta = rac{3}{4}$, what is the value of $ an(180^\circ - heta)$?

-rac{3}{4} (B) Signup and view all the answers

What is the importance of ensuring the equation of a given line is in gradient-intercept form?

To easily identify the gradient. (A) Signup and view all the answers

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

The product of the gradients is -1. (C) Signup and view all the answers

If $\sin heta = rac{2}{3}$, what is the value of $\cos(90^\circ + heta)$?

-rac{2}{3} (B) Signup and view all the answers

If $\cos heta = rac{1}{2}$, what is the value of $\sin(360^\circ - heta)$?

rac{1}{2} (D) Signup and view all the answers

What is the equation of a line in point-slope form that passes through the point (3, 4) and has a gradient of 2?

y - 4 = 2(x - 3) (B) Signup and view all the answers

If $ an(180^\circ + heta) = x$, what is the value of $ an heta$?

-x (D) Signup and view all the answers

If $\sin heta = rac{3}{5}$ and $\cos heta = rac{4}{5}$, what is the value of $ an(90^\circ - heta)$?

rac{3}{4} (A) Signup and view all the answers

If $\cos(180^\circ + heta) = x$, what is the value of $\cos heta$?

-x (C) Signup and view all the answers

If $ an heta = rac{2}{3}$, what is the value of $\sin(180^\circ - heta)$?

rac{2}{\sqrt{13}} (A) Signup and view all the answers

If $\cos heta = rac{1}{2}$ and $\sin heta = rac{\sqrt{3}}{2}$, what is the value of $ an(90^\circ + heta)$?

-rac{\sqrt{3}}{1} (A) Signup and view all the answers

What is the value of cos(180° + θ) in terms of θ, if the reduction formula is applied?

-cos(θ) (B) Signup and view all the answers

If points P and P' are symmetrical about the line y = x, what are the coordinates of P' if P is (x, y)?

(y, x) (A) Signup and view all the answers

What is the value of sin(90° - θ) in terms of θ, if the reduction formula is applied?

cos(θ) (A) Signup and view all the answers

What is the value of tan(360° - θ) in terms of θ, if the reduction formula is applied?

tan(θ) (D) Signup and view all the answers

What is the value of cos(360° + θ) in terms of θ, if the reduction formula is applied?

cos(θ) (C) Signup and view all the answers

What is the value of sin(-θ) in terms of θ, if the reduction formula is applied?

-sin(θ) (D) Signup and view all the answers

What is the value of tan(90° + θ) in terms of θ, if the reduction formula is applied?

-tan(θ) (D) Signup and view all the answers

What is the value of sin(180° - θ) in terms of θ, if the reduction formula is applied?

sin(θ) (D) Signup and view all the answers

What is the value of cos(90° + θ) in terms of θ, if the reduction formula is applied?

-cos(θ) (A) Signup and view all the answers

What is the value of tan(180° + θ) in terms of θ, if the reduction formula is applied?

tan(θ) (C) 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 (A) Signup and view all the answers

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

A vertical shift upwards by q units (D) Signup and view all the answers

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

[-1, 1] (B) Signup and view all the answers

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

1/3 × base area × height (B) Signup and view all the answers

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

kV (C) Signup and view all the answers

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

|a> (A) Signup and view all the answers

What is the general approach to solve trigonometric equations?

Use a calculator to find the reference angle, then use the CAST diagram to determine the quadrants where the trigonometric function is positive or negative. (B) Signup and view all the answers

What is the surface area of a right cone with radius r and height h?

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

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

(360, 0) (B) Signup and view all the answers

What is the formula for the area of a parallelogram?

A = b × h (B) Signup and view all the answers

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

A change in amplitude (A) Signup and view all the answers

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

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

What is the surface area of a prism or cylinder?

The sum of the areas of all its faces. (B) Signup and view all the answers

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

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

What is the first step in solving a quadratic trigonometric equation?

Simplify the equation and determine the reference angle. (D) Signup and view all the answers

If a cylinder has a radius of 2 cm and a height of 5 cm, what is its volume?

40π cm^3 (B) Signup and view all the answers

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

360° (B) Signup and view all the answers

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

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

What is the purpose of the CAST diagram in solving trigonometric equations?

To identify the quadrants where the trigonometric function is positive or negative. (A) Signup and view all the answers

What is the formula for the area of a trapezium?

A = (a + b) × h (B) Signup and view all the answers

What is the maximum turning point of the function y = sin(θ)?

(90, 1) (B) Signup and view all the answers

If a prism has a base area of 20 cm^2 and a height of 5 cm, what is its volume?

100 cm^3 (D) Signup and view all the answers

What is the definition of a right prism?

A geometric solid with a polygon as its base and vertical sides perpendicular to the base. (B) Signup and view all the answers

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

b(h_b + 3h_s) (B) Signup and view all the answers

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

A horizontal shift to the left by p units (C) Signup and view all the answers

What is the importance of ensuring the equation of a given line is in gradient-intercept form?

To identify the gradient and y-intercept of the line. (B) Signup and view all the answers

If a cylinder has a radius of 4 cm and a height of 10 cm, what is its surface area?

160π cm^2 (C) Signup and view all the answers

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

1/3πr^2h (C) Signup and view all the answers

What is the formula for the area of a trapezium?

0.5 × (a + b) × h (A) Signup and view all the answers

What is the formula for the circumference of a circle?

C = 2πr (D) Signup and view all the answers

What is the difference between a right prism and a cylinder?

A right prism has a polygon as its base, while a cylinder has a circular base. (A) Signup and view all the answers

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

0.5 × b × h × H (B) Signup and view all the answers

If the dimensions of a rectangular prism are multiplied by a factor of 2, what happens to its volume?

It is multiplied by 8 (D) Signup and view all the answers

What is the angle at the center of a circle if the angle at the circumference is 30°?

60° (C) Signup and view all the answers

What is the tangent-chord theorem?

The angle between a tangent and a chord is equal to the angle in the alternate segment. (A) Signup and view all the answers

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

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

What is the formula for the volume of a sphere?

4/3πr^3 (B) Signup and view all the answers

What is the theorem that states a perpendicular line from the center of a circle bisects the chord?

Perpendicular line from circle center bisects chord (C) Signup and view all the answers

What is the formula for the area of a parallelogram?

b × h (A) Signup and view all the answers

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

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

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

The period is calculated as 360°/k (C) Signup and view all the answers

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

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

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

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

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

The domain of one branch is {θ : -90°/k < θ < 90°/k, θ ∈ ℝ} (A) Signup and view all the answers

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

The branches of the graph are steeper if a > 1 and less steep if 0 < a < 1 (B) Signup and view all the answers

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

180°/k (A) Signup and view all the answers

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

The graph shifts vertically by q units (B) Signup and view all the answers

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

The x-intercept is determined by setting f(θ) = 0 and solving for θ (B) Signup and view all the answers

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

The y-intercept is determined by setting θ = 0 and solving for f(θ) (D) Signup and view all the answers

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

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

Gr 11 Math June P2 (Mix)

Choose a study mode

Podcast

Questions and Answers

What is the quotient identity of trigonometry?

What is the square identity of trigonometry?

What is the value of sin(180˚ - θ) in terms of θ?

What is the value of cos(180˚ - θ) in terms of θ?

What is the value of tan(180˚ - θ) in terms of θ?

What is the value of sin(180˚ + θ) in terms of θ?

What is the value of cos(180˚ + θ) in terms of θ?

What is the value of tan(180˚ + θ) in terms of θ?

What is the condition for two lines to be parallel?

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

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

What is the inclination of a vertical line?

What is the first step in finding the equation of a perpendicular line?

What is the equation form used when the gradient and the y-intercept are known?

What is the quotient identity for tangent in terms of sine and cosine?

What is the condition for two lines to be parallel?

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 square identity, also known as the Pythagorean identity?

What is the trigonometric relationship for acute angles?

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

What is a useful tip for proving trigonometric identities?

What is the equation form used to find the equation of a parallel line?

What is the condition for a line to be perpendicular to another line?

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

What is the inclination of a horizontal line?

What is the definition of the constant c in the gradient-intercept form of the straight line equation y = mx + c?

What is the purpose of trigonometric identities?

What is the formula to derive the gradient-point form of the straight line equation from the two-point form?

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

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

What is the measurement of the steepness of a line?

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

What is the importance of ensuring the equation of a given line is in gradient-intercept form?

What is the importance of identifying the gradient of the given line in finding the equation of a parallel line?

What is the formula to derive the gradient-intercept form of the straight line equation from the gradient-point form?

What are the three forms of the straight line equation mentioned in the content?

What is the value of sin(180° + θ) in terms of sin(θ)?

What is the value of cos(360° - θ) in terms of cos(θ)?

What is the value of tan(-θ) in terms of tan(θ)?

What is the value of sin(90° + θ) in terms of cos(θ)?

What is the value of cos(90° - θ) in terms of sin(θ)?

If points P and P' are symmetrical about the origin, what are the coordinates of P' if P is (x, y)?

If points P and P' are symmetrical about the x-axis, what are the coordinates of P' if P is (x, y)?

What is the value of sin(360° + θ) in terms of sin(θ)?

What is the value of cos(180° + θ) in terms of cos(θ)?

What is the value of tan(90° - θ) in terms of tan(θ)?

What is the formula for the area of a triangle?

What is the formula to calculate the volume of a rectangular prism?

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

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

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

What is the formula for the area of a circle?

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

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

What is the effect of scaling on the volume of a shape?

What is the formula to calculate the volume of a right cone?

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

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

What is the definition of a chord in a circle?

What is the formula to calculate the surface area of a triangular pyramid?

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

What is the volume of a cylinder with radius r and height h?

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

What happens to the surface area of a prism if one of its dimensions is multiplied by a constant factor k?

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

What is the definition of a segment in a circle?

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

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

What is the formula to calculate the volume of a triangular pyramid?

What is the formula to calculate the surface area of a right cone?

What is the effect of a > 1 on the graph of the function y = a*tan(θ) + q?

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

What is the volume of a sphere with radius r?

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

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

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