Gr 11 Math June P2 (Medium)

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) (correct)
y = mx + c
y - y_1 = m(x - x_1)
x = mx + c

What is the gradient of the line when the gradient-point form is y - y_1 = m(x - x_1)?

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

What is the value of c in the gradient-intercept form y = mx + c?

c = y_1 + mx_1
c = x_1 - y_1
c = y_2 - mx_2
c = y_1 - mx_1 (correct)

What is the y-intercept of the line when the equation is in the gradient-intercept form?

y = c (B) 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?

Gradient-point form (A) 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) in the two-point form?

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

What is the 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 standard form of the straight line equation?

y = mx + c (A) Signup and view all the answers

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

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

What is the condition for two lines to be perpendicular?

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

What is the inclination of a vertical line?

90° (B) 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 quotient identity for tangent?

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

If the gradient of a line is -2, what is the angle of inclination?

120° (B) Signup and view all the answers

What is the value of tan(30°) in terms of sine and cosine?

sin(30°)/cos(30°) (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 square identity in trigonometry?

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

Which of the following is a fundamental trigonometric identity?

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

What is the condition for parallel lines?

They have the same gradient (C) 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?

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

What is the gradient of a horizontal line?

0 (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 value of sin(180° - θ) in terms of sin(θ)?

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

What is the importance of the gradient-intercept form in finding the equation of a parallel line?

It is used to find the gradient (B) Signup and view all the answers

What is the formula to calculate the perpendicular gradient?

m_1 = -1 / m_2 (A) 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 relationship between the tangent function and the angle of inclination?

tan(θ) is positive for acute angles (B) Signup and view all the answers

Why is tan θ undefined when cos θ = 0?

Because the ratio of opposite side to adjacent side is undefined (C) Signup and view all the answers

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

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

What is the common technique used to prove trigonometric identities?

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

What is the coordinate of P' if P is (-√3, 1) and P' is symmetrical about the y-axis?

(-√3, 1) (C) Signup and view all the answers

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

45° (C) Signup and view all the answers

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

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

What is the value of sin^2(θ) + cos^2(θ) for all values of θ?

1 (C) Signup and view all the answers

What is the purpose of the CAST diagram in trigonometry?

To determine the quadrant of the angle (A) Signup and view all the answers

What is the value of cos^2(θ) in terms of sin(θ)?

1 - sin^2(θ) (B) Signup and view all the answers

If points P and P' are symmetrical about the origin, what are the coordinates of P'?

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

What is the value of sin(180° + θ)?

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

What is the value of cos(360° - θ)?

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

If points P and P' are symmetrical about the x-axis, what are the coordinates of P'?

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

What is the value of tan(-θ)?

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

What is the value of sin(90° + θ)?

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

What is the value of cos(90° - θ)?

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

What is the value of sin(360° + θ)?

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

What is the value of cos(360° + θ)?

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

What is the value of tan(360° + θ)?

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

What is the value of sin(68°) / cos(22°)?

1 (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. (A) 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. (C) Signup and view all the answers

What is the formula for the area of a triangle?

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

What is the formula for the area of a circle?

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

What is the surface area of a prism?

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

What is the shape of the base of a right prism?

A polygon (B) Signup and view all the answers

What is the shape of the unfolded net of a cube?

Six identical squares (A) Signup and view all the answers

What is the characteristic of a right prism?

The base and top surface are the same shape and size. (C) Signup and view all the answers

What is the shape of a right prism that has a triangular base?

A triangular prism (A) Signup and view all the answers

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

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

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

Vertical shift (C) Signup and view all the answers

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

a (B) Signup and view all the answers

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

Increase in amplitude (A) 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 x-intercept of the function y = sin(θ)?

(360°, 0) (D) Signup and view all the answers

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

Change in period (C) 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 period of the function y = cos(θ)?

360° (D) Signup and view all the answers

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

Increase in amplitude (B) Signup and view all the answers

What is the formula for the area of a trapezium?

b(h1 + h2)/2 (A) Signup and view all the answers

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

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

If a triangle has a base of 5 units and a height of 6 units, what is its area?

15 units^2 (D) Signup and view all the answers

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

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

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

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

What happens to the surface area of a shape when its dimensions are scaled by a factor of 2?

It increases by a factor of 4 (D) Signup and view all the answers

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

A = 2πr × h + 2πr^2 (B) Signup and view all the answers

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

V = 1/3 × πr^2 × h (B) 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 (A) 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 (B) Signup and view all the answers

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

A = 4πr^2 (B) 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 formula for the volume of a triangular prism?

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

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

Segment (C) Signup and view all the answers

If the length of a rectangular prism is multiplied by a constant factor k, what is the new volume?

V = k × l × b × h (B) Signup and view all the answers

What is the formula for the area of a circle?

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

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

A = b^2 + 4 × (1/2 × b × h) (D) Signup and view all the answers

What is the formula for the volume of a sphere?

V = 4/3 × πr^3 (A) Signup and view all the answers

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

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

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

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

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

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

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

For k > 1, the period decreases (C) Signup and view all the answers

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

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

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

{f(θ): -1 ≤ f(θ) ≤ 1} (B) Signup and view all the answers

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

180° (A) Signup and view all the answers

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

For p > 0, the graph shifts to the left (C) Signup and view all the answers

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

For a > 1, the branches of the graph are steeper (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 effect of k on the period of the function y = tan kθ?

For k > 1, the period decreases (B) Signup and view all the answers

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

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

Which of the following forms 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 the value of y when x = 0 in the gradient-intercept form of the straight line equation?

c (C) Signup and view all the answers

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

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

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

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

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

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

What is the relationship between the gradient and the y-intercept of a straight line?

The gradient is independent of the y-intercept (A) Signup and view all the answers

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

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

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

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

What is the process of deriving the gradient-intercept form from the gradient-point form?

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

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

It is the y-intercept of the line (A) Signup and view all the answers

What is the value of tan(θ) in terms of sin(θ) and cos(θ)?

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

What is the value of sin^2(θ) + cos^2(θ) for all values of θ?

1 (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

If the gradient of a line is 2, what is the angle of inclination?

atan(2) (C) Signup and view all the answers

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

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

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

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

Which of the following is true about a line with a negative gradient?

The angle of inclination is obtuse. (C) Signup and view all the answers

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

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

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

3 (D) Signup and view all the answers

What is the inclination of a line that is parallel to the x-axis?

0° (A) Signup and view all the answers

If the gradient of a line is undefined, what is the inclination of the line?

90° (A) Signup and view all the answers

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

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

What is the equation form used to find the equation of a line that passes through two points?

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

What is the purpose of the CAST diagram in trigonometry?

To relate the tangent function to the angle of inclination (D) Signup and view all the answers

What is the condition for two lines to be parallel?

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

What is the condition for two lines to be perpendicular in terms of their gradients?

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

If point P is rotated through 90°, what are the coordinates of P'?

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

What is the purpose of trigonometric identities?

To simplify equations and solve trigonometric problems (B) Signup and view all the answers

How can you determine the equation of a perpendicular line?

Identify the gradient of the given line and calculate the perpendicular gradient (C) Signup and view all the answers

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

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

If points P and P' are symmetrical about the origin, what are the coordinates of P'?

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

What is the square identity in trigonometry?

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

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

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

If points P and P' are symmetrical about the x-axis, what are the coordinates of P'?

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

What is the importance of the gradient-intercept form in finding the equation of a parallel line?

It makes it easier to identify the gradient (A) Signup and view all the answers

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

tan(θ) (D) 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

Why is tan(θ) undefined when cos(θ) = 0?

Because the cosine function is equal to 0 (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'?

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

What is the common technique used to prove trigonometric identities?

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

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

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

What is the value of sin^2(θ) + cos^2(θ) for all values of θ?

1 (B) Signup and view all the answers

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

-tan(θ) (C) 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 (D) 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?

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

What is the formula for the area of a circle?

A = π r^2 (B) 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 (D) Signup and view all the answers

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

SA = 2lw + 2lh + 2wh (D) 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 formula for the circumference of a circle?

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

What is the formula for the area of a rectangle?

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

What is the formula for the area of a square?

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

What is the formula for the volume of a cylinder?

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

What is the formula for the area of a square?

s^2 (A) 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 surface area of a sphere?

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

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

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

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

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

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

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

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

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

If the dimensions of a rectangular prism are multiplied by a constant factor k, what is the new volume?

k^3V (A) 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 is Twice the Angle at the Circumference (A) Signup and view all the answers

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

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

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

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

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

Tangent (C) Signup and view all the answers

What is the formula for the area of a trapezium?

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

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

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

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

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

If the dimensions of a rectangular prism are multiplied by a constant factor k, what is the new surface area?

k^2A (A), k^2A (D) Signup and view all the answers

What is the formula for the volume of a cylinder?

π × r^2 × 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 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 = sin(kθ)?

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

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

The amplitude increases for a > 1 (A) Signup and view all the answers

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

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

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

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

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

{θ: θ ∈ ℝ} (B) 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 effect of k on the period of the function y = sin(kθ)?

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

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

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

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

(360, 1) (D) Signup and view all the answers

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

The graph shifts horizontally to the left by p units (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 = tan kθ?

The period is equal to 180°/|k| (A) Signup and view all the answers

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

[-1, 1] (C) 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 to the left by p units (D) Signup and view all the answers

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

{θ: θ ∈ ℝ, θ ≠ 90°/k, 270°/k} (C) 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 for a > 1 (B) Signup and view all the answers

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

(0, 1) (B) 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 upwards by q units (D) Signup and view all the answers

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

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

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

θ = 90°/k (A) Signup and view all the answers

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

To find the equation of a line passing through two points (C) Signup and view all the answers

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

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 one point on the line are known?

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

What is the purpose of expanding the brackets in the gradient-point form?

To derive the gradient-intercept form (B) Signup and view all the answers

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

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

What is the definition of the gradient of a line?

The ratio of the vertical change to the horizontal change (C) Signup and view all the answers

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

They are two different forms of the same equation (B) Signup and view all the answers

Why is the gradient-intercept form useful in finding the equation of a parallel line?

It helps to find the y-intercept of the line (D) Signup and view all the answers

What is the correct expression for tan(θ) in terms of sin(θ) and cos(θ)?

sin(θ) / cos(θ) (D) 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 correct expression for cos²(θ) + sin²(θ)?

1 (B) Signup and view all the answers

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

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

If P is (-√3, 1) and P' is symmetrical about the y-axis, what are the coordinates of P'?

(-√3, -1) (C) Signup and view all the answers

What is the correct expression for cos(180° - θ) in terms of cos(θ)?

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

What is the value of sin²(θ) in terms of cos(θ)?

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

What is the purpose of the quotient identity in trigonometry?

To express tan(θ) in terms of sin(θ) and cos(θ) (A) Signup and view all the answers

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

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

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

135° (D) 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 equation form used to find the equation of a line that is parallel to a given line?

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

What is the condition for two lines to be perpendicular?

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

What is the gradient of a horizontal line?

0 (A) Signup and view all the answers

What is the quotient identity for tangent?

tan θ = sin θ / cos θ (D) 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 tangent of an angle θ in a right-angled triangle?

Opposite side / Adjacent side (B) Signup and view all the answers

What is the square identity in trigonometry?

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

What is the importance of the Gradient-Intercept Form in finding the equation of a parallel line?

It allows us to find the gradient (A) Signup and view all the answers

What is the relationship between the gradient and the y-intercept of a line in the Gradient-Intercept Form?

m is independent of c (B) Signup and view all the answers

What is the purpose of trigonometric identities?

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

What is the formula to calculate the perpendicular gradient?

m_1 = -1 / m_2 (D) Signup and view all the answers

What is the condition for a line to have a negative gradient?

The line is obtuse (D) Signup and view all the answers

Why is tan θ undefined when cos θ = 0?

Because tan θ is not defined for all angles. (C) Signup and view all the answers

What is the common technique used to prove trigonometric identities?

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

What is the importance of the gradient-intercept form in finding the equation of a parallel line?

It makes it easier to identify the gradient of the line. (B) Signup and view all the answers

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

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

If point P is rotated through 90°, what are the coordinates of P'?

(-y, x) (C) 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(90° + θ) in terms of sin(θ)?

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

If points P and P' are symmetrical about the origin, what are the coordinates of P'?

(-x, -y) (B) 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 value of cos(180° + θ) in terms of cos(θ)?

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

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

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

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

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

If points P 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 value of cos(90° - θ) in terms of sin(θ)?

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

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

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

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

The amplitude increases. (B) Signup and view all the answers

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

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

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

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

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

The graph shifts horizontally to the left by p units. (A) 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 amplitude of the function y = a sin(θ)?

a (B) Signup and view all the answers

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

(270, 0) (C) 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

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

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

What is the formula for the area of a triangle?

½ b × h (A) Signup and view all the answers

What is the formula for the area of a circle?

πr² (A) Signup and view all the answers

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

It bisects the chord (B) Signup and view all the answers

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

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

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

4πr² (C) Signup and view all the answers

What is the formula for the volume of a cylinder?

πr² × h (D) Signup and view all the answers

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

It scales by k³ (A) Signup and view all the answers

What is the formula for the area of a trapezium?

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

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

Twice the angle at the circumference (C) Signup and view all the answers

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

½b × h × H (A) Signup and view all the answers

What is the period of y = cos kθ?

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

Which of the following shapes is a geometric solid with a polygon as its base and sides that converge at a point called the apex?

Pyramid (C) Signup and view all the answers

What happens to the period of y = cos kθ when k > 1?

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

If the radius of a cylinder is doubled, what will be the effect on the surface area and volume of the cylinder?

Both surface area and volume will be quadrupled (D) Signup and view all the answers

What is the range of y = cos kθ?

(-1, 1) (D) 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 triangular prism?

(1/3)b(h)H (C) Signup and view all the answers

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

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

What is the period of y = tan kθ?

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

If the dimensions of a rectangular prism are tripled, what will be the effect on the surface area and volume of the prism?

Both surface area and volume will be nine times (C) Signup and view all the answers

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

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

What happens to the period of y = tan kθ when k > 1?

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

What is the formula for the volume of a cylinder?

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

What is the domain of y = tan kθ?

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

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

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

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

A change in the steepness of the branches (C) Signup and view all the answers

If the length of a rectangular prism is doubled, what will be the effect on the surface area and volume of the prism?

Surface area will be doubled and volume will be quadrupled (B) Signup and view all the answers

What is the general approach to solve trigonometric equations?

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

What is the y-intercept of y = tan kθ?

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

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

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

What is the formula for the area of a trapezium?

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

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

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

What is the name of the diagram used to determine the quadrants where the trigonometric function is positive or negative?

CAST diagram (C) Signup and view all the answers

What is the formula for the area of a circle?

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

What is the advantage of using reduction formulae in trigonometry?

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

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

SA = 2 × (A + B + C) (B) Signup and view all the answers

What is the name of the geometric solid that has a polygon as its base and vertical sides perpendicular to the base?

Right prism (B) Signup and view all the answers

What is the formula for the circumference of a circle?

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

What is the general approach to find the general solution of a trigonometric equation?

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

What is the value of tan(θ) in terms of sine and cosine?

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

What is the value of sin(180° - θ) in terms of sin(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) (D) Signup and view all the answers

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

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

What is the square identity in trigonometry?

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

What is the value of cos^2(θ) in terms of sin(θ)?

1 - sin^2(θ) (B) Signup and view all the answers

What is the value of sin^2(θ) in terms of cos(θ)?

1 - cos^2(θ) (B) Signup and view all the answers

What is the coordinate of P' if P is (√3, 1) and P' is symmetrical about the y-axis?

(-√3, 1) (B) Signup and view all the answers

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

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

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

c (D) Signup and view all the answers

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

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

How is the gradient-point form of the straight line equation derived?

By substituting m = (y2 - y1) / (x2 - x1) into the two-point form (B) Signup and view all the answers

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

The gradient is directly proportional to the inclination (C) Signup and view all the answers

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

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

How can the equation of a line be written in the gradient-intercept form?

By making y the subject of the formula in the gradient-point form (A) Signup and view all the answers

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

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

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

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

What is the purpose of trigonometric identities?

To simplify trigonometric expressions (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 (C) 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 quotient identity for tangent?

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

What is the formula to calculate the perpendicular gradient?

m_1 = -1/m_2 (A) Signup and view all the answers

Why is tan(θ) undefined when cos(θ) = 0?

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

What is the square identity in trigonometry?

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

What is the importance of the gradient-intercept form in finding the equation of a parallel line?

It allows us to find the gradient (A) Signup and view all the answers

What is the common technique used to prove trigonometric identities?

Changing all trigonometric ratios to sine and cosine (B) 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. (A) Signup and view all the answers

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

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

What is the inclination of a vertical line?

Undefined (C) Signup and view all the answers

If points P 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 condition for two lines to be parallel?

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

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

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

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

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

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

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

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

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

What is the purpose of the CAST diagram in trigonometry?

To identify the quadrant of an angle. (C) Signup and view all the answers

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

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

If the gradient of a line is -2, what is the angle of inclination?

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

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

It makes the angle obtuse. (D) Signup and view all the answers

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

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

What is the importance of the gradient-intercept form in finding the equation of a parallel line?

It is used to identify the gradient of the parallel line. (D) 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 opposite side to the adjacent side of the angle of inclination. (D) Signup and view all the answers

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

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

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

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

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

y = -1/mx + c (B) Signup and view all the answers

What is the purpose of the reduction formulae in trigonometry?

To simplify and evaluate trigonometric expressions (D) 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?

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

What is the purpose of the CAST diagram in trigonometry?

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

What is the formula for the area of a circle?

A = πr² (D) Signup and view all the answers

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

Surface area = sum of areas of each face (B) 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 (C) Signup and view all the answers

What is the formula for the circumference of a circle?

C = 2πr (C) 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 purpose of the general solution in trigonometric equations?

To determine the values of angles that satisfy the equation for all values of the angle (A) Signup and view all the answers

What is the formula for the volume of a cylinder?

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

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

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

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

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

If the length of a rectangular prism is multiplied by a factor of 2, what happens to the volume?

It doubles (A) Signup and view all the answers

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

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

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

1/3 × b^2 × H (A) Signup and view all the answers

If the height of a cylinder is multiplied by a factor of 3, what happens to the volume?

It triples (A) Signup and view all the answers

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

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

If the radius of a sphere is multiplied by a factor of 2, what happens to the surface area?

It quadruples (D) 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 period of y = cos kθ?

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

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

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

What is the domain of y = cos kθ?

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

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

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

What is the period of y = tan kθ?

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

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

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

What is the domain of y = tan kθ?

{θ : θ ∈ ℝ, θ ≠ 90°/k, 270°/k} (C) Signup and view all the answers

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

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

What is the y-intercept of y = tan kθ?

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

What is the effect of a > 1 on the shape of y = a tan θ + q?

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

What is the formula for the area of a square?

s^2 (B) Signup and view all the answers

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

unfolded into a net and find the area of each face (B) Signup and view all the answers

What is the formula for the volume of a cylinder?

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

What happens to the surface area of a shape when its dimensions are multiplied by a factor k?

It scales by k^2 (A) 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 is Twice the Angle at the Circumference (C) Signup and view all the answers

What is the period of the function y = sin(kθ) where k is a constant?

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

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

Tangent (D) Signup and view all the answers

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

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

What is the formula for the volume of a sphere?

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

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

Segment (D) Signup and view all the answers

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

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

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

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

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

The graph is shifted horizontally to the right by p units. (B) Signup and view all the answers

What happens to the volume of a shape when its dimensions are multiplied by a factor k?

It scales by k^3 (D) 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 effect of a on the graph of y = a cos(θ) when a < -1?

The amplitude of the graph increases with a reflection. (C) Signup and view all the answers

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

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

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

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

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

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

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

(0, 1), (360, 1) (D) Signup and view all the answers

Gr 11 Math June P2 (Medium)

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Questions and Answers

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

What is the gradient of the line when the gradient-point form is y - y_1 = m(x - x_1)?

What is the value of c in the gradient-intercept form y = mx + c?

What is the y-intercept of the line when the equation is in the gradient-intercept form?

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

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

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

What is the standard form of the straight line equation?

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

What is the condition for two lines to be perpendicular?

What is the inclination of a vertical line?

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

What is the quotient identity for tangent?

If the gradient of a line is -2, what is the angle of inclination?

What is the value of tan(30°) in terms of sine and cosine?

What is the condition for two lines to be parallel?

What is the square identity in trigonometry?

Which of the following is a fundamental trigonometric identity?

What is the condition for parallel lines?

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

What is the gradient of a horizontal line?

What is the purpose of trigonometric identities?

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

What is the importance of the gradient-intercept form in finding the equation of a parallel line?

What is the formula to calculate the perpendicular gradient?

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

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

Why is tan θ undefined when cos θ = 0?

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

What is the common technique used to prove trigonometric identities?

What is the coordinate of P' if P is (-√3, 1) and P' is symmetrical about the y-axis?

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

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

What is the value of sin^2(θ) + cos^2(θ) for all values of θ?

What is the purpose of the CAST diagram in trigonometry?

What is the value of cos^2(θ) in terms of sin(θ)?

If points P and P' are symmetrical about the origin, what are the coordinates of P'?

What is the value of sin(180° + θ)?

What is the value of cos(360° - θ)?

If points P and P' are symmetrical about the x-axis, what are the coordinates of P'?

What is the value of tan(-θ)?

What is the value of sin(90° + θ)?

What is the value of cos(90° - θ)?

What is the value of sin(360° + θ)?

What is the value of cos(360° + θ)?

What is the value of tan(360° + θ)?

What is the value of sin(68°) / cos(22°)?

What is the first step in solving a trigonometric equation?

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

What is the formula for the area of a triangle?

What is the formula for the area of a circle?

What is the surface area of a prism?

What is the shape of the base of a right prism?

What is the shape of the unfolded net of a cube?

What is the characteristic of a right prism?

What is the shape of a right prism that has a triangular base?

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

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

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

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

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

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

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

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

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

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

What is the formula for the area of a trapezium?

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

If a triangle has a base of 5 units and a height of 6 units, what is its area?

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

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

What happens to the surface area of a shape when its dimensions are scaled by a factor of 2?

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

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

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