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)?

  • (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?

<p>y = c (B)</p> 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?

<p>Gradient-point form (A)</p> 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?

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

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

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

What is the standard form of the straight line equation?

<p>y = mx + c (A)</p> Signup and view all the answers

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

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

What is the condition for two lines to be perpendicular?

<p>Their gradients multiply to -1 (A)</p> Signup and view all the answers

What is the inclination of a vertical line?

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

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

<p>Identify the gradient of the given line (D)</p> Signup and view all the answers

What is the quotient identity for tangent?

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

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

<p>120° (B)</p> Signup and view all the answers

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

<p>sin(30°)/cos(30°) (A)</p> Signup and view all the answers

What is the condition for two lines to be parallel?

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

What is the square identity in trigonometry?

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

Which of the following is a fundamental trigonometric identity?

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

What is the condition for parallel lines?

<p>They have the same gradient (C)</p> 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?

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

What is the gradient of a horizontal line?

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

What is the purpose of trigonometric identities?

<p>All of the above (D)</p> Signup and view all the answers

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

<p>sin(θ) (B)</p> Signup and view all the answers

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

<p>It is used to find the gradient (B)</p> Signup and view all the answers

What is the formula to calculate the perpendicular gradient?

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

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

<p>-cos(θ) (A)</p> Signup and view all the answers

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

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

Why is tan θ undefined when cos θ = 0?

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

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

<p>-tan(θ) (A)</p> Signup and view all the answers

What is the common technique used to prove trigonometric identities?

<p>All of the above (D)</p> 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?

<p>(-√3, 1) (C)</p> Signup and view all the answers

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

<p>45° (C)</p> 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?

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

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

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

What is the purpose of the CAST diagram in trigonometry?

<p>To determine the quadrant of the angle (A)</p> Signup and view all the answers

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

<p>1 - sin^2(θ) (B)</p> Signup and view all the answers

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

<p>(-x, -y) (D)</p> Signup and view all the answers

What is the value of sin(180° + θ)?

<p>-sin(θ) (B)</p> Signup and view all the answers

What is the value of cos(360° - θ)?

<p>cos(θ) (A)</p> Signup and view all the answers

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

<p>(x, -y) (A)</p> Signup and view all the answers

What is the value of tan(-θ)?

<p>-tan(θ) (A)</p> Signup and view all the answers

What is the value of sin(90° + θ)?

<p>cos(θ) (C)</p> Signup and view all the answers

What is the value of cos(90° - θ)?

<p>sin(θ) (A)</p> Signup and view all the answers

What is the value of sin(360° + θ)?

<p>sin(θ) (C)</p> Signup and view all the answers

What is the value of cos(360° + θ)?

<p>cos(θ) (C)</p> Signup and view all the answers

What is the value of tan(360° + θ)?

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

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

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

What is the first step in solving a trigonometric equation?

<p>Use a calculator to find the reference angle. (A)</p> Signup and view all the answers

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

<p>To determine the quadrants where the trigonometric function is positive or negative. (C)</p> Signup and view all the answers

What is the formula for the area of a triangle?

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

What is the formula for the area of a circle?

<p>π r^2 (B)</p> Signup and view all the answers

What is the surface area of a prism?

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

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

<p>A polygon (B)</p> Signup and view all the answers

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

<p>Six identical squares (A)</p> Signup and view all the answers

What is the characteristic of a right prism?

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

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

<p>A triangular prism (A)</p> Signup and view all the answers

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

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

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

<p>Vertical shift (C)</p> Signup and view all the answers

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

<p>a (B)</p> Signup and view all the answers

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

<p>Increase in amplitude (A)</p> Signup and view all the answers

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

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

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

<p>(360°, 0) (D)</p> Signup and view all the answers

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

<p>Change in period (C)</p> Signup and view all the answers

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

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

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

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

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

<p>Increase in amplitude (B)</p> Signup and view all the answers

What is the formula for the area of a trapezium?

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

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

<p>4πr^2 (D)</p> 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?

<p>15 units^2 (D)</p> Signup and view all the answers

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

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

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

<p>V = l × b × h (C)</p> 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?

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

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

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

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

<p>V = 1/3 × πr^2 × h (B)</p> 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?

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

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

<p>Tangent (B)</p> Signup and view all the answers

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

<p>A = 4πr^2 (B)</p> Signup and view all the answers

What is the formula for the volume of a cylinder?

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

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

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

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

<p>Segment (C)</p> 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?

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

What is the formula for the area of a circle?

<p>πr^2 (C)</p> Signup and view all the answers

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

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

What is the formula for the volume of a sphere?

<p>V = 4/3 × πr^3 (A)</p> 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?

<p>The volume is multiplied by k (B)</p> Signup and view all the answers

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

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

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

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

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

<p>For k &gt; 1, the period decreases (C)</p> Signup and view all the answers

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

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

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

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

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

<p>180° (A)</p> Signup and view all the answers

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

<p>For p &gt; 0, the graph shifts to the left (C)</p> Signup and view all the answers

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

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

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

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

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

<p>For k &gt; 1, the period decreases (B)</p> Signup and view all the answers

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

<p>{θ: -90°/k &lt; θ &lt; 90°/k, θ ∈ ℝ} (D)</p> 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?

<p>Gradient-point form (C)</p> 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?

<p>c (C)</p> Signup and view all the answers

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

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

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

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

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

<p>-tan(θ) (B)</p> Signup and view all the answers

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

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

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

<p>-cos(θ) (B)</p> Signup and view all the answers

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

<p>To find the equation of a line when the gradient and one point are known (B)</p> Signup and view all the answers

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

<p>sin(θ) (A)</p> Signup and view all the answers

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

<p>All of the above (D)</p> Signup and view all the answers

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

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

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

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

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

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

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

<p>-cos(θ) (A)</p> Signup and view all the answers

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

<p>atan(2) (C)</p> Signup and view all the answers

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

<p>sin(θ) (C)</p> Signup and view all the answers

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

<p>-tan(θ) (D)</p> Signup and view all the answers

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

<p>The angle of inclination is obtuse. (C)</p> 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?

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

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

<p>3 (D)</p> Signup and view all the answers

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

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

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

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

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

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

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

<p>Two-Point Form (A)</p> Signup and view all the answers

What is the purpose of the CAST diagram in trigonometry?

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

What is the condition for two lines to be parallel?

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

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

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

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

<p>(-y, x) (D)</p> Signup and view all the answers

What is the purpose of trigonometric identities?

<p>To simplify equations and solve trigonometric problems (B)</p> Signup and view all the answers

How can you determine the equation of a perpendicular line?

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

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

<p>sin(θ) (A)</p> Signup and view all the answers

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

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

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

<p>(-x, -y) (C)</p> Signup and view all the answers

What is the square identity in trigonometry?

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

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

<p>-sin(θ) (D)</p> Signup and view all the answers

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

<p>Identify the gradient of the given line (B)</p> Signup and view all the answers

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

<p>(x, -y) (B)</p> Signup and view all the answers

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

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

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

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

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

<p>cos(θ) (D)</p> Signup and view all the answers

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

<p>Because the cosine function is equal to 0 (D)</p> Signup and view all the answers

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

<p>(y, x) (C)</p> Signup and view all the answers

What is the common technique used to prove trigonometric identities?

<p>Change all trigonometric ratios to sine and cosine (D)</p> Signup and view all the answers

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

<p>cos(θ) (C)</p> Signup and view all the answers

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

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

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

<p>-tan(θ) (C)</p> Signup and view all the answers

What is the purpose of the CAST diagram in trigonometry?

<p>To determine the quadrants where the trigonometric function is positive or negative (D)</p> Signup and view all the answers

What is the first step in solving a trigonometric equation?

<p>Use a calculator to find the reference angle (D)</p> Signup and view all the answers

What is the formula for the area of a triangle?

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

What is the formula for the area of a circle?

<p>A = π r^2 (B)</p> Signup and view all the answers

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

<p>To determine the quadrants where the trigonometric function is positive or negative (D)</p> Signup and view all the answers

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

<p>SA = 2lw + 2lh + 2wh (D)</p> Signup and view all the answers

What is the formula for the area of a trapezium?

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

What is the formula for the circumference of a circle?

<p>C = 2π r (A)</p> Signup and view all the answers

What is the formula for the area of a rectangle?

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

What is the formula for the area of a square?

<p>A = s^2 (D)</p> Signup and view all the answers

What is the formula for the volume of a cylinder?

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

What is the formula for the area of a square?

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

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

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

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

<p>4 × π × r^2 (B)</p> Signup and view all the answers

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

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

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

<p>4πr^2 (A)</p> 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?

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

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

<p>1/3 × b × h × H (C)</p> 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?

<p>k^3V (A)</p> 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?

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

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

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

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

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

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

<p>Tangent (C)</p> Signup and view all the answers

What is the formula for the area of a trapezium?

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

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

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

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

<p>π × r (r + h) (C)</p> 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?

<p>k^2A (A), k^2A (D)</p> Signup and view all the answers

What is the formula for the volume of a cylinder?

<p>π × r^2 × h (D)</p> Signup and view all the answers

What is the formula for the volume of a sphere?

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

What is the formula for the area of a circle?

<p>π × r^2 (D)</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<p>(360, 1) (D)</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

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

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

<p>The branches of the graph are steeper for a &gt; 1 (B)</p> Signup and view all the answers

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

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

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

<p>The graph shifts vertically upwards by q units (D)</p> Signup and view all the answers

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

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

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

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

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

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

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

<p>The y-intercept of the line (C)</p> 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?

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

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

<p>To derive the gradient-intercept form (B)</p> 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'?

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

What is the definition of the gradient of a line?

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

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

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

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

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

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

<p>sin(θ) / cos(θ) (D)</p> Signup and view all the answers

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

<p>-sin(θ) (B)</p> Signup and view all the answers

What is the correct expression for cos²(θ) + sin²(θ)?

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

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

<p>tan(θ) (D)</p> 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'?

<p>(-√3, -1) (C)</p> Signup and view all the answers

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

<p>-cos(θ) (C)</p> Signup and view all the answers

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

<p>1 - cos(θ) (C)</p> Signup and view all the answers

What is the purpose of the quotient identity in trigonometry?

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

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

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

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

<p>135° (D)</p> Signup and view all the answers

What is the condition for two lines to be parallel?

<p>m1 = m2 (D)</p> 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?

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

What is the condition for two lines to be perpendicular?

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

What is the gradient of a horizontal line?

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

What is the quotient identity for tangent?

<p>tan θ = sin θ / cos θ (D)</p> Signup and view all the answers

What is the inclination of a vertical line?

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

What is the tangent of an angle θ in a right-angled triangle?

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

What is the square identity in trigonometry?

<p>sin^2 θ + cos^2 θ = 1 (C)</p> Signup and view all the answers

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

<p>Identify the gradient of the given line. (B)</p> Signup and view all the answers

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

<p>It allows us to find the gradient (A)</p> 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?

<p>m is independent of c (B)</p> Signup and view all the answers

What is the purpose of trigonometric identities?

<p>To simplify trigonometric expressions. (A)</p> Signup and view all the answers

What is the formula to calculate the perpendicular gradient?

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

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

<p>The line is obtuse (D)</p> Signup and view all the answers

Why is tan θ undefined when cos θ = 0?

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

What is the common technique used to prove trigonometric identities?

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

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

<p>It makes it easier to identify the gradient of the line. (B)</p> 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?

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

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

<p>(-y, x) (C)</p> Signup and view all the answers

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

<p>sin(θ) (B)</p> Signup and view all the answers

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

<p>-sin(θ) (B)</p> Signup and view all the answers

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

<p>(-x, -y) (B)</p> Signup and view all the answers

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

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

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

<p>-cos(θ) (B)</p> Signup and view all the answers

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

<p>-sin(θ) (D)</p> Signup and view all the answers

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

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

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

<p>(-x, y) (D)</p> Signup and view all the answers

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

<p>sin(θ) (D)</p> Signup and view all the answers

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

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

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

<p>The amplitude increases. (B)</p> Signup and view all the answers

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

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

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

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

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

<p>The graph shifts horizontally to the left by p units. (A)</p> Signup and view all the answers

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

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

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

<p>a (B)</p> Signup and view all the answers

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

<p>(270, 0) (C)</p> Signup and view all the answers

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

<p>(90, 1) (B)</p> Signup and view all the answers

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

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

What is the formula for the area of a triangle?

<p>½ b × h (A)</p> Signup and view all the answers

What is the formula for the area of a circle?

<p>πr² (A)</p> Signup and view all the answers

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

<p>It bisects the chord (B)</p> Signup and view all the answers

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

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

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

<p>4πr² (C)</p> Signup and view all the answers

What is the formula for the volume of a cylinder?

<p>πr² × h (D)</p> 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?

<p>It scales by k³ (A)</p> Signup and view all the answers

What is the formula for the area of a trapezium?

<p>½(a + b) × h (C)</p> Signup and view all the answers

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

<p>Twice the angle at the circumference (C)</p> Signup and view all the answers

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

<p>½b × h × H (A)</p> Signup and view all the answers

What is the period of y = cos kθ?

<p>360°/|k| (A)</p> 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?

<p>Pyramid (C)</p> Signup and view all the answers

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

<p>The period decreases (A)</p> 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?

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

What is the range of y = cos kθ?

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

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

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

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

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

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

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

What is the period of y = tan kθ?

<p>180°/|k| (D)</p> 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?

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

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

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

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

<p>The period decreases (C)</p> Signup and view all the answers

What is the formula for the volume of a cylinder?

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

What is the domain of y = tan kθ?

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

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

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

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

<p>A change in the steepness of the branches (C)</p> 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?

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

What is the general approach to solve trigonometric equations?

<p>All of the above (D)</p> Signup and view all the answers

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

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

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

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

What is the formula for the area of a trapezium?

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

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

<p>A vertical shift upwards by q units (B)</p> 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?

<p>CAST diagram (C)</p> Signup and view all the answers

What is the formula for the area of a circle?

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

What is the advantage of using reduction formulae in trigonometry?

<p>All of the above (D)</p> Signup and view all the answers

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

<p>SA = 2 × (A + B + C) (B)</p> 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?

<p>Right prism (B)</p> Signup and view all the answers

What is the formula for the circumference of a circle?

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

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

<p>To determine the quadrants where the trigonometric function is positive or negative. (C)</p> Signup and view all the answers

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

<p>All of the above (D)</p> Signup and view all the answers

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

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

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

<p>sin(θ) (C)</p> Signup and view all the answers

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

<p>-cos(θ) (D)</p> Signup and view all the answers

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

<p>-tan(θ) (A)</p> Signup and view all the answers

What is the square identity in trigonometry?

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

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

<p>1 - sin^2(θ) (B)</p> Signup and view all the answers

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

<p>1 - cos^2(θ) (B)</p> 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?

<p>(-√3, 1) (B)</p> Signup and view all the answers

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

<p>Two-Point Form (A)</p> Signup and view all the answers

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

<p>c (D)</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

<p>By making y the subject of the formula in the gradient-point form (A)</p> 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?

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

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

<p>Their product is -1 (A)</p> Signup and view all the answers

What is the purpose of trigonometric identities?

<p>To simplify trigonometric expressions (C)</p> Signup and view all the answers

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

<p>Identify the gradient of the given line (C)</p> Signup and view all the answers

What is the condition for two lines to be parallel?

<p>They have the same gradient (B)</p> Signup and view all the answers

What is the quotient identity for tangent?

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

What is the formula to calculate the perpendicular gradient?

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

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

<p>Because cos(θ) = 0 (A)</p> Signup and view all the answers

What is the square identity in trigonometry?

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

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

<p>It allows us to find the gradient (A)</p> Signup and view all the answers

What is the common technique used to prove trigonometric identities?

<p>Changing all trigonometric ratios to sine and cosine (B)</p> Signup and view all the answers

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

<p>The gradient of a line is equal to the tangent of its inclination. (A)</p> Signup and view all the answers

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

<p>-sin(θ) (C)</p> Signup and view all the answers

What is the inclination of a vertical line?

<p>Undefined (C)</p> Signup and view all the answers

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

<p>(-x, y) (D)</p> Signup and view all the answers

What is the condition for two lines to be parallel?

<p>They have the same gradient. (C)</p> Signup and view all the answers

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

<p>sin(θ) (D)</p> 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?

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

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

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

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

<p>sin(θ) (D)</p> Signup and view all the answers

What is the purpose of the CAST diagram in trigonometry?

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

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

<p>cos(θ) (A)</p> Signup and view all the answers

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

<p>tan^(-1)(-2) (B)</p> Signup and view all the answers

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

<p>It makes the angle obtuse. (D)</p> Signup and view all the answers

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

<p>-tan(θ) (C)</p> Signup and view all the answers

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

<p>It is used to identify the gradient of the parallel line. (D)</p> Signup and view all the answers

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

<p>The tangent function is equal to the ratio of the opposite side to the adjacent side of the angle of inclination. (D)</p> Signup and view all the answers

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

<p>-cos(θ) (B)</p> Signup and view all the answers

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

<p>tan(θ) (D)</p> 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?

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

What is the purpose of the reduction formulae in trigonometry?

<p>To simplify and evaluate trigonometric expressions (D)</p> Signup and view all the answers

What is the first step in solving a trigonometric equation?

<p>Use a calculator to find the reference angle (B)</p> Signup and view all the answers

What is the formula for the area of a trapezium?

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

What is the purpose of the CAST diagram in trigonometry?

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

What is the formula for the area of a circle?

<p>A = πr² (D)</p> Signup and view all the answers

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

<p>Surface area = sum of areas of each face (B)</p> Signup and view all the answers

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

<p>Simplify the equation and determine the reference angle (C)</p> Signup and view all the answers

What is the formula for the circumference of a circle?

<p>C = 2πr (C)</p> Signup and view all the answers

What is the definition of a right prism?

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

What is the purpose of the general solution in trigonometric equations?

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

What is the formula for the volume of a cylinder?

<p>πr^2 × h (A)</p> Signup and view all the answers

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

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

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

<p>1/3 × b × h × H (A)</p> 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?

<p>It doubles (A)</p> Signup and view all the answers

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

<p>πr^2 + πr × h (A)</p> Signup and view all the answers

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

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

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

<p>It triples (A)</p> Signup and view all the answers

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

<p>b × h + 3 × (b × h_s)/2 (D)</p> 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?

<p>It quadruples (D)</p> Signup and view all the answers

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

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

What is the period of y = cos kθ?

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

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

<p>The period decreases (D)</p> Signup and view all the answers

What is the domain of y = cos kθ?

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

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

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

What is the period of y = tan kθ?

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

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

<p>The period decreases (B)</p> Signup and view all the answers

What is the domain of y = tan kθ?

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

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

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

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

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

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

<p>The branches of the graph become steeper (C)</p> Signup and view all the answers

What is the formula for the area of a square?

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

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

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

What is the formula for the volume of a cylinder?

<p>πr^2 × h (A)</p> Signup and view all the answers

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

<p>It scales by k^2 (A)</p> 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?

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

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

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

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

<p>Tangent (D)</p> Signup and view all the answers

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

<p>The amplitude of the graph increases. (C)</p> Signup and view all the answers

What is the formula for the volume of a sphere?

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

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

<p>Segment (D)</p> Signup and view all the answers

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

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

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

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

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

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

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

<p>It scales by k^3 (D)</p> Signup and view all the answers

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

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

What is the effect of a on the graph of y = a cos(θ) when a < -1?

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

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

<p>(0, 0), (180, 0), (360, 0) (A)</p> Signup and view all the answers

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

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

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

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

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

<p>(0, 1), (360, 1) (D)</p> Signup and view all the answers

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