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</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</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)</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</p> Signup and view all the answers

    What is the standard form of the straight line equation?

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

    What is the condition for two lines to be perpendicular?

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

    What is the inclination of a vertical line?

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

    What is the quotient identity for tangent?

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

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

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

    What is the condition for two lines to be parallel?

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

    What is the square identity in trigonometry?

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

    Which of the following is a fundamental trigonometric identity?

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

    What is the condition for parallel lines?

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

    What is the gradient of a horizontal line?

    <p>0</p> Signup and view all the answers

    What is the purpose of trigonometric identities?

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

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

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

    What is the formula to calculate the perpendicular gradient?

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

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

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

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

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

    What is the common technique used to prove trigonometric identities?

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

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

    <p>45°</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)</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</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</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)</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)</p> Signup and view all the answers

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

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

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

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

    What is the value of tan(-θ)?

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

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

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

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

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

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

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

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

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

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

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

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

    <p>1</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.</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.</p> Signup and view all the answers

    What is the formula for the area of a triangle?

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

    What is the formula for the area of a circle?

    <p>π r^2</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.</p> Signup and view all the answers

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

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

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

    <p>Six identical squares</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.</p> Signup and view all the answers

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

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

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

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

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

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

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

    <p>a</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    What is the formula for the area of a trapezium?

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

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

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

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

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

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

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

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

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

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

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

    What is the formula for the volume of a cylinder?

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

    What is the formula for the area of a circle?

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

    What is the formula for the volume of a sphere?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    What is the condition for two lines to be parallel?

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

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

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

    What is the purpose of trigonometric identities?

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

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

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

    What is the square identity in trigonometry?

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

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

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

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

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

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

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

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

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

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

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

    What is the formula for the area of a triangle?

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

    What is the formula for the area of a circle?

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

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

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

    What is the formula for the area of a trapezium?

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

    What is the formula for the circumference of a circle?

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

    What is the formula for the area of a rectangle?

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

    What is the formula for the area of a square?

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

    What is the formula for the volume of a cylinder?

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

    What is the formula for the area of a square?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    <p>Tangent</p> Signup and view all the answers

    What is the formula for the area of a trapezium?

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

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

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

    What is the formula for the volume of a cylinder?

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

    What is the formula for the volume of a sphere?

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

    What is the formula for the area of a circle?

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

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

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

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

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

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

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

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

    <p>|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</p> Signup and view all the answers

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

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

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

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

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

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

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

    <p>[-1, 1]</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</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}</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</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

    <p>1</p> Signup and view all the answers

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

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

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

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

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

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

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

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

    What is the condition for two lines to be parallel?

    <p>m1 = m2</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</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.</p> Signup and view all the answers

    What is the gradient of a horizontal line?

    <p>0</p> Signup and view all the answers

    What is the quotient identity for tangent?

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

    What is the inclination of a vertical line?

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

    What is the square identity in trigonometry?

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

    What is the purpose of trigonometric identities?

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

    What is the formula to calculate the perpendicular gradient?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    <p>360°/k</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.</p> Signup and view all the answers

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

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

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

    <p>[-1, 1]</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.</p> Signup and view all the answers

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

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

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

    <p>a</p> Signup and view all the answers

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

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

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

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

    What is the formula for the area of a triangle?

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

    What is the formula for the area of a circle?

    <p>πr²</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</p> Signup and view all the answers

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

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

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

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

    What is the formula for the volume of a cylinder?

    <p>πr² × h</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</p> Signup and view all the answers

    What is the formula for the area of a trapezium?

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

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

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

    What is the period of y = cos kθ?

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

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

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

    What is the range of y = cos kθ?

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

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

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

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

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

    What is the period of y = tan kθ?

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

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

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

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

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

    What is the formula for the volume of a cylinder?

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

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

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

    What is the general approach to solve trigonometric equations?

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

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

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

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

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

    What is the formula for the area of a trapezium?

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

    What is the formula for the area of a circle?

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

    What is the advantage of using reduction formulae in trigonometry?

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

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

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

    What is the formula for the circumference of a circle?

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

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

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

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

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

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

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

    What is the square identity in trigonometry?

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

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

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

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

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

    What is the purpose of trigonometric identities?

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

    What is the condition for two lines to be parallel?

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

    What is the quotient identity for tangent?

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

    What is the formula to calculate the perpendicular gradient?

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

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

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

    What is the square identity in trigonometry?

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

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

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

    What is the inclination of a vertical line?

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

    What is the condition for two lines to be parallel?

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

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

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

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

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

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

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

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

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

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

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

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

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

    What is the purpose of the reduction formulae in trigonometry?

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

    What is the formula for the area of a trapezium?

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

    What is the formula for the area of a circle?

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

    What is the formula for the circumference of a circle?

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

    What is the formula for the volume of a cylinder?

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

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

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

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

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

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

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

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

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

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

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

    What is the period of y = cos kθ?

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

    What is the domain of y = cos kθ?

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

    What is the period of y = tan kθ?

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

    What is the domain of y = tan kθ?

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

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

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

    What is the formula for the area of a square?

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

    What is the formula for the volume of a cylinder?

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

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

    <p>Tangent</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.</p> Signup and view all the answers

    What is the formula for the volume of a sphere?

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

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

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

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

    <p>1/3 × bh × H</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.</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</p> Signup and view all the answers

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

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

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

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

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

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

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