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Gr 11 Math June P2 (Mix)
384 Questions
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Gr 11 Math June P2 (Mix)

Created by
@GreatestTiger

Questions and Answers

What is the quotient identity of trigonometry?

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

    • What is the square identity of trigonometry?

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

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

  • sin θ (correct)
  • -cos θ
  • -sin θ
  • cos θ

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

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

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

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

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

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

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

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

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

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

    What is the condition for two lines to be parallel?

    <p>They have the same gradient but can have different y-intercepts.</p> Signup and view all the answers

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

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

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

    <p>m = tan(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 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 equation form used when the gradient and the y-intercept are known?

    <p>Gradient-Intercept Form</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

    What is the condition for two lines to be parallel?

    <p>m1 = m2</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)?

    <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 square identity, also known as the Pythagorean identity?

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

    What is the trigonometric relationship for acute angles?

    <p>tan(θ) is positive</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 a useful tip for proving trigonometric identities?

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

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

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

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

    <p>The gradients of the two lines must multiply to -1.</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 y = mx + c?

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

    What is the inclination of a horizontal line?

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

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

    <p>c = y_1 - mx_1</p> Signup and view all the answers

    What is the purpose of trigonometric identities?

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

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

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

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

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

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

    <p>θ = 180° + tan^(-1)(m)</p> Signup and view all the answers

    What is the measurement of the steepness of a line?

    <p>Gradient (m)</p> Signup and view all the answers

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

    <p>Gradient-Intercept Form</p> Signup and view all the answers

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

    <p>To directly read off the gradient.</p> Signup and view all the answers

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

    <p>To directly read off the gradient</p> Signup and view all the answers

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

    <p>y = mx + (y_1 - mx_1)</p> Signup and view all the answers

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

    <p>Two-Point Form, Gradient-Point Form, and Gradient-Intercept Form</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(360° - θ) in terms of cos(θ)?

    <p>cos(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

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

    <p>cos(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' if P is (x, y)?

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

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

    <p>(x, -y)</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(180° + θ) in terms of cos(θ)?

    <p>-cos(θ)</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 formula for the area of a triangle?

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

    What is the formula to calculate 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>4 × π × r^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 surface area of a sphere with radius r?

    <p>4πr^2</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 = cos(kθ)?

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

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

    <p>It is multiplied by k^3</p> Signup and view all the answers

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

    <p>Volume scales by k^3</p> Signup and view all the answers

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

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

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

    <p>The period decreases</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 definition of a chord in a circle?

    <p>A straight line joining the ends of an arc</p> Signup and view all the answers

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

    <p>1/2bh + 3bh_s</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 volume of a cylinder with radius r and height h?

    <p>πr^2h</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 happens to the surface area of a prism if one of its dimensions is multiplied by a constant factor k?

    <p>It is multiplied by k</p> Signup and view all the answers

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

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

    What is the definition of a segment in a circle?

    <p>A part of the circle that is cut off by a chord</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 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 to calculate the volume of a triangular pyramid?

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

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

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

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

    <p>The branches of the graph are steeper</p> Signup and view all the answers

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

    <p>1/3 × π × r^2 × h</p> Signup and view all the answers

    What is the volume of a sphere with radius r?

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

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

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

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

    <p>All real numbers except θ = 90°/k and θ = 270°/k</p> Signup and view all the answers

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

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

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

    <p>Twice the angle on the circle subtended by the same chord</p> Signup and view all the answers

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

    <p>A vertical shift upwards by q units</p> Signup and view all the answers

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

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

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

    <p>A reflection about the y-axis</p> Signup and view all the answers

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

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

    What is the domain of y = sin(θ)?

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

    What is the range of y = sin(θ)?

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

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

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

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

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

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

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

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

    <p>To evaluate trigonometric functions without using a calculator</p> Signup and view all the answers

    What is the first step in solving trigonometric equations?

    <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 circumference of a circle?

    <p>C = 2π r</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 formula for the area of a trapezium?

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

    What is the general solution to a trigonometric equation?

    <p>The solution in the interval [0°; 360°] and adding multiples of the period</p> Signup and view all the answers

    What is 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 unfolding a prism into a net?

    <p>To calculate the surface area</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 form of the straight line equation used when two points on the line are known?

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

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

    <p>The y-intercept of the line</p> Signup and view all the answers

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

    <p>To derive the gradient-intercept form of the straight line equation</p> Signup and view all the answers

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

    <p>It is used when the gradient and one point on the line are known</p> Signup and view all the answers

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

    <p>m and c are independent</p> Signup and view all the answers

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

    <p>Because it is the simplest form of the straight line equation</p> Signup and view all the answers

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

    <p>It is used when two points on the line are known</p> Signup and view all the answers

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

    <p>y - y1 = m(x - x1)</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

    If $P(x, y)$ 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 relationship between the gradient and inclination of a line?

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

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

    <p>$\sin heta$</p> Signup and view all the answers

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

    <p>150°</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 equation form used to find the equation of a line that is parallel to a given line and passes through a specific point?

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

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

    <p>$- an heta$</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?

    <p>Their gradients are negative reciprocals of each other</p> Signup and view all the answers

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

    <p>To directly read off the gradient</p> Signup and view all the answers

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

    <p>$\sin heta$</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 value of $ an ( heta)$ in terms of $\sin heta$ and $\cos heta$?

    <p>$rac{\sin heta}{\cos heta}$</p> Signup and view all the answers

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

    <p>Gradient-Intercept Form</p> Signup and view all the answers

    What is the trigonometric relationship for obtuse angles?

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

    What is the measurement of the steepness of a line?

    <p>Gradient</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

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

    <p>Gradient-Intercept Form</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 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 trigonometric identity derived from the Pythagorean theorem?

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

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

    <p>Point-slope form</p> Signup and view all the answers

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

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

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

    <p>To identify the gradient</p> Signup and view all the answers

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

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

    What is the measurement of the steepness of a line?

    <p>Gradient</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' if P is (x, y)?

    <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 θ?

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

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

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

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

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

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

    <p>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' if P is (x, y)?

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

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

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

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

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

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

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

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

    <p>The solution is found by adding multiples of the period to each answer.</p> Signup and view all the answers

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

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

    What is the formula for the area of a circle?

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

    What is the purpose of using the CAST diagram when 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 circumference of a circle?

    <p>Circumference = 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 formula for the area of a triangle?

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

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

    <p>To find the surface area.</p> Signup and view all the answers

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

    <p>It shifts the graph vertically upwards by q units.</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 graph of y = a sin θ?

    <p>It changes the amplitude of the graph by a factor of a.</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 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 graph of y = sin(θ + p)?

    <p>It shifts the graph horizontally to the right by p units.</p> Signup and view all the answers

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

    <p>(90°, 0)</p> Signup and view all the answers

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

    <p>a</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 period of the function y = cos θ?

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

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

    <p>(180°, -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>1/2bhH</p> Signup and view all the answers

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

    <p>The surface area increases by k and the volume increases by k^2</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 surface area of a triangular pyramid?

    <p>1/2bh + 3bh_s</p> Signup and view all the answers

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

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

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

    <p>b^2 + 4bh_s</p> Signup and view all the answers

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

    <p>The volume increases by k^3</p> Signup and view all the answers

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

    <p>2πr(r + 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) when k > 1?

    <p>The period decreases</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 formula for the area of a square?

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

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

    <p>The sum of the areas of all faces</p> Signup and view all the answers

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

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

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

    <p>$rac{1}{2}b imes h imes H$</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 a on the shape of the function y = a tan(θ) + q?

    <p>The branches of the graph are steeper</p> Signup and view all the answers

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

    <p>It increases by a factor of 27</p> Signup and view all the answers

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

    <p>$rac{1}{3} \pi r^2 imes H$</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

    What is the formula for the area of a trapezium?

    <p>$rac{1}{2} (a + b) imes h$</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 is shifted vertically by q units</p> Signup and view all the answers

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

    <p>Determined by setting f(θ) = 0 and solving for θ</p> Signup and view all the answers

    What is the theorem that states that a tangent to a circle is perpendicular to the radius drawn to the point of contact?

    <p>Tangent Perpendicular to Radius</p> Signup and view all the answers

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

    <p>60</p> Signup and view all the answers

    What is the definition of a segment in circle geometry?

    <p>A part of the circle cut off by a chord</p> Signup and view all the answers

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

    <p>$2 \pi r (r + h)$</p> Signup and view all the answers

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

    <p>y = (y_2 - y_1)/(x_2 - x_1) * (x - x_1) + y_1</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 y = mx + c?

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

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

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

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

    <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 the y-intercept are known?

    <p>Gradient-intercept form</p> Signup and view all the answers

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

    <p>y = mx - mx_1 + y_1</p> Signup and view all the answers

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

    <p>Two-point form, gradient-point form, gradient-intercept form</p> Signup and view all the answers

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

    <p>To use depending on the information provided in the problem</p> Signup and view all the answers

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

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

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

    <p>210°</p> Signup and view all the answers

    What is the equation form 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 condition for two lines to be parallel?

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

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

    <p>To find the equation of a line when given the gradient and one point on the line</p> Signup and view all the answers

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

    <p>To easily identify the gradient</p> Signup and view all the answers

    What is the trigonometric relationship for obtuse angles?

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

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

    <p>y = 2x + 5</p> Signup and view all the answers

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

    <p>36.9°</p> Signup and view all the answers

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

    <p>To ensure the lines are parallel</p> Signup and view all the answers

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

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

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

    <p>x^2 / r^2 + y^2 / r^2</p> Signup and view all the answers

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

    <p>y/x</p> Signup and view all the answers

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

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

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

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

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

    <p>P' = (-x, -y)</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 first step in determining the equation of a perpendicular line?

    <p>Identify the gradient of the given line.</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 form of the straight line equation is used when the gradient and one point on the line are known?

    <p>Point-slope form.</p> Signup and view all the answers

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

    <p>To easily identify the gradient.</p> Signup and view all the answers

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

    <p>The y-intercept.</p> Signup and view all the answers

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

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

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

    <p>sin²(θ) + cos²(θ) = 1.</p> Signup and view all the answers

    What is a useful tip for proving trigonometric identities?

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

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

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

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

    <p>sin(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' if P is (x, y)?

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

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

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

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

    <p>tan(θ)</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' if P is (x, y)?

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

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

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

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

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

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

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

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

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

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

    <p>cos(θ)</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>Area = 1/2 b × h</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 parallelogram?

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

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

    <p>Find the values of the angle in the interval [0°; 360°] and add multiples of the period to each answer.</p> Signup and view all the answers

    What is the formula for the area of a circle?

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

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

    <p>To find the values of the angle.</p> Signup and view all the answers

    What is the surface area of a prism or cylinder?

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

    What is the formula for the circumference of a circle?

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

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

    <p>To find the surface area of the prism or cylinder.</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 period of the function y = cos kθ?

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

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

    <p>$2(lb + lh + bh)$</p> Signup and view all the answers

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

    <p>The period decreases</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 formula for the volume of a right cone?

    <p>$rac{1}{3} \pi r^2 h$</p> Signup and view all the answers

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

    <p>It is multiplied by $k^2$</p> Signup and view all the answers

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

    <p>The graph shifts to the left</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 formula for the area of a trapezium?

    <p>$rac{1}{2} (a + b) h$</p> Signup and view all the answers

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

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

    What is the tangent to a circle?

    <p>A line that touches the circle at only one point</p> Signup and view all the answers

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

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

    What is the formula for the volume of a sphere?

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

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

    <p>$2 \pi r^2 + 2 \pi r h$</p> Signup and view all the answers

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

    <p>The graph shifts upwards</p> Signup and view all the answers

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

    <p>The graph becomes steeper</p> Signup and view all the answers

    What is the formula for the area of a circle?

    <p>$\pi r^2$</p> Signup and view all the answers

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

    <p>$rac{1}{2} b h H$</p> Signup and view all the answers

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

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

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

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

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

    <p>It shifts the graph vertically.</p> Signup and view all the answers

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

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

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

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

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

    <p>It reflects the graph about the y-axis.</p> Signup and view all the answers

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

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

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

    <p>It decreases the period of the function.</p> Signup and view all the answers

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

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

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

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

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

    <p>It shifts the graph to the left.</p> Signup and view all the answers

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

    <p>$\pi r (r + h)$</p> Signup and view all the answers

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

    <p>[0°, 360°]</p> Signup and view all the answers

    What is the formula for the volume of a cylinder?

    <p>$\pi r^2 imes h$</p> Signup and view all the answers

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

    <p>The volume increases by a factor of k^3</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

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

    <p>The surface area increases by a factor of k^2</p> Signup and view all the answers

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

    <p>$rac{1}{3}b^2 imes H$</p> Signup and view all the answers

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

    <p>$rac{1}{2}b (h_b + 3h_s)$</p> Signup and view all the answers

    What is the formula for the volume of a sphere?

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

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

    <p>$4\pi r^2$</p> Signup and view all the answers

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

    <p>The y-intercept of the line</p> Signup and view all the answers

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

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

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

    <p>To derive the gradient-intercept form of the straight line equation</p> Signup and view all the answers

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

    <p>It is used to find the y-intercept of a line when the gradient is given.</p> Signup and view all the answers

    What is the main difference between the two-point form and the gradient-point form of the straight line equation?

    <p>The two-point form requires two points, while the gradient-point form requires the gradient and one point.</p> Signup and view all the answers

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

    <p>Gradient-intercept form</p> Signup and view all the answers

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

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

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

    <p>150°</p> Signup and view all the answers

    Which of the following is true about two parallel lines?

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

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

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

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

    <p>The gradient of the line</p> Signup and view all the answers

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

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

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

    <p>Gradient-Intercept Form</p> Signup and view all the answers

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

    <p>They are negative reciprocals of each other</p> Signup and view all the answers

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

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

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

    <p>To find the equation of a parallel line</p> Signup and view all the answers

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

    <p>The lines are perpendicular.</p> Signup and view all the answers

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

    <p>y - 3 = 3/2(x - 2)</p> Signup and view all the answers

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

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

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

    <p>Determine the gradient of the given line.</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

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

    <p>y = -3/4x + 5</p> Signup and view all the answers

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

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

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

    <p>-rac{3}{4}</p> Signup and view all the answers

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

    <p>To easily identify the gradient.</p> Signup and view all the answers

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

    <p>The product of the gradients is -1.</p> Signup and view all the answers

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

    <p>-rac{2}{3}</p> Signup and view all the answers

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

    <p>rac{1}{2}</p> Signup and view all the answers

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

    <p>y - 4 = 2(x - 3)</p> Signup and view all the answers

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

    <p>-x</p> Signup and view all the answers

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

    <p>rac{3}{4}</p> Signup and view all the answers

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

    <p>-x</p> Signup and view all the answers

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

    <p>rac{2}{\sqrt{13}}</p> Signup and view all the answers

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

    <p>-rac{\sqrt{3}}{1}</p> Signup and view all the answers

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

    <p>-cos(θ)</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' if P is (x, y)?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    <p>tan(θ)</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 is calculated as 360°/k</p> Signup and view all the answers

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

    <p>A vertical shift upwards by q units</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 prism?

    <p>1/3 × base area × height</p> Signup and view all the answers

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

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

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

    <p>|a&gt;</p> Signup and view all the answers

    What is the general approach to solve trigonometric equations?

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

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

    <p>πr(r + h)</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 formula for the area of a parallelogram?

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

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

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

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

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

    What is the surface area of a prism or cylinder?

    <p>The sum of the areas of all its faces.</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 first step in solving a quadratic trigonometric equation?

    <p>Simplify the equation and determine the reference angle.</p> Signup and view all the answers

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

    <p>40π cm^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 surface area of a square pyramid with base side length b and slant height h?

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

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

    <p>To identify 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 trapezium?

    <p>A = (a + b) × h</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

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

    <p>100 cm^3</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 formula for the surface area of a triangular pyramid with base side length b and slant height h?

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

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

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

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

    <p>To identify the gradient and y-intercept of the line.</p> Signup and view all the answers

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

    <p>160π cm^2</p> Signup and view all the answers

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

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

    What is the formula for the area of a trapezium?

    <p>0.5 × (a + b) × h</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 difference between a right prism and a cylinder?

    <p>A right prism has a polygon as its base, while a cylinder has a circular base.</p> Signup and view all the answers

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

    <p>0.5 × b × h × H</p> Signup and view all the answers

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

    <p>It is multiplied by 8</p> Signup and view all the answers

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

    <p>60°</p> Signup and view all the answers

    What is the tangent-chord theorem?

    <p>The angle between a tangent and a chord is equal to the angle in the alternate segment.</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 sphere?

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

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

    <p>Perpendicular line from circle center bisects chord</p> Signup and view all the answers

    What is the formula for the area of a parallelogram?

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

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

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

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

    <p>The period is calculated as 360°/k</p> Signup and view all the answers

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

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

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

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

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

    <p>The domain of one branch is {θ : -90°/k &lt; θ &lt; 90°/k, θ ∈ ℝ}</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 if a &gt; 1 and less steep if 0 &lt; a &lt; 1</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 q on the graph of the function y = a tan(θ) + q?

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

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

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

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

    <p>The y-intercept is determined by setting θ = 0 and solving for f(θ)</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 by p units</p> Signup and view all the answers

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