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Gr 11 Math June P2 (Easy)
407 Questions
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Gr 11 Math June P2 (Easy)

Created by
@GreatestTiger

Questions and Answers

What is the equation of the line in the two-point form?

  • y - y_1 / x - x_1 = y_2 - y_1 / x_2 - x_1 (correct)
  • y = mx_1 + y_1
  • y = mx + c
  • y - y_1 = m(x - x_1)

    • What is the equation of the line in the gradient-point form?

  • y = mx_1 + y_1
  • y - y_1 = x - x_1
  • y - y_1 = m(x - x_1) (correct)
  • y = mx + c

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

  • y - y_1 = m(x - x_1)
  • y = mx + c (correct)
  • y = mx_1 + y_1
  • y - y_1 / x - x_1 = y_2 - y_1 / x_2 - x_1

    • When is the two-point form of the straight line equation used?

    <p>When two points on the line are known</p> Signup and view all the answers

    What is the value of c in the gradient-intercept form?

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

    What is the relationship between the gradient and the two-point form?

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

    What is the value of y when x = 0 in the gradient-intercept form?

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

    What is the name of the equation y = mx + c?

    <p>Standard Form</p> Signup and view all the answers

    What is the quotient identity in trigonometry?

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

    What is the value of sin² θ + cos² θ?

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

    What is the value of cos² θ in terms of sin θ?

    <p>1 - sin² 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 value of sin(180° + θ) in terms of θ?

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

    Why are the function values of 180° ± θ derived separately?

    <p>Because the points are symmetrical about the y-axis</p> Signup and view all the answers

    What is the measure of the steepness of a line?

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

    Which form 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 angle formed by a line with the positive x-axis?

    <p>Inclination (θ)</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 gradient of a vertical line?

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

    What is the angle of inclination for a horizontal line?

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

    How do you find the equation of a line that is parallel to a given line and passes through a specific point?

    <p>Use the point-slope form with the given point and the gradient of the given line</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 relationship between the gradient and inclination of a line for obtuse angles?

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

    What is the formula to adjust the angle of inclination for a line with a negative gradient?

    <p>θ = 180° + tan^(-1)(m)</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 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 shape of the base of a cylinder when it is unfolded into a net?

    <p>Two identical circles</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 the formula for the volume of a triangular prism?

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

    What should you do when proving trigonometric identities?

    <p>Change all trigonometric ratios to sine and cosine, and then simplify both sides of the equation.</p> Signup and view all the answers

    What should you do when finding the equation of a perpendicular line?

    <p>Identify the gradient of the given line, calculate the perpendicular gradient, and use the point-slope form.</p> Signup and view all the answers

    What is the surface area of a sphere?

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

    Why is tan θ undefined when cos θ = 0?

    <p>Because the cosine function is zero, making the tangent function undefined.</p> Signup and view all the answers

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

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

    What is the shape of a triangular prism when it is unfolded into a net?

    <p>Two triangles and three rectangles</p> Signup and view all the answers

    What is the purpose of trigonometric identities?

    <p>To simplify a given expression so that it contains only sine and cosine ratios.</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 should you do when a square root sign appears in a trigonometric identity?

    <p>Use the square identity to simplify the expression.</p> Signup and view all the answers

    What is the condition for two lines to be parallel?

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

    What happens to the surface area and volume of a prism or cylinder when one or more dimensions are multiplied by a constant factor?

    <p>They change according to the relationships between the original and new dimensions</p> Signup and view all the answers

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

    <p>1/2 × b(hb + 3hs)</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 shape of a cube when it is unfolded into a net?

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

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

    <p>To express trigonometric functions in terms of acute angles</p> Signup and view all the answers

    When solving trigonometric equations, what is the first step?

    <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 formula for the circumference of a circle?

    <p>Circumference = 2 × π × 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 parallelogram?

    <p>Area = b × h</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

    How do you calculate the surface area of a prism?

    <p>By calculating the area of each face and adding them together</p> Signup and view all the answers

    What is the purpose of finding the general solution in trigonometry?

    <p>To find all possible values of the angle that satisfy the equation</p> Signup and view all the answers

    What is the formula for the area of a square?

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

    What are the coordinates of P' if points P and P' are symmetrical about the origin and P is ($\sqrt{3}$, 1)?

    <p>(-$\sqrt{3}$, -1)</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

    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 cos(360° - θ)?

    <p>cos θ</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

    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 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(180° + θ)?

    <p>-cos θ</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 range of the function y = tan kθ?

    <p>(-∞, ∞)</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 effect of p > 0 on the graph of y = tan(θ + p)?

    <p>The graph shifts to the left by p.</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 y-intercept of the function y = tan kθ?

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

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

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

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

    <p>It is multiplied by k^3</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 triangle?

    <p>1/2(b × h)</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 circumference of a circle?

    <p>2πr</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

    If an arc subtends an angle at the center of a circle and at the circumference, what is the relationship between the two angles?

    <p>The angle at the center is twice the angle at the circumference</p> Signup and view all the answers

    What is the definition of a tangent to a circle?

    <p>A straight line that touches the circle at only one point on the circumference</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 relationship between opposite angles of a cyclic quadrilateral?

    <p>They are supplementary</p> Signup and view all the answers

    What is the angle between a tangent to a circle and a chord drawn from the point of contact?

    <p>The angle is equal to the angle subtended by the chord in the alternate segment</p> Signup and view all the answers

    What is the length of two tangents drawn from the same point outside a circle?

    <p>They are equal in length</p> Signup and view all the answers

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

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

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

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

    What is the period of the sine function?

    <p>360°</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</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 p on the graph of y = sin(θ + p)?

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

    What is the range of the sine function?

    <p>[-1, 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 q on the graph of y = a cos θ + q?

    <p>Vertical shift</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 effect of k on the period of the function y = cos kθ?

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

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

    <p>{θ : θ ∈ ℝ, θ ≠ 90°, 270°}</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 a on the graph of y = a tan θ + q?

    <p>Steeper branches</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 decreases</p> Signup and view all the answers

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

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

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

    <p>Horizontal shift to the right</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 definition of the constant 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 of the following is a characteristic of the gradient–intercept form of the straight line equation?

    <p>It is used when the gradient and y-intercept are known</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

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

    <p>Gradient–Point Form</p> Signup and view all the answers

    What is the relationship between the gradient and the y-intercept in the gradient–intercept form of the straight line equation?

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

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

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

    What is the fundamental identity that relates the tangent function to the sine and cosine functions?

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

    What is the value of sin² θ + cos² θ?

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

    What is the value of cos² θ in terms of sin θ?

    <p>1 - sin² 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 relationship between the gradient and the angle of inclination for a line?

    <p>m = tan(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 inclination of a vertical line?

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

    What is the formula to adjust the angle of inclination for a line with a negative gradient?

    <p>θ = 180° + tan⁻¹(m)</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>m₁ = m₂</p> Signup and view all the answers

    What is the purpose of reduction formulae in trigonometry?

    <p>To derive function values of 180° ± θ</p> Signup and view all the answers

    Why are the function values of 180° ± θ derived separately?

    <p>Because they have different values</p> Signup and view all the answers

    What is the equation of a line that is parallel to a given line with gradient m and passes through a specific point (x₁, y₁)?

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

    What is the value of tan(θ) for an acute angle?

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

    What is the value of tan(θ) for an obtuse angle?

    <p>Negative</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 condition for two lines to be perpendicular?

    <p>They have gradients that multiply to -1</p> Signup and view all the answers

    What is the purpose of trigonometric identities?

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

    What is the angle of inclination for a horizontal line?

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

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

    <p>y - y1 = (-1/m)(x - x1)</p> Signup and view all the answers

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

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

    What is the value of sin² θ + cos² θ?

    <p>1</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

    Why is tan θ undefined when cos θ = 0?

    <p>Because the tangent function is undefined when the cosine is zero</p> Signup and view all the answers

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

    <p>-1/m</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 quotient identity in trigonometry?

    <p>tan θ = sin θ / cos θ</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

    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 first step in proving trigonometric identities?

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

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

    <p>They multiply to -1</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(90° + θ) in terms of θ?

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

    What is the purpose of the square identity?

    <p>To simplify trigonometric expressions and solve equations</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 sin(360° + θ) in terms of θ?

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

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

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

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

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

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

    <p>θ ∈ ℝ, θ ≠ -90°/k and θ ≠ 90°/k</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 y-intercept of the function y = tan kθ?

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

    What happens to the graph of the tangent function when p > 0 in the function y = tan(θ + p)?

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

    What is the effect of p on the graph of the tangent function when p < 0 in the function y = tan(θ + p)?

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

    What are the asymptotes of the function y = tan kθ?

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

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

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

    What is the first step when 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 shape of a cylinder when it is unfolded into a net?

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

    What is the purpose of the CAST diagram in trigonometry?

    <p>To determine the quadrants of a trigonometric function</p> Signup and view all the answers

    How do you find the values of the angle when solving trigonometric equations?

    <p>Use reduction formulae to find the values of the angle</p> Signup and view all the answers

    What is the shape of a right prism when it is unfolded into a net?

    <p>A polygon</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 area of a trapezium?

    <p>A = (1/2) (a + b) × h</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 shape of a cylinder when it is unfolded into a net?

    <p>Two identical circles and a rectangle</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 triangular prism?

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

    What happens to the surface area and volume of a prism or cylinder when one or more dimensions are multiplied by a constant factor?

    <p>The surface area and volume change according to the relationships between the original and new dimensions</p> Signup and view all the answers

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

    <p>1/3 × πr² × H</p> Signup and view all the answers

    What is the shape of the base of a triangular prism when it is unfolded into a net?

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

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

    <p>b² + 4bh_s</p> Signup and view all the answers

    What is the formula for the volume of a sphere?

    <p>4/3 × πr³</p> Signup and view all the answers

    What is the shape of a cube when it is unfolded into a net?

    <p>Six identical squares</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

    If a prism has a base area of 10 cm² and a height of 5 cm, what is its volume?

    <p>50 cm³</p> Signup and view all the answers

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

    <p>4 × π × r²</p> Signup and view all the answers

    What happens to the volume of a prism or cylinder when one or more dimensions are multiplied by a constant factor k?

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

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

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

    What is the formula for the volume of a cylinder?

    <p>π × r² × h</p> Signup and view all the answers

    What is the formula for the area of a circle?

    <p>π × r²</p> Signup and view all the answers

    What happens to the surface area of a prism or cylinder when one or more dimensions are multiplied by a constant factor k?

    <p>It scales by k²</p> Signup and view all the answers

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

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

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

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

    What is true about the opposite angles of a cyclic quadrilateral?

    <p>They are supplementary</p> Signup and view all the answers

    What is the angle between a tangent to a circle and a chord drawn from the point of contact?

    <p>The angle which the chord subtends in the alternate segment</p> Signup and view all the answers

    What is true about two tangents drawn from the same point outside a circle?

    <p>They are equal in length</p> Signup and view all the answers

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

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

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

    <p>It is calculated as 360°/k</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</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 domain of the function y = sin kθ?

    <p>All real numbers</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 shape of the function y = a cos θ?

    <p>It increases the amplitude</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 = 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>It shifts the graph vertically</p> Signup and view all the answers

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

    <p>{θ: 0° ≤ θ ≤ 360°}</p> Signup and view all the answers

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

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

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

    <p>{f(θ): f(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 + q?

    <p>It increases the steepness of the branches</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 quotient identity in trigonometry?

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

    What is the value of cos² θ in terms of sin θ?

    <p>1 - sin² 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

    Why are the function values of 180° ± θ derived separately?

    <p>Because of the symmetry of the unit circle about the y-axis</p> Signup and view all the answers

    What is the purpose of reduction formulae in trigonometry?

    <p>To simplify trigonometric functions with arguments of 180° ± 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

    Why is tan θ undefined when cos θ = 0?

    <p>Because the tangent function is undefined when the cosine function is zero</p> Signup and view all the answers

    What is the primary purpose of reduction formulae in trigonometry?

    <p>To simplify trigonometric functions with arguments of 90° ± θ and 360° ± θ</p> Signup and view all the answers

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

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

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

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

    When is the two-point form of the straight line equation used?

    <p>When two points on the line are known</p> Signup and view all the answers

    What is the name of the equation y = mx + c?

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

    What is the gradient of a line that is parallel to a given line?

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

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

    <p>To find the equation of a line when two points on the line are known</p> Signup and view all the answers

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

    <p>The gradient is the slope of the line and the y-intercept is the point where the line crosses the y-axis</p> Signup and view all the answers

    What is the difference between the gradient-point form and the gradient-intercept form?

    <p>The gradient-point form is used when the gradient and the coordinates of one point on the line are known, while the gradient-intercept form is used when the gradient and the y-intercept are known</p> Signup and view all the answers

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

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

    What is the angle of inclination for a vertical line?

    <p>Undefined</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 condition for two lines to be parallel?

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

    What is the formula to adjust the angle of inclination for a line with a negative gradient?

    <p>θ = 180° + tan^(-1)(m)</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 x-axis, what are the coordinates of P'?

    <p>(x, -y)</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 relationship between the gradient and the inclination of a line for obtuse angles?

    <p>m = tan(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 cos(90° - θ) in terms of θ?

    <p>sin θ</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 value of sin(360° + θ) in terms of θ?

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

    What is the measure of the steepness of a line?

    <p>Gradient</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 formula for the gradient of a line?

    <p>m = Δy/Δx</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 purpose of the trigonometric relationship between the gradient and inclination of a line?

    <p>To find the inclination of a line</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 purpose of reduction formulae in trigonometry?

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

    What is the condition for two lines to be perpendicular?

    <p>They have gradients that multiply to -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 equation of a line that is perpendicular 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 θ 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 should you do when proving trigonometric identities?

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

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

    <p>-1/m</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 = mx + c, where m is the same as the given line</p> Signup and view all the answers

    Why is tan θ undefined when cos θ = 0?

    <p>Because the tangent function is undefined when the denominator is zero.</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 domain of one branch 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 range of the function y = tan kθ?

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

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

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

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

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

    What happens to the graph of y = tan kθ when p > 0 is added to θ?

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

    What happens to the graph of y = tan kθ when p < 0 is added to θ?

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

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

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

    What is the first step when solving trigonometric equations?

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

    What is the shape of the base of a cylinder when it is unfolded into a net?

    <p>Two identical circles</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 volume of a rectangular prism?

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

    What happens to the surface area and volume of a prism or cylinder when one or more dimensions are multiplied by a constant factor?

    <p>The surface area and volume change according to the relationships between the original and new dimensions</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 surface area of a sphere?

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

    What is the shape of the base of a right prism when it is unfolded into a net?

    <p>Polygon</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 shape of a triangular prism when it is unfolded into a net?

    <p>Two triangles and three rectangles</p> Signup and view all the answers

    How do you find the general solution of a trigonometric equation?

    <p>Find the angles in the interval [0°; 360°] that satisfy the equation and add multiples of the period to each answer</p> Signup and view all the answers

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

    <p>1/3 × πr² × H</p> Signup and view all the answers

    What is the formula for the area of a rectangle?

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

    What is the shape of a cube when it is unfolded into a net?

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

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

    <p>SA = Σ(area of each face)</p> Signup and view all the answers

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

    <p>1/2 × b × h × 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 formula for the volume of a sphere?

    <p>4/3 × πr³</p> Signup and view all the answers

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

    <p>b² + 3bh</p> Signup and view all the answers

    What is the effect on the volume of a rectangular prism when all three dimensions are multiplied by a factor k?

    <p>It scales by k^3</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 effect on the surface area of a rectangular prism when one dimension is multiplied by a factor k?

    <p>It scales by k</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 is the formula for the area of a circle?

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

    What is the effect on the volume of a rectangular prism when two dimensions are multiplied by a factor k?

    <p>It scales by k^2</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 rectangular prism?

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

    What is the effect on the surface area of a rectangular prism when all three dimensions are multiplied by a factor k?

    <p>It scales by k^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 period of the function y = cos θ?

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

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

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

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

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

    What is the angle between a tangent to a circle and a chord drawn from the point of contact?

    <p>Equal to the angle which the chord subtends in the alternate segment</p> Signup and view all the answers

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

    <p>Amplitude change</p> Signup and view all the answers

    What is the period of the sine function?

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

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

    <p>Vertical shift</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 period of the function y = tan θ?

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

    What is the range of the sine function?

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

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

    <p>Changes the amplitude</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 a on the shape of the graph of y = a tan θ?

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

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

    <p>The graph is shifted horizontally to the left</p> Signup and view all the answers

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

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

    What is the perpendicular bisector of a chord?

    <p>A line segment bisecting a chord and passing through the center of a circle</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 effect of p on the graph of y = sin(θ + p)?

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

    What is the diameter of a circle?

    <p>The longest chord</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 sin²(θ) + cos²(θ)?

    <p>1</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 sin(180° + θ) in terms of θ?

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

    Why are the function values of 180° ± θ derived separately?

    <p>Because of the symmetry about the y-axis</p> Signup and view all the answers

    What is the purpose of the reduction formulae in trigonometry?

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

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

    <p>1 - cos²(θ)</p> Signup and view all the answers

    What is the advantage of using the quotient identity in trigonometry?

    <p>It relates tangent to sine and cosine</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>One is used when two points are known and the other is used when the gradient and one point are known.</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

    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 relationship between the gradient and the y-intercept of a line in the gradient-intercept form?

    <p>The gradient and y-intercept are independent of each other.</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 formula for the gradient-point form of the straight line equation?

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

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

    <p>One is used when the gradient and one point are known, and the other is used when the gradient and the y-intercept are known.</p> Signup and view all the answers

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

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

    What is the measure of the steepness of a line?

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

    Which of the following is true for obtuse angles?

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

    What is the special case for the angle of inclination of a horizontal line?

    <p>θ = 0°</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 formula to adjust the angle of inclination for a line with a negative gradient?

    <p>θ = 180° + tan⁻¹(m)</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 special case for the gradient of a vertical line?

    <p>m is undefined</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 relationship between the gradient and inclination of a line for acute angles?

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

    What is the name of the equation that represents the relationship between the gradient and inclination of a line?

    <p>Trigonometric relationship</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 formula for 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 purpose of using the point-slope form of a line when finding the equation of a perpendicular line?

    <p>To use the gradient and a point to find the equation of the perpendicular line.</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 the first step when proving trigonometric identities?

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

    What is the condition for two lines to be parallel?

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

    What is the purpose of the gradient-intercept form of a line?

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

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

    <p>Because the denominator of the tangent function is zero.</p> Signup and view all the answers

    What is the formula for finding the gradient of a perpendicular line?

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

    What is the importance of the equation form when finding the equation of a perpendicular line?

    <p>It is essential to ensure the given line's equation is in the gradient-intercept form.</p> Signup and view all the answers

    What are the coordinates of point P' when points P and P' are symmetrical about the origin?

    <p>(-x, -y)</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(360° - θ) in terms of θ?

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

    What are the coordinates of point P' when points P and P' are symmetrical about the x-axis?

    <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 cos(90° - θ) in terms of θ?

    <p>sin(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 tan(180° + θ) in terms of θ?

    <p>tan(θ)</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(360° + θ) in terms of θ?

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

    What is the shape of the base of a cylinder when it is unfolded into a net?

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

    What happens to the surface area and volume of a prism or cylinder when one or more dimensions are multiplied by a constant factor?

    <p>They increase by a factor of the square of the constant</p> Signup and view all the answers

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

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

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

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

    What is the shape of a triangular prism when it is unfolded into a net?

    <p>Two triangles and three rectangles</p> Signup and view all the answers

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

    <p>1/2 × b × h × H</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 purpose of reduction formulae and co-function rules in trigonometry?

    <p>To express trigonometric functions in terms of acute angles, facilitating simplification and evaluation</p> Signup and view all the answers

    When solving trigonometric equations, what is the first step?

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

    What is the shape of a cube when it is unfolded into a net?

    <p>Six identical squares</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 = 2 × π × r</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 shape of a right prism when it is unfolded into a net?

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

    What is the primary 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 surface area of a prism or cylinder?

    <p>SA is calculated by finding the area of each face and adding them together</p> Signup and view all the answers

    What is the purpose of trigonometric equations?

    <p>To find the values of angles that satisfy the equation</p> Signup and view all the answers

    What is the condition for a trigonometric equation to have a solution?

    <p>The equation must be given a specific interval</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 q on the graph of y = a cos θ + q?

    <p>Vertical shift</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 effect of p on the graph of y = cos(θ + p)?

    <p>Horizontal shift</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 y = a tan θ + q?

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

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

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

    In a cyclic quadrilateral, what is the relationship between the opposite angles?

    <p>They are supplementary</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 angle between a tangent to a circle and a chord drawn from the point of contact equal to?

    <p>The angle which the chord subtends in the alternate segment</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 graph of y = a sin(θ) + q?

    <p>It causes a vertical shift</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 a on the graph of y = a sin(θ)?

    <p>It changes the amplitude</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 angle formed by a line with the positive x-axis?

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

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

    <p>It causes a horizontal shift</p> Signup and view all the answers

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

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

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

    <p>All real values of θ except θ = -90°/k and θ = 90°/k</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 y-intercept of the function y = tan(kθ)?

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

    What happens to the graph of the function y = tan(θ) when p is added to θ, resulting in y = tan(θ + p)?

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

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

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

    What are the asymptotes of the function y = tan(kθ)?

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

    What is the effect of multiplying all three dimensions of a prism or cylinder by a constant factor k on its volume?

    <p>It is scaled by k³</p> Signup and view all the answers

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

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

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

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

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

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

    What is the effect of multiplying one dimension of a prism or cylinder by a constant factor k on its surface area?

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

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

    <p>⅓ × b² × H</p> Signup and view all the answers

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

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

    What is the formula for the circumference of a circle?

    <p>2 × πr</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 formula for the volume of a right cone?

    <p>⅓ × πr² × H</p> Signup and view all the answers

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