Gr 11 Math Term 2 Test
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Questions and Answers

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

  • (y - y1) / (x - x1) = (y2 - y1) / (x2 - x1) (correct)
  • y - y1 = m(x - x1)
  • y - y1 = (y2 - y1) / (x2 - x1)
  • y = mx + c

    • What is the definition of the gradient of a line?

  • The x-intercept of the line
  • The y-intercept of the line
  • Rise over run (correct)
  • Run over rise

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

  • To find the equation of a line given its gradient and a point on the line (correct)
  • To find the y-intercept of a line
  • To find the x-intercept of a line
  • To find the gradient of a line

    • What is the standard form of the straight line equation?

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

    What information is required to use the two-point form of a straight line equation?

    <p>Two points on the line</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

    What is the relationship between the gradient-point form and the two-point form of a straight line equation?

    <p>The gradient-point form is derived from the two-point form</p> Signup and view all the answers

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

    <p>It is easier to find the y-intercept</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 relationship between the gradient and the y-intercept of a line?

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

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

    <p>-30°</p> Signup and view all the answers

    What is the equation form used when given two points on a line?

    <p>Two-Point Form</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 characteristic of parallel lines?

    <p>Same gradient but different y-intercepts</p> Signup and view all the answers

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

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

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

    <p>The gradient is the tangent of the inclination</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 characteristic of a vertical line?

    <p>Gradient is undefined</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 relationship between the gradients of two perpendicular lines?

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

    What is the effect of q on the graph of y = ax^2 + q?

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

    What is the effect of a on the graph of y = ax^2 + q?

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

    What is the domain of the function f(x) = ax^2 + q?

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

    What is the range of the function f(x) = ax^2 + q when a > 0?

    <p>{y : y ≥ q, y ∈ ℝ}</p> Signup and view all the answers

    What is the equation of the axis of symmetry of the graph of y = a(x + p)^2 + q?

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

    What is the effect of p on the graph of y = a(x + p)^2 + q?

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

    What is the condition for the graph of y = ax^2 + q to be a 'frown'?

    <p>a &lt; 0</p> Signup and view all the answers

    What happens to the graph of y = ax^2 + q when a = 0?

    <p>It becomes a horizontal line</p> Signup and view all the answers

    What is the range of a quadratic function when a < 0?

    <p>{y : y ≤ q, y ∈ ℝ}</p> Signup and view all the answers

    How do you find the y-intercept of a quadratic function?

    <p>Set x = 0 and solve for y</p> Signup and view all the answers

    What is the turning point of the quadratic function f(x) = a(x + p)^2 + q?

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

    What is the axis of symmetry of the quadratic function f(x) = a(x + p)^2 + q?

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

    How do you shift the graph of a quadratic function m units to the right?

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

    What is the formula to find the average gradient of a curve between two points?

    <p>Gradient = (y_A - y_C) / (x_A - x_C)</p> Signup and view all the answers

    What is the general form of a hyperbolic function?

    <p>y = a/x + q</p> Signup and view all the answers

    What is the effect of q on the graph of a hyperbolic function?

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

    What is the effect of a on the shape of a hyperbolic function?

    <p>It changes the shape and quadrants</p> Signup and view all the answers

    What is the vertical asymptote of a hyperbolic function?

    <p>The line x = 0</p> Signup and view all the answers

    What is the period of the function y = sinθ?

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

    What is the effect of q on the graph of y = asinθ + q?

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

    What is the maximum value of the function y = sinθ?

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

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

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

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

    <p>The period decreases</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 period of the function y = cosθ?

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

    What is the y-intercept of the function y = cosθ?

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

    What is the effect of a on the amplitude of the function y = acosθ?

    <p>The amplitude increases</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 period of the tangent function?

    <p>180°</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 range of the tangent function?

    <p>All real numbers</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 formula for the area of a circle?

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

    What is the formula for the area of a triangle?

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

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

    <p>Horizontal shift</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 circumference of a circle?

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

    What is the effect of a change in parameter p on the graph of y = a/(x + p) + q?

    <p>A horizontal shift only</p> Signup and view all the answers

    What is the equation of the vertical asymptote of y = a/(x + p) + q?

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

    What is the effect of a change in parameter q on the graph of y = a/(x + p) + q?

    <p>A vertical shift</p> Signup and view all the answers

    What is the equation of the horizontal asymptote of y = a/(x + p) + q?

    <p>y = q</p> Signup and view all the answers

    What is the point of intersection of the axes of symmetry of y = a/(x + p) + q?

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

    What is the effect of a change in parameter a on the graph of y = ab^x + q?

    <p>A change in the shape of the graph</p> Signup and view all the answers

    What is the effect of a change in parameter p on the graph of y = ab^(x + p) + q?

    <p>A horizontal shift</p> Signup and view all the answers

    What is the domain of y = ab^(x + p) + q?

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

    What is the range of y = ab^(x + p) + q when a > 0?

    <p>{y: y &gt; q, y ∈ ℝ}</p> Signup and view all the answers

    What is the horizontal asymptote of y = ab^(x + p) + q?

    <p>y = q</p> Signup and view all the answers

    What is the total area of the exposed or outer surfaces of a prism?

    <p>Surface area</p> Signup and view all the answers

    How many rectangles are there in a rectangular prism unfolded into a net?

    <p>6</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 cylinder?

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

    What is the formula for the volume of a sphere?

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

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

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

    What happens to the surface area and volume when one or more dimensions of a prism or cylinder is 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 volume of a square pyramid?

    <p>1/3 × b^2 × 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_b + 3h_s)</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 formula for the surface area of a right prism?

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

    If we multiply all three dimensions of a rectangular prism by a constant factor k, what is the effect on the volume?

    <p>The volume 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

    If we multiply one dimension of a rectangular prism by a constant factor k, what is the effect on the volume?

    <p>The volume scales by k</p> Signup and view all the answers

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

    <p>1/2lhH</p> Signup and view all the answers

    If we multiply two dimensions of a rectangular prism by a constant factor k, what is the effect on the volume?

    <p>The volume scales by k^2</p> Signup and view all the answers

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

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

    If we multiply all three dimensions of a rectangular prism by a constant factor k, what is the effect on the surface area?

    <p>The surface area 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 formula for the surface area of a triangular pyramid?

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

    In a cyclic quadrilateral, what can be said about the opposite angles?

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

    What is the relationship between the exterior angle of a cyclic quadrilateral and the interior opposite angle?

    <p>They are equal</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 can be said 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 angle at the center of a circle when subtended by a chord?

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

    What is the relationship between equal chords of a circle?

    <p>They subtend equal angles at the center</p> Signup and view all the answers

    What is the relationship between a diameter and the circle?

    <p>It subtends a right angle on the circle</p> Signup and view all the answers

    When a line segment subtends equal angles on the same side, what can be said about the four points?

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

    Which equation form is used when the gradient and a point on the line are known?

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

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

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

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

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

    What is the name of the form derived from the definition of gradient and the two-point form?

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

    What information is required to use the gradient-point form of a straight line equation?

    <p>The gradient and a point on the line</p> Signup and view all the answers

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

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

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

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

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

    <p>It is easier to graph the line</p> Signup and view all the answers

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

    <p>m = 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 equation form used when given a gradient and a point on a line?

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

    What is the angle of inclination for a vertical line?

    <p>90°</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 significance of the y-intercept in the equation of a line?

    <p>It represents the point where the line crosses the y-axis</p> Signup and view all the answers

    What is the formula for finding the equation of a line parallel to a given line and passing through a specific point?

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

    What is the characteristic of a line with a negative gradient?

    <p>The line falls from left to right</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) and θ is obtuse</p> Signup and view all the answers

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

    <p>To find the equation of a line given a gradient and a point</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

    Given a line with equation y = mx + c, what does the gradient m represent?

    <p>The rate of change of the line.</p> Signup and view all the answers

    What is the effect of a positive value of q on the graph of y = ax^2 + q?

    <p>The graph is shifted vertically upwards.</p> Signup and view all the answers

    What is the equation of the axis of symmetry of the graph of y = a(x + p)^2 + q?

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

    What is the range of the function f(x) = ax^2 + q when a < 0?

    <p>{y : y ≤ q, y ∈ ℝ}</p> Signup and view all the answers

    What is the effect of a negative value of p on the graph of y = a(x + p)^2 + q?

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

    What is the characteristic of the graph of y = ax^2 + q when a > 0?

    <p>It is a 'smile' shape.</p> Signup and view all the answers

    What is the effect of a on the shape of the graph of y = ax^2 + q?

    <p>It affects the shape of the graph.</p> Signup and view all the answers

    What is the turning point of the quadratic function f(x) = a(x + p)^2 + q?

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

    What is the domain of the function f(x) = ax^2 + q?

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

    What is the effect of p on the graph of y = a/(x + p) + q?

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

    What is the domain of the function y = a/(x + p) + q?

    <p>All real numbers except x = -p</p> Signup and view all the answers

    What is the horizontal asymptote of the function y = a/(x + p) + q?

    <p>The line y = q</p> Signup and view all the answers

    What are the axes of symmetry of the hyperbola y = a/(x + p) + q?

    <p>The lines x = -p and y = q</p> Signup and view all the answers

    What is the effect of q on the graph of y = ab^x + q?

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

    What is the effect of a on the graph of y = ab^x + q?

    <p>The graph is stretched or compressed</p> Signup and view all the answers

    What is the turning point of the function f(x) = a(x + p)^2 + q?

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

    What is the range of the function y = ab^x + q when a > 0?

    <p>{y: y &gt; q, y ∈ ℝ}</p> Signup and view all the answers

    What is the effect of p on the graph of y = ab^(x + p) + q?

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

    If a < 0, what is the range of the function f(x) = ax^2 + q?

    <p>{y : y ≤ q, y ∈ ℝ}</p> Signup and view all the answers

    How do you find the y-intercept of a quadratic function?

    <p>Set x = 0 and solve for y</p> Signup and view all the answers

    What is the domain of the function y = ab^(x + p) + q?

    <p>All real numbers</p> Signup and view all the answers

    What is the axis of symmetry of the function f(x) = a(x + p)^2 + q?

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

    What is the horizontal asymptote of the function y = ab^(x + p) + q?

    <p>The line y = q</p> Signup and view all the answers

    What is the effect of p on the graph of y = a(x + p)^2 + q?

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

    What is the average gradient of a curve between two points A(x_A, y_A) and C(x_C, y_C)?

    <p>y_C - y_A / x_C - x_A</p> Signup and view all the answers

    What is the effect of a > 0 on the graph of y = ax^2 + q?

    <p>The graph is a 'smile' shape</p> Signup and view all the answers

    What is the effect of q on the graph of a hyperbolic function?

    <p>Shifts the graph vertically upwards by q units</p> Signup and view all the answers

    What is the general form of a hyperbolic function?

    <p>y = a/x + q</p> Signup and view all the answers

    What is the vertical asymptote of a hyperbolic function?

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

    What is the amplitude of the function y = sinθ?

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

    What is the effect of a on the amplitude of the function y = acosθ?

    <p>The amplitude is multiplied by a</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 p on the graph of y = sin(θ + p)?

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

    What is the x-intercept of the function y = cosθ?

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

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

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

    What is the effect of q on the graph of y = acosθ + q?

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

    What is the maximum value of the function y = cosθ?

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

    What is the y-intercept of the function y = sinθ?

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

    What is the domain of the function y = coskθ?

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

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

    <p>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 equal to?

    <p>The angle which the chord subtends in the alternate segment</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

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

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

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

    <p>Equal</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 angle at the center of a circle when subtended by a chord?

    <p>Twice the angle on the circle</p> Signup and view all the answers

    What can be said about the angles on a circle subtended by the same arc?

    <p>They are equal</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 characteristic of a diameter in a circle?

    <p>It is the longest chord</p> Signup and view all the answers

    What is the effect on the surface area of a rectangular prism if its dimensions are multiplied by a factor k?

    <p>The surface area is multiplied by k^2</p> Signup and view all the answers

    What is the formula for the volume of a cylinder?

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

    What can be said about the perpendicular bisector of a chord?

    <p>It passes through the center of the circle</p> Signup and view all the answers

    What is the relationship between equal chords in a circle?

    <p>They subtend equal angles at the center</p> Signup and view all the answers

    What is the formula for the area of a circle?

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

    What is the formula for the volume of a 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(l + h_s)</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 total area of the exposed or outer surfaces of a prism?

    <p>Surface area</p> Signup and view all the answers

    What is the formula to calculate the volume of a triangular prism?

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

    What is the surface area of a sphere?

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

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

    <p>1/3 × π × r^2 × 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>They change according to the relationships between the original and new dimensions</p> Signup and view all the answers

    What is the formula to calculate the surface area of a rectangular prism?

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

    What is the formula to calculate the volume of a cube?

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

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

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

    What is the formula to calculate the volume of a sphere?

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

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

    <p>π × r × (r + 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)?

    <p>a &gt; 1: the graph is steeper, a &lt; 1: the graph is less steep</p> Signup and view all the answers

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

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

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

    <p>For p &gt; 0, the graph is shifted to the right, for p &lt; 0, the graph is shifted to the left</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>A = (a + b) × h</p> Signup and view all the answers

    What is the formula for the area of a circle?

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

    What is the formula for the circumference of a circle?

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

    What is the definition of a right prism?

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

    What is the characteristic of parallel lines?

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

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

    <p>To determine the equation of a line given its gradient and a point on the line</p> Signup and view all the answers

    Given a line with a gradient of 3 and passing through the point (2, 5), what is the equation of the line in gradient-intercept form?

    <p>y = 3x + 1</p> Signup and view all the answers

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

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

    Given two points (3, 4) and (5, 6), what is the equation of the line passing through these points in two-point form?

    <p>y - 4 = (6 - 4)/(5 - 3)(x - 3)</p> Signup and view all the answers

    What is the primary advantage of using the gradient-intercept form of a 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 equation of the line passing through the point (2, 3) with a gradient of -2?

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

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

    <p>The gradient is directly proportional to the steepness</p> Signup and view all the answers

    Given a line with a gradient of 1/2 and passing through the point (4, 3), what is the equation of the line in gradient-intercept form?

    <p>y = (1/2)x + 1</p> Signup and view all the answers

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

    <p>m = tan(θ) for 0° ≤ θ &lt; 180°</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

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

    What is the characteristic of parallel lines?

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

    What is the angle of inclination of a vertical line?

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

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

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

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

    <p>The angle of inclination is obtuse</p> Signup and view all the answers

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

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

    What is the range of the function f(x) = a(x+p)^2 + q if a < 0?

    <p>{y : y ≤ q, y ∈ ℝ}</p> Signup and view all the answers

    What is the effect of shifting the graph of y = a(x+p)^2 + q m units to the left?

    <p>Replace x with x + m.</p> Signup and view all the answers

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

    <p>m = 0</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 axis of symmetry of the graph of f(x) = a(x+p)^2 + q?

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

    What is the formula to find the average gradient of a curve between two points A(x_A, y_A) and C(x_C, y_C)?

    <p>Gradient = (y_C - y_A) / (x_C - x_A)</p> Signup and view all the answers

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

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

    What is the effect of q on the graph of a hyperbolic function y = a/x + q?

    <p>Vertical shift by q units.</p> Signup and view all the answers

    What is the effect of a on the shape of a hyperbolic function y = a/x + q if a > 1?

    <p>The graph moves further away from the axes.</p> Signup and view all the answers

    What is the effect of p on the graph of y = a(x + p)^2 + q?

    <p>A horizontal shift.</p> Signup and view all the answers

    What is the vertical asymptote of a hyperbolic function y = a/x + q?

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

    What is the characteristic of a quadratic function with a > 0?

    <p>A minimum turning point.</p> Signup and view all the answers

    What is the effect of q on the graph of y = ax^2 + q?

    <p>A vertical shift.</p> Signup and view all the answers

    What is the average gradient of a curve between points A(a, g(a)) and Q(a + h, g(a + h))?

    <p>(g(a + h) - g(a)) / h</p> Signup and view all the answers

    What is the axis of symmetry of the graph of y = a(x + p)^2 + q?

    <p>The line x = -p.</p> Signup and view all the answers

    What is the effect of h on the average gradient formula?

    <p>As h tends to 0, the average gradient approaches the gradient at point P.</p> Signup and view all the answers

    What is the general form of a hyperbolic function?

    <p>y = a/x + q</p> Signup and view all the answers

    What is the range of a quadratic function with a < 0?

    <p>{y : y ≤ q, y ∈ ℝ}.</p> Signup and view all the answers

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

    <p>The gradient is the tangent of the inclination.</p> Signup and view all the answers

    What is the effect of a on the shape of the graph of y = ax^2 + q?

    <p>It affects the steepness of the graph.</p> Signup and view all the answers

    What is the domain of the function f(x) = ax^2 + q?

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

    What is the turning point of the quadratic function f(x) = a(x + p)^2 + q?

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

    What is the effect of p on the graph of y = a/(x+p) + q?

    <p>A horizontal shift occurs</p> Signup and view all the answers

    What is the range of the function y = a/(x+p) + q?

    <p>All real numbers except y = q</p> Signup and view all the answers

    What is the vertical asymptote of the function y = a/(x+p) + q?

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

    What is the axes of symmetry of the function y = a/(x+p) + q?

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

    What is the effect of q on the graph of y = ab^x + q?

    <p>A vertical shift occurs</p> Signup and view all the answers

    What is the range of the function y = ab^(x+p) + q?

    <p>y &gt; q if a &gt; 0, y &lt; q if a &lt; 0</p> Signup and view all the answers

    What is the effect of p on the graph of y = ab^(x+p) + q?

    <p>A horizontal shift occurs</p> Signup and view all the answers

    What is the domain of the function y = ab^(x+p) + q?

    <p>All real numbers</p> Signup and view all the answers

    What is the effect of a on the shape of the function y = ab^(x+p) + q?

    <p>The graph is increasing if a &gt; 0, decreasing if a &lt; 0</p> Signup and view all the answers

    What is the horizontal asymptote of the function y = ab^(x+p) + q?

    <p>y = q</p> Signup and view all the answers

    What is the relationship between the interior opposite angle and the exterior angle 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>It is equal to the angle which the chord subtends in the alternate segment</p> Signup and view all the answers

    What is the relationship between 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 angle subtended by a diameter at the circumference of a circle?

    <p>Right angle</p> Signup and view all the answers

    What is the relationship between the angles subtended by the same arc at the center and on the circle?

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

    What is the condition for a line segment to be a perpendicular bisector of a chord?

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

    What is the relationship between the length of two tangents drawn from the same point to a circle?

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

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

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

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

    <p>The amplitude increases and the graph is not reflected about the x-axis.</p> Signup and view all the answers

    What is the period of the function y = sin(2θ)?

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

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

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

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

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

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

    <p>[-1, 1]</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 when k &gt; 1.</p> Signup and view all the answers

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

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

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

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

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

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

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

    <p>The amplitude increases and the graph is not reflected about the x-axis.</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 by a factor of k</p> Signup and view all the answers

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

    <p>All real numbers except multiples of 90 degrees</p> Signup and view all the answers

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

    <p>The graph is stretched vertically by a factor of a</p> Signup and view all the answers

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

    <p>The graph is shifted horizontally by p units</p> Signup and view all the answers

    What is the formula for the area of a trapezium?

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

    What is the formula for the area of a circle?

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

    What is the formula for the circumference of a circle?

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

    What is the definition of a right prism?

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

    What is the characteristic of a right prism?

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

    What is the formula for the area of a triangle?

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

    What is the surface area of a triangular prism unfolded into a net?

    <p>The sum of the areas of the two triangles and the three rectangles</p> Signup and view all the answers

    What is the formula for the volume of a cylinder?

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

    What is the surface area of a right cone?

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

    What is the volume of a sphere?

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

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

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

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

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

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

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

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

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

    What is the surface area of a rectangular prism unfolded into a net?

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

    If a rectangular prism has a length of 6 cm, a breadth of 4 cm, and a height of 3 cm, and its dimensions are multiplied by a factor of 2, what will be its new surface area?

    <p>176 cm²</p> Signup and view all the answers

    What is the effect of multiplying the dimensions of a rectangular prism by a factor of k on its volume?

    <p>The volume is multiplied by k³</p> Signup and view all the answers

    If a sphere has a radius of 4 cm, what is its surface area?

    <p>160π cm²</p> Signup and view all the answers

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

    <p>½ b (h_b + 3h_s)</p> Signup and view all the answers

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

    <p>⅓ πr²h</p> Signup and view all the answers

    What is the effect of multiplying the dimensions of a rectangular prism by a factor of k on its surface area?

    <p>The surface area is multiplied by k²</p> Signup and view all the answers

    What is the formula for the volume of a sphere?

    <p>⅔ πr³</p> Signup and view all the answers

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

    <p>2πr² + 2πrh</p> Signup and view all the answers

    What is the effect of multiplying the dimensions of a rectangular prism by a factor of k on its volume and surface area?

    <p>The volume is multiplied by k³, and the surface area is multiplied by k²</p> Signup and view all the answers

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

    <p>b² + 2bh_s</p> Signup and view all the answers

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

    <p>The two-point form is used when the gradient is known, while the gradient-point form is used when two points are known.</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>The gradient-intercept form is used when the equation of the line is in the form y = mx + c.</p> Signup and view all the answers

    What is the condition for two lines to be perpendicular?

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

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

    <p>It is easier to find the y-intercept of a line using the gradient-intercept form.</p> Signup and view all the answers

    What is the effect of a on the graph of y = ax^2 + q?

    <p>It affects the shape of the graph.</p> Signup and view all the answers

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

    <p>The gradient of a line is unrelated to the y-intercept of a line.</p> Signup and view all the answers

    What is the equation of the axis of symmetry of the graph of y = a(x + p)^2 + q?

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

    What is the range of the function f(x) = ax^2 + q when a > 0?

    <p>{y : y ≥ q, y ∈ ℝ}</p> Signup and view all the answers

    What is the equation of the line that passes through the points (2, 3) and (4, 5)?

    <p>y = x + 1</p> Signup and view all the answers

    What is the gradient of the line that passes through the points (1, 2) and (3, 4)?

    <p>2/3</p> Signup and view all the answers

    What is the effect of p on the graph of y = a(x + p)^2 + q?

    <p>It affects the horizontal shift of the graph.</p> Signup and view all the answers

    What is the condition for the graph of y = ax^2 + q to be a 'frown'?

    <p>a &lt; 0</p> Signup and view all the answers

    What is the y-intercept of the line that passes through the point (2, 3) with a gradient of 2?

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

    What is the equation of the line that passes through the point (1, 2) with a gradient of 1/2?

    <p>y = 1/2x + 3/2</p> Signup and view all the answers

    What happens to the graph of y = ax^2 + q when a = 0?

    <p>The graph becomes a horizontal line.</p> Signup and view all the answers

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

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

    What is the range of a quadratic function when a < 0?

    <p>{y : y ≤ q, y ∈ ℝ}</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 turning point of the quadratic function f(x) = a(x + p)^2 + q?

    <p>(-p, q)</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

    How do you shift the graph of a quadratic function m units to the right?

    <p>Replace x with x - m.</p> Signup and view all the answers

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

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

    What is the characteristic of a vertical line?

    <p>It has an undefined gradient</p> Signup and view all the answers

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

    <p>The gradient of a line has no relation to its y-intercept</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 inclination of a horizontal line?

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

    What is the tangent of the angle of inclination for a line with a gradient of 0.5?

    <p>0.5</p> Signup and view all the answers

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

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

    If the quadratic function f(x) = ax^2 + q has a range of {y : y ≤ q, y ∈ ℝ}, what is the sign of a?

    <p>a &lt; 0</p> Signup and view all the answers

    What is the x-coordinate of the turning point of the quadratic function f(x) = a(x + p)^2 + q?

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

    If the graph of a quadratic function is shifted horizontally by 2 units to the right, what is the new equation of the function?

    <p>f(x) = a(x - 2)^2 + q</p> Signup and view all the answers

    What is the equation of the axis of symmetry of the quadratic function f(x) = a(x + p)^2 + q?

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

    What is the effect of q on the graph of the quadratic function f(x) = ax^2 + q?

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

    What is the average gradient of the curve between two points A(x_A, y_A) and C(x_C, y_C)?

    <p>y_A - y_C / x_A - x_C</p> Signup and view all the answers

    What is the effect of a on the shape of the hyperbolic function f(x) = a/x + q?

    <p>The graph is closer to the axes for larger values of a</p> Signup and view all the answers

    What is the vertical asymptote of the hyperbolic function f(x) = a/x + q?

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

    What is the equation of the hyperbolic function that has a horizontal asymptote at y = 2 and a vertical asymptote at x = 0?

    <p>f(x) = 2/x + 2</p> Signup and view all the answers

    What is the effect of q on the graph of the hyperbolic function f(x) = a/x + q?

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

    What is the effect of a on the graph of y = \frac{a}{x + p} + q?

    <p>The graph is reflected about the horizontal asymptote.</p> Signup and view all the answers

    What is the equation of the vertical asymptote of the graph of y = \frac{a}{x + p} + q?

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

    What is the effect of p on the graph of y = ab^{x + p} + q?

    <p>The graph is shifted horizontally by p units.</p> Signup and view all the answers

    What is the range of the function y = ab^{x + p} + q when a > 0?

    <p>{y : y ∈ ℝ, y &gt; q}</p> Signup and view all the answers

    What is the axes of symmetry of the graph of y = \frac{a}{x + p} + q?

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

    What is the effect of q on the graph of y = ab^{x + p} + q?

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

    What is the domain of the function y = \frac{a}{x + p} + q?

    <p>{x : x ∈ ℝ, x ≠ -p}</p> Signup and view all the answers

    What is the equation of the horizontal asymptote of the graph of y = ab^{x + p} + q?

    <p>y = q</p> Signup and view all the answers

    What is the effect of a on the shape of the graph of y = ab^{x + p} + q?

    <p>The graph is reflected about the horizontal asymptote.</p> Signup and view all the answers

    What is the characteristic of the graph of y = \frac{a}{x + p} + q?

    <p>The graph is a hyperbola.</p> Signup and view all the answers

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

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

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

    <p>The graph is reflected about the x-axis.</p> Signup and view all the answers

    What is the period of the function y = cos(2θ)?

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

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

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

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

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

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

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

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

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

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

    <p>The graph is shifted horizontally by p units.</p> Signup and view all the answers

    What is the minimum value of the function y = a cos(θ)?

    <p>-a</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 formula to calculate the surface area of a triangular prism?

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

    What is the formula to calculate the volume of a cylinder?

    <p>πr^2h</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 formula to calculate the volume of a sphere?

    <p>4/3πr^3</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?

    <p>The surface area is multiplied by the square of the factor and the volume is multiplied by the cube of the factor.</p> Signup and view all the answers

    What is the formula to calculate 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>1/3(bh_bH)</p> Signup and view all the answers

    What is the formula to calculate the surface area of a cylinder?

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

    What is the formula to calculate the volume of a square pyramid?

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

    What is the formula to calculate the surface area of a sphere?

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

    What is the relationship between the opposite angles of a cyclic quadrilateral?

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

    If a tangent is drawn to a circle at a point, what is the angle between the tangent and the 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 relationship between the length of two tangents drawn from the same point outside a circle?

    <p>The tangents are equal in length.</p> Signup and view all the answers

    What is the relationship between the angle at the center of a circle and the angle subtended by the same arc?

    <p>The angle at the center is twice the angle subtended by the same arc.</p> Signup and view all the answers

    What is the relationship between the chords of a circle that subtend equal angles at the center?

    <p>The chords are equal in length.</p> Signup and view all the answers

    What is the relationship between the angles subtended by the same arc on the same side of a circle?

    <p>The angles are equal.</p> Signup and view all the answers

    What is the characteristic of a diameter of a circle?

    <p>It is a chord that passes through the center.</p> Signup and view all the answers

    What is the period of the function y = tan(2θ)?

    <p>90°/2</p> Signup and view all the answers

    What is the condition for four points to be cyclic?

    <p>When a line segment subtends equal angles on the same side.</p> Signup and view all the answers

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

    <p>It makes the branches steeper.</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(θ)?

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

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

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

    What is the area of a polygon with a base of 5 units and a height of 6 units?

    <p>30</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 characteristic of a right prism?

    <p>It has 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 trapezium?

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

    What is the characteristic of a cylinder?

    <p>It has a circle as its base and vertical sides perpendicular to the base.</p> Signup and view all the answers

    If a rectangular prism has dimensions of length 8, breadth 6, and height 4, what is the volume of the prism if all its dimensions are multiplied by a factor of 2?

    <p>768</p> Signup and view all the answers

    What is the surface area of a sphere with a radius of 4 cm?

    <p>256π</p> Signup and view all the answers

    A rectangular prism has dimensions of length 10, breadth 8, and height 6. If the length and breadth are multiplied by a factor of 3, what is the surface area of the new prism?

    <p>720</p> Signup and view all the answers

    What is the volume of a cone with a radius of 3 cm and a height of 6 cm?

    <p>54π</p> Signup and view all the answers

    If the dimensions of a rectangular prism are multiplied by a factor of 4, what is the scale factor of the surface area?

    <p>16</p> Signup and view all the answers

    What is the surface area of a triangular prism with base dimensions of 5 cm and 6 cm, and a height of 8 cm?

    <p>140</p> Signup and view all the answers

    If the radius of a sphere is doubled, what is the scale factor of the surface area?

    <p>8</p> Signup and view all the answers

    What is the volume of a cylinder with a radius of 2 cm and a height of 10 cm?

    <p>80π</p> Signup and view all the answers

    A triangular pyramid has a base area of 20 cm² and a height of 8 cm. What is the volume of the pyramid?

    <p>80</p> Signup and view all the answers

    What is the scale factor of the volume of a rectangular prism when its dimensions are multiplied by a factor of 3?

    <p>27</p> Signup and view all the answers

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