DP Mathematics: Applications and Interpretation Questionbank

SL 2.3—Graphing
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[N/A]Directly related questions
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21M.2.SL.TZ2.5c:
Sketch the graph of V=300√3x-94x3, for 0≤x≤16.
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21N.2.SL.TZ0.3a.i:
maximum value of h.
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21N.2.SL.TZ0.3c.ii:
Find the period of the function.
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21N.2.SL.TZ0.3e.i:
Find the height of C above the ground when t=2.
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21N.2.SL.TZ0.3f.i:
At any given instant, find the probability that point C is visible from Tim’s window.
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21N.2.SL.TZ0.3a.ii:
minimum value of h.
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21N.2.SL.TZ0.3e.ii:
Find the time, in seconds, that point C is above a height of 100 m, during each complete rotation.
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21N.2.SL.TZ0.3f.ii:
The wind speed increases. The blades rotate at twice the speed, but still at a constant rate.
At any given instant, find the probability that Tim can see point C from his window. Justify your answer.
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21N.2.SL.TZ0.3b.i:
Find the time, in seconds, it takes for the blade [BC] to make one complete rotation under these conditions.
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21N.2.SL.TZ0.3c.i:
Write down the amplitude of the function.
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21N.2.SL.TZ0.3b.ii:
Calculate the angle, in degrees, that the blade [BC] turns through in one second.
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21N.2.SL.TZ0.3d:
Sketch the function h(t) for 0≤t≤5, clearly labelling the coordinates of the maximum and minimum points.
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21N.2.AHL.TZ0.2b.ii:
Calculate the angle, in degrees, that the blade [BC] turns through in one second.
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21N.2.AHL.TZ0.2f:
The wind speed increases and the blades rotate faster, but still at a constant rate.
Given that point C is now higher than 110 m for 1 second during each complete rotation, find the time for one complete rotation.
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21N.2.AHL.TZ0.2c.ii:
Find the period of the function.
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21N.2.AHL.TZ0.2a.i:
maximum value of h.
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21N.2.AHL.TZ0.2a.ii:
minimum value of h.
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21N.2.AHL.TZ0.2e.i:
Find the height of C above the ground when t=2.
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21N.2.AHL.TZ0.2b.i:
Find the time, in seconds, it takes for the blade [BC] to make one complete rotation under these conditions.
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21N.2.AHL.TZ0.2c.i:
Write down the amplitude of the function.
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21N.2.AHL.TZ0.2d:
Sketch the function h(t) for 0≤t≤5, clearly labelling the coordinates of the maximum and minimum points.
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21N.2.AHL.TZ0.2e.ii:
Find the time, in seconds, that point C is above a height of 100 m, during each complete rotation.
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SPM.1.SL.TZ0.8b:
A rock concert has an intensity level of 112 dB. Find the sound intensity, S.
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SPM.1.SL.TZ0.8a:
An orchestra has a sound intensity of 6.4 × 10−3 W m−2 . Calculate the intensity level, L of the orchestra.
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22M.2.SL.TZ2.5d:
Sketch the graph of C against x, labelling the maximum point and the x-intercepts with their coordinates.
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22M.2.AHL.TZ2.4b:
Given that limT→∞k=A and limT→0k=0, sketch the graph of k against T.
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22M.2.AHL.TZ2.7d:
Sketch the graph of x against t, labelling the maximum point of the graph with its coordinates.
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17N.2.SL.TZ0.T_5a:
Find the exact value of each of the zeros of f.
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17N.2.SL.TZ0.T_5b.i:
Expand the expression for f(x).
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17N.2.SL.TZ0.T_5b.ii:
Find f′(x).
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17N.2.SL.TZ0.T_5c:
Use your answer to part (b)(ii) to find the values of x for which f is increasing.
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17N.2.SL.TZ0.T_5d:
Draw the graph of f for −3⩽x⩽3 and −40⩽y⩽20. Use a scale of 2 cm to represent 1 unit on the x-axis and 1 cm to represent 5 units on the y-axis.
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17N.2.SL.TZ0.T_5e:
Write down the coordinates of the point of intersection.
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18M.2.SL.TZ1.T_4a:
Find the value of k.
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18M.2.SL.TZ1.T_4b:
Using your value of k , find f ′(x).
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18M.2.SL.TZ1.T_4c:
Use your answer to part (b) to show that the minimum value of f(x) is −22 .
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18M.2.SL.TZ1.T_4e:
Sketch the graph of y = f (x) for 0 < x ≤ 6 and −30 ≤ y ≤ 60.
Clearly indicate the minimum point P and the x-intercepts on your graph. -
18M.2.SL.TZ2.T_6a:
Sketch the curve for −1 < x < 3 and −2 < y < 12.
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18M.2.SL.TZ2.T_6b:
A teacher asks her students to make some observations about the curve.
Three students responded.
Nadia said “The x-intercept of the curve is between −1 and zero”.
Rick said “The curve is decreasing when x < 1 ”.
Paula said “The gradient of the curve is less than zero between x = 1 and x = 2 ”.State the name of the student who made an incorrect observation.
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18M.2.SL.TZ2.T_6d:
Find dydx.
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18M.2.SL.TZ2.T_6f:
Given that y = 2x3 − 9x2 + 12x + 2 = k has three solutions, find the possible values of k.
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17M.1.SL.TZ2.T_13a:
Write down the value of f(1).
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17M.1.SL.TZ2.T_13b:
Find the equation of N. Give your answer in the form ax+by+d=0 where a, b, d∈Z.
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17M.1.SL.TZ2.T_13c:
Draw the line N on the diagram above.
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17M.1.SL.TZ1.T_12a:
Write down the domain of the function.
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17M.1.SL.TZ1.T_12b.i:
Draw the line y=−6 on the axes.
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17M.1.SL.TZ1.T_12b.ii:
Write down the number of solutions to f(x)=−6.
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17M.1.SL.TZ1.T_12c:
Find the range of values of k for which f(x)=k has no solution.
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18N.2.SL.TZ0.T_4a:
Sketch the graph of y = f (x), for −4 ≤ x ≤ 3 and −50 ≤ y ≤ 100.
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18N.2.SL.TZ0.T_4b.i:
Use your graphic display calculator to find the zero of f (x).
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18N.2.SL.TZ0.T_4b.ii:
Use your graphic display calculator to find the coordinates of the local minimum point.
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18N.2.SL.TZ0.T_4b.iii:
Use your graphic display calculator to find the equation of the tangent to the graph of y = f (x) at the point (–2, 38.75).
Give your answer in the form y = mx + c.
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19M.2.SL.TZ2.T_5d:
Find f′(x).
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19M.2.SL.TZ2.T_5e:
Find the gradient of the graph of y=f(x) at x=2.
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19M.2.SL.TZ2.T_5f:
Find the equation of the tangent line to the graph of y=f(x) at x=2. Give the equation in the form ax+by+d=0 where, a, b, and d∈Z.
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19N.2.SL.TZ0.T_4a:
Find the value of c.
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19N.2.SL.TZ0.T_4b:
Write down the equation for the axis of symmetry of the graph.
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19N.2.SL.TZ0.T_4c:
Use the symmetry of the graph to show that the second solution is x=4.
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19N.2.SL.TZ0.T_4d:
Write down the x-intercepts of the graph.
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19N.2.SL.TZ0.T_4e:
On graph paper, draw the graph of y=f(x) for -10≤x≤4 and -14≤y≤14. Use a scale of 1 to represent unit on the -axis and to represent units on the -axis.
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19N.2.SL.TZ0.T_4f.i:
Write down the equation of .
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19N.2.SL.TZ0.T_4f.ii:
Draw the tangent on your graph.
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19N.2.SL.TZ0.T_4g:
Given and , state whether the function, , is increasing or decreasing at . Give a reason for your answer.