DP Mathematics: Applications and Interpretation Questionbank

AHL 2.8—Transformations of graphs, composite transformations
Description
[N/A]Directly related questions
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20N.1.SL.TZ0.S_10a.i:
Find f'(p) in terms of k and p.
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20N.1.SL.TZ0.S_10a.ii:
Show that the equation of L1 is kx+p2y-2pk=0.
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20N.1.SL.TZ0.S_10b:
Find the area of triangle AOB in terms of k.
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20N.1.SL.TZ0.S_10c:
The graph of f is translated by (43) to give the graph of g.
In the following diagram:- point Q lies on the graph of g
- points C, D and E lie on the vertical asymptote of g
- points D and F lie on the horizontal asymptote of g
- point G lies on the x-axis such that FG is parallel to DC.
Line L2 is the tangent to the graph of g at Q, and passes through E and F.
Given that triangle EDF and rectangle CDFG have equal areas, find the gradient of L2 in terms of p.
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EXN.1.AHL.TZ0.8b:
Write down a sequence of transformations that will transform the graph of y=cos x onto the graph of y=f(x).
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21M.1.AHL.TZ1.17:
The graph of the function f(x)=ln x is translated by (ab) so that it then passes through the points (0, 1) and (e3, 1+ln 2) .
Find the value of a and the value of b.
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21N.1.AHL.TZ0.10a:
Find g(0).
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21N.1.AHL.TZ0.10b:
On the same set of axes draw the graph of y=g(x), showing any intercepts and asymptotes.
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22M.2.AHL.TZ1.6b:
Find the value of p and the value of q.
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SPM.1.AHL.TZ0.14a.i:
Write down the value of a.
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SPM.1.AHL.TZ0.14a.ii:
Find the value of b.
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SPM.1.AHL.TZ0.14b:
The outer dome of a large cathedral has the shape of a hemisphere of diameter 32 m, supported by vertical walls of height 17 m. It is also supported by an inner dome which can be modelled by rotating the curve y=33−0.08x3 through 360° about the y-axis between y = 0 and y = 33, as indicated in the diagram.
Find the volume of the space between the two domes.
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22M.2.AHL.TZ2.6e:
Determine the two positions where the path of the arrow intersects the path of the ball.
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22M.2.AHL.TZ2.6f:
Determine the time when the arrow should be released to hit the ball before the ball reaches its maximum height.
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19M.1.AHL.TZ2.H_11a:
Describe the transformation by which f(x) is transformed to g(x).
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19M.1.AHL.TZ2.H_11b:
State the range of g.
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19M.1.AHL.TZ2.H_11c:
Sketch the graphs of y=f(x) and y=g(x) on the same axes, clearly stating the points of intersection with any axes.
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19M.1.AHL.TZ2.H_11d:
Find the coordinates of P.
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19M.1.AHL.TZ2.H_11e:
The tangent to y=f(x) at P passes through the origin (0, 0).
Determine the value of k.
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19M.1.AHL.TZ2.H_3:
Consider the function f(x)=x4−6x2−2x+4, x∈R.
The graph of f is translated two units to the left to form the function g(x).
Express g(x) in the form ax4+bx3+cx2+dx+e where a, b, c, d, e∈Z.
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19M.1.AHL.TZ1.H_10a.i:
Find the remainder when p(x) is divided by (x−2).
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19M.1.AHL.TZ1.H_10a.ii:
Find the remainder when p(x) is divided by (x−3).
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19M.1.AHL.TZ1.H_10b:
Prove that p(x) has only one real zero.
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19M.1.AHL.TZ1.H_10c:
Write down the transformation that will transform the graph of y=p(x) onto the graph of y=8x3−12x2+16x−24.
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19M.1.AHL.TZ1.H_10d:
The random variable X follows a Poisson distribution with a mean of λ and 6P(X=3)=3P(X=2)−2P(X=1)+3P(X=0).
Find the value of λ.
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19M.2.AHL.TZ1.H_10a:
Write down the maximum and minimum value of v.
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19M.2.AHL.TZ1.H_10b:
Write down two transformations that will transform the graph of y=v(t) onto the graph of y=i(t).
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19M.2.AHL.TZ1.H_10c:
Sketch the graph of y=p(t) for 0 ≤ t ≤ 0.02 , showing clearly the coordinates of the first maximum and the first minimum.
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19M.2.AHL.TZ1.H_10d:
Find the total time in the interval 0 ≤ t ≤ 0.02 for which p(t) ≥ 3.
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19M.2.AHL.TZ1.H_10e:
Find pav(0.007).
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19M.2.AHL.TZ1.H_10f:
With reference to your graph of y=p(t) explain why pav(T) > 0 for all T > 0.
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19M.2.AHL.TZ1.H_10g:
Given that p(t) can be written as p(t)=asin(b(t−c))+d where a, b, c, d > 0, use your graph to find the values of a, b, c and d.
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18M.1.SL.TZ2.S_5a:
On the same axes, sketch the graph of f(−x).
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18M.1.SL.TZ2.S_5b:
Another function, g, can be written in the form g(x)=a×f(x+b). The following diagram shows the graph of g.
Write down the value of a and of b.
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18N.1.SL.TZ0.S_8b:
Find the equation of the axis of symmetry of the graph of f.
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18N.1.SL.TZ0.S_8c.i:
Write down the value of h.
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18N.1.SL.TZ0.S_8c.ii:
Find the value of k.
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18N.1.SL.TZ0.S_8d:
The graph of a second function, g, is obtained by a reflection of the graph of f in the y-axis, followed by a translation of (−36).
Find the coordinates of the vertex of the graph of g.
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19M.1.SL.TZ2.S_4a.i:
Find the y-intercept of the graph of f(x)+3.
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19M.1.SL.TZ2.S_4a.ii:
Find the y-intercept of the graph of f(4x).
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19M.1.SL.TZ2.S_4b:
Find the x-intercept of the graph of f(2x).
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19M.1.SL.TZ2.S_4c:
Describe the transformation f(x+1).
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18N.1.AHL.TZ0.H_3b:
Write down the least value of a such that g has an inverse.
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18N.1.AHL.TZ0.H_3a:
For a=−π2, sketch the graph of y=g(x). Indicate clearly the maximum and minimum values of the function.
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19M.2.SL.TZ1.S_8c.i:
Find the value of b and of c.
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19M.2.SL.TZ1.S_8a:
The range of f is k ≤ f(x) ≤ m. Find k and m.
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19M.2.SL.TZ1.S_8d:
The equation g(x)=12 has two solutions where π ≤ x ≤ 4π3. Find both solutions.
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19M.2.SL.TZ1.S_8c.ii:
Find the period of g.
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19M.2.SL.TZ1.S_8b:
Find the range of g.
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18N.1.AHL.TZ0.H_3c.i:
For the value of a found in part (b), write down the domain of g−1.
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18N.1.AHL.TZ0.H_3c.ii:
For the value of a found in part (b), find an expression for g−1(x).