DP Mathematics: Analysis and Approaches Questionbank

SL 2.10—Solving equations graphically and analytically
Description
[N/A]Directly related questions
-
22M.2.SL.TZ2.6b:
Find the times when the particle’s acceleration is -1.9 m s-2−1.9ms−2.
-
22M.2.SL.TZ2.6c:
Find the particle’s acceleration when its speed is at its greatest.
-
22M.2.SL.TZ2.8c:
For 0≤t≤90≤t≤9, find the total amount of time when the rate of growth of Plant BB was greater than the rate of growth of Plant AA.
-
22M.2.SL.TZ2.8b:
Find the values of tt when hA(t)=hB(t)hA(t)=hB(t).
-
22M.2.AHL.TZ2.10d:
For 0≤t≤90≤t≤9, find the total amount of time when the rate of growth of Plant BB was greater than the rate of growth of Plant AA.
-
22M.2.AHL.TZ2.12f:
After 1010 years, the population of marsupials is 3P03P0. It is known that N=4P0N=4P0.
Find the value of kk for this population model.
-
22M.1.SL.TZ2.8a:
Find the coordinates of BB.
-
22M.1.AHL.TZ2.3c:
Hence, solve the inequality 0<2x-1x+1<20<2x−1x+1<2.
-
22M.2.AHL.TZ1.6b:
Solve the inequality f(x)≥g(x)f(x)≥g(x).
-
22M.2.AHL.TZ2.11d.ii:
Determine the length of time between the first airplane arriving at PP and the second airplane arriving at PP.
-
22M.2.AHL.TZ2.11d.i:
Find the coordinates of PP.
-
SPM.2.SL.TZ0.9a:
Find the period of ff.
-
SPM.2.SL.TZ0.9d:
Find the value of xx for which the functions have the greatest difference.
-
SPM.2.SL.TZ0.9b.i:
Find the value of bb.
-
SPM.2.SL.TZ0.9b.ii:
Hence, find the value of ff(6).
-
SPM.2.SL.TZ0.9c:
Find the value of pp and the value of qq.
-
16N.1.AHL.TZ0.H_5:
The quadratic equation x2−2kx+(k−1)=0x2−2kx+(k−1)=0 has roots αα and ββ such that α2+β2=4α2+β2=4. Without solving the equation, find the possible values of the real number kk.
-
17N.1.SL.TZ0.S_8d:
Find the area of the region enclosed by the graph of ff and the line LL.
-
18M.2.SL.TZ1.S_1c:
Solve f '(x) = f "(x).
-
18M.2.SL.TZ1.S_7a:
Given that xk + 1 = xk + a, find a.
-
18M.2.SL.TZ1.S_7b:
Hence find the value of n such that n∑k=1xk=861n∑k=1xk=861.
-
17M.1.SL.TZ1.S_10a:
Show that cosθ=34cosθ=34.
-
17M.1.SL.TZ1.S_10b:
Given that tanθ>0tanθ>0, find tanθtanθ.
-
17M.1.SL.TZ1.S_10c:
Let y=1cosxy=1cosx, for 0<x<π20<x<π2. The graph of yybetween x=θx=θ and x=π4x=π4 is rotated 360° about the xx-axis. Find the volume of the solid formed.
-
16N.2.SL.TZ0.S_4a:
Find the value of pp and of qq.
-
16N.2.SL.TZ0.S_4b:
Hence, find the area of the region enclosed by the graphs of ff and gg.
-
17N.2.SL.TZ0.S_5a:
Find the value of pp.
-
17N.2.SL.TZ0.S_5b:
The following diagram shows part of the graph of ff.
The region enclosed by the graph of ff, the xx-axis and the lines x=−px=−p and x=px=p is rotated 360° about the xx-axis. Find the volume of the solid formed.
-
18N.1.SL.TZ0.S_5:
Consider the vectors a = (32p)(32p) and b = (p+18)(p+18).
Find the possible values of p for which a and b are parallel.
-
19M.2.SL.TZ2.S_4a:
Show that OC=rcosθOC=rcosθ.
-
19M.2.SL.TZ2.S_4b:
Find the area of triangle OBC in terms of rr and θ.
-
19M.2.SL.TZ2.S_4c:
Given that the area of triangle OBC is 3535 of the area of sector OAB, find θ.
-
17M.2.SL.TZ2.S_10a.i:
Find qq.
-
17M.2.SL.TZ2.S_10a.ii:
Find pp.
-
17M.2.SL.TZ2.S_10b.i:
Write down the probability of drawing three blue marbles.
-
17M.2.SL.TZ2.S_10b.ii:
Explain why the probability of drawing three white marbles is 1616.
-
17M.2.SL.TZ2.S_10b.iii:
The bag contains a total of ten marbles of which ww are white. Find ww.
-
17M.2.SL.TZ2.S_10d:
Grant plays the game until he wins two prizes. Find the probability that he wins his second prize on his eighth attempt.
-
17M.2.SL.TZ2.S_10c:
Jill plays the game nine times. Find the probability that she wins exactly two prizes.
-
19N.1.SL.TZ0.S_10a:
Write down the coordinates of BB.
-
19N.1.SL.TZ0.S_10b:
Given that f′(a)=1lnp, find the equation of L1 in terms of x, p and q.
-
19N.1.SL.TZ0.S_10c:
The line L2 is tangent to the graph of g at A and has equation y=(lnp)x+q+1.
The line L2 passes through the point (−2, −2).
The gradient of the normal to g at A is 1ln(13).
Find the equation of L1 in terms of x.
-
19N.1.SL.TZ0.S_9a.i:
→OA∙→OC.
-
19N.1.SL.TZ0.S_9a.ii:
→OB∙→OC.
-
19N.1.SL.TZ0.S_9b:
Given that AˆOC=BˆOC, show that k=7.
-
19N.1.SL.TZ0.S_9c:
Calculate the area of triangle AOC.
-
19N.2.SL.TZ0.S_10a:
Find an expression for the velocity, v m s−1, of the rocket during the first stage.
-
19N.2.SL.TZ0.S_10b:
Find the distance that the rocket travels during the first stage.
-
19N.2.SL.TZ0.S_10c:
During the second stage, the rocket accelerates at a constant rate. The distance which the rocket travels during the second stage is the same as the distance it travels during the first stage.
Find the total time taken for the two stages.
-
19N.2.SL.TZ0.S_2a:
Find the point of intersection of L1 and L2.
-
19N.2.SL.TZ0.S_2b:
Write down a direction vector for L3.
-
19N.2.SL.TZ0.S_2c:
L3 passes through the intersection of L1 and L2.
Write down a vector equation for L3.
-
19N.2.SL.TZ0.S_9a:
Calculate the probability a flight is not late.
-
19N.2.SL.TZ0.S_9b:
Find the value of m.
-
19N.2.SL.TZ0.S_9c.i:
Calculate the probability that at least 7 of these flights are on time.
-
19N.2.SL.TZ0.S_9c.ii:
Given that at least 7 of these flights are on time, find the probability that exactly 10 flights are on time.
-
19N.2.SL.TZ0.S_9d:
SpeedWay increases the number of flights from city A to city B to 20 flights each week, and improves their efficiency so that more flights are on time. The probability that at least 19 flights are on time is 0.788.
A flight is chosen at random. Calculate the probability that it is on time.