IB Questionbank

Updates to Questionbank

User interface language: English | Español

Date	May 2017	Marks available	2	Reference code	17M.2.SL.TZ1.S_10
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 1
Command term	Find	Question number	S_10	Adapted from	N/A

Question

Let $f(x) = \ln x$ and $g(x) = 3 + \ln \left( {\frac{x}{2}} \right)$ , for $x > 0$ .

The graph of $g$ can be obtained from the graph of $f$ by two transformations:

$\begin{array}{*{20}{l}} {{\text{a horizontal stretch of scale factor }}q{\text{ followed by}}} \\ {{\text{a translation of }}\left( {\begin{array}{*{20}{c}} h \\ k \end{array}} \right).} \end{array}$

Let $h(x) = g(x) \times \cos (0.1x)$ , for $0 < x < 4$ . The following diagram shows the graph of $h$ and the line $y = x$ .

M17/5/MATME/SP2/ENG/TZ1/10.b.c

The graph of $h$ intersects the graph of ${h^{ - 1}}$ at two points. These points have $x$ coordinates 0.111 and 3.31 correct to three significant figures.

Write down the value of $q$ ;

[1]

a.i.

Write down the value of $h$ ;

[1]

a.ii.

Write down the value of $k$ .

[1]

a.iii.

Find $\int_{0.111}^{3.31} {\left( {h(x) - x} \right){\text{d}}x}$ .

[2]

b.i.

Hence, find the area of the region enclosed by the graphs of $h$ and ${h^{ - 1}}$ .

[3]

b.ii.

Let $d$ be the vertical distance from a point on the graph of $h$ to the line $y = x$ . There is a point ${\text{P}}(a,{\text{ }}b)$ on the graph of $h$ where $d$ is a maximum.

Find the coordinates of P, where $0.111 < a < 3.31$ .

[7]

c.

Markscheme

$q = 2$ A1 N1

Note: Accept $q = 1$ , $h = 0$ , and $k = 3 - \ln (2)$ , 2.31 as candidate may have rewritten $g(x)$ as equal to $3 + \ln (x) - \ln (2)$ .

[1 mark]

a.i.

$h = 0$ A1 N1

Note: Accept $q = 1$ , $h = 0$ , and $k = 3 - \ln (2)$ , 2.31 as candidate may have rewritten $g(x)$ as equal to $3 + \ln (x) - \ln (2)$ .

[1 mark]

a.ii.

$k = 3$ A1 N1

Note: Accept $q = 1$ , $h = 0$ , and $k = 3 - \ln (2)$ , 2.31 as candidate may have rewritten $g(x)$ as equal to $3 + \ln (x) - \ln (2)$ .

[1 mark]

a.iii.

2.72409

2.72 A2 N2

[2 marks]

b.i.

recognizing area between $y = x$ and $h$ equals 2.72 (M1)

eg $\,\,\,\,\,$ M17/5/MATME/SP2/ENG/TZ1/10.b.ii/M

recognizing graphs of $h$ and ${h^{ - 1}}$ are reflections of each other in $y = x$ (M1)

eg $\,\,\,\,\,$ area between $y = x$ and $h$ equals between $y = x$ and ${h^{ - 1}}$

$2 \times 2.72\int_{0.111}^{3.31} {\left( {x - {h^{ - 1}}(x)} \right){\text{d}}x = 2.72}$

5.44819

5.45 A1 N3

[??? marks]

b.ii.

valid attempt to find $d$ (M1)

eg $\,\,\,\,\,$ difference in $y$ -coordinates, $d = h(x) - x$

correct expression for $d$ (A1)

eg $\,\,\,\,\,$ $\left( {\ln \frac{1}{2}x + 3} \right)(\cos 0.1x) - x$

valid approach to find when $d$ is a maximum (M1)

eg $\,\,\,\,\,$ max on sketch of $d$ , attempt to solve $d’ = 0$

0.973679

$x = 0.974$ A2 N4

substituting their $x$ value into $h(x)$ (M1)

2.26938

$y = 2.27$ A1 N2

[7 marks]

c.

Examiners report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

a.iii.

[N/A]

b.i.

[N/A]

b.ii.

[N/A]

c.

Syllabus sections

Topic 5 —Calculus » SL 5.5—Integration introduction, areas between curve and x axis

Show 162 related questions

18M.2.SL.TZ1.S_4a:
Write down the coordinates of the vertex of the graph of g.
18M.2.SL.TZ2.S_9a:
Find the initial velocity of P.
18M.2.SL.TZ2.S_9d:
Find the acceleration of P when it changes direction.
19M.1.SL.TZ1.S_7b:
Find the total distance travelled in the first 5 seconds.
19M.2.SL.TZ2.S_8c:
Find the value of $t$ when particle A first changes direction.
19M.1.AHL.TZ1.H_8d:
Sketch the curve $y = f\left( x \right)$ , 0 ≤ $x$ ≤ 5 indicating clearly the coordinates of the maximum and minimum points and any intercepts with the coordinate axes.
18M.2.SL.TZ1.S_4b:
On the grid above, sketch the graph of g for −2 ≤ x ≤ 4.
21N.1.SL.TZ0.7b:
Sketch a graph of $v$ against $t$ , clearly showing any points of intersection with the axes.
18M.3.AHL.TZ0.Hca_3c:
Hence write down a lower bound for $\sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}}$ .
18M.2.SL.TZ1.T_2a:
State the alternative hypothesis.
18M.2.SL.TZ1.T_2d.i:
Write down the χ² statistic.
18M.2.SL.TZ1.T_2d.ii:
Write down the associated p-value.
18M.2.SL.TZ2.T_1c.i:
Find the value of x.
18M.2.SL.TZ1.T_5c:
Copy the probability tree diagram and write down the relevant probabilities along the branches.
18M.2.SL.TZ1.T_5e:
120 contestants attempted this game.

Find the expected number of contestants who fell into a trap while attempting to pass through a door in the third wall.
19M.2.SL.TZ2.T_1c.i:
the expected frequency of female students who chose to take the Chinese class.
16N.2.SL.TZ0.S_9b:
Find the value of $p$ .
17M.2.SL.TZ1.S_7a.i:
Write down the first value of $t$ at which P changes direction.
17M.2.SL.TZ1.S_7a.ii:
Find the total distance travelled by P, for $0 \leqslant t \leqslant 8$ .
18M.2.SL.TZ1.T_5a:
Write down the probability that Ayako avoids the trap in this wall.
17N.2.SL.TZ0.S_9b:
Hence or otherwise, find all possible values of $t$ for which the velocity of P is decreasing.
17N.1.SL.TZ0.T_7a:
Complete the Venn diagram for these students.
19M.1.SL.TZ2.T_5a:
Using the given information, complete the following Venn diagram.
18N.2.SL.TZ0.T_2b.i:
Write down $n\left( {S \cap \left( {M \cup B} \right)} \right)$ .
18N.2.SL.TZ0.T_2b.ii:
Write down $n\left( {B \cap M \cap S'} \right)$ .
18M.2.SL.TZ2.S_9e:
Find the total distance travelled by P.
SPM.2.AHL.TZ0.11a:
Show that $t$ + 1 is an integrating factor for this differential equation.
18M.2.SL.TZ2.T_1c.ii:
Find the value of y.
19N.1.SL.TZ0.S_8a:
Write down an expression for $y$ in terms of $x$ .
SPM.2.AHL.TZ0.11d:
Find the value of $t$ at which the amount of salt in the tank is decreasing most rapidly.
19N.1.SL.TZ0.S_8d.i:
Find the value of $x$ for which $V$ is a maximum.
17M.1.SL.TZ1.S_10b:
Given that $\tan \theta > 0$ , find $\tan \theta$ .
19M.2.SL.TZ2.S_8d:
Find the total distance travelled by particle A in the first 3 seconds.
19M.2.SL.TZ2.T_1e.iii:
Find the probability that at least one of the two students is female.
19M.2.SL.TZ2.T_1c.ii:
the ${\chi ^2}$ statistic.
17N.2.SL.TZ0.T_4g:
Estimate the number of employees, from this 38, who are allergic to nuts.
19M.2.SL.TZ2.T_1a:
Write down the null hypothesis, H₀, for this test.
16N.2.SL.TZ0.S_9a:
Find the initial velocity of $P$ .
18M.2.SL.TZ2.T_1a.ii:
Write down the value of b.
18M.2.SL.TZ2.T_1d:
Find the number of employees who, in the last year, did not travel to work by car, bicycle or public transportation.
19M.1.SL.TZ1.T_12c:
Write down the probability that the second spin is yellow, given that the first spin is blue.
18N.2.SL.TZ0.T_2a.ii:
Find the number of students in the school that study Mathematics in English.
18M.1.SL.TZ2.T_7b:
Find the probability that the boy answered questions in Hindi.
18M.2.SL.TZ2.S_9b:
Find the maximum speed of P.
19M.1.SL.TZ2.S_10c:
Write down an expression for the area of $R$ .
17N.2.SL.TZ0.S_5b:
The following diagram shows part of the graph of $f$ .

The region enclosed by the graph of $f$ , the $x$ -axis and the lines $x = - p$ and $x = p$ is rotated 360° about the $x$ -axis. Find the volume of the solid formed.
18M.2.SL.TZ1.T_2g:
Given that this flight was not heavily delayed, find the probability that it travelled between 500 km and 5000 km.
17M.1.SL.TZ1.S_10c:
Let $y = \frac{1}{{\cos x}}$ , for $0 < x < \frac{\pi }{2}$ . The graph of $y$ between $x = \theta$ and $x = \frac{\pi }{4}$ is rotated 360° about the $x$ -axis. Find the volume of the solid formed.
16N.2.SL.TZ0.S_9c:
(i) Find the value of $q$ .

(ii) Hence, find the speed of P when $t = q$ .
18M.3.AHL.TZ0.Hca_3b:
Illustrate graphically the inequality $\sum\limits_{n = 5}^\infty {\frac{1}{{{n^3}}}} < \int\limits_4^\infty {\frac{1}{{{x^3}}}{\text{d}}x} < \sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}}$ .
19N.1.SL.TZ0.S_8b:
Find an expression for $V$ in terms of $x$ .
18M.1.SL.TZ1.S_5a:
Find $\int {{{\left( {f\left( x \right)} \right)}^2}{\text{d}}x}$ .
17N.2.SL.TZ0.T_4d:
Find the probability that this adult is allergic to nuts and the liquid turns blue.
17N.2.SL.TZ0.S_5a:
Find the value of $p$ .
22M.1.SL.TZ1.2b:
Hence, find the value of $\int_{1}^{9} (\frac{3 \sqrt{x} - 5}{\sqrt{x}}) d x$ .
18M.1.SL.TZ1.S_5b:
Part of the graph of f is shown in the following diagram.

The shaded region R is enclosed by the graph of f, the x-axis, and the lines x = 1 and x = 9 . Find the volume of the solid formed when R is revolved 360° about the x-axis.
19M.2.SL.TZ2.S_8e.i:
Given that particles A and B start at the same point, find the displacement function ${s_{\text{B}}}$ for particle B.
22M.1.AHL.TZ1.12b:
Hence, find an approximate value for $\int_{0}^{1} e^{x^{2}} \sin (x^{2}) d x$ .
20N.1.AHL.TZ0.H_12b:
State the equation of the horizontal asymptote on the graph of $y = f (x)$ .
20N.1.AHL.TZ0.H_12d:
Sketch the graph of $y = f (x)$ , stating clearly the equations of any asymptotes and the coordinates of any points of intersections with the coordinate axes.
20N.2.AHL.TZ0.H_3b:
Hence find the area of the shaded region.
17N.2.SL.TZ0.S_9a:
Write down the values of $t$ when $a = 0$ .
18M.3.AHL.TZ0.Hca_3a:
Find the value of $\int\limits_4^\infty {\frac{1}{{{x^3}}}{\text{d}}x}$ .
19M.1.AHL.TZ1.H_8b:
find the value of $f\left( 1 \right)$ .
18M.2.SL.TZ2.S_3a:
Find the x-intercept of the graph of $f$ .
16N.2.SL.TZ0.S_4b:
Hence, find the area of the region enclosed by the graphs of $f$ and $g$ .
17N.1.SL.TZ0.S_8d:
Find the area of the region enclosed by the graph of $f$ and the line $L$ .
21M.2.SL.TZ1.9d.i:
Find the $x$ -coordinate of the point where $L$ intersects the line $y = x$ .
21M.2.SL.TZ1.9d.ii:
Hence, find the area of $A$ .
19M.1.SL.TZ2.S_10d:
Hence find the exact area of $R$ .
19M.2.SL.TZ2.S_8a:
Find the initial displacement of particle A from point P.
19M.2.SL.TZ2.S_8e.ii:
Find the other value of $t$ when particles A and B meet.
16N.2.SL.TZ0.S_6a:
Use the model to find the volume of the barrel.
20N.2.AHL.TZ0.H_3a:
Determine the values of $p$ , $q$ and $r$ .
19N.2.AHL.TZ0.H_11c:
The region $R$ is now rotated about the $y$ -axis, through $2\pi$ radians, to form a solid.

By writing ${{\text{si}}{{\text{n}}^3}\,y}$ as $\left( {1 - {\text{co}}{{\text{s}}^2}\,y} \right){\text{sin}}\,y$ , show that the volume of the solid formed is $\frac{{2\pi }}{3}$ .
18M.2.SL.TZ2.S_3b:
The region enclosed by the graph of $f$ , the y-axis and the x-axis is rotated 360° about the x-axis.

Find the volume of the solid formed.
19M.2.SL.TZ2.S_2b:
The region enclosed by the graph of $f$ , the $x$ -axis and the $y$ -axis is rotated 360º about the $x$ -axis. Find the volume of the solid formed.
18M.2.SL.TZ2.S_9c:
Write down the number of times that the acceleration of P is 0 m s⁻² .
19N.1.SL.TZ0.S_8e:
Find the maximum volume.
19N.1.SL.TZ0.S_8d.ii:
Justify your answer.
17N.2.SL.TZ0.S_9d:
Find the total distance travelled by P when its velocity is increasing.
19N.1.SL.TZ0.S_8c:
Find $\frac{{{\text{d}}V}}{{{\text{d}}x}}$ .
19M.1.AHL.TZ1.H_8c:
find the value of $f\left( 4 \right)$ .
SPM.2.AHL.TZ0.11c:
Sketch the graph of $x$ versus $t$ for 0 ≤ $t$ ≤ 60 and hence find the maximum amount of salt in the tank and the value of $t$ at which this occurs.
19M.2.SL.TZ2.S_2a:
Find the $x$ -intercept of the graph of $f$ .
21M.2.SL.TZ1.1a:
Find $\int (6 x + 7) d x$ .
17M.2.SL.TZ1.S_10a.i:
Write down the value of $q$ ;
22M.2.SL.TZ2.2:
The derivative of a function $g$ is given by $g' (x) = 3 x^{2} + 5 e^{x}$ , where $x \in ℝ$ . The graph of $g$ passes through the point $(0, 4)$ . Find $g (x)$ .
21N.1.SL.TZ0.7c:
Find the total distance travelled by $P$ .
21N.1.SL.TZ0.7a.ii:
Show that the distance of $P$ from $O$ at this time is $\frac{88}{27}$ metres.
22M.1.AHL.TZ1.1:
Find the value of $\int_{1}^{9} (\frac{3 \sqrt{x} - 5}{\sqrt{x}}) d x$ .
18M.1.SL.TZ2.T_7a:
State the number of boys who answered questions in Portuguese.
19M.1.SL.TZ1.T_12a:
Find the probability that both spins are yellow.
17N.1.SL.TZ0.T_7b:
One of the students who joined the sports club is chosen at random. Find the probability that this student joined both clubs.
16N.2.SL.TZ0.T_2d:
Find the probability that this person

(i) went on at most one trip;

(ii) went on the coach trip, given that this person also went on both the helicopter trip and the boat trip.
19M.1.SL.TZ2.T_5c:
A student is chosen at random from the surveyed students.

Find the probability that this student likes kiwi fruit smoothies given that they like mango smoothies.
18M.2.SL.TZ1.T_2e:
State, with a reason, whether you would reject the null hypothesis.
17N.1.SL.TZ0.T_7c:
Determine whether the events $S$ and $M$ are independent.
16N.2.SL.TZ0.T_6b:
Express this volume in ${\text{c}}{{\text{m}}^3}$ .
16N.2.SL.TZ0.T_6c:
Write down, in terms of $r$ and $h$ , an equation for the volume of this water container.
16N.2.SL.TZ0.T_6e:
Find $\frac{{{\text{d}}A}}{{{\text{d}}r}}$ .
16N.2.SL.TZ0.T_6f:
Using your answer to part (e), find the value of $r$ which minimizes $A$ .
SPM.2.AHL.TZ0.11b:
Hence, by solving this differential equation, show that $x\left( t \right) = \frac{{200 - 40{{\text{e}}^{ - \frac{t}{4}}}\left( {t + 5} \right)}}{{t + 1}}$ .
19M.2.SL.TZ2.S_8b:
Find the value of $t$ when particle A first reaches point P.
17N.2.SL.TZ0.S_9c:
Find an expression for the velocity of P at time $t$ .
18M.2.SL.TZ1.T_2h:
Two flights are chosen at random from those which were slightly delayed.

Find the probability that each of these flights travelled at least 5000 km.
SPM.2.AHL.TZ0.11e:
The rate of change of the amount of salt leaving the tank is equal to $\frac{x}{{t + 1}}$ .

Find the amount of salt that left the tank during the first 60 minutes.
18M.2.SL.TZ1.S_4c:
Find the area of the region enclosed by the graphs of f and g.
17M.2.SL.TZ2.S_7:
Note: In this question, distance is in metres and time is in seconds.

A particle moves along a horizontal line starting at a fixed point A. The velocity $v$ of the particle, at time $t$ , is given by $v(t) = \frac{{2{t^2} - 4t}}{{{t^2} - 2t + 2}}$ , for $0 \leqslant t \leqslant 5$ . The following diagram shows the graph of $v$

There are $t$ -intercepts at $(0,{\text{ }}0)$ and $(2,{\text{ }}0)$ .

Find the maximum distance of the particle from A during the time $0 \leqslant t \leqslant 5$ and justify your answer.
17M.1.SL.TZ1.S_10a:
Show that $\cos \theta = \frac{3}{4}$ .
20N.1.AHL.TZ0.H_12a:
State the equation of the vertical asymptote on the graph of $y = f (x)$ .
20N.1.AHL.TZ0.H_12c:
Use an algebraic method to determine whether $f$ is a self-inverse function.
19N.1.AHL.TZ0.H_10c:
Show that $\frac{3}{{x + 1}} - \frac{1}{{x - 1}} = \frac{{2x - 4}}{{{x^2} - 1}}$ .
19M.1.SL.TZ2.S_10b:
Hence find $\int {\left( {3{x^2} + 1} \right)\sqrt {{x^3} + x} } \,{\text{d}}x$ .
20N.1.AHL.TZ0.H_12e:
The region bounded by the $x$ -axis, the curve $y = f (x)$ , and the lines $x = 5$ and $x = 7$ is rotated through $2 π$ about the $x$ -axis. Find the volume of the solid generated, giving your answer in the form $π (a + b \ln 2)$ , where $a, b \in ℤ$ .
17M.2.SL.TZ1.S_7b:
A second particle Q also moves along a straight line. Its velocity, ${v_{\text{Q}}}{\text{ m}}\,{{\text{s}}^{ - 1}}$ after $t$ seconds is given by ${v_{\text{Q}}} = \sqrt t$ for $0 \leqslant t \leqslant 8$ . After $k$ seconds Q has travelled the same total distance as P.

Find $k$ .
16N.2.SL.TZ0.S_4a:
Find the value of $p$ and of $q$ .
19N.2.AHL.TZ0.H_11b:
Find the area of $R$ .
18N.2.SL.TZ0.T_2c.iii:
Find the probability that this student is taught in Spanish, given that the student studies Biology.
19N.1.AHL.TZ0.H_10d:
The area enclosed by the graph of $y = f\left( x \right)$ and the line $y = 4$ can be expressed as ${\text{ln}}\,v$ . Find the value of $v$ .
18M.3.AHL.TZ0.Hca_3d:
Find an upper bound for $\sum\limits_{n = 4}^\infty {\frac{1}{{{n^3}}}}$ .
19M.1.SL.TZ1.S_7a:
Find the value of $s\left( 4 \right) - s\left( 2 \right)$ .
18M.2.SL.TZ1.T_2b:
Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed.
16N.2.SL.TZ0.S_9d:
(i) Find the total distance travelled by P between $t = 1$ and $t = p$ .

(ii) Hence or otherwise, find the displacement of P from A when $t = p$ .
21M.2.SL.TZ1.1b:
Given $f' (x) = 6 x + 7$ and $f (1.2) = 7.32$ , find $f (x)$ .
17M.2.SL.TZ1.S_10a.iii:
Write down the value of $k$ .
17M.2.SL.TZ1.S_10c:
Let $d$ be the vertical distance from a point on the graph of $h$ to the line $y = x$ . There is a point ${\text{P}}(a,{\text{ }}b)$ on the graph of $h$ where $d$ is a maximum.

Find the coordinates of P, where $0.111 < a < 3.31$ .
17M.2.SL.TZ1.S_10a.ii:
Write down the value of $h$ ;
17M.2.SL.TZ1.S_10b.ii:
Hence, find the area of the region enclosed by the graphs of $h$ and ${h^{ - 1}}$ .
18N.2.SL.TZ0.T_2a.i:
Find the number of students in the school that are taught in Spanish.
18N.2.SL.TZ0.T_2a.iii:
Find the number of students in the school that study both Biology and Mathematics.
19M.2.SL.TZ2.T_1d:
State whether or not H₀ should be rejected. Justify your statement.
17N.2.SL.TZ0.T_4c:
Copy and complete the tree diagram.
18M.2.SL.TZ1.T_2c:
Write down the number of degrees of freedom.
19M.1.SL.TZ2.T_5b:
Find the number of surveyed students who did not like any of the three flavours.
18M.2.SL.TZ1.T_5d.ii:
A contestant is chosen at random. Find the probability that this contestant fell into a trap.
18N.2.SL.TZ0.T_2c.i:
Find the probability that this student studies Mathematics.
19M.2.SL.TZ2.T_1e.i:
Find the probability that the student does not take the Spanish class.
16N.2.SL.TZ0.T_2b:
Show that $x = 3$ .
18M.2.SL.TZ1.T_5d.i:
A contestant is chosen at random. Find the probability that this contestant fell into a trap while attempting to pass through a door in the second wall.
18M.1.SL.TZ2.T_7c:
Two girls are selected at random.

Calculate the probability that one girl answered questions in Mandarin and the other answered questions in Hindi.
19M.1.SL.TZ1.T_12b:
Find the probability that at least one of the spins is yellow.
17N.2.SL.TZ0.T_4e:
Find the probability that the liquid turns blue.
16N.2.SL.TZ0.T_6d:
Show that $A = \pi {r^2} + \frac{{1\,000\,000}}{r}$ .
16N.2.SL.TZ0.T_6g:
Find the value of this minimum area.
21N.1.SL.TZ0.7a.i:
Find the value of $t$ when $P$ reaches its maximum velocity.
16N.2.SL.TZ0.T_6a:
Write down a formula for $A$ , the surface area to be coated.
16N.2.SL.TZ0.T_6h:
Find the least number of cans of water-resistant material that will coat the area in part (g).
18M.2.SL.TZ1.T_2f:
Write down the probability that this flight arrived on time.
19M.2.SL.TZ2.T_1e.ii:
Find the probability that neither of the two students take the Spanish class.
18M.2.SL.TZ2.T_1a.i:
Write down the value of a.
18M.2.SL.TZ2.T_1b.i:
Use the tree diagram to find the probability that an employee encountered traffic and was late for work.
18M.2.SL.TZ2.T_1b.ii:
Use the tree diagram to find the probability that an employee was late for work.
18M.2.SL.TZ2.T_1b.iii:
Use the tree diagram to find the probability that an employee encountered traffic given that they were late for work.
18M.2.SL.TZ2.T_1e:
Find $n\left( {\left( {C \cup B} \right) \cap P'} \right)$ .
16N.2.SL.TZ0.T_2a:
Draw a Venn diagram to represent the given information, using sets labelled $B$ , $C$ and $H$ .
16N.2.SL.TZ0.T_2c:
Write down the value of $n(B \cap C)$ .
18N.2.SL.TZ0.T_2c.ii:
Find the probability that this student studies neither Biology nor Mathematics.
17N.2.SL.TZ0.T_4b:
Find the probability that both people chosen are not allergic to nuts.
17N.2.SL.TZ0.T_4f:
Find the probability that the tested adult is allergic to nuts given that the liquid turned blue.
18M.2.SL.TZ1.T_5b:
Find the probability that only one of Ayako and Natsuko falls into a trap while attempting to pass through a door in the first wall.
19M.2.SL.TZ2.T_1b:
State the number of degrees of freedom.

Hide related questions

Topic 5 —Calculus » SL 5.6—Differentiating polynomials n E Q. Chain, product and quotient rules

Topic 5 —Calculus » SL 5.8—Testing for max and min, optimisation. Points of inflexion

Topic 5 —Calculus » SL 5.11—Definite integrals, areas under curve onto x-axis and areas between curves

Topic 5 —Calculus