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Date	May 2018	Marks available	2	Reference code	18M.2.SL.TZ2.T_1
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 2
Command term	Find and Use	Question number	T_1	Adapted from	N/A

Question

In a company it is found that 25 % of the employees encountered traffic on their way to work. From those who encountered traffic the probability of being late for work is 80 %.

From those who did not encounter traffic, the probability of being late for work is 15 %.

The tree diagram illustrates the information.

The company investigates the different means of transport used by their employees in the past year to travel to work. It was found that the three most common means of transport used to travel to work were public transportation (P ), car (C ) and bicycle (B ).

The company finds that 20 employees travelled by car, 28 travelled by bicycle and 19 travelled by public transportation in the last year.

Some of the information is shown in the Venn diagram.

There are 54 employees in the company.

Write down the value of a.

[1]

a.i.

Write down the value of b.

[1]

a.ii.

Use the tree diagram to find the probability that an employee encountered traffic and was late for work.

[2]

b.i.

Use the tree diagram to find the probability that an employee was late for work.

[3]

b.ii.

Use the tree diagram to find the probability that an employee encountered traffic given that they were late for work.

[3]

b.iii.

Find the value of x.

[1]

c.i.

Find the value of y.

[1]

c.ii.

Find the number of employees who, in the last year, did not travel to work by car, bicycle or public transportation.

[2]

d.

Find $n\left( {\left( {C \cup B} \right) \cap P'} \right)$ .

[2]

e.

Markscheme

a = 0.2 (A1)

[1 mark]

a.i.

b = 0.85 (A1)

[1 mark]

a.ii.

0.25 × 0.8 (M1)

Note: Award (M1) for a correct product.

$= 0.2\,\,\,\left( {\,\frac{1}{5},\,\,\,20\% } \right)$ (A1)(G2)

[2 marks]

b.i.

0.25 × 0.8 + 0.75 × 0.15 (A1)(ft)(M1)

Note: Award (A1)(ft) for their (0.25 × 0.8) and (0.75 × 0.15), (M1) for adding two products.

$= 0.313\,\,\,\left( {0.3125,\,\,\,\frac{5}{{16}},\,\,\,31.3\% } \right)$ (A1)(ft)(G3)

Note: Award the final (A1)(ft) only if answer does not exceed 1. Follow through from part (b)(i).

[3 marks]

b.ii.

$\frac{{0.25 \times 0.8}}{{0.25 \times 0.8 + 0.75 \times 0.15}}$ (A1)(ft)(A1)(ft)

Note: Award (A1)(ft) for a correct numerator (their part (b)(i)), (A1)(ft) for a correct denominator (their part (b)(ii)). Follow through from parts (b)(i) and (b)(ii).

$= 0.64\,\,\,\left( {\frac{{16}}{{25}},\,\,64{\text{% }}} \right)$ (A1)(ft)(G3)

Note: Award final (A1)(ft) only if answer does not exceed 1.

[3 marks]

b.iii.

(x =) 3 (A1)

[1 Mark]

c.i.

(y =) 10 (A1)(ft)

Note: Following through from part (c)(i) but only if their x is less than or equal to 13.

[1 Mark]

c.ii.

54 − (10 + 3 + 4 + 2 + 6 + 8 + 13) (M1)

Note: Award (M1) for subtracting their correct sum from 54. Follow through from their part (c).

= 8 (A1)(ft)(G2)

Note: Award (A1)(ft) only if their sum does not exceed 54. Follow through from their part (c).

[2 marks]

d.

6 + 8 + 13 (M1)

Note: Award (M1) for summing 6, 8 and 13.

27 (A1)(G2)

[2 marks]

e.

Examiners report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

b.i.

[N/A]

b.ii.

[N/A]

b.iii.

[N/A]

c.i.

[N/A]

c.ii.

[N/A]

d.

[N/A]

e.

Syllabus sections

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

Show 85 related questions

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22M.1.SL.TZ1.12b:
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22M.1.SL.TZ1.6c:
Find the area of the unshaded region in the painting.
22M.2.AHL.TZ1.2d:
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Find the total volume of grass eaten by the goat during this time.
22M.2.AHL.TZ1.6d.i:
Find the area enclosed by $y = f (x)$ , the $x$ -axis and the line $x = 0.5$ .
21N.1.SL.TZ0.13a.iii:
Hence find the equation of the quadratic curve.
21N.1.SL.TZ0.13a.ii:
Hence form two equations in terms of $a$ and $b$ .
16N.2.SL.TZ0.T_6b:
Express this volume in ${\text{c}}{{\text{m}}^3}$ .
17M.2.SL.TZ2.S_8b.i:
Write down the coordinates of A.
19M.2.SL.TZ2.T_1b:
State the number of degrees of freedom.
19M.2.SL.TZ2.T_1c.i:
the expected frequency of female students who chose to take the Chinese class.
19M.2.SL.TZ2.T_1d:
State whether or not H₀ should be rejected. Justify your statement.
18M.2.SL.TZ1.S_4b:
On the grid above, sketch the graph of g for −2 ≤ x ≤ 4.
17M.2.SL.TZ2.S_8b.ii:
Write down the rate of change of $f$ at A.
17N.2.SL.TZ0.T_4d:
Find the probability that this adult is allergic to nuts and the liquid turns blue.
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Find the area of region R.
19M.1.SL.TZ1.T_12c:
Write down the probability that the second spin is yellow, given that the first spin is blue.
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Estimate the number of employees, from this 38, who are allergic to nuts.
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Find the coordinates of B.
18M.3.AHL.TZ0.Hca_3c:
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Find the probability that at least one of the two students is female.
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Find the probability that both spins are yellow.
16N.2.SL.TZ0.S_6b:
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18M.2.SL.TZ2.S_3b:
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19M.2.SL.TZ2.S_2b:
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Find the minimum volume of empty space in the container during the 4 hour period.
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Let $R$ be the region enclosed by the graph of $f$ , the $x$ -axis, the line $x = b$ and the line $x = a$ . The region $R$ is rotated 360° about the $x$ -axis. Find the volume of the solid formed.
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Find the value of $p$ .
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State in context what this value represents.
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Find the range of $h$ .
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Find $\int_{0}^{5} \frac{1000}{2 + t} d t$ .
18M.1.SL.TZ1.S_5b:
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17N.2.SL.TZ0.S_5b:
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21M.1.SL.TZ2.13a:
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18M.3.AHL.TZ0.Hca_3b:
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18M.1.SL.TZ2.T_7c:
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Calculate the probability that one girl answered questions in Mandarin and the other answered questions in Hindi.
21M.1.SL.TZ1.13a:
Determine whether the graph of $l$ against $θ$ is increasing or decreasing at $θ = 50 °$ .
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Find $\frac{d y}{d x}$ .
18M.1.SL.TZ2.S_2b:
Find the area of the region enclosed by the graph of $f$ , the x-axis and the lines x = 1 and x = 2 .
16N.2.SL.TZ0.S_6a:
Use the model to find the volume of the barrel.
21M.2.AHL.TZ1.2d.ii:
Hence find the cross-sectional area of the tunnel.
18N.2.SL.TZ0.S_10b.i:
Find the value of $p$ and of $q$ .
21M.1.SL.TZ2.13b:
The company regularly increases the number of cars it produces.

Describe how their profit changes if they increase production to over $30$ cars per month and up to $50$ cars per month. Justify your answer.
17M.2.SL.TZ2.S_8c.ii:
Find the the rate of change of $f$ at B.
21M.2.SL.TZ1.5c.i:
Write down the integral which can be used to find the cross-sectional area of the tunnel.
21M.2.SL.TZ1.5c.ii:
Hence find the cross-sectional area of the tunnel.
21M.2.AHL.TZ1.2d.i:
Write down the integral which can be used to find the cross-sectional area of the tunnel.
21N.1.SL.TZ0.13b:
Find the area of the shaded region in Irina’s design.
EXN.2.SL.TZ0.3b.i:
Find the value of $t$ at which the ball hits the ground.
EXN.1.AHL.TZ0.10c:
Determine $\int_{0}^{365} P (t) d t$ and state what it represents.
EXN.1.AHL.TZ0.10b:
Find an expression for $P$ in terms of $t$ .
EXN.2.SL.TZ0.3a:
Find an expression for the height $h$ of the ball at time $t$ .
EXN.2.SL.TZ0.6g:
Use the expression found in (f) to calculate a value for $A$ .
21N.1.SL.TZ0.13a.i:
Write down the value of $c$ .

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