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Date	May Specimen paper	Marks available	2	Reference code	SPM.1.SL.TZ0.8
Level	Standard Level	Paper	Paper 1	Time zone	Time zone 0
Command term	Find	Question number	8	Adapted from	N/A

Question

The intensity level of sound, $L$ measured in decibels (dB), is a function of the sound intensity, $S$ watts per square metre (W m⁻²). The intensity level is given by the following formula.

$L = 10\,{\text{lo}}{{\text{g}}_{10}}\left( {S \times {{10}^{12}}} \right)$ , $S$ ≥ 0.

An orchestra has a sound intensity of 6.4 × 10⁻³W m⁻² . Calculate the intensity level, $L$ of the orchestra.

[2]

A rock concert has an intensity level of 112 dB. Find the sound intensity, $S$ .

[2]

Markscheme

$10\,{\text{lo}}{{\text{g}}_{10}}\left( {6.4 \times {{10}^{ - 3}} \times {{10}^{12}}} \right)$ (M1)

= 98.1(dB) (98.06179…) A1

[2 marks]

$112 = 10\,{\text{lo}}{{\text{g}}_{10}}\left( {S \times {{10}^{12}}} \right)$ (M1)

0.158 (W m⁻²) (0.158489… (W m⁻²)) A1

[2 marks]

Examiners report

[N/A]

Syllabus sections

Topic 2—Functions » SL 2.3—Graphing

Show 62 related questions

22M.2.SL.TZ2.5d:
Sketch the graph of $C$ against $x$ , labelling the maximum point and the $x$ -intercepts with their coordinates.
22M.2.AHL.TZ2.7d:
Sketch the graph of $x$ against $t$ , labelling the maximum point of the graph with its coordinates.
18N.2.SL.TZ0.T_4a:
Sketch the graph of y = f (x), for −4 ≤ x ≤ 3 and −50 ≤ y ≤ 100.
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.
19N.2.SL.TZ0.T_4c:
Use the symmetry of the graph to show that the second solution is $x = 4$ .
22M.2.AHL.TZ2.4b:
Given that $\lim_{T \to \infty} k = A$ and $\lim_{T \to 0} k = 0$ , sketch the graph of $k$ against $T$ .
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.
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.
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.
21N.2.SL.TZ0.3c.i:
Write down the amplitude of the function.
21N.2.SL.TZ0.3e.i:
Find the height of $C$ above the ground when $t = 2$ .
21N.2.AHL.TZ0.2d:
Sketch the function $h (t)$ for $0 \leq t \leq 5$ , clearly labelling the coordinates of the maximum and minimum points.
17M.1.SL.TZ2.T_13a:
Write down the value of $f(1)$ .
18N.2.SL.TZ0.T_4b.i:
Use your graphic display calculator to find the zero of f (x).
19M.2.SL.TZ2.T_5f:
Find the equation of the tangent line to the graph of $y = f\left( x \right)$ at $x = 2$ . Give the equation in the form $ax + by + d = 0$ where, $a$ , $b$ , and $d \in \mathbb{Z}$ .
18M.2.SL.TZ1.T_4a:
Find the value of k.
18M.2.SL.TZ2.T_6f:
Given that y = 2x³ − 9x² + 12x + 2 = k has three solutions, find the possible values of k.
18M.2.SL.TZ2.T_6a:
Sketch the curve for −1 < x < 3 and −2 < y < 12.
17N.2.SL.TZ0.T_5b.ii:
Find $f’(x)$ .
17M.1.SL.TZ2.T_13c:
Draw the line $N$ on the diagram above.
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.
18M.2.SL.TZ1.T_4b:
Using your value of k , find f ′(x).
19N.2.SL.TZ0.T_4b:
Write down the equation for the axis of symmetry of the graph.
19N.2.SL.TZ0.T_4d:
Write down the $x$ -intercepts of the graph.
18N.2.SL.TZ0.T_4b.ii:
Use your graphic display calculator to find the coordinates of the local minimum point.
19N.2.SL.TZ0.T_4f.ii:
Draw the tangent $T$ on your graph.
17N.2.SL.TZ0.T_5b.i:
Expand the expression for $f(x)$ .
17N.2.SL.TZ0.T_5e:
Write down the coordinates of the point of intersection.
19N.2.SL.TZ0.T_4e:
On graph paper, draw the graph of $y = f (x)$ for $- 10 \leq x \leq 4$ and $- 14 \leq y \leq 14$ . Use a scale of $1 cm$ to represent $1$ unit on the $x$ -axis and $1 cm$ to represent $2$ units on the $y$ -axis.
19N.2.SL.TZ0.T_4f.i:
Write down the equation of $T$ .
17M.1.SL.TZ1.T_12a:
Write down the domain of the function.
17N.2.SL.TZ0.T_5c:
Use your answer to part (b)(ii) to find the values of $x$ for which $f$ is increasing.
18M.2.SL.TZ2.T_6d:
Find $\frac{{{\text{dy}}}}{{{\text{dx}}}}$ .
17N.2.SL.TZ0.T_5a:
Find the exact value of each of the zeros of $f$ .
18M.2.SL.TZ1.T_4c:
Use your answer to part (b) to show that the minimum value of f(x) is −22 .
19M.2.SL.TZ2.T_5d:
Find $f'\left( x \right)$ .
17M.1.SL.TZ2.T_13b:
Find the equation of $N$ . Give your answer in the form $ax + by + d = 0$ where $a$ , $b$ , $d \in \mathbb{Z}$ .
17M.1.SL.TZ1.T_12b.i:
Draw the line $y = - 6$ on the axes.
SPM.1.SL.TZ0.8a:
An orchestra has a sound intensity of 6.4 × 10⁻³W m⁻² . Calculate the intensity level, $L$ of the orchestra.
17N.2.SL.TZ0.T_5d:
Draw the graph of $f$ for $- 3 \leqslant x \leqslant 3$ and $- 40 \leqslant y \leqslant 20$ . 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.
19N.2.SL.TZ0.T_4a:
Find the value of $c$ .
19N.2.SL.TZ0.T_4g:
Given $f (a) = 5.5$ and $f' (a) = - 6$ , state whether the function, $f$ , is increasing or decreasing at $x = a$ . Give a reason for your answer.
17M.1.SL.TZ1.T_12c:
Find the range of values of $k$ for which $f(x) = k$ has no solution.
17M.1.SL.TZ1.T_12b.ii:
Write down the number of solutions to $f(x) = - 6$ .
21M.2.SL.TZ2.5c:
Sketch the graph of $V = 300 \sqrt{3} x - \frac{9}{4} x^{3}$ , for $0 \leq x \leq 16$ .
19M.2.SL.TZ2.T_5e:
Find the gradient of the graph of $y = f\left( x \right)$ at $x = 2$ .
21N.2.AHL.TZ0.2a.ii:
minimum value of $h$ .
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.
21N.2.SL.TZ0.3a.i:
maximum value of $h$ .
21N.2.SL.TZ0.3a.ii:
minimum value of $h$ .
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.
21N.2.SL.TZ0.3b.ii:
Calculate the angle, in degrees, that the blade $[BC]$ turns through in one second.
21N.2.SL.TZ0.3c.ii:
Find the period of the function.
21N.2.SL.TZ0.3d:
Sketch the function $h (t)$ for $0 \leq t \leq 5$ , clearly labelling the coordinates of the maximum and minimum points.
21N.2.SL.TZ0.3f.i:
At any given instant, find the probability that point $C$ is visible from Tim’s window.
21N.2.AHL.TZ0.2a.i:
maximum value of $h$ .
21N.2.AHL.TZ0.2b.ii:
Calculate the angle, in degrees, that the blade $[BC]$ turns through in one second.
21N.2.AHL.TZ0.2c.i:
Write down the amplitude of the function.
21N.2.AHL.TZ0.2c.ii:
Find the period of the function.
21N.2.AHL.TZ0.2e.i:
Find the height of $C$ above the ground when $t = 2$ .
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.
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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