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Date November 2020 Marks available 3 Reference code 20N.1.SL.TZ0.T_12
Level Standard Level Paper Paper 1 (with calculator from previous syllabus) Time zone Time zone 0
Command term Find Question number T_12 Adapted from N/A

Question

Jean-Pierre jumps out of an airplane that is flying at constant altitude. Before opening his parachute, he goes through a period of freefall.

Jean-Pierre’s vertical speed during the time of freefall, SS, in m s-1ms1, is modelled by the following function.

S(t)=K-60(1.2-t) , t0S(t)=K60(1.2t) , t0

where tt, is the number of seconds after he jumps out of the airplane, and KK is a constant. A sketch of Jean-Pierre’s vertical speed against time is shown below.

Jean-Pierre’s initial vertical speed is 0m s-10ms1.

Find the value of KK.

[2]
a.

In the context of the model, state what the horizontal asymptote represents.

[1]
b.

Find Jean-Pierre’s vertical speed after 1010 seconds. Give your answer in kmh1kmh1 .

[3]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure. It appeared in a paper that permitted the use of a calculator, and so might not be suitable for all forms of practice.

0=K-60(1.20)0=K60(1.20)      (M1)


Note:
Award (M1) for correctly substituted function equated to zero.


(K=) 60(K=) 60      (A1)    (C2)


[2 marks]

a.

the (vertical) speed that Jean-Pierre is approaching (as tt increases)     (A1)    (C1)
OR
the limit of the (vertical) speed of Jean-Pierre     (A1)    (C1)


Note: Accept “maximum speed” or “terminal speed”.


[1 mark]

b.

(S=) 60-60(1.2-10)(S=) 6060(1.210)     (M1)


Note: Award (M1) for correctly substituted function.


(S=) 50.3096(m s-1)(S=) 50.3096(ms1)     (A1)(ft)


Note:
Follow through from part (a).


181 (km h-1)  (181.114(km h-1))181 (kmh1)  (181.114(kmh1))     (A1)(ft)       (C3)


Note: Award the final (A1)(ft) for correct conversion of their speed to kmh1kmh1.


[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 2—Functions » SL 2.9—Exponential and logarithmic functions
Topic 2—Functions

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