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Date November Example question Marks available 1 Reference code EXN.2.SL.TZ0.3
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Write down and Hence Question number 3 Adapted from N/A

Question

The rate of change of the height (h) of a ball above horizontal ground, measured in metres, t seconds after it has been thrown and until it hits the ground, can be modelled by the equation

dhdt=11.4-9.8t

The height of the ball when t=0 is 1.2m.

Find an expression for the height h of the ball at time t.

[6]
a.

Find the value of t at which the ball hits the ground.

[2]
b.i.

Hence write down the domain of h.

[1]
b.ii.

Find the range of h.

[3]
c.

Markscheme

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

h=11.4-9.8tdt        M1

h=11.4t-4.9t2+c        A1A1

When t=0, h=1.2         (M1)

c=1.2         (A1)

h=1.2+11.4t-4.9t2        A1

 

[6 marks]

a.

2.43 2.42741 seconds           (M1)A1      

 

[2 marks]

b.i.

0t2.43         A1      

 

Note: Accept 0t<2.43.

 

[1 mark]

b.ii.

Maximum value is 7.83061        (M1)

Range is 0h7.83         A1A1      

 

Note: Accept 0h<7.83.

 

[3 marks]

c.

Examiners report

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

Syllabus sections

Topic 2—Functions » SL 2.2—Functions, notation domain, range and inverse as reflection
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Topic 2—Functions
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