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Date May 2022 Marks available 2 Reference code 22M.1.SL.TZ1.3
Level Standard Level Paper Paper 1 Time zone Time zone 1
Command term State Question number 3 Adapted from N/A

Question

The height of a baseball after it is hit by a bat is modelled by the function

ht=-4.8t2+21t+1.2

where h(t) is the height in metres above the ground and t is the time in seconds after the ball was hit.

Write down the height of the ball above the ground at the instant it is hit by the bat.

[1]
a.

Find the value of t when the ball hits the ground.

[2]
b.

State an appropriate domain for t in this model.

[2]
c.

Markscheme

1.2 metres        A1

 

[1 mark]

a.

-4.8t2+21t+1.2=0         (M1)

t=  4.43s   4.431415 s        A1

 

 
Note: If both values for t are seen do not award the A1 mark unless the negative is explicitly excluded.

[2 marks]

b.

0t4.43  OR  0, 4.43        A1A1

 
Note: Award A1 for correct endpoints and A1 for expressing answer with correct notation. Award at most A1A0 for use of x instead of t.

[2 marks]

c.

Examiners report

Probably the best answered question on the paper with many correct answers seen.

 

a.

Many candidates correctly solved the quadratic equation.

 

b.

Some cases, the lower bound was given as 1.2 from confusing height with time. Often the variable x was used in the interval notation which lost a mark.

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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