User interface language: English | Español

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

Question

Urvashi wants to model the height of a moving object. She collects the following data showing the height, h   metres, of the object at time t seconds.

She believes the height can be modeled by a quadratic function,  h ( t ) = a t 2 + b t + c , where  a , b , c R .

Hence find

Show that 4 a + 2 b + c = 34 .

[1]
a.

Write down two more equations for a , b and c .

[3]
b.

Solve this system of three equations to find the value of a , b and c .

[4]
c.

when the height of the object is zero.

[3]
d.i.

the maximum height of the object.

[2]
d.ii.

Markscheme

t = 2 , h = 34 34 = a 2 2 + 2 b + c      M1

  34 = 4 a + 2 b + c      AG

[1 mark]

a.

attempt to substitute either (5, 38) or (7, 24)      M1

25 a + 5 b + c = 38       A1

49 a + 7 b + c = 24       A1

[3 marks]

b.

a = 5 3 , b = 13 , c = 44 3      M1A1A1A1

[3 marks]

c.

5 3 t 2 + 13 t + 44 3 = 0       M1

t = 8.8 seconds    M1A1

[3 marks]

d.i.

attempt to find maximum height, e.g. sketch of graph     M1

h = 40.0  metres    A1

[2 marks]

d.ii.

Examiners report

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

Syllabus sections

Topic 2—Functions » SL 2.6—Modelling skills
Show 75 related questions
Topic 2—Functions

View options