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Date May 2017 Marks available 2 Reference code 17M.2.SL.TZ1.T_3
Level Standard Level Paper Paper 2 Time zone Time zone 1
Command term Find Question number T_3 Adapted from N/A

Question

Consider the function f ( x ) = 0.3 x 3 + 10 x + 2 x .

Consider a second function, g ( x ) = 2 x 3 .

Calculate f ( 1 ) .

[2]
a.

Sketch the graph of y = f ( x ) for 7 x 4 and 30 y 30 .

[4]
b.

Write down the equation of the vertical asymptote.

[2]
c.

Write down the coordinates of the x -intercept.

[2]
d.

Write down the possible values of x for which x < 0 and f ( x ) > 0 .

[2]
e.

Find the solution of f ( x ) = g ( x ) .

[2]
f.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

0.3 ( 1 ) 3 + 10 1 + 2 1     (M1)

 

Note:     Award (M1) for correct substitution into function.

 

= 10.8     (A1)(G2)

[2 marks]

a.

M17/5/MATSD/SP2/ENG/TZ1/03.b/M     (A1)(A1)(A1)(A1)

 

Note:     Award (A1) for indication of correct window and labelled axes.

Award (A1) for correct shape and position for x < 0 (with the local maximum, local minimum and x -intercept in relative approximate location in 3 rd quadrant).

Award (A1) for correct shape and position for x > 0 (with the local minimum in relative approximate location in 1 st quadrant).

Award (A1) for smooth curve with indication of asymptote (graph should not touch y -axis and should not curve away from the y -axis). The asymptote is only assessed in this mark.

 

[4 marks]

b.

x = 0     (A2)

 

Note:     Award (A1) for “ x = (a constant) ” and (A1) for “ (a constant) = 0 ”.

The answer must be an equation.

 

[2 marks]

c.

( 6.18 ,   0 )   ( 6.17516 ,   0 )     (A1)(A1)

 

Note:     Award (A1) for each correct coordinate. Award (A0)(A1) if parentheses are missing.

 

[2 marks]

d.

4.99 < x < 2.47   ( 4.98688 < x < 2.46635 )     (A1)(A1)

 

Note:     Award (A1) for both correct end points, (A1) for strict inequalities used with 2 endpoints.

 

[2 marks]

e.

0.3 x 3 + 10 x + 2 x = 2 x 3     (M1)

 

Note:     Award (M1) for equating the expressions for f and g or for the line y = 2 x 3 sketched (positive gradient, negative y -intercept) on their graph from part (a).

 

( x = )   1.34   ( 1.33650 )     (A1)(G2)

 

Note:     Award a maximum of (M1)(A0) or (G1) for coordinate pair seen as final answer.

 

[2 marks]

f.

Examiners report

[N/A]
a.
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b.
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c.
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d.
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e.
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f.

Syllabus sections

Topic 2—Functions » SL 2.5—Modelling functions
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Topic 2—Functions

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