User interface language: English | Español

Date May 2017 Marks available 1 Reference code 17M.1.SL.TZ1.T_12
Level Standard Level Paper Paper 1 Time zone Time zone 1
Command term Write down Question number T_12 Adapted from N/A

Question

The function f is of the form f ( x ) = a x + b + c x , where a , b and c are positive integers.

Part of the graph of y = f ( x ) is shown on the axes below. The graph of the function has its local maximum at ( 2 ,   2 ) and its local minimum at ( 2 ,   6 ) .

M17/5/MATSD/SP1/ENG/TZ1/12

Write down the domain of the function.

[2]
a.

Draw the line y = 6 on the axes.

[1]
b.i.

Write down the number of solutions to f ( x ) = 6 .

[1]
b.ii.

Find the range of values of k for which f ( x ) = k has no solution.

[2]
c.

Markscheme

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

( x R ) ,   x 0     (A2)     (C2)

 

Note:     Accept equivalent notation. Award (A1)(A0) for y 0 .

Award (A1) for a clear statement that demonstrates understanding of the meaning of domain. For example, D : ( ,   0 ) ( 1 ,   ) should be awarded (A1)(A0).

 

[2 marks]

a.

M17/5/MATSD/SP1/ENG/TZ1/21.b.i/M     (A1)     (C1)

 

Note:     The command term “Draw” states: “A ruler (straight edge) should be used for straight lines”; do not accept a freehand y = 6 line.

 

[1 mark]

b.i.

2     (A1)(ft)     (C1)

 

Note:     Follow through from part (b)(i).

 

[1 mark]

b.ii.

2 < k < 6     (A1)(A1)     (C2)

 

Note:     Award (A1) for both end points correct and (A1) for correct strict inequalities.

Award at most (A1)(A0) if the stated variable is different from k or y for example 2 < x < 6 is (A1)(A0).

 

[2 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
Show 123 related questions
Topic 2—Functions » SL 2.3—Graphing
Topic 2—Functions

View options