Processing math: 100%

User interface language: English | Español

Date May 2010 Marks available 8 Reference code 10M.1.sl.TZ1.8
Level SL only Paper 1 Time zone TZ1
Command term Find Question number 8 Adapted from N/A

Question

Let f(x)=12x3x23x . Part of the graph of f is shown below.


There is a maximum point at A and a minimum point at B(3, − 9) .

Find the coordinates of A.

[8]
a.

Write down the coordinates of

(i)     the image of B after reflection in the y-axis;

(ii)    the image of B after translation by the vector (25) ;

(iii)   the image of B after reflection in the x-axis followed by a horizontal stretch with scale factor 12 .

[6]
b(i), (ii) and (iii).

Markscheme

f(x)=x22x3     A1A1A1

evidence of solving f(x)=0     (M1)

e.g. x22x3=0

evidence of correct working     A1

e.g. (x+1)(x3) ,  2±162

x=1 (ignore x=3 )     (A1)

evidence of substituting their negative x-value into f(x)     (M1)

e.g. 13(1)3(1)23(1) , 131+3

y=53     A1

coordinates are (1,53)     N3

[8 marks]

a.

(i) (39)     A1     N1

(ii) (14)     A1A1    N2

(iii) reflection gives (39)     (A1)

stretch gives (329)     A1A1     N3

[6 marks]

b(i), (ii) and (iii).

Examiners report

A majority of candidates answered part (a) completely.

a.

Candidates were generally successful in finding images after single transformations in part (b). Common incorrect answers for (biii) included (32,92) , (6, 9) and (6, 18) , demonstrating difficulty with images from horizontal stretches.

b(i), (ii) and (iii).

Syllabus sections

Topic 2 - Functions and equations » 2.3 » Transformations of graphs.
Show 43 related questions

View options