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Date May 2018 Marks available 4 Reference code 18M.1.AHL.TZ2.H_2
Level Additional Higher Level Paper Paper 1 Time zone Time zone 2
Command term Solve Question number H_2 Adapted from N/A

Question

Sketch the graphs of y=x2+1 and y=|x2| on the following axes.

[3]
a.

Solve the equation x2+1=|x2|.

[4]
b.

Markscheme

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

straight line graph with correct axis intercepts      A1

modulus graph: V shape in upper half plane      A1

modulus graph having correct vertex and y-intercept      A1

[3 marks]

a.

METHOD 1

attempt to solve x2+1=x2     (M1)

x=6      A1

Note: Accept x=6 using the graph.

attempt to solve (algebraically) x2+1=2x     M1

x=23     A1

[4 marks]

 

 

METHOD 2

(x2+1)2=(x2)2      M1

x24+x+1=x24x+4

0=3x245x+3

3x220x+12=0

attempt to factorise (or equivalent)       M1

(3x2)(x6)=0

x=23     A1

x=6      A1

[4 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 2—Functions » SL 2.2—Functions, notation domain, range and inverse as reflection
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Topic 2—Functions » SL 2.4—Key features of graphs, intersections using technology
Topic 2—Functions

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