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Date May 2010 Marks available 6 Reference code 10M.1.sl.TZ1.4
Level SL only Paper 1 Time zone TZ1
Command term Find Question number 4 Adapted from N/A

Question

The straight line with equation y=34x makes an acute angle θ with the x-axis.

Write down the value of tanθ .

[1]
a.

Find the value of

(i)     sin2θ ;

(ii)    cos2θ .

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

Markscheme

tanθ=34 (do not accept 34x )     A1     N1

[1 mark]

a.

(i) sinθ=35 , cosθ=45     (A1)(A1)

correct substitution     A1

e.g. sin2θ=2(35)(45)

sin2θ=2425     A1     N3

(ii) correct substitution     A1

e.g. cos2θ=12(35)2 ,  (45)2(35)2

cos2θ=725     A1     N1

[6 marks]

b(i) and (ii).

Examiners report

Many candidates drew a diagram to correctly find tanθ , although few recognized that a line through the origin can be expressed as y=xtanθ , with gradient tanθ , which is explicit in the syllabus.

a.

A surprising number were unable to find the ratios for sinθ and cosθ from tanθ . It was not uncommon for candidates to use unreasonable values, such as sinθ=3 and cosθ=4 , or to write nonsense such as 2sin35cos45 .

b(i) and (ii).

Syllabus sections

Prior learning topics » Coordinate geometry » Elementary geometry of the plane, including the concepts of dimension for point, line, plane and space.The equation of a line in the form ymxc= +.

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