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Date May 2015 Marks available 2 Reference code 15M.1.sl.TZ2.8
Level SL only Paper 1 Time zone TZ2
Command term Find Question number 8 Adapted from N/A

Question

The diagram shows a triangle ABC. The size of angle CˆAB is 55 and the length of AM is 10 m, where M is the midpoint of AB. Triangle CMB is isosceles with CM=MB.

Write down the length of MB.

[1]
a.

Find the size of angle CˆMB.

[2]
b.

Find the length of CB.

[3]
c.

Markscheme

10    (A1)(C1)

a.

AˆMC=70ORAˆCM=55     (A1)

CˆMB=110     (A1)     (C2)

b.

CB2=102+1022×10×10×cos110     (M1)(A1)(ft)

Notes: Award (M1) for substitution into the cosine rule formula, (A1)(ft) for correct substitution. Follow through from their answer to part (b).

 

OR

CBsin110=10sin35     (M1)(A1)(ft)

Notes: Award (M1) for substitution into the sine rule formula, (A1)(ft) for correct substitution. Follow through from their answer to part (b).

 

OR

AˆCB=90     (A1)

sin55=CB55ORcos35=CB20     (M1)

Note: Award (A1) for some indication that AˆCB=90, (M1) for correct trigonometric equation.

 

OR

Perpendicular MN is drawn from M to CB.     (A1)

12CB10=cos35     (M1)

Note: Award (A1) for some indication of the perpendicular bisector of BC, (M1) for correct trigonometric equation.

 

CB=16.4 (m)(16.3830 (m))     (A1)(ft)(C3)

Notes: Where a candidate uses CˆMB=90 and finds CB=14.1 (m) award, at most, (M1)(A1)(A0).

Where a candidate uses CˆMB=60 and finds CB=10 (m) award, at most, (M1)(A1)(A0).

c.

Examiners report

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

Syllabus sections

Topic 5 - Geometry and trigonometry » 5.0 » Basic geometric concepts: point, line, plane, angle

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