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Date November 2017 Marks available 4 Reference code 17N.1.sl.TZ0.4
Level SL only Paper 1 Time zone TZ0
Command term Show that Question number 4 Adapted from N/A

Question

The following diagram shows triangle ABC, with AB=3 cm, BC=8 cm, and AˆBC=π3.

N17/5/MATME/SP1/ENG/TZ0/04

Show that AC=7 cm.

[4]
a.

The shape in the following diagram is formed by adding a semicircle with diameter [AC] to the triangle.

N17/5/MATME/SP1/ENG/TZ0/04.b

Find the exact perimeter of this shape.

[3]
b.

Markscheme

evidence of choosing the cosine rule     (M1)

egc2=a2+b2abcosC

correct substitution into RHS of cosine rule     (A1)

eg32+822×3×8×cosπ3

evidence of correct value for cosπ3 (may be seen anywhere, including in cosine rule)     A1

egcosπ3=12, AC2=9+64(48×12), 9+6424

correct working clearly leading to answer     A1

egAC2=49, b=49

AC=7 (cm)     AG     N0

 

Note:     Award no marks if the only working seen is AC2=49 or AC=49 (or similar).

 

[4 marks]

a.

correct substitution for semicircle     (A1)

egsemicircle=12(2π×3.5), 12×π×7, 3.5π

valid approach (seen anywhere)     (M1)

egperimeter=AB+BC+semicircle, 3+8+(12×2×π×72), 8+3+3.5π

11+72π (=3.5π+11) (cm)     A1     N2

[3 marks]

b.

Examiners report

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

Syllabus sections

Topic 3 - Circular functions and trigonometry » 3.1 » The circle: radian measure of angles; length of an arc; area of a sector.
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