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Date November 2017 Marks available 4 Reference code 17N.1.SL.TZ0.S_4
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Show that Question number S_4 Adapted from N/A

Question

The following diagram shows triangle ABC, with AB = 3  cm , BC = 8  cm , and A B ^ C = π 3 .

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

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

evidence of choosing the cosine rule     (M1)

eg c 2 = a 2 + b 2 a b cos C

correct substitution into RHS of cosine rule     (A1)

eg 3 2 + 8 2 2 × 3 × 8 × cos π 3

evidence of correct value for cos π 3 (may be seen anywhere, including in cosine rule)     A1

eg cos π 3 = 1 2 ,  A C 2 = 9 + 64 ( 48 × 1 2 ) ,   9 + 64 24

correct working clearly leading to answer     A1

eg A C 2 = 49 ,   b = 49

AC = 7  (cm)     AG     N0

 

Note:     Award no marks if the only working seen is A C 2 = 49 or AC = 49 (or similar).

 

[4 marks]

a.

correct substitution for semicircle     (A1)

eg semicircle = 1 2 ( 2 π × 3.5 ) ,   1 2 × π × 7 ,   3.5 π

valid approach (seen anywhere)     (M1)

eg perimeter = AB + BC + semicircle,  3 + 8 + ( 1 2 × 2 × π × 7 2 ) ,   8 + 3 + 3.5 π

11 + 7 2 π   ( = 3.5 π + 11 )  (cm)     A1     N2

[3 marks]

b.

Examiners report

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

Syllabus sections

Topic 3—Geometry and trigonometry » AHL 3.7—Radians
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Topic 3—Geometry and trigonometry

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