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.
Show that AC=7 cm.
The shape in the following diagram is formed by adding a semicircle with diameter [AC] to the triangle.
Find the exact perimeter of this shape.
Markscheme
evidence of choosing the cosine rule (M1)
egc2=a2+b2−abcosC
correct substitution into RHS of cosine rule (A1)
eg32+82−2×3×8×cosπ3
evidence of correct value for cosπ3 (may be seen anywhere, including in cosine rule) A1
egcosπ3=12, AC2=9+64−(48×12), 9+64−24
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]
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]