Term 1 review
Answers are for parents and teachers.
1
Divide (5 + i)/(2 − i) and write the answer as a + bi.
(5 + i)(2 + i)/5 = (10 + 5i + 2i + i²)/5 = (9 + 7i)/5 = 9/5 + 7i/5.
2
Solve x² − 2x − 15 < 0 and write the solution as an interval.
Roots −3 and 5: ]−3, 5[.
3
A map has scale 1 : 25 000 and a lake covers 8 cm² on it. Find the real area in hectares.
1 cm = 250 m, 1 cm² = 62 500 m², 8 cm² = 500 000 m² = 50 ha.
4
DE ∥ BC with AD = 6, DB = 9 and AE = 4. Find EC, and find DE when BC = 25.
6/9 = 4/EC, EC = 6; DE = 6/15 × 25 = 10.
5
Find the smallest positive measure of −950°, then find sin of that angle to 2 decimal places.
−950° + 1080° = 130° = 180° − 50°, so sin 130° = sin 50° ≈ 0.77.