1.i) For the arithmetic sequence below, determine the equation that describes the sequence and the values of d. State the missing terms of the sequence __, 0, -3, __, -9 (2 marks)

ii) A marble is rolling down an inclined ramp, picking up speed as it goes.

The marble travels 2 cm in the first second, 5 cm in the 2nd-second, and 8 cm in the 3rd second and so on.

A)How far does the marble travel in the 25th second? (1 mark)

B)Determine the total distance that the marble travels in 25 seconds. (1 mark)

2.For the arithmetic series, determine the value of n and the value of Sn to the correct number of terms. 5+9+13+17+...+81.

3. An excavating company has a digger that was purchased for $240 000. It is depreciating at 12% per year. (4 marks)

a) Determine the next three terms of this geometric sequence.

b) Determine the general term (tn). Define your variables.

c) How much will the digger be worth in 7 years?

d) How long will it take before the equipment is worth less than $120 000?

4.A company stores 9 kg of a radioactive material. After one year, 91% of the radioactive material remains. How much radioactive material will be left after 10 years? State your answer to the nearest tenth of a kilogram. (2 marks)

5.In a geometric series, t1 = 12, t3 = 48 and the sum of the series is 98292. How many terms are in the series? (2 marks)

6. State whether each geometric series is convergent or divergent. Show your work. If the series is convergent, find the sum of the infinite series. (4 marks)

a)80+20+5+5/4 +...

b) t1 = 1/3, r= -2

7. State the reference angle for each angle in standard position. Draw a diagram and show your calculations. State the Quadrant that the reference angle belongs in. (4 marks)

a) 55

b) 155

c) 255

d) 355

8. The point P(-9,-12) lies on the terminal arm of an angle, q , in standard position.

Determine the exact trigonometric ratios for sin , cos , and tan . (3 marks)

9. Sketch each triangle. Then, determine the unknown side and angles. If two solutions are possible, give both. Round your angle measures to the nearest degree and the side measurements to the nearest tenth.

a) In PQR, PQ = 12.5 cm, QR = 13.0 cm, and P = 103. (3 marks)

b) In DEF, DE = 8.0 cm, EF = 6.0 cm, and D = 40 (3 marks)

10. At noon, two tracking stations on earth (A and B), 30 km apart, measure the angles of elevation of a rocket that was launched with a weather satellite.

From Station A, the angle of elevation is 46 and from Station B it is 77. The tracking stations are equal distances vertically from the Earth. Find the altitude (height) of the rocket above Station B to the nearest tenth of a km. The rocket is not between the stations. Draw a diagram and show your work. (3 marks)

11. Determine the length of the third side of each triangle to the nearest tenth of a centimetre. Show your work. (2 marks)

12. A bicycle race follows a triangular course. The 3 legs of the race are, in order, 2.5 km, 6.2 km and 6.3 km. Find the angle between the starting leg to the finishing leg to the nearest degree. Draw a diagram and show your work. (2 marks)