Algebra IIAB 2nd semester review
In 1-13, graph the function. State the domain and range.
1. 2. 3.
4. 5. 6. y = log 2 x
7. 8. 9.
10. 11. 12. 5
13. Graph:
14. You have $1500 in an account that pays 4% interest. Find amount in the account after 2 years if it is compounded:
a. Quarterly b. Monthly c. Continuously
15. The value of a boat decreases by 10% each year. How much is a boat worth after 6 years that cost $15000 new?
16. Simplify the expression. All answers should be in exact form.
a. b. c. d.
e. f. g. h.
j. k. m. n.
p. q. r. t.
u. v. w. x.
y. aa. bb. cc.
17. Solve the equation.
a. b. c.
d. e. f.
g. (then give the general solution)
h. 2 =0 (then give the general solution)
18. Y varies directly with x and z. Y = 8 when x=2 and z=12. Write an equation relating x, y, and z.
19. Y varies inversely with t. Y=10 when t=6. Write an equation relating y and t.
20. Find the midpoint of AB. A(2,-4) B(8,10) 21. Find AB. A(2,-4) B(8,10)
22. Graph each conic section, or system. Label vertices and foci if appropriate.
a. b. c.
d. e. f,
g. h.
j.
23a. Solve the system: , b. What does this system and solution represent?
24. Write the first 5 terms of the sequence. Determine the 40th term.
a. an = 3n+2 b. an = n2 – 3 c. an = 30
d. a1 = 4, an = an-1-3 e. a1 = , an = 2an-1
25. Find the sum. a.
b. Find the sum, then write the formula for the nth term, and then write the summation notation.
7+11+15+19+…+399+403
c. Write the formula for the nth term of each:
1. 6, 10, 14, 18, . . . 2. the arithmetic sequence: a4 = 18; a5 = 23
3. the geometric sequence a4 = 128; a5 = 712
26. 20,10,5,2.5,… a. Find the sum of the first 8 terms. b. Find the sum of the infinite series.
27. Al earns $32,000 in his first year on the job. Under payment plan A, he gets a 4% raise every year. Under
payment plan B he gets a raise of $4000 every year.
a. Under plan A, how much will he make in his 15th year on the job?
b. Under plan B, how much will he make in his 15th year on the job?
c. Under plan A, how much will he make in his first 15 years on the job?
d. Under plan B, how much will he make in his first 15 years on the job?
28. Given that and , find the other 5 trig functions in exact form.
29. Give two angles, one positive and one negative, that are coterminal with the given angle
a. 120° b.
30. Give the reference angle for the given angle.
a. 98° b. -20° c.
31. Convert to radians: 210° 32. Convert to degrees:
33. A minute hand on a clock is 20 inches long. How far does a point on the end of the minute hand travel
in 45 minutes?
34. Solve the given triangle.
a. A = 20°, B = 80°, a = 8cm b. A = 42°, a = 15cm, b = 20cm c. a = 9m, b = 12m, c = 18m
35. From 150’ away the angle of elevation to the top of a cliff is 40°. What is the height of the cliff?
36. A = 30°, b = 20m, c = 15cm. What is the area of ∆ABC?
37. What is the period, amplitude, vertical shift, and horizontal shift?
a. b. c.
38. Given sin ϴ = 1/8 and Find the following in exact form.
a. Cos2ϴ b. Tan(ϴ/2)
39. Simplify: a. b.
40. Find a trigonometric model for the data.
a.
x / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12y / 16 / 15.3 / 14.2 / 13.4 / 12.5 / 11.4 / 11.0 / 11.3 / 12.1 / 13.0 / 14.2 / 15.3
b.
x / 1 / 2 / 3 / 4 / 5 / 6y / 2.73 / 5.73 / 12.04 / 25.28 / 53.09 / 111.5
41. Write each in standard form, then identify which conic it is.
a. b.