Honors PreCalculus Semester 1 2017 Final Exam Review 1[A]1. From a distance of 75 m from the base, you look to the top of a building with an angle of elevation of 27°. Approximate the height of the building to the nearest whole meter.2. Solve using Cramer’s rule.

−4 x+ y=19

3 x−2 y=−183. Find the area of a triangle given A = 98°, b = 13 cm, c = 8 cm to the nearest whole unit squared.4. Given 3i is a zero of the polynomial function f(x) = 2 x5+x4−7 x3+21 x2−225 x+108, find all remaining zeroes.

5. Solve ln (4 x2−3 x )=ln (16 x−12 )−ln x.6. Given f(x) = 3 x2−2x+5 and g(x) = x + 8, find f(g(x)).7. Solve 6e2x=72.8. Verify

sin(x+ y )sin (x− y )=¿ sin2 x−¿ sin2 y¿¿.9. Find the exact value of sin−1(−1

2) .

10. Write a polynomial function with zeroes 0, 3, 1 + i.11. Give one positive and one negative coterminal angle to θ=−7 π8 .

12. Divide using long division.2x4−7 x3−38 x2+103 x+60

x−3

13. Find one complementary and one supplementary angle to θ=2 π7 .

[B]1. Two sides of a triangle have lengths 22 and 29

inches. The included angle is 108°. Solve the triangle.

2. Solve the multivariable system using method of choice.

−2 x+ y−3 z= 0

3 x−4 y+10 z=−7

5 x+2 y+8 z=23

3. Find the inverse of f(x).

f(x) = √5−x

4. Solve sin2 x+2sin x=−1

5. Write the equation of the line parallel to 5 x−3 y=7 through (-2, 5).

6. Find the zeroes of f(x) = x3+ x2−4 x−4 and state the multiplicity wherever necessary.

7. Find the domain, all zeroes, and any and all asymptotes.

f(x) = x2+3 x−4x2+2x−3

8. Find the exact value of cos 17π12 using a sum or

difference formula.

9. Factor e2x+3ex−130.

10. Find all solutions on the interval [0, 2π).

sin 2θ−¿ sin θ=0¿

11. Find any and all relative extrema and state any and all intervals of increase and decrease.

f(x) = 3 x4−2 x3+3 x2+5 x−3

12. Solve 25x +6=42 x+1.

13. Given that sin θ=12 , determine the exact value

of csc(90°−θ).