Weekly Workout Solve: Simplify Solve: Simplify #1 #2 #3 #4 #5 #6 #7 Solve #8.
PC Semester 2 Exam Review · 2018. 9. 9. · Pre$Cal($(Semester(2($(Review((1....
Transcript of PC Semester 2 Exam Review · 2018. 9. 9. · Pre$Cal($(Semester(2($(Review((1....
Pre-‐Cal -‐ Semester 2 -‐ Review
1. Simplify 34− 92 ∗ (4+ 87)− 2 ∗ 6. 2. Simplify 𝑖!". 3. Solve the equation 2𝑥 + 5− 6𝑥 = 2𝑥 + 87. 4. Factor the equation 𝑥! − 16𝑥 + 64. 5. Solve the equation 2𝑥! + 3𝑥 + 1 = 0. 6. Rewrite the equation log!" 324 = 2 in exponential form. 7. Rewrite the equation 125
!! = 5 in logarithmic form.
8. Solve the equation log! 𝑥 = log! 455. 9. Solve the equation log!(2𝑚) = log!(𝑚 − 3). 10. Solve the equation log!! −12𝑥 − 2 = log!! 𝑥! + 18 . 11. Solve the equation 6 log! 𝑦 − 3 = 12. 12. Solve the equation log 𝑥 + 6 + 4 = 7. 13. Condense the logarithmic expression 7 log! 𝑥 − 13 log! 𝑦 into a single logarithm.
14. Expand the logarithm log !"!
! completely.
15. Solve the exponential equation 3!!! = 2!!!. 16. Simplify ln 1. 17. Simplify log 10. 18. Convert 152° to radians. 19. Convert !"!
! to degrees.
20. What is a coterminal angle of !!!?
21. What is a coterminal angle of −213°? 22. Evaluate cot 34°. 23. Evaluate sin 30°. 24. You are standing 20 feet away from a tree. The angle of elevation formed between you and the top
of the tree is 48°. Find the height of the tree to the nearest foot. 25. An airplane is flying at an altitude of 1500 m. From the plane the angle of depression of a tree on
the ground is measured as 25°. What is the distance from the plane to the tree? 26. If ∆𝐴𝐵𝐶 ℎ𝑎𝑠 𝑎 = 9.4, 𝑏 = 6.5,𝑎𝑛𝑑 ∠𝐶 = 131°, 𝑓𝑖𝑛𝑑 𝑐. 27. Find the 6th term of the arithmetic sequence where a1=12 and d=5. 28. Write a simplified equation for the nth term of the arithmetic sequence -‐45, -‐36, -‐27, … 29. Find Sn for the arithmetic series where a1=3, d=5, and n=12. 30. Find the sum of the arithmetic series (5𝑛 − 12)!
!!! . 31. Find the 4th term of the geometric sequence where a1=36 and r=-‐1/2. 32. Write a simplified equation for the nth term of the geometric sequence 4, 16, 64, …
33. Find Sn of the geometric series 3 !!
!!!!!!! .
34. Find the sum of the infinite geometric series, 3 − !!
!!!,!
!!! if it exits.
35. Use the following matrices for questions.
A= 1 2 46 9 0
225
9 1 22 4 6
80
B= 2 −73 5 C=[
235−9
] D= −22 53 0
36. What is the size of the matrix A?
37. What is the size of matrix C? 38. What is B+D? 39. What is A+C? 40. What is AC? 41. What is BD? 42. What is D-‐1? 43. If a taco joint has two types of shells, three types of meat, and 7 toppings, how many possible tacos
can be made if you select one thing from each category? 44. You have to make a 6 digit passcode using numerals only. How many passcodes are there if you
cannot repeat digits? 45. Find the number of distinguishable permutations of the name SAVANNAH? 46. Given a standard deck of cards, what is the probability that you would select a 10 of diamonds or a
5 of hearts? 47. What is the probability of rolling an even number if you toss a 6-‐sided die once? 48. If the probability of winning a game is !
!, what is the probability that you will not win the game?
49. A bag contains 3 blue marbles, 4 red marbles and 2 green marbles. What is the probability of selecting a blue marble, and then a green marble, without replacement?
50. A class is give a list of 50 study problems from which 30 will be part of an upcoming exam. If a student knows how to solve 40 of the problems, what is the probability that the student will be able to answer all 30 questions on the exam?