Complex numbers Questions and Answers

Solve the right triangle E G EG FG 9 mZE 26 Write your answers as integers or as decimals rounded to the nearest tenth F O

Simplify each expression 3x 7x 6 9 6x 3x 9 5 A 7 A 8 8 x 10 x 2 1 2x 28x 8x 14 x B x 4 3 D 4 2k 9 5k 2 5k 8 15x 51x 18 15x 16x 4 D 0 Simplify each and state the excluded values k k 12 k 6k 40 k 3 A 10 4 k 10 5k 3 0 B B 5 x 8 D 5k 8 0 5k 2 x 3 1 x 3 x 9 x 2 2 52 556 6 Factor each completely 9 2x48x 10x A 2x x 1 x 5 B 2x x 1 x 5 C 2 x 1 x 5 D 2x x 1 x 5 6 3a 9a 3 5a 9a 5 C 10a A B 8 D 49

1 Evaluate each function 10 w t 1 Find w 10 A 7 B 0 D 10 C 4 Evaluate each function Round to the nearest hundredth if necessary TWO DIGITS 11 p n n 4 2 Find p 1 4 A 3 9 B 5 6 C 7 3 D 6 4 Each graph represents a relation Determine if the relation is a function 2 12 AV 6 A The relation is not a function B The relation is a function Y

2 Find the component form of v given its magnitude and the angle it makes with the positive x axis Magnitude Angle v 4 0 O 0 0 O 4 4 O 0 4 O 4 0

2 Find the component form of v given its magnitude and the angle it makes with the positive x a Magnitude Angle v 4 0 0 0 0 0 4 4 0 0 4 4 0

3 The initial and terminal points of vector v are 3 8 and 7 1 respectively Select v in component form v 4 9 v 4 9 v 4 9 v 4 9 v 9 4

1 Find the component form and the magnitude of the vector v Initial Point 1 3 Ov 1 8 v 15 Ov 9 12 v 8 Ov 9 12 v 15 Ov 1 8 v 8 v 8 9 v 12 Terminal Point 8 9

9 Evaluate tan 1 without using a calculator Leave your answer in radians using as part of your answer and explain your process

4 An airplane flies at an altitude of a 9 miles toward a point directly over an observer Consider and x as shown in the figure Write as a function of x a mi

2 Use an inverse trigonometric function to write as a function of x e a x 5 Lo a

1 Use the properties of inverse trigonometric functions to evaluate the expressio sin arcsin 0 9 O 0 9 O sin 0 9 O 0 9 O sin 0 9

8 Use a graphing utility to select the graph of the two equations in the same viewing window Use the graphs to determine whether the expression are equivalent 3 sinx cscxX y1 V 3

7 Determine whether the function below is even odd or neither f x x csc O Odd O Neither X Even

3x Determine lim 6 6 2 O infinity O 1 2 O infinity O 3

2 2 2 i12 2

E Consider the following sets A 1 2 3 4 B 2 4 6 8 C 2 3 5 7 Find A A U B B An B C AUB n C D n A U B

otal number of papers that he has left to deliver at any given time can be approximated by the equation P 200 4m where m is the number of minutes since he left for the paper route and P is the number of papers he has left to deliver 13 How many minutes will it take Michael to have 100 papers left to deliver a 25 b 50 c 75 d 200 14 How many papers will Michael have left to deliver after half an hour a 198 b 80

d 9 12 Which of the following is the sum 5 2i 6 5i a 1 7i b 11 7i c 11 3i d 11 7i 7 2 1 59 6 79

10 If 3x 4 11 what is the value of 2x a 4 66 b 5 c 10 d 90 6 4 11

6 Find the measure of each indicated angle

8 If 2t 12 what is the value of 4t 4 a 6 b 10 20 d 42

erything at a store is on sale The store offers a 20 discount a The regular price of a T shirt is 18 What is the discount price Boya Unit OF b If the regular price of an item is x dollars what is the discount price in dollars c The discount price of a hat is 18 What is the regular price

ens con 1511 3 829 501 0 2x c 1 2 x 60 d 2 it S 2x33 E 381 mo

Rewrite the quadratic function 2 y x 2x 3 in vertex form Answer y x 2 x 3 y x 2 3 Oy x 1 2 x 2x 3 0 O y

What is the vertex for the quadratic 2 function y x 2x 3 Answer 2 3 O 1 2 3 2 2 1

Factor completely 46x yz 29z

Factor the expression completely 4 x y xy

Factor the expression completely 60x 54x Answer

Solve for all values of x by factoring Answer x 6x 10 Additional Solution X No Solution

Write the quadratic equation in standard form 2x 9 4x Answer 2x 1

11 A 34 22 C 36 02 Find each quotient 11 z I WIN Al A 1 C 38 B B 29 72 D 39 52 D l c w 8

Given the angle 3 4 To which quadrant does belong Write your answer as a numerical value 2 T Find the reference angle for IN RADIANS 4 Find the point where intersects the unit circle

Find RS S R 21 RS 7 9 T Write your answer as an integer or as a decimal rounded to the nearest tenth

Graph the image of ABCD after a dilation with a scale factor of 4 centered at the origin 6 4 D 2 B 1 0 8 6 4 2 2 4 6 8 Y N 2 C 4 6 00 8

Graph the image of trapezoid CDEF after a dilation with a scale factor of centered at the origin 1 4 F 1 0 8 6 4 C 2 10 8 6 4 2 2 4 6 8 1 0 y 2 E 4 6

4 The daily consumption C in gallons of diesel fuel on a farm is modeled by C 30 1 21 6 sin 2 t 365 10 5 10 where t is the time in days with t 1 corresponding to January 1 What is the period of the model

a 3 points Sketch the graph of f x 2 e by transforming the graph of y e Include any relevant asymptote on your graph

sig mot no estoq vodotesibi ol sua stel motorun ein to ten 12 Prove the following identity tan x sin x sec x cos x sec x

12 Let A 2 40 120 a 3 b Which of the following vectors is in the column space of A c 6 13 Let W be the subspace of R spanned by the vectors u 0 1 1 and u 1 2 1 Use the Gram Schmidt process to find an orthonormal basis for W b a 0 1 0 0 0 e 0 oto 0 to to to e 0

9 Let V be an n dimensional vector space Which of the following statements are true i Every linearly independent subset of V is a basis for V ii Every set of vectors that spans V is a basis for V iii If V span V1 V2 Vn then V V2 Vn is a basis for V a all of them b none of them c iii only d ii only e i only

6 Which of the following sets of polynomials form a basis for P 1 1 2 3x ii iii 1 1 a i and ii only b i only c none of them d all of them e ii and iii only 1 2 1 1 1

Decem 1 Let V be a vector space with dimension n 2 Which of the following statements are true 1 Every set of n vectors in V is a basis for V ii Every set with less than n vectors must be linearly independent iii Every set with more than n vectors must span V a all of them b none of them c ii and iii only d i and iii only e i and ii only

14 Let y 3 sin x a Determine the amplitude and period b Sketch the graph of this function Make sure to indicate key points on your graph 6 5 4 3 2 1 87 77 6 5 4 3 27 1 2 3 4 5 56 6 K 2 3 4 5 6 7 8

4 Find the values of 0 in degrees 0 0 90 and radians s 0 0 7 2 sec Not defined and cot 0 0 without the aid of a calculat

5 Use the given function value s and trigonometric identities including the cofunction identities to find the indicated trigonometric functi sin 0 0 tan 0 0 in 00 and ton 008

Video The graph shows g x which is a translation of f x x Write the function rule for g x 2 10 8 6 4 2 g x 1 0 8 6 4 2 O 2 4 6 8 10 y 2 4 6 8 Write your answer in the form a x h k where a h and k are integers or simplified fractions

b log x 4 log x 7 2

13 Solve the following equation 2 sin 0 cos 0 2 for 0 0 2 v atqso i a viem wolnoitonuri sno of onos si s t que botix moy aislyx Torsd 2 noionit sit to setovat oitonut oil to dagodt i

9 Explain how you can use the unit triangle 45 45 90 and it s side measures to find exact values for sin 45 and cos 45

7 6 8 Find the point x y on the unit circle that corresponds to the real number Use your results to evaluate cos t