Complex numbers Questions and Answers

9 Given cos 0 and 0 lies in Quadrant III what is the exact value of sin 0 in simplified form 3

12 What is the exact value of 117 6 T 3 5T 6 5TT 3 3 in radians Circle the answer be sure to show work and explain

7 What is the exact value of the trigonometric expression Note You should be able to find exact sine and cosine values as well tan 27 3

8 What is the exact value of the trigonometric expression in simplest form TL 2 cos 2 tan TT 3

6 A point on the unit circle lies on the terminal side of an angle in standard position in Quadrant I Indicate whether each measurement is positive or negative The cosine of the angle is circle one positive The sine of the angle is circle one positive negative negative

3 t A circle has a radius of 28 cm What is the arc length intercepted by a central angle that measures 4 radians Express the answer in terms of 7 Note You should be able to set up and solve for radius central angle and arc length

What is the product of 71 and 3 2i O 14 21i O 14 21i O 14 21i O 14 21i

What is the value of 6 2i 7 8i 01 6i O 13 10i O 13 10i O 1 61

Simplify the polynomial given the operation 3x 4x 10x 7x 2

Subtract 9a 6a 5 from 10a 3a 25 Your answer should be a polynomial in standard form

8x 27 0 3

Write the ploynomial function in factored form with real and rational coefficients with given zeros 3 2 and 1 i

Write the polynomial function in factored form with real and rational coefficients with the given en zeros

olve the ploynomial equation by finding all roots x 2x x 2 0

4 The graph shows a linear relationship between and y Suppose a represents the number of months Jada plans to make equal payments to her mother for the money she borrowed for a new laptop and y represents the amount of money in dollars she still owes her mother a b C Find and interpret the and y intercept of this line Write an equation of this line Amount owed 30 600 700 600 Kiran s work 3x y 5 3 1 2 5 3 2 5 500 100 Xntercer 6000 15 The point 2 1 is not a solution to the equation 400 Find and interpret the slope of this line 1 intercent 30 300 200 2 20 18 16 Number of month d If Jada has made 12 months of equal payments how much money does she still owe her mother Explain your thinking 250 Since the ordered Peir is 12 250 4 6 8 10 12 14 5 Kiran is determining if the ordered pair 2 1 is a solution to the equation 3x y 5 His work is shown Is he correct Explain your thinking No 6 The ordered pairs 0 5 1 7 5 and 2 10 are solutions to a linear equation What is the linear equation Express your answer in the form Ax By C Show your thinking 21 1

And 6x 6x 6 7x 6x 5

According to the data from the U S Census Bureau for 1990 2009 the number of commercially owned automobiles in the United States can be modeled by the function A x 1 4x 130 6x 1831 3x 128141 where x is the number of years after 1990 and A x is the number of automobiles in thousands The number of privately owned automobiles in the United States can be modeled by the function P x x 24 9x 177 9x 1709 5 where x is the number of years after 1990 and P x is the number of automobiles in thousands Create a polynomial that represents the total number of automobiles owned

Which angle has a cosine value of O ZA O ZB LC B 2

Mia is standing 210 yd from a radio tower The angle of elevation from where she is standing on the ground to the top of the tower is 11 How tall is the radio tower Round the final answer to the nearest tenth Enter your answer in the box A

Solve for z In 63 In z ln 7 Enter your answer in the box Z 9

Which of the following is a complex number that is not in the set of real numbers O 8 O 2 5 C O T 3 7i

Which expression is equivalent to i 256 O i 01 O 1

Which of the following is a complex number that is not in the set of real numbers 0 7 4 9i 0 O2 3

Simplify 64 81 O 8i O 32i O 8

4 Zero x ai x ai x 2i x

1 Algebra Prep Solving Rational Expressions Solve each equation Remember to check for extraneous solutions 1 1 S 4 5 22 2 2 5

7 2n 7n 5

5 3b 25b 50

3 m 7m 6

9 Find the product x 2 2x

8 y 4x 20x 24 1

5 2m 16m 32

2 3 If y 3x x 5 and z 5 and z 4x 34 3 6x 4x 22 1 6x 4x 2 x 12 which polynomial is equivalent to 2 y z 2 6x 3x 17 4 6x 2x 17

2023 2024E T M RET M YILI KIR EH R MESLEK ve TEKN K ANADOLU L SES 10 SINIFLAR MATEMATI DERSIL D NEM 2 YAZILI SINAV SORULARI ADI SOYADI 1 22255 5 basamakl 2 6 ki inin i inden 4 ki i ka farkl se ilebilir ekilde say s n n rakamlar ile ka farkl say yaz l r 3 Bir torbada ve 6 Sari top vard r secilen bir topun K rm z olas l ka t r 4 fiR R f 7 5 S Z Z birim fonksiyon m 5 k rm z ka t r 4 Beyaz Rastgele olma f x 4x 5 f x m 2 X ise NO 6 2 12 0 SINIFI YA 4 2 34 Spru Sayis Ac 2 00 mert 0 1 fou Ise91f R R 3 Zaman G n 8 A 0 3 m 7 B 5 8 10 12 f A B f x x 5 fonts m kaati Birebir oldu una g re 9 RR fog 3 Asli ile ment in 4 g nde G zd kleri toplam soru say s ka t r f 2 f 3 5x 3 fix 3x 1 g x 5x 7 10 A a daki fonksiyonlar n tersini yaz n z f x 3x 2 ise f x 1

The data below shows the estimated population of a highly populated area of the United States during a period of 6 decades Decade Population in millions 1950 1960 1970 1980 1990 2000 2010 10 6 13 16 19 7 24 2 29 8 36 7 3 Use a graphing calculator to find an exponential model that shows the relationship between the decades x since 1950 and the population y Use 0 for 1950 1 for 1960 4 How can you rewrite the exponential growth function in Exercise 3 to find the yearly growth rate 5 In 2015 Allie inherited land that was valued at 200 000 In 2016 the value of the land increased to 212 000 If this rate of increase continues what exponential model can you use to describe the increase in the value of the land over time

Y Y 168 In a shop the price of a jacket is 168 more expensive than a T shirt If the total price of 2 T shirts and a jacket is 528 find the total price of a T shirt and a jacket 6 marks

02 05 HC The functions f x x 4 2 and g x x 2 2 have been rewritten using the completing the square method Apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning

Show all work to solve 3x 5x 2 0

Which of the following leading terms would make the expression a perfect square trinomial 156xy 169y A B C D 36x2 81x 25x 49x

POSSIBLE POINTS 2 Match each polynomial from the first column with a factoring technique in the second column If none of the techniques can be used to factor the polynomial choose none 49x 100y 64a 48ab 96 a 3a 2a 6 144m 25m Factor out GCF Perfect Square Trinomial Difference of Squares Factor by Grouping None 1 of E

3 x 2

5 Given the points A 3 0 1 and B 2 1 0 a Find the point Con the YZ plane i e the plane spanned by j and k such the points A B and Care collinear b Find the distance between the origin and the line passing through the points A and B c Determine whether the points A and Bare on the same side of the plane 7x y z 1 6 a If u 0 1 1 and v p 4 p then find the parameter p such that the angle between vectors u and v is 3 b Show that if u and v are vectors in R such that u vand u v have the same length then u and v are orthogonal c If u v and w are vectors in R then prove the identity 6u vxw u 3w 2v

Select all expressions that are equivalent to 16 a C 3 16 2 b 16 163 d 32

X 15 x 16 3 Select one O a 15 16 b All real numbers Oc No solution O d 1 3

Write an equation for a function that has the given characteristics The shape of y x but shifted left 7 units and up 6 units Select one x 71 6 O a y O b y x 71 6 O c y O d y x 71 6 x 7 6

For the piecewise function find g 2 x 3 for x 2 4 x for x 2 g x Select one O a g 2 2 O b g 2 5 O c g 2 1 O d g 2 6

5 Elena is planning to go camping for the weekend and has already spent 40 on supplies She goes to the store and buys more supplies Which inequality represents d the total amount in dollars that Elena spends on supplies Od 40 Od 40 Od 40 Od 40

8 Find the constant term in the expansion of 6x 2 3x

b cscx sin x cot x cosx

2 There are 13 animals in the barn Some are chickens and some are pigs There are 40 legs in all How many of each animal are there