Algebra Questions

8 A 1 1

A B 2T 5 C 3x D V

2 3n A 3n B 2n C 3n D D 9n

Simplify the expression 2 xo QC X

15 1 Determine the force in each member of the truss and state if the members are in tension or compression Set P 45 kN P 30 kN CY P2 D MEMIN B 1 5 m

Find two functions f and g such that h x can be expressed as the function indicated Several answers are possib h x 3x x f g f x g x

Compute the partial sums S2 S4 and S6 S S4 S6 3 3 3 3 22 32 42

Calculate S3 S4 and S and then find the sum for the telescoping series n 1 72 where S is the partial sum using the first k values of n S3 S4 S S5

2 413 A 4v 1 2v 15 C B 4 D 2v 16 2x A 4x C x B D 3x 2 2

Sketch and find the coordinates of the point corresponding to each angle on the unit circle P is at 90 P Q is at 90 Q i R is at 360 And i

oblem 6 A linear dynamical system can be created for two masses connected by springs between one another and connected to opposing walls The state vector at time t is a 4 x 1 vector consisting of the displacement and velocity of each of the two masses The transition matrix for this dynamical system is given by the following matrix 1 0 33232 16 5 1 i 0 1 16 5 30 O 00 25 0 0 8 25 Because the system oscillates there will be complex valued eigenvalues Find the eigenvalue associated with the following eigenvector 1 3323 0 1 5

11 13 Simplify Your answer should contain only positive exponents 11 a 12 12 4k A 16a A k 2 C 1 1 256a C 13 w w w w 3 3 A 36 26 B D D B 1 1113 1 1 14 4 3 4 A 4 C 4 14 B 64k D 16k B D IT ZO

7 9 Simplify Your answer should contain only positive exponents 8 8 xx 7 3v2v v A 9 Simplify 9 2p A p C 9p 12 B US D 4 B p 2 D 4p 10 A 4x 2 12 6 10 3v A 16v C 16 12 212 B D B 16 2 D 81v4

Integer Exponents Simplify 11 3p 3p 2p A 6p C 6p 3 B 4p D 18p Simplify Your answer should contain only positive exponents 3 2 2 4 2 2 4 A 2 C 1 122 B D 25 2 2 34 34 A 94 C 4 K C 2 B 44 D 945 B 2 D 1

blem 2 In any given year a person may or may not get the flu Past records show that if a person has the flu one year then due to a build up of antibodies there is a 90 chance that they will not get the flu in the following year If they don t have a flu in a given year then there is a 20 chance that they will get the flu the following year a If a person does not have the flu one year what is the probability that they will also not have the flu 2 years later b In the long run what proportion of years does a person not have the flu

5 Simplify 5 2b ba 2a b A 4b a C 4a b 77 3v 20 v A 9 B 16ba D 48 B Simplify Your answer should contain only positive exponents 8 12 S 6 D 4v 6 451 2 A 6y x 8 A 4x 02 B 24x D 8x 12 2 B D

13 15 13 3 3 A 36 9 7 15 4 A 4 c 2 1 2v B 1 D 1113 B 4 D 2v 14 16 14 4 A 4 C 4 X 2x A 4x C 16 B D B 4 3 x 2

oblem 3 a Express the complex number 4 3i 3 in the form a bi b Express the below complex number in the form a bi 7 3i i 3 6i c Consider the following matrix A 2 4i 2 4i 1 5i 1 2i Let B A Find b22 i e find the entry in row 2 column 2 of 4

Problem 4 Which of the following is a solution to the equation 3 i A 2 3 cos 17 18 i sin 17 18 B 2 cos 11 9 i sin 117 9 C 21 3 cos 23 18 i sin 23 18 D 2 3 cos 8 9 i sin 8 9 E 2 3 cos 10 9 i sin 10 9 F 2 3 cos 13 18 i sin 13 18 G 2 3 cos 7 9 i sin 7 9 H 2 3 cos 19 18 i sin 19 18

Problem 7 Find the values of c c2 and c3 so that c 2 4 1 0 3 4 0 c3 1 0 0 3 12 3 Problem 7 enter the values of c c2 and c3 separated by commas

5 em 5 Express 2 3 67 in the form a bi Enter the values of a and b in that order into the answer box below separated with a comma Enter your answer symbolically ac in these examples if your answer is a bi then enter a b in the answer box

K Use an identity to write the expression as a single trigonometric function 1 1 cos 142 2 cos 142 2 0 Type an exact answer

Determine whether the positive or negative square root should be selected 1 cos 401 2 sin 200 5 Since 200 5 is in quadrant the 1 5 6 square root should be selected C

K A 1 1 and 0 x 2 determine the exact value of cos 2 Given that cos cos Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators

Use a half angle identity to find the exact value cos 165 Which half angle formula should be used to find the exact value of cos 165 Select the correct choice below and fill in the answer boxes to complete your choice Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OA cos 165 cos OB cos 165 cos OC cos 165 cos 5 2 OD cos 165 cos H 2 2 t 2 1 cos 2 1 cos 2 1 cos 1 cos 1 cos 1 cos

Simplify the expression by using an appropriate identity Do not use a calculator cos57 cos33 sin57 sin33 COL Write the expression using the sum or difference formula for sine or cosine Choose the correct answer below OA cos57 cos33 sin57 sin33 cos 57 33 cos 24 B cos57 cos33 sin57 sin33 cos 57 33 cos 90 OC cos57 cos33 sin57 sin33 s sin 57 33 sin 90 OD cos57 cos33 sin57 sin33 sin 57 33 sin 90 Points 0 5 of The exact value of cos57 cos33 sin57 sin33 is Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators

K Given that sin 0 sin 20 cos 20 2184 7225 13 and cos 0 0 determine the values of the sine and cosine functions for 20 85 Type an integer or a simplified fraction Type an integer or a simplified fraction

Write the expression as a function of x with no angle measure involved sin sin ALG T 4 cosx sinx C X 2 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

rite the expression as a function of x with no angle measure involved sin TO 4 X 1 cos x sinx 2 mplify your answer including any radicals Use integers or fractions for any numbers in the expressi

Question 7 5 5 9 Part 1 of 2 Use identities to find values of the sine and cosine functions of the function for the angle measure 2x given tan x 4 and cos x 0 cos 2x 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Given that sin 8 sin 20 Question 1 5 5 7 Part 1 of 2 Type an integer or a simplified fraction 7 and cos 8 0 determine the values of the sine and cosine functions for 20 25

Use identities to find values of the sine and cosine functions of the function for the angle measure 7 3 20 given sin Question 8 5 5 11 Part 1 of 2 and cos 0 0 cos 20 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Question 4 5 5 37 Use a double angle identity to find the exact value of the expression cos 2120 sin 2120 cos 2120 sin2 120 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

5 COS Use an identity to simplify the expression Do not use a calculator T 2 9 sin 2 COS Sin 2 9 9 Type an exact answer using as needed Question 5 5 5

Determine the solution set of the quadratic equation by observing the graphing calculator screens Then verify your solutions by solving the equation X Simplify your answers Type an integer or a decimal Use commas to separate answers ED f x 4x 7x 15 Zero x 3 y 0 Q o Q Q 2

Find the zero s of the following function x x 14x 4 The zero s of the function is are Simplify your answer including any radicals Usent numbers in the expression Use a comma to separate Express complex numbers in terms of i Type each m

Save The formula S 16t is used to approximate the distance S in feet that an object falls freely from rest in t seconds The height of a building is 1317 feet How long would take for an object to fall from the top The object would fall for seconds Simplify your answer Type an integer or a decimal rounded to the nearest tenth

Find the zero s of the following function f w w 10w 21 The zero s of the function is are Simplify your answer including any radicals Use integers or fe numbers in the expression Use a comma to separate answers Express complex numbers in terms of i Type each solution of

7 9 points Given the polynomial p x x x 1 x 5 do the following a Determine all of the x intercepts of the graph of p x X b For each x intercept found in a give the multiplicity of each AND then tell whether the graph CROSSES or TOUCHES TURNS at each of the x intercepts answer both for each intercept

8 9 points Match each of the three given graphs to the one function that is MOST LIKELY the one with the given graph Look at the DEGREE and the LEADING COEFFICIENTS as well as what is happening at the x intercepts Simply write the letter of the function on the line under the matching graph ONLY ONE function will go with each graph thus TWO of the functions will NOT be used at all a x ax x 3 x 1 for a 0 b f x ax 2x 3x 4 for a 0 c f x a x 3 x 1 for a 0 d f x ax 2x 3x 4 for a 0 e f x a x 2 x 0 5 x 1 5 for a 0 y 10 4 pdf 5 2 1 5 1 0 5 0 5 1 1 5 2 2 6 8 10 8692 x 4 40 20 A 20 100 0 100 200 300 X

12 10 points Solve the rational inequality Write your answer using interval notation x 1 0 2x 9

11 8 points Given that given that x 2 is a zero of the polynomial p x x 2x 16x 32 use any appropriate method either division method and factoring to find the remaining zeroes of p x

Suppose A B and C are positive constants and x y C Show that the minimum value of Ax By occurs when BC and y AC A B A B N

4 10 points The profit that the vendor makes per day by selling x pretzels is given by the function P x 0 004 x 2 8x 300 A Find the number of pretzels that must be sold to maximize the daily profit

6 6 points What is the end behavior of p x You may describe it with words symbols or a sketch

9 8 points Use long division to perform the indicated operation x 4x 11 x 5

10 8 points Use synthetic division to perform the indicated operation x x 4x 11 x 5

Use the polynomial p x 3600x 0 4x 500x 24x to answer questions 5 and 6 5 6 points Find the degree of p x and leading coefficient of p x

1 8 points Sketch the graph of y x 3 2 using transformations be sure to label the vertex

3 10 points Write an equation for the parabola given below in vertex form i e y a x h k 1 2