Permutations and Combinations Questions and Answers

Factor the following polynomials or identify it as irreducible 8x 125 Below is a list cube roots 1 1 8 2 27 3 64 4 125 5 216 6 343 7 512 8 729 9 1000 10

A rectangle has a length of 2x 9 and a width of x2 3x 4 What is the polynomial that models the are of the rectangle A x 5x 13 B 2x 15x 19x 36 C 2x 3x 35x 36

7x x 4x 10x 6x 6x x

6x58x4 3 8x5 6x 3x

13x6 x5 6x4 7x5 6x4 5x

7x 13x8x5 20x 2x5 9x

17x 8x 9x7 4 2x 11x 8x 12

Which expression is equivalent to 60 O 47 15 O 2i 15 2 15

x 4 x y

3m 2 3m 2m 1

13 pq Given 3 r express p in terms of q and r 9 Diberi P 3 r ungkapkan p dalam sebutan q dan r Answer Jawapan 14 Solve each of the following linear equations Selesaikan tiap tiap persamaan linear berikut a 2k 6

A financial analyst constructs a statistical model to represent the market shares of several similar companies She then collects data over the next month to evaluate her model At the end of the month she finds that for one of the companies the difference between her model and the data is 5 She decides to collect data for an additional two months If her model is valid what could she expect from the total data collected after three months OA The difference between the data and the model will get smaller OB The difference between the data and the model will get larger OC The difference between the data and the model will stay the same O D It is impossible to predict how the difference between the data and the model change

Drag the appropriate factor to the missing box to factor each trinomial completely 6x 8x8 x 5x 1 5x 19x 12 5x 5x 18x 9 5x 4x 15x25 x

Find a subset of the vectors v 02 03 7 1 v 3 V V3 H That forms a basis for the subspace of R spanned by these vecto b Express each vector not in the basis as a linear combination of the basis vectors 5 Marks

03 04 HC The function f x x 7x 7x 15 has zeros located at 5 3 1 Verify the zeros of f x and explain how you verified them Describe the end behavior of the function

10 AB BA EN AB BA 45 A 5 B 6 min A C 7 The right D 8 answer is E 9

10 B 150 a 10 b

5 The school that Stefan goes to is selling tickets to a choral performance On the first day of ticket sales the school sold 3 senior tickets and 1 child ticket for a total of 38 The school took in 52 on the second day by selling 3 senior tickets and 2 child tickets Find the price of a senior ticket and the price of a child ticket

4 Emilee has a total of 580 She has 76 bills in all consisting of 5 bills and 10 billo How mo no of hill dono cho h

Factor each completely 15 2x 18x 28 17 4x 16x 12 19 3x 9x 12 21 5a 15a 200 23 2n 4n 70 25 4p 28p 24 27 3v 36v 96 16 6n 66n 180 18 6x 6x 336 20 3x 9x 84 22 6p 42p 180 24 3r 9r 30 26 2 10 28 28 2n 4n 6

9 4x 15x 9 completely 11 9v 24v 7 13 6x 5x 6 Har n 162 7 10 8v 6v 1 12 6m 7m 3 14 9a 55a 6 16 9n 18m 7

3 29 Find the exact value of sin u v given that sin u 5 sin u v sin u v sin u v sin u v sin u v 3 44 125 44 126 and cos v 24 25 Both u and v are in Quadrant II

1 4 A weight is oscillating on the end of a spring see figure The position of the weight relative to the point of equilibrium is given by y 12 displacement in meters and t is the time in seconds Find the times when the weight is at the point of equilibrium y 0 for 0 t 1 Equilibrium www cos7t 3sin 7t where y is

13 Use a graphing utility to graph the function f x 1 1 2 sin r cos2x

X 21 Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of 0 where 0 x 16 x x 4cos 0 16 cos O 4 sin 0 4 cos 0 16 sin 0 4 sin 0

X 12 Find the exact solutions of the given equation in the interval 0 2 sin 2x sin x 2 4 0 O X 3 Ox 75 11 X 2 6 6 O x 0 Ox 0 5 7 x 0 O x 0 2 T 3 2 3 5 TL 4 T 3 2 5 TL 3

1 4 5 12 21 2 5 3 6 8 11

b COS X 1 sinx COS X 1 sin x x15ml 1 2 tan x

15 Find the exact solutions to the trig equations for x 0 27 a 4 sinx 2 0 b 6cosx 3 0 c 2 tan x 2 0

32 y csc 2x

Sinx tanx cosx secx sin x cos x serx cosx 1 losx Seix

Write the polynomial in standard form Then classify the polynomial by degree and by number of terms 6x 5x 3x Write the polynomial in standard form Simplify your answer Classify the polynomial The polynomial is a

Find the midpoint between the interval 9 2

1 Use the Heron s formula to find the area of the triangle Round your answer upto one decimal plac a 3 08 b 0 78 c 2 48 3 5 0 4 0 4 0 1 0 7

5 Graph the expression on each side of the equals symbol to determine whether the equation might be an identity 2tan x sin x CSC X sin x csc X Identity Not an Identity

4 ANSWERS GIVEN AS A DECIMAL WILL BE COUNTED AS INCORRE 3 13 2 Solve each inequality 14 1 2 5x 4 s61 A x 7 or x 5 27 27 B 7 x 5 C 1 x 2 D x 1 or x 2 4 Find Solve each inequality and graph its solution 515 3x 5 3 3 27 A x orx 1 16 B 4 x 9 C x 5 or x 15 D 2 x 4 3 2 1 0 1 2 3 4 5 6 7 8 8 7 6 5 4 3 2 1 20 16 12 8 8 7 6 5 4 3 2 10 0 1 2 3 4 4 e 12 0 ZO

9 Explain what the period of a function is and how it affects the normal graph of a trig function

lain the products and reactants of photosynthesis a What factors limit the rate of photosynthesis Why b Why is oxygen a good indicator to determine if a plant is undergoing photosynthesis

6 In New York state sales tax rates vary by county In Allegany County the sales tax rate is 8 a A book costs 12 99 and a video game costs 39 99 Rounded to the nearest cent how much more is the tax on the video game than the tax on the book b Using n to represent the cost of an item in dollars before tax and t to represent the amount of sales tax in dollars for that item write an equation to show the relationship between n and t c Using your equation create a table that includes five possible pairs of solutions to the equation Label each column appropriately

6 The projected monthly sales in thousands of units of lawn mowers a seasonal product are modeled by S 71 3t 40cos Tt 6 where t is the time in months with t 1 corresponding to January Select the graph of the sales function over 1 year

xatol 1700 ts bios bus bybubong add you 7 The following transformations applied to the graph of the function f x ln x a shift left 2 units b reflect the result from a over x axis c shift up the result from b 3 units ne or bru Write the equation of the resulting graph and describe the end behavior of the function

1 Function g is related to a parent function f x sin x g x 8 sin 8x 7 Use function notation to write g in terms of f g x 8f 8x 10 g x 7f 8x 14 g x 8f 8x 7 g x 8f 8x 12

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 a 0 1 0 2 0 0 22 6 0 2 20 to to 6 e 0 2

5 The revenue R x of producing and selling AirPads is modeled by the function R x 5x 175x a How many AirPads need to be produced and sold in order to maximize the revenue Round to the nearest whole number ant of boilans enojnolans thean ainer d most juzex b What is the maximum revenue Round to the nearest cent

12 Prove the following identity tan x sin x sec x cos x sec x

EXPONENTS a a 5 so Estimating Square Roots A number is called a if its square root is an integer For example 25 and 36 are both perfect squares since 25 52 and 36 6 so 25 5 and 36 6 If we don t know the square root of some number x and don t have a calculator handy we can estimate the square root by bracketing it betweer two perfect squares for which we do know the square roots For example to estimate IO we know and 10 10 8 is between 2 Estimate the following square 23 Therefore 10 lies somewhere between and closer to 9 than to 16 According to a calculator 10 and 642 roots where and are perfect squares probably closer to because 10 is 95 is between and

1 Use the Law of Sines to solve for b Round your answers to two decimal places A 100 a 75 c 6 b 83 72 b 75 1 72 73

3 Use the sum to product formulas to rewrite the sum or difference as a product cos 30 cos 80

Find all solutions of the equation in the interval 0 27 List the solutions in increasing order If there is no solution enter NO SOLUTI 24 sin x 24 12 cos x X X X TU 3 X n 2 50 2 t 4 3 n 2 57 3 n 2 X n 2 X smallest value largest value

Which transformation changed f x to g x f x 3x 1 g x 3x 1 Vertical translation of 6 units Horizontal translation of 6 units Reflection across the x axis Reflection across the y axis