Algebra Questions

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

3 6x 9x 1 Find

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

1 2 Factor each completely 1 16x 36x 70 A 2 2x 7 4x 5 B 2 2x 7 4x 5 C 4x 7 2x 5 D 2 4x 7 2x 5 Simplify each expression 2 m 3 A B C D Sum 2 2m 1 m 3 2m 1 5 m 3m 4 4 2m m 3 2m 1 6m 8 m 3 2m 1 Find each product 4 4p 8 6p p 4 A 32p 24p 44p 12 B 10p 19p 46p 16 C 5p 32p 7p 2 D 24p 44p 24p 32 3 3 2 2 v1 A C 1 v v 1 2 2v 7 2v 2 v B D 8v 15 v 3 6v 15 v 2v v 3

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

8 A traffic light weighing 15 pounds is suspended by two cables see figure Find the tension in each cable if 0 40 and 0 35 Approximat the answers to one decimal place 0 0

10 Find the component form of v if v 10 and the angle it makes with the x axis is 120 O 10 10 3 5 2 5 2 0 5 3 5 0 5 3 10

5 Find the component form of v if v 6 and the angle it makes with the x axis is 150 O 6 3 6 O 3 2 3 2 O 3 3 3 O 3 3 3 6 6 3

9 Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vec Initial Point 9i 5j O 5i 9j O 9i 5j O9i 5j 9 7 Terminal Point 0 2

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

6 Find u v u 6 1 v 1 7 O 8 7 O 7 7 O 8 9 O 8 8

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

8 Find an algebraic expression that is equivalent to the expression tan arccos

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

6 Evaluate arccos without using a calculator 3 2 E 6 OF OF F M O F O 37 4

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

3 A television camera at ground level is filming the lift off of a space shuttle at a point a 600 meters from the launch pad see figure Let 0 be th angle of elevation to the shuttle and let s be the height of the shuttle Write as a function of s m XX Not drawn to scale

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

10 How are the GRAPHS of sin x and cos x different How are they similar Explain in detail your answer U Font Family AA A 3 C D

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

etermine the values of a for which the following system of linear equations has no solutions a unique solution or infinitely many solutions You can select always ever a or a then specify a value or comma separated list of values X1 2x2 2x3 1 3x7 6x2 9x3 12 2x7 ax2 7x3 12 Ho Solutions Unique Solution nfinitely Many Solutions Always Always Always Always Never When a SUBMIT AND MARK SAVE AND CLO

Use the method of corners to solve the linear programming problem An investor has decided to commit no more than 80 000 to the purchase of the common stocks of two companies Company A and Company 8 He has also estimated that there is a chance of at most a 1 capital loss on his investment in Company A and a chance of at most a 4 loss on his investment in Company B and he has decided that these losses should not exceed 2 000 On the other hand he expects to make a 15 profit from his investment in Company A and a 21 profit from his investment in Company B Determine how much he should invest in the stock of each company x dollars in Company A and y dollars in Company B in order to maximize his investment returns x y What is the maximum return in dollars

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

Use long division to divide Simplify your answer completely 7 x 1 x 1

a Explain how biotic and abiotic factors can impact growth of populations b How does one feeding niche impact others in

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

Lion Elephant Nitrogen Digestion Lab a How do carnivores utilize food items to complete necessary biological functions b How do herbivores utilize food items to complete necessary biological functions c Which element is lacking from the major components of herbivore diets d Explain how this element can be transferred from the environment into a form that can be consumed by animals

2 2 2 i12 2

Find the exact value of sec 0 if a 7 C 8

Refer to the sets A B C and D Determine the union or intersection as indicated Express the answer in interval notation if possible A x x 1 B x x 1 C x x2 9 D x 1 x 0 Bn C 0 0 0 0 0 0 0 0 OVO 8 8

Furthermore for the rules of exponents to be consistent then am n RATIONAL EXPONENTS T 16 116 23 3 64 2 am avnjm Examples

b c 3 5ab3 Write your answer using only positive exponents 0 15a

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

16 A publishing company orders black and blue ink in bulk for its 2 color printing press To keep things simple with its ink supplier each time it places an order for blue ink it buys B gallons and each time places an order for black ink it buys K gallons Over a one month period the company places m blue ink and n order of black ink a The company placed twice as many orders for black ink than for blue ink in January Create an equation to represent this situation in terms of m and n b Given an interpretation for the expression c Find the value of 72 m n in terms of the orders placed in January

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

3 Lydia is deciding which company she should hire to clean her carpet Company A 140 plus an extra 15 off Company B 0 50 per square foot Company C 42 50 per room 0 50 11 62 Lydia has 3 rooms to clean Each room is 8 feet by 11 feet Which company offers Lydia the best price Show your work and explain how you found your answer

2 Derrick went to the grocery store and purchased of a pound of ham for 6 99 per pound of a pound of cheese for 3 99 p r pound a loaf of bread for 2 49 and 1 gallon of milk for 2 89 The sales tax on food items in his tate is 4 3 What is Derrick s total for the groceries 544 after tax Round your answer to the nearest cent Sub total

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

17 Which values of x satisfy the inequality 2x 3 11 a X 4 B x 4 c X 4 d X 4

7 Without solving identify whether each of the following equations has a unique solution no solution or infinitely many solutions a 3x 5 2 b 6 x 11 15 4x c 12x 9 8x 1 4x d 2 x 3 10x 6 8x e 5x 6 5x 4

11 If 2x 4 5 what is the value of 6x 3 a 0 b 0 5 c 4 5

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

a 3x 5 2 b 6 x 11 15 4x c 12x 9 8x 1 4x d 2 x 3 10x 6 8x e 5x 6 5x 4 8 If 21 12 what is the value of 4t 4 a 6 b 10 20 d 42 9 If kand k 5 what is the value of x a 4 5 b 5 c 12 d 18 18 2 5 4

4 Debbie s employee has reached her 1 year anniversary with the company and gets a 10 raise The employee used to earn 15 00 per hour How much does the employee earn in a 40 hour week with the 10 raise a 540 00 b 600 00 c 606 00 d 660 00