Algebra Questions

3 2022 Kuta Software LLC All rights Subtrating Rational Expressions Simplify each expression 1 2 6n A C A 4x 2 B n 5 C D 18n 5 6n 18n n 8 3n 9n 6 6n 18n n 1 4x 6x 3x 12x 6x 4 3 2x 1 37 x x 1 x 5 x 37 x 1 x 5 36 x 1 x 5 B D 2 3n 9n n 5 6n 18n 4 2 reserved 2 4 6b A B D A b 5 B 18b 1 96 36 6b 18b 1 6b 18b 4k 3 3b 1 b 2 3 b 3 6b 186 k 6 6k 15 C D 0 3k 7 6 3 k 30 k 4k 3 k 6 8k 21k 6 3 2k 5

5 A B 4a 10a C 77 9 D A B 4n n 2 C D A 6 B C D 21 5a 2a 2a 5 21 6a 2a 2a 5 21 15a 4a 3 2a 2a 2a 5 21 10a 2a 2a 2a 5 2n 3n 6 5 5n 6 21n 27n 10 5n 6 n 2 7 2n 3 21n 22n 16 5n 6 n 2 20n 29n 10 5n 6 n 2 2 4n 20n 1 3 n 2 n 5 2n 2 17n 6 4n 4n 20n 3n 6 6n n 2 n 5 1 4 n 5 6 8 10 A 4 n 2 B C D 8 A 2 r 2 B D 10 A B C 5n n 6 20n 5n n 6 n 2 11 6n D 3n 4n 8n 24 n 6 n 2 14n 24 5n n 6 n 2 4 3r 3 12 8r 3 r 2 r 1 2 2r 2r 5 5r 14 3 3 r 2 r 1 2r 14 3 r 2 r 1 6 2x 2x 18x 12x 48x 6 18x 12x 49x 2x 7 18x 12x 49x 2 x 9x 6x 24x 3 X 27x 17x 72 3x 3x 4 x 2

3 Subtrating Rational Expressions Simplify each expression 1 A 6n C A 4x 2 B n 5 C D 18n 5 2 6n 18n n 1 6n 18n n 8 3n 9n 6 4x 6x 3x 12x 6x 4 3 2x 1 37 x x 1 x 5 x 37 x 1 x 5 36 x 1 x 5 B D 2 3n 9n n 5 6n 18n 4 2 2 4 b 5 6b 186 A B C D A B 66 4k 3 23 1 3b 9b 3b 1 b C D 0 186 1 6b 18b b 3 6b 186 k 6 6k 15 3k 7 6 3 k 30 k 4k 3 k 6 8k 21k 6 3 2k 5

4 Find a un vector in the O 13 13 O VIS VTS V13 O VTVT 13 13 13 8 13 13 13 26 12 13 13 Ion o1

A population characteristic is normally distributed Approximately what percentage of the population lies within two standard deviations of the mean A 48 B C 68 95

Maggle claims that the function g x Which statement provides a correct analysis of Maggie s claim A B C D 4 is the inverse of the function of f x 3x 4 Maggie s claim is correct because if you add 4 to g x and then multiply it by 3 you get x Maggle s claim is correct because when g x is substituted into every occurrence of x in f x f g x x and when f x is substituted into every occurrence of x in g x Maggie s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x 8 therefore g x is not the inverse of f x Maggie s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x therefore g x is not the inverse of f x

19 What famous rap star does the following represent ICE Type a response

0 State the domain of the relation or function 10 8 A The relation is not a function B The relation is a function

Maggle claims that the function g z 3 4 is the inverse of the function of f x 3x 4 Which statement provides a correct analysis of Maggie s claim A B C D Maggie s claim is correct because if you add 4 to g x and then multiply it by 3 you get x Maggie s claim is correct because when g x is substituted into every occurrence of x in f x f g x x and when x is substituted into every occurrence of x in g x gl Maggie s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x 8 therefore g x is not the inverse of f x Maggie s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x therefore g x is not the inverse of f x

Researchers are conducting a study to test the effectiveness of a new medication Subjects are randomly divided into two groups the first group is given the medication and the second group is given s placebe herove the s two months after which subjects are asked to answer a questionnaire about their response to the drug and any potential side effects that they may have had This is an example of an experiment A B O D a sample survey an observational study a random phenomenon

Solve Simplify your answer log x 1 BIUEX X

A B C D y x

A student was finding solutions to the equation 4 2 5 0 and wrote down these steps Step 1 2 5 Step 2 x 5 4 Step 3 2 5 16 Step 4 2 11 Which statement is an accurate interpretation of the student s work e A B D The student found the correct solution to the original equation 11 x 11 is a solution to the equation in Step 2 but not to the original equation The student made an error in Step 3 The student made an error in Step 1

12 Write the slope of the line that passes through the given points 12 through 4 2 and 5 4 Write the point slope form of the equation of the line that passes through the given points 13 13 through 3 2 and 0 3 x 3 A y 2 5 B y 2 x 3 C y 3 x 2 D y 3 x 2 Solve each system by elimination 414 9x 6y 18 21 9x 7y Divide 5 15 a 8a 9a 6 a 2 A a 6a 2 B a 6a 3 C a 8a 3 D a 8a 2 2 a 2 4 a 2 Find each product 16 16 2x 8x 8 2x 3x 2 A 4x4 24x 16 B 4x4 22x 36x 8x 16

7 Sketch the solution to each system of inequalities 17 x 3y 9 x 3y 3 A B 6 D 1 y x X x

Given 2 64 Which of the following expressions is the value of x log264 log64 O OC A C B U 64 64

Solve for x logg4 x O A B C 312 213 32

11 4 7x 1 1 2 6 18 71 A No solution B x 0 6 or x 2 C All real numbers D x 46 4 or x 0 4 2 CUMMULATIVE EXTRA CREDIT Solve each inequality and graph its solution 3 Find each quotient 2 VIAG N A C 10 7 7 10 5 B D 8 7 6 5 4 3 2 1 0 1 2 3 A 15b 2b 20 C 15b 2b 8 4 34 35 10 7 0 3 2 1 0 1 2 3 4 5 4 3 2 1 0 456 6 7 8 Simplify each difference 3 3b3b 1 8b 7b 3 5b b 6b 3b 4 5b B 15b 2b 14 D 15b 2b 20 8b 2 3 4 5 6 05 10 15 20 25 30 35 40 45 50 Simplify each sum 4 n 8n 4n 2 1 n 3n 3n 2n 5n 4n 7n A 7n 12n n 8n 3 B 7n 12n n 8n 4 D 7n 12n n 8n 7 C 7n 12n n 8n 1 Simplify Your answer should contain only positive exponents x y 2x

66 It takes DeShawn 9 5 hours to mop a warehouse Perry can mop the same warehouse in 8 4 hours Find how long it would take them if they worked together 3 Solve each question Round your answer to two digits 7 0 1 9 9 x x Find f 1 4 Evaluate each function Round to the nearest HUNDREDTH if necessary TWO DIGITS 8 h a 2 1a 1 3a Find h 1 9 Evaluate each function ANSWER SHOULD BE A FRACTION OR MIXED NUMBER ANSWERS GIVEN AS A DECIMAL WILL BE COUNTED AS INCORRECT State the domain of the relation or function 10 7 An aircraft carrier left Port 51 and traveled east A submarine left two hours later traveling 10 km h faster in an effort to catch up to it After four hours the submarine finally caught up Find the aircraft carrier s average speed Ay A The relation is not a function B The relation is a function 11 Determine the slope of the line represented by the equation 16 4 y x

2 Solve for 0 where 0 0 360 in the following equations Round to the nearest tenth of a degree if necessary Drawing an appropriate triangle finding a reference angle general solutions and applying restrictions are suggestions for full credit a sec 0 3 0 QII

3 cos x 0 351 0 x

3tan x sec x 5 0

6 sin3x 1 0 x

2 4 2 sin x 3 sin x 1 0

2 tan 0 3

3 Does 2 1 2 3n n 0 converge or diverge If it converges what is the sum

Function f x x 6x 3x 26x 24 a Verify the given factors of f x x 3 3 1 6 x 2 1 3 2 1 6 2 Factors x 3 x 2 3 9 m 16 Nice 26 26 X X 24 24 X X

Find the standard deviation for the following 11 13 14 15 17 Round the answer to two 2 decimal places 2 24 1 23 O2 78 3 45

Let q represent the following statement q Chris can sing Symbolically express the statement Chris cannot sing 1 q 2 q 3 q N 4 q

A TI 84 calculator costs 79 99 What is the total cost of the graphing calculator if sales tax is 7 Round to the nearest cent 135 98 74 39 55 99 O 85 59

A paper manufacturing company converts wood pulp to writing paper The profit per unit of writing paper is modeled by p x 2x 15x 105 Evaluate the profit for converting 5 units of writing paper 1 170 2 230 3 130 4 118

Based on the scatter plot choose the best estimate of the correlation coefficient O 0 9 0 0 5 00 5

Write an equation in the form y mx b for the average cost y of a textbook x years after 1990 Use the data points 0 38 and 8 86 to find the equation Then use the equation to predict the average cost in 2012 1 y 38x 6 the cost in 2012 is 842 2 y 6x 38 the cost in 2012 is 86 3 y 6x 38 the cost in 2012 is 170 O 4 y y 38x 6 the cost in 2012 is 234

D Determine drug dosage by patient s weight For each kilograms of a person s weight 15 milligrams of a drug is to be given What dosage should be given to a person who weighs 240 pounds Use 1 pound 0 45 kg Multiply by 10 for each step to the right x 10 km hm dam m dm cm mm Divide by 10 for each step to the left 1 1 620 mg 2 8 000 mg 3 26 67 mg 4 3 600 mg 10

A garden is in the shape of a rectangle 43 feet long and 13 feet wide If fencing costs 6 25 a foot what will it cost to place fencing around the garden 118 25 3 493 75 350 00 700 00

3 3 31 244 3 y 3x 3 Oy 3x 3 Oy 3x 1 Oy x 3

3 ft 13 ft 6 ft 3 ft Determine the area of the given polygon 66 ft 25 ft 50 ft

nt Future Value A P 1 Present Value P mulas below 147 044 162 240 Suppose 15 000 is deposited into a savings account earning 4 interest compounded semi annually The balance in the account after 10 years rounded to the nearest dollar is O 22 289 10 095 A 1 nt

Position Administrative Assistant Sales CEO Project Management IT Human Resources Rounded to the nearest dollar what is the mean salary of these employees O a 55 650 b 29 500 c 43 500 Salary 31 400 29 500 109 000 49 500 77 000 37 500 d 31 436

Use the table along with dimensional analysis to convert the given square unit to the square unit indicated 59 cm2 to in 1 in 2 1 ft 1 yd 1 mi2 acre 6 5 cm 0 09 m 0 8 m 2 6 km 0 4 hectare ha 62 5 square inches 65 5 square inches 9 08 square inches 383 5 square inches

If 1 m 3 28 ft then use dimensional analysis and the given information to convert 4 km to feet kilo O 1 13 120 ft hecto 2 1 219 51 ft 3 13 12 ft 4 1 22 ft deka base meter liter gram deci 3 centi milli

Evaluate the function at the given value of the variable f x 2x 4x 2 f 3 4 28 14 46 None of these

Use the chart to convert 5 621 cm to m kilo 56 21 m 5 621 m 56 210 m 562 100 m hecto deka base meter liter gram decl centi

A flagpole casts a shadow of 25 ft Nearby a 7 ft tree casts a shadow of 5 ft What the height of the flag pole 35 ft 1 4 ft 875 ft 17 9 ft

What is the next number in the list 8 12 20 32 1 36 2 48 3 42 4 40

Only one of five possible answers of a multiple choice is correct What is the probability that your answer choice will be correct if you are selecting the answer at random 01 1323 01 1 20

Find the volume of the solid below 5 cm 6 cm 14 8 cm 4 cm 6 cm 8 cm

Evaluate the expression using the graphs of y f x and y g x Evaluate fog 2 99 g x 4 f x 8 x O A O B O C O D

1 7 12 Which function describes a parabola that opens downward and has a vertex of 2 3 a f x x 2 3 b f x x 2 3 c f x x 2 3 d f x x 1 2 7 d f x x 2 3 13 List the sequences of steps required to graph the function f x x 4 6 a horizontal translation 4 units to the right vertical stretch by a factor of 1 and a translation 6 units down b horizontal translation 4 units to the right reflection over the x axis and a vertical translation 6 units down c horizontal translation 4 units to the left vertical translation 6 units up and a reflection over the x axis d horizontal translation 4 units to the left reflection over the x axis and a vertical translation 6 units down 14 List the sequences of steps required to graph the function f x 3 x 7 1 a horizontal translation 7 units to the right vertical stretch by a factor of 1 and a translation 6 units down b horizontal translation 7 units to the right vertical stretch by a factor of 3 and a translation 1 unit down c horizontal translation 7 units to the left vertical stretch by a factor of 3 and a translation 1 unit up d horizontal translation 7 units left reflection over the x axis by a factor of 3 and a translation 1 unit down 15 Consider a parabola P that opens upward and has a vertex 1 3 Now find the equation of a new parabole that results if P is reflected over the x axis and translated 3 units down a f x x 4 3 b f x x 1 6

Multiple Cholce Identify the choice that best completes the statement or answers the question 9 Which function has a translation of 3 units to the left a f x 3x 1 b f x x 3 1 c f x x 3 1 10 Which function has a translation a f x 5 x 2 b f x 5 x 2 of 2 units right and a vertical stretch by a factor of 57 c f x x 2 5 d f x 27 5 1 Which function has a translation of 7 units down and reflects over the x axis a f x x 7 1 b f x x 7 1 d f x x 1 3 f x x 7 1 c f x x 17 7 f x x 1 7 Which function describes a parabola that opens downward and has a vertex of 2 312 a f x x 2 3 b f x x 2 3 c f x x 29 3 alt