High School Algebra Questions

Listen An arch of a walkway can be modeled by y 0 06x2 where x and y are meas meters Find the height and width of the arch when the arch meets the ground at 10 6 and 10 6 10 8 6 6 8 10x Height m Width m

Graph the line with the equation y 52 2 10

Select the correct answer Solve the following equation for x x 8x 7 0 O A x 1 x 7 OB x 1 x 7 O c x 1 x 7 O D x 1 x 7

The table shows values for functions f z and g z X 1 3 5 f x 14 2 5 7 9 11 6 6 11 What are the known solutions to f x g x Select each correct answer D 1 05 07 9 g x 14 4 3 7 9 3

Noelle stands at the edge of a cliff and drops a rock The height of the rock in meters is given by the function f x 4 9x 17 where x is the number of seconds after Noelle releases her rock Cesar who is standing nearby on the ground throws a rock straight up in the air The height of Cesar s rock in meters is given by the function g x 4 92 13z where x is the number of seconds after he releases his rock There is a moment when the rocks are at the same height What is this height Enter your answer rounded to the nearest tenth of a meter in the box

Construct the vector 0 7 c 1 2 d having initial point P Use the tools provided to move and scale the given vectors then don t forget to draw your final answer 1 0 d X P G

George is 7 and his mother is 37 In how many years will his mother be 3 times as old as he is in 8 years old when George is is is mother wil be 45 Pete is 14 and his grandfather is 54 How many years ago was his grandfather 6 times as old as Pete 7 Years ago pete s grandfather

38 3 poly 3a 3 na n 6 6mx 2m 9x 3 38 4a 7kn 6k 14n 12 6 7x 7a Bach 50 38 5 a 5y y y 5 6 y3 4 2y 2y c ax 3x 4a 12 d 2mx3m 4x 6 B 9m 9mn 5m 5n r be 3ac 2ab 6a B 2 21 3z 72 r 2 322 23 3

This system has one solution y x 3x 7 y 3x 2 What is the y coordinate of the solution Enter your answer in the box

How many real solutions does the system have y 3x 1 y x 3x 4 Enter your answer in the box

Quick Fix Inc repairs bikes The company s revenue is modeled by the function R h 220h 160 for every h hours spent repairing bikes The company s overhead cost is modeled by the function C h 20h 400 After how many hours does the company break even Enter your answer in the box

Write the rational expression in factored form by dragging the correct factors in the box provided 7x 56 x2 5x 24 7 1 x 3 x 8 x 6 x 7 8

Write the rational expression in factored form by dragging the correct factors from the box provided Note not all responses will be needed and some responses may be used more than once POSSIBL 12x 4x 20x2 8x 4x 3 3x 1 3x 1 4x 8x 12x 52 2 8x 2 3x 1

Simplify the rational expression into lowest terms A B 4 2 322 48 3 x 4 3 x 4 C 3 x 4 D 3 x 4

Simplify the rational expression into lowest terms x 6x 9 2 9 A 2 3 x 3 B 3 C D 6z 1 3 2 3

11 Perform the indicated operations Simplify the answer 5i 125 5 25 25i

15 Perform the operation and write your answer in standard form Explain your process 8 7i

13 Solve the quadratic equation and express all nonreal complex solutions in terms of i x2 5x 10

3 Perform the operation and write the result in standard form 19i 1 6i 118 19i 116 19i 115 19i

12 Solve the quadratic equation and express all nonreal complex solutions in terms of i x2 x 8 0 31

10 Perform the indicated operation Write the result in standard form 4 5i 7 i 11 4i 11 4i 11 4i 3 6i

8 Simplify the power of i i 26 1

1 Perform the addition or subtraction and write the result in standard form 7 i 5 5i 13 5i 12 4i 15 7i 16 8i 14 6i

9 Perform the indicated operation Write the result in standard form 7 8i 2 4i 9 12i 9 12i 9 12i

7 Indicate whether the statement is true always sometimes or never When i is raised to an odd power the result is 1 Sometimes Always

5 Write the complex conjugate of the complex number Then multiply the number by its complex conjuga 5 37 5 31 9 5 31 34 5 31 34 5 31 9

D 4 Perform the operation and write the result in standard form 27 29 28 21 19 8 19 81

2 Perform the addition or subtraction and write the result in standard form 191 15 31 15 22i 15 251 15 22i 15 22i 15 22i

Choose the correct value from each dropdown menu f x 3x 12x 9 r2 5 4 There is a vertical asymptote at x There is a hole at x This graph is

DACK L USE YOUR MATH SKILLS TO FIND THE VALUE OF EACH ICON

Example 4 The cold water tap can fill a tub 2 hours faster than the hot water tap The 2 taps together can fill the tub in 80 mins How long does it take for each tap to fill the tub

24 Let f x 1 1 What is the point of maximum growth rate for the logistic function f x Round your answer to the nearest hundredth 0 42 3 O 0 85 24 O 0 85 12 0 4

Let f z 11 1 24 1 3e 1z What are the asymptotes of the graph of f x Select each correct answer O y 24 y 0 O y 3 y 1 3

3 Graph the following function f x 2x 7 Instructions Click the graph tab Click on the graph background to add a point Add two points to create a graph Drag a point or type in x and y coordinates to edit its position Click on a point to delete it Graph 1 6 CO 6 6 Co 6 Zoom In Q Zoom Ou Focus

1 f x 2 2 Make and fill in a table of values using 3 random x values You will need to use values near the turn of the graph X y Select Select Select Select

EVALUATE round all answers correctly to three decimal places 1

12 EVALUATE AT X 3 ANSWERS SHOULD BE ROUNDED TO 3 DECIMAL PLACES g x 3e 0 5X 5

mine the solution to the system of equations below You must show work for all questions to get credit 1 y 1 y 3x 1 2 8x 4y 16 6x 20 A 0 1 B 1 0 2 8 C 7 1 B 2 1 D 7 1 C 2 1 D 2 1 3 2x 3y 4 y x 4 4 x y 7 6x 2y 18 A 8 1 8 4 B 2 1 D 1 1 A 1 6 C 1 6 5 7x 2y 18 x y 9 6 5x 3y 2 4x y 10 B 1 6 D 2 6 4 5 C 4 1 B 4 1 D 7 4 A 4 6 C 3 6 B 3 6 D 3 6

Work 3x 2y 16 x 3y 10 Substitute 3y 10 equation Distribute muljely 3x 2y 16 3y 10 3y 16 3 3 2x 16 gy ay 16 3 3x 10 ay 16 30 16 7y 30 16 30 v Combine XP Tw Cancel the constant w Concel the coefficien Plug in 2 value ind 2 FG Solve Plug in 2 valle inte 210 Jolye Write as ordered Pair Try It Again Problem Solve the system shown below listing your answer as an ordered pair 3x 2y 14 y 5 2x 3 5 2y 14 315x 27 14 3 3x 2 2y 14 15x 10 2y 14 13y 10 14 10 10

solve problems involving quadratic functions including problems arising from real world applications 3M B 3 Mathematics Overall Expectation Problem Solving develop select apply compare and adapt a variety of problem solving strategies as they pose and solve problems and conduct investigations to help deepen their mathematical understanding 3M A 1 Mathematics Mathematical Process Expectation Reasoning and Proving develop and apply reasoning skills e g use of inductive reasoning deductive reasoning and counte examples construction of proofs to make mathematical conjectures assess conjectures and justify conclusions and plan and construct organized mathematical arguments 3M A 2 Mathematics Mathematical Process Expectation Connecting make connections among mathematical concepts and procedures and relate mathematical ideas to situations or phenomena drawn from other contexts e g other curriculum areas daily life current events art and culture sports 3M A 5 Mathematics Mathematical Process Expectation Repreconti

4 You roll a 6 sided die two times What is the probability of rolling a 1 and then rolling a 1 Write your answer as a percentage Independent or Dependent

3 You pick a card at random put it back and then pick another card at random What is th probability of picking a number less than 7 and then picking an even number Write yo answer as a fraction Independent or Dependent 678

1 Convert the equation from point slope form to slope intercept form y 3 5 x 10 2 In the question below what information are you given What type of line equation can you create with that information Answer the question below and show all of your work What is the equation for a line that passes through the points 4 1 and 8 14 OA y 4 B y x 6 Oc y x 6 O D y 2 4

3 Which ordered pair below is a solution to the system of equations a 1 1 b 2 4 c 1 1 d 4 2 x y 3x 4 y

4 What value for x 2x 7x 4 0 makes the equation true 2x 1 a 6 b 5 c 4 d 3

Extend look at the equation What other value of x would make the equation true 2 What value for t below is a solution to the equation 6t2 8t 8 a 0 b 1 c 2 d 3

3 Given the syst Extension Questions 1 Which value for x below is a solution to the equation x 3 x 5 0 a 3 b 5 c 7 d 9 Extend look at the equation What other value of x would make the equation true

Given the following exponential function identify whether the change represents growth or decay and determine the percentage rate of increase Hecrease y 420 1 04

2 Previous There was a study done on oxygen consumption of snails as a function of pH and the result was a degree 4 polynomial whose graph is shown below 0 101 Oxygen Consumption co hr 0 08 0 06 0 04 0 02 0 00 6 7 8 pH 9 10 Which of the following statements about this function is INCORRECT There is a positive leading coefficient B The degree of the polynomial is even There are two intervals where the function is decreasing At two pH values there is an absolute maximum value

S Given the following graph write a possible equation that could represent the function in factored and standard form LA Factored Form Standard Form