Algebra Questions

ALGEBRA 2 DIAGNOSTIC TEST REFRESHER NAME 2 SOLVE and Graph using key features 0 5x2 12

Period 8 14 2023 1 g x 2 x 1 3 State the parent function f x State the transformation of g x

X y input 5 2 1 0 6 4 X 5 5 5 5 y 1 2 3 4 2 8 10 12 14 output 2 8 7 6 6 11 14 13 14 3 12 114 4 11 4 6 8 6 8 11 14 9 4 2 8 0 1 input 3 6 9 12 6 5 2 3 X 9 11 15 20 9 8 8 6 output 2 4 6 y 4 3 1 0

Set A Set B E U IV On the Venn diagram which region s represent the intersection of Set A and Set B ANB OII OI and III OI II and III O I II III and IV

Consider U x x is a negative real number Which is an empty set O x x EU and x has a negative cube root O x x EU and x has a negative square root O x x EU and x is equal to the product of a positive number and 1 O x x EU and x is equal to the sum of one negative and one positive num

The Venn diagram shows the number of patients seen at a pediatrician s office in one week for colds C ear infections E and allergies A U 5 2 10 15 A 3 E 9 How many patients total were seen for only a cold onl an ear infection and only allergies O 16 O 28 O44 O 49

Carrie is finding the set of even numbers within the set of prime numbers Of the sets described which is the universal set all real numbers O all integers Oprime numbers even numbers

Which explains how to find the radius of a circle whose equation is in the form x y z O The radius is the constant term z The radius is the constant term z divided by 2 O The radius is the square root of the constant term z The radius is the square of the constant term z

What is the center of a circle whose equation is x y2 4x 8y 11 0 O 2 4 O 4 8 O 2 4 O 4 8

Mrs Culland is finding the center of a circle whose equation is x y2 6x 4y 3 0 by completing the square Her work is shown 2 6x 4y 3 0 6x y 4y 3 0 x 6x y 4y 3 x2 6x 9 2 4y 4 3 9 4 Which completes the work correctly O x 3 y 2 2 42 so the center is 3 2 O x 3 2 y 2 2 42 so the center is 3 2 O x 3 y 2 2 42 so the center is 3 2 x 3 y 2 2 42 so the center is 3 2

2 41 2 0 543 2 IN 4 4 4 4 3 X Distance formula x x V V Does the point 1 7 lie on the circle shown Explain O Yes the distance from 2 4 to 1 7 is 4 units O Yes the distance from 2 0 to 1 7 is 4 units O No the distance from 2 0 to 1 7 is not 4 units O No the distance from 2 4 to 1 7 is not 4 units

An arc on a circle measures 85 The measure of the central angle in radians is within which range O 0 to radians Oto radians O to 37 radians 2 O 37 to 7 radians

3 F G In circle G r 3 units Maria draws a circle with do the area of circle G What is the area of Maria s circle 6 units O O 9 units 12 units 18 units

D C B A The smallest of the three circles with center D has a radius of 8 inches and CB BA 4 inches What is the sum of the areas of all three circles 80 min 96 in 208 in 464 in

T 14 ft n circle V r 14ft What is the area of circle V 14m O 28tf O 49m O 196

The measure of central angle RST is a radians What is the area of the shaded sector 4 units 8 units 16m units 20 units

H G 6 cm X 8 cm Point G is the center of the small circle Point X is the center of the large circle Points G H and X are on lin segment GX What would be the area of a new circle that has line segment GX as its diameter O 16 cm O 36 cm 49 cm 98 cm

The measure of central angle YCZ is 80 degrees X 9 W 80 C Z What is the sum of the areas of the two shaded sectors O 18 units 36 units 45 units 817 units

In each circle below a 50 angle with a vertex at the center of the circle is drawn How are minor arc lengths CD and EF related A 50 8 cm C D B 50 2 cm F LL E O They are the same because the central angle measure is the same

Circle P has a circumference of approximately 75 inches P T What is the approximate length of the radius r Use 3 14 for T Round to the nearest inch O 12 inches 24 inches 38 inches O 46 inches

An arc on a circle measures 125 The measure of the central angle in radians is within which range 0 to radians to to radians T to 3 radians O 03 O3 to 2 radians

In the diagram below O is measured in radians Which equation represents the relationship between the radius r and arc length s Os r Or 0 s Os 0 r Or 0 s 0 A T B

Circle O has a circumference of approximately 250m ft d What is the approximate length of the diameter d O 40 ft O 80 ft O125 ft 250 ft

36 C 106 In the diagram of circle C what is the measure c 17 35 70 O 71

36 B D 48 E n circle O what is 84 96 O 120 168

P M 83 45 N What is MPO O 128 173 192 256

72 x P 360 x In the diagram of circle P mzXYZ is 72 What is th value of x 108 O 144 16 O216 O252

R 21 119 U What is m O 49 O 77 98 O 161

TRIANGLES Apply your knowledge of angles in similar triangles to answer each question below 1 Three students sketched the triangles shown Which students sketched similar triangles Explain Beau 180 116 3 Use the triangles below to answer a b B E 14 cm A 63 48 10 cm C 20 D 2 Spencer constructed triangle XYZ where ZX 76 and 2Y 49 Morgan constructed triangle JKL where J 49 and ZK 65 Are the two triangles yes Tho corresponding angles similar Explain your reasoning 89 48 15 cm b If possible find the value of x X 21 116 61 F a Is triangle ABC similar to DEF Explain yes two corresponding angles BEAU 55 55 61 KAI D 64 4 Use the triangles to answer a b 12 in A 5 Richard believes the two triangles shown are similar while Penelope believes there is not enough information to tell Who do you agree with Explain your choice C 55 NYLANA 4 in 55 51 61 b If possible find the value of x B 8 in a Is triangle ABC similar to CDE Explain yes 70 61 51

Given Circle O with diameter LN and inscribed angle LMN Prove ZLMN is a right angle K M N What is the missing reason in step 5 Statements 1 circle O has diameter LN and inscribed angle LMN 2 LKN is a semicircle 3 circle O measures 360 m LKN 180 5 m2LMN 90 6 LMN is a right angle OHL theorem 1 given Reasons 2 diameter o divides into 2 semicircles 3 measure of a circle is 360 4 definition of semicircle 5 6 definition of right angle

CY 48 B What is the measure of angle CAB in circle O 24 48 72 96

Write an equation of the line Price of pair of shoes dollars 50 40 20 10 30 0 50 20 units 0 y Shoe Sales 0 10 units 20 40 60 80 Percent discount X

4 Listen Write an equation of the line Balance dollars Bank Account YA 800 600 400 3 600 200 y 0 0 2 400 4 Weeks 2

Slope 3 passing through 6 7 OA y 3x 11 OB y 3x 11 OC y 7 3x 6 OD y 7 x 6

K use the train also have the option of purchasing a frequent rider pass for 18 75 each month With the pass a ticket costs only 1 75 per ride How many train ride month make the frequent rider pass a better deal than standard train tickets OA 24 or more rides OB 27 or more rides OC 25 or more rides OD 26 or more rides

Q8 If z a ib Z c id then Z Z Z Z l a ac bd bc ad ac b d ac b d b ac bd bc ad ad a c ac bd bc ad a c b d d ac bd bc ad a c b d

h x X 1 2 X 1 A x 1 OB x 1 x 1 O C x 1 O D no vertical asymptote

K Solve the system by the addition method x y 4 4x 25y 100 OA 2 0 2 0 OB 0 2 0 2 OC 0 5 0 5 O D 5 0 5 0

K Find the y intercept of the polynomial f f x x 2x 8 OA 0 OB 1 O C 8 O D 8

K x 30 x OA 0 5 U 6 00 O C 6 5 0 12 8 8 10 8 12 12 CL OB 6 U 5 00 O D 5 6 12 12 8 8

April shoots an arrow upward into the air at a speed of 64 feet per second from a platform that is 16 feet high The height of the arrow is given by the function h t 1612 64t 16 where t is the time is seconds What is the maximum height of the arrow OA 64 ft OB 16 ft OC 12 ft OD 80 ft

The logistic growth function f t nearest whole number OA 175 butterflies OB 375 butterflies OC 275 butterflies OD 4 800 butterflies 320 1 7e 0 25t describes the population of a species of butterflies t months after they are introduced to a non threatening habitat How many butterflies are expected in the habitat after 1 GELEB

than juniors in an 8 AM algebra class If there are 68 students in this class find the number of sophomores and the number of junior OA 39 sophomores 29 juniors OB 29 sophomores 39 juniors OC 78 sophomores 58 juniors O D 68 sophomores 58 juniors EXCE

Graph the solution set of the system of inequalities or indicate that the system has no solution 2x y 6 2x y 1 O A 10 B 10 C S D

Problem 4 24 points Consider the conic equation with equation 7 6ry y 1 a Identify this equation as a hyperbola or ellipse b Find the change of variables RT needed to eliminate the mixed term ry and have the conic equation in standard form A a The symmetric matrix is A equation will correspond to a hyperbola b The eigenvectors are 1 2 1 2 1 2 1 2 rotation matrix R A y2 1 1 3 s since the eigenvalues are 4 2 which have opposite sign the 3 1 for 4 and 1 for 2 After normalizing the eigenvectors we have the 1 2 1 2 1 2 1 V so the change of variables is

3 Two cereal companies A and B find that the number of people who will buy one of their products in the first month that it is introduced is linearly related to the amount of money they spend on advertising If company A spends 40 000 on advertising then 100 000 boxes of cereal will be sold and if it spends 60 000 then 200 000 boxes will be sold However if company B spends 40 000 on advertising then 135 000 boxes of cereal will be sold For both companies the number of boxes of cereal sold increases by the same amount for each additional 1 000 they spent on ad vertising How much advertising does each company need to sell 300 000 boxes of cereal 8 marks

54 2ab 5 ab 20 a b A 6 B 9 C 12 D 13 E 15

C B H For each of the growing patterns A B C and D shown above do the following 2 1 Draw the next pattern 2 2 Complete a table that shows the number of figures for each step 2 3 Describe how each pattern grows in words You must relate the number of figures to the step number 4 4 8 M161

COSO sino 3 i tanh 6 i sech 6 tanh 3 i F

points The matrix as three distinct real eigenvalues if and only if k 4 6 A 2 k F C