Questions

3 y 1 1

A boy whirls a stone in a horizontal circle of radius 1 55 m and at height 2 08 m above level ground The string breaks and the stone flies off horizontally and strikes the ground after traveling a horizontal distance of 8 80 m What is the magnitude of the centripetal acceleration of the stone while in circular motion Use g 9 81 m s Number i Units

The bases for a cylinder must be two discs that are parallel and O A similar B congruent C squares D have one lying directly above the other

Use the graph of h in the given figure to find the following values or state that they do not exist a h 4 b lim h x X 4 c h 6 d lim h x X 6 e lim h x X 7 n 4 Type an integer or a decimal A lim h x x 4 Type an integer or a decimal 10 OB The limit does not exist b x OB h 4 is undefined b Find lim h x Select the correct choice and if necessary fill in the answer box to complete your choice

What valid inference can be made from the following proposition Take the truth value as specified All amusement parks are crowded places T Some crowded places are not amusement parks T All crowded places are amusement parks F No amusement parks are crowded places F All crowded places are amusement parks T

6 1 point The pentagon shown could be reflected over which line to be carried onto itself x axis y axis line y x not possible

A right cone has a slant height of 6 and a radius of 2 What is its surface area O A 48 units2 O B 16 units2 C 12 units D 24 units2

The ratio of the surface areas of two similar solids is 49 100 What is the ratio of their corresponding side lengths OA 7 10 OB 1 24 O C 10 10 OD 7 100

In the surveys of the credibility of makeup products according to users statistics will be used in this IA to evaluate and measure the patterns that are present in makeup reviews Descriptive statistics will be used to summarize and present the significant characteristic features of the different features Hypothesis testing will be used within the investigation to understand whether certain observed trends and patterns are significant so that it is possible to determine if some makeup products were positively or negatively reviewed throughout all of them It is possible to use regression analysis to identify correlations between certain product attributes and user satisfaction thus developing a more precise perspective on credibility factors I will be providing a framework that will allow the reader to understand the trustworthiness of beauty products when new reviews become available This adaptive approach enables the fine tuning nature of evaluations with changing datasets Finally statistical methods will not only help quantify the validity of makeup products but also increase the reliability and rigor embedded in our conclusions hence making this potential discipline more evidence driven

7 3a 12 2a 4 1 6a 24 8 4a

4 x 5x 6 x 4 x 3x 2 x 2x 3

the graph of f in the figure to find the following values or state that they do not st If a limit does not exist explain why 3 lim f x 3 im f x 3 im f x 3 2 3 IN B The value of f 3 is undefined Find the limit Select the correct choice and if necessary fill in the answer box within your choice A lim f x Type an integer or a fraction X 3 3 The limit does not exist because f is not defined for all x near 3 with x 3 Alim f x 1 Type an integer or a fraction x 3 B The limit does not exist because f is not defined for all x near 3 with x 3 ind the limit Select the correct choice and if necessary fill in the answer box within your choice X

highway that runs east to west and you know you are north of the highway Based on the signal delay it can ose there are two cell phone towers within range of you located 3000 feet apart along a straight be determined you are 2050 feet from the first tower and 1420 feet from the second Determine the angle 0 between your line of sight to the first tower and the highway to the nearest tenth of a degree 300024 20 2050 2 1420 2050 cos 90 2050 ALLA 420 3

5 x x 2x 1 3x x 1

5 1 point If the pentagon below is to be reflected over the y axis which point would not move at all L K 1 Point H Point J Point K Point G 1 G H 3 1

3 x 4 x 1 x 1 x 2x

3 6x 6y y x 14 18 5x 5y

y 5y 6 y 3y 10 y 4y

7 12 points Name the three ways a function fails to be differentiable at a point 8 12 points The following will be two separate graphs Draw a possible graph of a function f x with the given description 1 f is continuous on all of R but f is not differentiable at x 2 f is continuous at all x except for x 1 2 and the tangent line to f at the point 0 2 is a vertical line

G 2 1 D If point C is rotated 180 degrees counter clockwise around the origin what is the resulting point Point D Point A Point F

K Use the graph of f in the figure to find the following values or state that they do not exist a f 1 b lim f x X 1 c lim f x X 4 d lim f x X 5 a Select the correct answer and if necessary fill in the answer box within your choice OA f 1 Type an integer or a decimal B f 1 is undefined 3 y f x in

2 Write the linear combination as a matrix vector nmdu 3 1 10 1 x3

1 1 point The transformation shown is a translation True False

2x 12 6 2x 3x 9 3x 8

A geometric solid has only length and height O A True OB False

N What side is congruent to side ON Side MN Side QR Side MO Side QP

13 M 1 point 44 0000 N P R F Which two triangles are congruent AMNO APRQ OAMNO APQR OAMNO ARPQ Not congruent

AV What criteria can be used to prove these two triangles congruent ASA SSA SAS HL

Find A Begin by finding A 1 and then evaluate its determinant Verify your result by finding A and then applying the formula A1 1 A A 0 1 1 A 9 1 9 1 9 6

2 1 point If point x y is rotated 180 degrees about the origin the resulting point is x y True False

dy dx 5 12 points Find using the limit process for y 1 x 6 6 12 points The graph of f x is shown below State the domains of f x and x

The triangle has been reflected over the line Find x y and z 3z x 1 y 11 Z 4 15 X 1 y 8 2y 4 18 12 not enough information to determine x 2 y 8 Z 4 9x 6

Which of the following is a solid consisting of a disc a point not in the same plane as the disc but directly above the center of the disc and all the points between them OA Oblique cone OB Oblique pyramid C Right cone D Right pyramid

Use the determinant of the coefficient matrix to determine whether the system of linear equations has a unique solution 5x1 X2 6x3 x4 7 x2 3x3 4x4 5 3x4 9 1 X1 2x1 5x 2x3 Xi 5X2 6x3 O The system has a unique solution because the determinant of the coefficient matrix is nonzero O The system has a unique solution because the determinant of the coefficient matrix is zero O The system does not have a unique solution because the determinant of the coefficient matrix is nonzero O The system does not have a unique solution because the determinant of the coefficient matrix is zero

8 1 point If point x y is reflected over the line y x the resulting point is y x True False

Let f x x 4 lim X 2 X 2 a Calculate f x for each value of x in the following table 1 9 1 999 1 9999 3 9 3 999 3 9999 2 001 2 0001 x 4 4 1 4 01 4 001 4 0001 f x x 2 Type integers or decimals rounded to four decimal places as needed X f x x 4 a Calculate f x for each value of x in the following table b Make a conjecture about the valu lim X 4 x 2 X 2 1 1 99 3 99 2 01 X b Make a conjecture about the value of lim X 2 X 2 Type an integer or a decimal

Determine which property of determinants the equation illustrates 3 1 4 00 0 0 97 8 O If one row of a matrix is a multiple of another row then the determinant of the matrix is zero O If one row of a matrix consists entirely of zeros then the determinant of the matrix is zero If two columns of a matrix are interchanged then the determinant of the matrix changes sign O If a row of a matrix is multiplied by a scalar then the determinant of the matrix is multiplied by that scalar O none of these

2 Point Slope Form 1 3 Graph the line that represents each linear equation 1 y2 2 x 3 2 y 3 2 x 1 P 5 1 3 y 1 x 5 2

Use either elementary row or column operations or cofactor expansion to find the determinant by hand Then use a software program or a graphing utility to verify your answer 0 1 10 1 1 90 1 9 10 5 1

A right cylinder has a radius of 5 and a height of 9 What is its surface area A 45 units2 B 140 units C 70 units D 90 units2

A local carnival features a booth where a person guesses the participant s age Suppose that a 21 year old person has his ag guessed as 30 years a Compute the absolute error Simplify your answer completely AE Interpret the result The guesser estimates a person s age correctly this proportion of the time The guesser s estimate was off by this much relative to the participant s age This is the ratio of the guesser s estimate to the participant s age The guesser s estimate had this percent error The guesser s estimate was off by this many years b Compute the relative error Round to three decimal places Simplify your answer completely RE Interpret the result The guesser estimates a person s age correctly this proportion of the time The guesser s estimate was off by this much relative to the participant s age This is the ratio of the guesser s estimate to the participant s age The guesser s estimate had this percent error The guesser s estimate was off by this many years

Which solid figure has a base that is a polygon and triangular faces that meet at a vertex A Cylinder B Prism C Cone D Pyramid

Let f x x 3x 1 1 Find a simplified expression for f x h and f x h f x 2 Find f x 3 Calculate f 1 and f 1 What do these values tell you about the tangent lines at the points with a values 1 and 1 5 12 points Find using the limit process for y dy dx 1 x 6 6 12 points The graph of f x is shown below State the domains of f x and x 0 34 7 12 points Name the three ways a function fails to be differentiable at a point 8 12 points The following will be two separate graphs Draw a possible graph of a function f x with the given description 1 f is continuous on all of R but f is not differentiable at x 1 2 f is continuous at all except for x 2 and the tangent line to f at the point 0 2 is a vertical line

Which types of polygons are the faces of a tetrahedron O A Regular pentagons B Regular hexagons OC Squares OD Equilateral triangles

pizza 1 5 5 2 94 99 units 4 4 94 2 unite 80 08 units 171 95 units 5 unit

nd IAI IBI AB and IABI Then verify that IA B AB 49 2 A 4 2 B 3 1 94 0 a A b B c AB d AB A

Let A and B be square matrices of order 3 such that A 6 and B 9 a Find ABI b Find 2A c Are A and B singular or nonsingular Explain O A and B are both singular because they both have nonzero determinants O A and B are both nonsingular because they both have nonzero determinants OA is singular but B is nonsingular because A B OB is singular but A is nonsingular because A BI d If A and B are nonsingular find A1 and B 1 If the inverse is undefined enter UNDEFINED A 1 B e Find AB 1

x 45 10 Explain why it does not matter which point you choose when writing the equation of the line in point slope form given two points

A line passes through 1 3 and has slope 2 Find an equation of the line Explain your steps Step y y m x x y 3 2 x 1 y 3 2 x 1 Written Explanation Use the point slope form Substitute 1 for x 3 for y and 2 for m Simplify inside grouping symbols

Find the value of k such that A is singular Enter your answers as a comma separated list 0 k 1 k 1 k 1 k O