2D Geometry Questions and Answers

Basic Trigonometry Which expression represent tan 9 for the triangle shown a O O O O 00 8 114 100 OF 20 points Question 2 20 points Basic Trigonometry Approximate the unknown side x in the diagram 3 356

In the exercises find the value of x Then tell whether the side lengths form a Pythagorean triple 1 13 X 6 2 30 X 16 In the following exercises verify that the segment lengths form a triangle Is the triangle acute right or obtuse 3 5 12 and 13 4 2 10 and 11 5 8 4 and 6

ind the translation rule and the scale factor of the dilation that transforms Ol to Ol x x 4x x A x y x 8 y 7 scale factor 3 B x y x 8 y 7 scale factor 2 C D x y x 7 y 8 scale factor 3 x y x 7 y 8 scale factor 2 10 8 6 4 104 2 0 10 r 10

x 4x Various dilations of square A are shown Which square was obtained by dilating square A by the scale factor of 3 A B C D Square D Square C Square E D Square B C A B E

For questions 9 15 give each answer as a fraction in simplest form 9 Natalie randomly answered the last three true or false questions on her math quiz What is the probability that she got at least two correct probability of getting at least two is 1 2 1 2 x 1 2 1 4 0 25 11 The probability of winning a coupon at the grocery store checkout is 2 25 What is the probability of not winning the probability of winning 2 25 the probability of not winning 1 2 25 23 25 Instrument 14 8 Sport 3 A group of students were asked if they play a sport or play an instrument The results are shown in the Venn diagram below If one of these students is chosen at random find each probability a P instrument b P does not play a sport 24 50 18 Counting Outcomes 22 50 c P both 12 10 Two dice are rolled What is the prob that the sum on the two dice is less th 0 1 36 2 36 3 36 4 36 10 36 12 A number from 1 30 is chosen at random What is the probability that the number is not a prime number non prime 1 4 6 8 9 10 12 14 15 16 18 20 21 22 24 25 26 2 28 30 total 20 p not prime 20 30 2 3 0 667

b Draw a curve y f x given the sign chart of its 2nd derivative of y 5 Use derivatives to find approximate changes in geometric measurements For all the formulas below be able to find the differential of one variable with respect to another variable and find the rate of changes at given specified values Perimeter and Area of Plane Figures Triangle Rectangle P 2 2 Parallelogram PA333 Trapezoid Postboced Circle C 2xr Amar Volume and Surface Area of Solid Figures Rectangular Prim V luk 5 2 2 2 Right Circular Cylinder Vwar k S 2 2 Sphere V Smar Right Circular Con Swar 7 For the circle and sphere 1 a Find dC in term of dr What is dC if dr 1cm b Express the radius r in terms of the circumference C Find dr in terms of dC Find dr if dC 2 cm Ans a dC 2ndr dC 2 cm if dr 1 cm b r C 2n dr dC 2n dr 1 n cm

6 POINTS EACH 7 AB 2422 CB 2 122 8 AB 9 AB CB 02 CB 10 AC CB 11 AC AB 12 AB CB 13 AC 14 AC CB CB AC 5 8 AC 14 AB 15 CB 2 A 45 AC 3 7 AC 6 2 48 3 CH AB 3 2 AB 4 2 46 59 B 5852 18 5 4 2 1182 72 2CB 2 712 AB 3 2 MB ACC 602 CB 622

1 5 6 How many times does sin x 0 5 between x 630 and x 630 C 7 d 8

Let s Exercise A 10 meter light post cast a shadow of 5 meters when a tower casts a shadow of is meters What is the height of the tower A tree casts a 12 feet shadow At the same time a 10tt flagpole carto a 6 teet shadow how high ie thetree

43 If the length of each leg of an isosceles triangle is 17 and the base is 16 the length of the altitude to the base is A 8 1 2 B 8 C 32 D 15

03 03 MC Jamal drew ALMN in which mzLMN 90 He then drew APQR which was a dilation of ALMN by a scale factor of 2 from the center of dilation at point M Which of these can be used to prove ALMN APQR by the AA similarity postulate OmzP mzN this can be confirmed by translating point P to point N OLM 2PQ this can be confirmed translating point P to point L mzR mzN this can be confirmed by translating point R to point N MN 20R this can be confirmed translating point R to point N

Develop a fractal by beginning with the following figur side with a L Repeat this process twice

Question 4 Multiple Choice Worth 1 points 03 03 MC If AONP is dilated from point N by a scale factor of w NL NP k

Question 6 Multiple Choice Worth 1 points 03 03 MC If a translation maps 21 onto ZK which of the following st Ho G I

Question 8 Multiple Choice Worth 1 points 03 03 MC B E

Write an 10 equation for the function 7177579 1

In circle Z VZ ZW and SV 12 Find the following 3 lengths S N U Y X T a UT b WT c ST

Liam needs to find the range of prices at which he can sell mums and make a profit Based on the equation what are the points between which he will earn a profit on his mums Type your response here

INTS EACH TES 8 FORM A PG AR POLYGONS Use the similar triangles below to determine whether each of the following statements is TRUE or FALSE Circle one 7 TRUE or FALSE ZC ZD 8 TRUE or FALSE 9 TRUE or FALSE 10 TRUE or FALSE For pr 20 is included between DO and GO AT OD OD is included between 20 and ZG

A B 63 is congruent with is congruent with is greater than Y is longer than D E 82 F

A 9 B E D X C E XEZ m BDC 45 max x

a Shade 4 n B U X universal set U B b Shade A UB B X B

1 Find the surface area of the figure 8 in 2 in 3 in

To determine how far a boat is from shore two radar stations 490 feet apart find the angles out to the boat as shown in the figure A boat 490 shore 62 B Determine the distance of the boat from station A Round your answers to the nearest whole foot and the distance from shore feet

Is quadrilateral ABCD a parallelogram Explain why or why not D B C Ono both pairs of opposite sides need to be congruent Ono all angles must be congruent O yes diagonals bisect each other O yes opposite sides are congruent

Symmetry Ox axis Oy axis origin Onone of these Symmetry Ox axis Oy axis Dorigin Onone of these 5

A parabolic satelite receiver is initially positioned so its axis of symmetry is parallel to the x axis A motor allows the receiver to rotate and track the satellite signal If the rotated receiver han equation 2x 4 19xy 19 19x 25y 179 329 0 through what acute angle did the receiver rotate to the nearest tenth of a degree The acute angle the receiver rotated is approximately Type your answer in degrees Round to the nearest tenth as needed CTED

Ft James Bond the Directions Find the indicated M 5

above If the horisontal distance bebwean the hellcopter en 3 055 feet and the angle of elevation la 71 find the airplane A helicopter flying 1500 fee above If the horizontal dist 3 055 feet and the angle of

Kurt spots a bird sitting at the top of a 60 the angle of elevation from the ground wh is 59 how far is Kurt standing from the be 13 13 Kurt spots a bird sitt the angle of elevatio is 59 how far is Ku

Find the surface area of the figure on the right 13 yd 5 yd 29 yd 5 yd 35 yd 13 yd 13 yd

1 Find the exact value of the following from the unit circle no decimals 4 points sin 240 tan 270 7 sec Sz tan 3

Find the measure of angle 2 m22 Z 2 W 80 C Y X 160

Find the area of the shap Find the area of the figure Use 3 14 for 16 m 16 m sq meters 456 96 C

Lee picks a card at random puts it back and then picks another card at random 234 Are these two events dependent or independent dependent independent

Question 10 Find x Assume that segments that appear to be tange R 5 A 10 15

Question 11 Find x Assume that segments that ap a 14 b 10 20 B 12

H a 5 b 7 A A B B C c assume that segments that appear tangent are tan 11 18 N K M c 13 d 11 9 38

12 BJ 6 what Is JD 9 W D Note The figure is not drawn to scale

Note The figure is not drawn to scale and PM 4 what is the length of PJ

B Question 4 Which of the following represents 4 1 97 A

Question 1 The graph of a circle is shown below A Which equation is best represented by this graph B 6 C y x 4 y 5 4 x 4 y 5 4 x 4 y 5 16 x 4 y 5 16 x

ERS The graph of which equation is a circle with its center at 16 25 A x 4 y 5 100 x 4 y 5 100 16 2 y 25 100 x 16 y 25 100 B C C D

8 A card is chosen at ran simplest form decimal a P ace

8 Find the scale factor of the perimeter area and volume of the given pair of similar solids SA 67 cm SA 24 cm

Perimeter Area c a rectangular solid P A B C P 4s P 2 1 w or P 21 2w e a triangle A bh A s A lw r A 14 d Circumference 10 Volume 1 By drawing a sketch giving an example or providing a written description please indicate the meaning of each of the following shapes 9 marks a a rectangle b a square C 2 r nd d a cylinder V lwh V r h V 14 d h f the circumference of a circle

7 Find the surface area of a cone if the height is 14 centimeters and the slant height is 16 4 centimeters a 669 3 cm b 440 1 cm c 950 4 cm d 3988 2 cm

Shown to the right are two functions The dashed graph in red is the parent function p x The vertical intercept of p x is 0 1 The solid graph in blue is the child function c x The vertical intercept of c x is 0 2 a Use the pull down menus to describe the transformation b Find a formula for the child function c x in terms of the parent function p x a The graph of c x is a Click for List of p x by a factor of Number Click for List b c x Your formula involves p x followed by of the graph 8 7 65 wa 4 3 2 8 7 6 5 4 3 2 P 2 4 8 y p x 5 6 23 15 6 y c x

A triangle has side lengths of 6 2g 3 4 centimeters 1 9g 5 3 centimeters and 9 3h 1 2 centimeters Which expression represents the perimeter in centimeters of the triangle

2 A patio is being landscaped with trees and shrubs How many square feet of landscaping will be around the patio 14 ft 8 ft 1 3 ft landscape 3 ft 3 ft landscape 14 ft 3 ft 8 ft