Geometry Questions

AABC has vertices at A 3 4 B 2 1 and C 3 8 The longest side of AABC is units and AABC is a triangle Select one O a 8 6 scalene O b 11 5 scalene Oc 11 5 isosceles O d 8 6 isosceles

ct one a m BAC 90 b m BAC 30 cm BAC 45 d m BAC 60 The vertices of a triangle are as follows A 3 2 B 7 2 and C 7 6 What is the m BAC Here is the link to Geogebra

Points P and Q are located at P 2 1 and Q 1 7 Line PQ can be represented by the equation y 2x 5 Line RS is parallel to line PQ with point at R 2 1 What is the equation that represents line RS Select one O a y 1 2 x 3 O b y 1 2x 3 Oc y 2x 3 O d y 2x 3

e 5 3 4 3 1 2 2 5 Circle A has a center at 3 4 and has a radius of 4 47 units Which of the following points lies on Circle A

Given the vector with magnitude 15 and directional angle 120 Write the vector in unit vector form

What is the volume of the original sculpture What is the volume of the new sculpture How much greater of a volume is the new sculpture Select one O a The original sphere s volume is 33 ft the new sphere s volume is 904 ft and the new sculpture s volume is approximately 27 times the volume of the original O b The original sphere s volume is 33 ft the new sphere s volume is 904 ft and the new sculpture s volume is approximately 9 times the volume of the original Oc The original sphere s volume is 268 ft the new sphere s volume is 7235 ft and the new sculpture s volume is approximately 27 times the volume of the original

Select one O a 560 units O b 580 units OC 160 units What is the volume of 14 units Area of base 40 square units 10 units

Select one O a 103 62 in O b 75 36 in Oc 103 62 in O d 75 36 in What is the lateral surface area of the given cone 8 in r 3 in

Given a vector begins at 1 3 and ends at 3 1 then the components of the vector are 45

Choose the correct vector Select one O a O b O C 2 5 2 8

The diameter of a sphere is 8 units What are the radius and volume elect one a The radius is 4 units and the volume is 803 85 units O b The radius is 4 units and the volume is 267 95 units Oc The radius is 16 units and the volume is 51 445 76 units Od The radius is 16 units and the volume is 17 148 59 units

A cone has a radius of 5 inches and a height of 13 inches If its radius and height were enlarged by a scale factor of 2 5 how much larger would the volume of the new cone be Select one O a 32 5 times larger O b 6 25 times larger OC 12 5 times larger O d 15 625 times larger

ven a 6i 4j 4k and b 37 xj 9k find x when a b 2

Find the angle between vectors 2 6 and 11 7 Select one O a 39 01 O b 72 4 OC 82 04 O d Do not have enough information

Vectors can be Select one or more O a inverted O b scaled O c squared O d subtracted

The dot product of two vectors is NEVER Select one or more O a a vector O b a real number O c a magnitude d an integer

E 2 5 Py 17 1 0 5 0 5 0 1 5 ey 6 The vector above has a magnitude of 0 5 B 25

Given the graph Q 17 Find the following v u v u 6 19 o where is the angle formed by the vectors

What is the surface area of the triangular prism 3 cm 4 cm 4 cm 4 cm 5 cm 3 cm 5 cm Jhry

OO C 38 yd C 44 yd What is the ratio of the diameter of the smaller circle to the diameter of the larger

The radius of a circle is 8 inches What is the length of a 180 arc 180 r 8 in

Let 0 be an angle in quadrant I such that cos035 Find the exact values of csc0 and cote

10 3 Dilate by using the origin 8 6 A 4 2 4 2 2 4 6 8 10 B 2 4 C A 4 6 A B 0 6 B C 0 10 C 1 6 8 S 10 8 6 R A 2 104 8 6 4 2 2 6 8 R 8 8 R S 8 8 S 2 1 T 1 4 U T 4 8 T 1 U 4 8 U 6 8 10

Graph the image of the figure using the 1 Dilate by 2 using the center 0 0 10 8 6 7 2 H E G 2 2 F zut 4 9 6 8 10 E 2 4 E F 1 4 F G 1 2 G H 2 2 H 2 1 4 6 2 Dilate by 5 using the center 0 0 104 10 8 6 4 2 B 6 4 2 2 4 6 E D 4 6 D 1 1 D E 1 2 E F 2 0 F B AS 10

A community swimming pool is 8 yards 4 79 feet wide How wide is the pool in meters and centimeters Conversion ratios 1 m 1 09 yd 1 ft 0 3048 m 1 m 100 cm Round the centimeters to the nearest hundredth C 0 0070 08 Speed 1x Paused

Find the area K of the triangle K square units

MATHEMATICS WRITTEN WORK 1 A Write Draw the correct relation symbol to show the relationship Use a separate sheet of paper 1 AB 4 105 m2 1 6 7 DE 110 S Quarter 4 mZ2 6 B Find the measurement of the missing angles U 70 50 6 T 3 m21 Grade 8 Statements C Directions Complete the two column proof 10 15 Given A LMN where LM IN MN Prove MN IN LM MN LM LN LM LN MN Proof m22 Y 4 ZLPN ZMPN 5 ZLNP ZMPN 6 ZMNP LNM ZLNP 1 IP IN 2 ALNP is an isosceles triangle 3 ZLNPZLPN 8 9 2 FG 5 MS M N Notice that since MN LN and that MN LM then it is obvious that MN LM IN and MN LN LM are true 95 Hence what remains to be proved is the third statement LM LN MN Let us construct LP as an extension of LM such that Lis between Mand P LP LN and A LMN is formed 50 M LM LS 115 MATH SCIENCE ENGLISH MAPEH Reasons Page 5 of 1 By construction 2 3 Base angles of isosceles triangles are congruent 4 5 6 Angle Addition Postulate

A tank in the shape of a hemisphere has a diameter of 6 feet If the liquid that fills the tank has a density of 91 7 pounds per cubic foot what is the total weight of the liquid in the tank to the nearest full pound

17 Steve drew line segments ABCD EFG BF and CF as shown in the diagram below Scalene ABFC is formed A E B 1 LCFG LFCB 2 LABF LBFC F C D G Which statement will allow Steve to prove ABCDEFG 3 LEFB 4 LCBF LCFB LGFC

II A parallelogram lot has an interior angle of 36 and a height of 3 m 1 Find the length of the side in ft a 0 7 b 7 c 17 d 27 2 Find the area in sqf a 289 b 729 c 49 d 5 3 Find the area of the triangle in sqf a 55 b 66 c 77 d 88 III A right trapezoidal wall has an angle of elevation 30 the smaller height the base lengths 8m with an area of 40sqm 1 Find the smaller height in m a 2 7 b 2 8 2 9 d 3 2 Find the larger height in m a 7 2 b 7 3 c 7 4 d 7 5 3 Find the perimeter in m a 22 9 b 23 9 c 24 9

32 In the diagram below EF intersects AB and CD at G and II respectively and GI is drawn such that GII III A C H E F If mZEGB 50 and m DIG 115 explain why AB CD B

33 Given Quadrilateral ABCD is a parallelogram with diagonals AC and BD intersecting at E A B Prove AAED ACEB D E C

19 What is an equation of a line that is perpendicular to the line whose equation is 2y 3x 10 and passes through 6 1 1 y 2 y 2 3 x 5 2 x 2 3 y 3 x x 1 2 4 y x 10 3

13 The diagram below shows parallelogram ABCD with diagonals AC and BD intersecting at E B C E X D A What additional information is sufficient to prove that parallelogram ABCD is also a rhombus 1 BD bisects AC 2 AB is parallel to CD 3 AC is congruent to BD 4 AC is perpendicular to BD

5 in 3 in Volume 6 in 9 in 2 in

14 Find the area of the shaded region 9 cm

Let 2 1 1 B 1 2 3 A 0 02 2 13 2 points Part c 6 points Part d Evaluate each of the following if possible If it is not possible justify your answer Show all your work 4 points Part a Evaluate CD 3AT 3 points Part b Evaluate Evaluate DB Evaluate 8E tr CD I C 2 D 2 1 1 E 3 E 2 6 BC 4 2

21 In parallelogram PQRS QP is extended to point T and ST is drawn S R 1 130 2 80 P If ST SP and m R 130 what is mZPST 3 65 4 50 T

gths 4 Will be used later as a theorem In triangle ABC let D be a point on BC and let E be a point on AD Prove that Let ABE ACE BD CD ABD U ACD V PBD u PCD v BD CD ABP x ACP y a Which theorem states that U V t t V t t b Conclude that Uv uV i e u x v u v y Then conclude the desired poult

33 Find two values of for the trigonometric equation cos 0 9135 Round your answer to the nearest degree 24 156 B 24 336 204 336 156 204

Which is the best name for the quadrilateral with vertices at 2 2 5 2 1 5 and 2 1 A parallelogram B rectangle C rhombus D square

Triangle ABC has coordinates A 1 3 B 2 0 and C 4 1 The image of the triangle after a sequence of transformations is triangle A B C where A 5 3 B 4 0 and C 2 1 Write a sequence of transformations that takes triangle ABC to triangle A B C yt 5 4 A 3 21 B 6 5 4 3 2C1 34 2 4 5 6 A C B 1 2 3 4 5 x

Elizabeth was playing with a spinner that has 3 equal areas numbered 1 2 and 3 Elizabeth spun the spinner 100 times and 23 of the 100 spins came up as a 3 She wanted to see how likely a result of 23 threes in 100 spins would be with a fair spinner so Elizabeth used a computer simulation to see the proportion of threes in 100 spins repeated 100 times assuming a probability of of spinning a 3 Create a 95 confidence interval based on the data from the simulation to the nearest hundredth and state whether the observed proportion of threes is within the margin of error of the simulation results 1 Mean 0 331 SD 0 048 0 2 0 25 ooooo oooooo 0 3 0 35 Proportion of Threes 0 4 0 45 0 5 Note don t use percents for the interval or sample proportion The confidence interval based on the simulation is observed proportion of threes of is spinner s simulation so the of the fair

linder 6 c m Surface Area 12 cm

Rectangular Prism Surface Aras Surface Area of Rec WWE 13 mm

C 2 Suppose V is a vector space that contains vectors u u us and us If u 2 0 which of the following would be a set that spans V Select that all applied 244 S ui uz ui ui S ui u u Sa ui ui ui S u u u 0 S 0 S

Find the surface area of following 6 cm 7 cm 4 cm 12 cm 8 cm 8 cm

In the circle below IK is a diameter Suppose m 1J 44 and mLIJL 28 Find the following a m JIK 0 b m 2 KJL X

Round Tree Manor is a hotel that provides two types of rooms with three rental classes Super Saver Deluxe and Business The profit per night for each type of room and rental class is as follows Room Type I Type II Super Saver Deluxe Business 30 Rental Class 20 35 30 40 Type I rooms do not have high speed Internet access and are not available for the Business rental class Round Tree s management makes a forecast of the demand by rental class for each night in the future A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class The demand forecast for a particular night is 160 rentals in the Super Saver class 60 rentals in the Deluxe class and 50 rentals in the Business class Round Tree has 100 Type I rooms and 120 Type II rooms a Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types Is the demand by any rental class not satisfied Explain If demand materializes as forecast there will be rooms not reserved in th Select Super Saver Deluxe Business b How many reservations can be accommodated in each rental class Super Saver Deluxe Business ss

1a If there exist any solutions find the all solutions of the following congruences i x 2x 35 0 mod 27 ii x ux 44 0 mod 49 b Investigate the solututions of the following congruences If there are any solutions or not i x 461 mod 773 ii x 219 Mod 383