Geometry Questions

The graph of f x 5 0 15 is given below click on graph to enlarge

b C 3 9 D 5 4 Find the midpoins of set of orderd pairs

Follow the steps for graphing a rational function to graph the function F x UL Ine domain is the set of all real numbers Write F x in lowest terms Select the correct choice below and if necessary fill in the answer box within your choice A F x Simplify your answer B F x is already in lowest terms x 17x 18 X 6 Find the intercepts of the graph Select the correct choice below and if necessary fill in the answer box es within your choice OA The graph has y intercept and x intercept s Simplify your answers Type integers or fractions Use a comma to separate answers as needed Type each answer only once OB The graph has y intercept and no x intercept Simplify your answer Type an integer or a fraction OC The graph has x intercept s and no y intercept Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once OD The graph has neither x intercepts nor y intercepts

2 Tell whether the transformation appears to be an isometry Explain your answer

9 Determine the number of lines of symmetry for each figure a b c

1 Name the transformation that maps the lighter turtle preimage to the darker turtle image a b c 2 Tell whether the transformation appears to be an isometry Explain your answer t

Steps for graphing a rational function to graph the function P x 1 The graph has y intercept and no x intercept 6 Simplify your answer Type an integer or a fraction OD The graph has neither x intercepts nor y intercepts 6 36 X Determine the behavior of the graph of P at any x intercepts Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The graph will cross the x axis at x and touch but not cross the x axis at x Type integers or simplified fractions Use a comma to separate answers as needed Type each answer only once OB The graph will touch but not cross the x axis at x Type an integer or a simplified fraction Use a comma to separate answers as needed Type each answer only once OC The graph will cross the x axis at x Type an integer or a simplified fraction Use a comma to separate answers as needed Type each answer only once OD There is no x intercept

7 Use your compass to construct two circles with the same radius intersecting at two points Label the centers P and Q Label the points of intersection of the two circles A and B Construct quadrilateral PAQB What type of quadrilateral is it

5 a Draw the vectors a 3 2 b 2 1 and C 7 1 b Show by means of a sketch that there are scalars s and t such that c sa tb c Use the sketch to estimate the values of s and t d Find the exact values of s and t

5 8 Find a vector a with representation given by the directed line segment AB Draw AB and the equivalent representation starting at the origin 5 A 1 1 B 3 2 6 A 4 1 B 1 2

9 12 Find the sum of the given vectors and illustrate geometrically 9 1 4 6 2 10 3 1 1 5

13 16 Find a b 2a 3b a and a b 13 a 5 12 b 3 6

Would you use SSS SAS ASA or AAS to prove the triangles congruent If there is not enough information write There is not enough information Explain your answer E P F R

A chord AB of a circle centre O and radius 21 cm is 36 cm long Express the angle AOB in radians Use your result in a to calculate correct to three significant figures i the length of the arc AB the area of the sector AOB the area of the minor segment cut off by the chord AB Take 3 142 ii iii

Question 12 of 14 12 Assume each outcome in the sample space S provided below is equally likely Find P AB S 0 1 2 3 4 5 6 A 0 1 2 5 B 1 2 4 Round your answer to the nearest hundredths Answer Previous Answer 0 29

The medians of AABC are AE BF and CD They meet at a single point In other words G is the centroid of AABC Suppose BF 27 AG 14 and CG 20 Find the following lengths Note that the figure is not drawn to scale A D F G B E C GD 0 GF AE

11 Find an equation of the sphere that passes through the point 4 3 1 and has center 3 8 1

5 Describe and sketch the surface in R represented by the equation x y 2 hu

5 Describe and sketch the surface in R represented by the equation x y 2

Write a rule to describe each transformation 31 G H H y A

36 reflection across the x axis v 5 1 W 5 3 X 1 3 AY X

4 Write the conditional converse and contrapositive to the following inverse statement If a triangle has 1 right angle then the triangle is a right triangle 40 Conditional Converse Contrapositive 15 Draw a counterexample to the following statement All isosceles triangles are acute triangles 16 A toddler s climbing ramp is designed with the profile of a right triangle The measure of one acute angle is who times the measure of the other acute angle Find the measure of each acute angle Find m2BDC M 28 58 b 84 c 56 d 112 the 5 sides lengths from shortest to longest on the es below 8 7 951 135 B 8 19 A Geometry student was using the following picture to find mzQ Identify the first step if any in which an error occurred R 2x 15 a Yes acute triangle b Yes obtuse triangle c Yes right triangle d No cannot e a triangle X 2 20 Determine if the following measures can be the sides of a triangle 6 14 13 If so classify the triangle by its angles Side 21 Find the value of x Then classify the triangle by its sides angles Angle TO113 22 Find the measure of the smallest angle H 4x 2x 9 W Step 1 Step 2 Step 3 Step 4 10x 3x 8 23 Determine the value of x x x 200 Student Work x 2 2x 15 180 5x 30 180 C mZQ 2 30 15 75 x 150 x 30 3x 28 B 5x 52 2x 10

2x 4 A C B 9 11 BC A A Sy 1 B y 2 C

Question 10 of 14 10 Suppose X is a normal random variable with probability density function defined by 1 16 What is the mean of X f x Answer e 16 Previous Answer 0 Return to overview

Solve the given equation Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTION 2 sin 9 cos 8 1 8

An equation is given Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTI 3 tan 30 1 0 a Find all solutions of the equation Tk TUTU 3 18 8 8 X b Find the solutions in the interval 0 2 T 7T 4 6 X

An equation is given Enter your answers as a comma separated list Let k be any integer Round terms to three decimal places where appropriate If there is no solution enter NO SOLUTION 2 cos 38 1 a Find all solutions of the equation 8 b Find the solutions in the interval 0 2m 8

Given AC L BD and BD bisects AC Prove AABD ACBD Step 1 2 try Statement AC L BD BD bisects AC BD BD Type of Statement Reason Given Reflexive Property A B D C

Given E is the midpoint of BD and AC L BD Prove ABAE ADAE Step 1 try Statement E is the midpoint of BD AC L BD Type of Statement Reason Given A B E D

Given AD AE and AB AC Prove AABE AACD Step 1 try Statement AD AE AB AC Type of Statement Reason Given A D F B

Given D is the midpoint of AC ZAED ZCFD and LEDA LFDC Prove AAED ACFD Step 1 try Statement D is the midpoint of AC LAED LCFD LEDA LFDC Type of Statement Reason Given E B F

Triangle FGH is congruent to triangle QRS Which congruence statements must be true Select ALL that apply FG RS OZGHF LRQS HF SQ OLHGF SQR LCE

Select the correct answer from each drop down menu Consider the figure formed by AAEB and ADCB sharing a common vertex B A The figure E has point symmetry does not have point symmetry D because rotating it 180 about point B maps AAEB onto ADCB The figure because point E is the same distance but in the opposite direction from point B as point C and point A is direction from point B as point D

Complete the proof 1 Given Line AB intersects line DC at point B LAEB and DEC are straight angles Prove LAEC DEB 10 Statements E Reasons 1 1 2 ZAEC is supplementary to CEB 2 3 ZDEB is supplementary to CEB 3 Def of Supplementary Zs 4 4 Supplements Theorem a ZAEB and DEC are straight angles b Substitution c Angle Addition Postulate d Given e Addition Property of Equality f Linear Pair Theorem g ZAEC is congruent to ZDEB B

2 3 pts 1 each For each part below all are separate from each other make up a list of FIVE scores from 0 to 100 inclusive that have the indicated properties If not possible explain WHY not discussing the meanings of all measures of central tendency or spread mentioned in the problem a There are three modes and the mean is 40 b The median is 50 but it changes to 54 if an extra sixth score of 80 is included Make it clear which FIVE scores are your originals n The range is 20 low score is 6 and mean is 15

Using the figure provided complete each congruence statement Explain your reasoning B A 2 E ZBED H D C

15 One litre of latex paint covers approximately 8 5 m and costs 12 a Copy and complete this table Volume of Paint p L Cost c 0 24 Area Covered A m 0 17 0 2468 b Graph the area covered as a function of the volume of paint c Graph the area covered as a function of the cost d Write the domain and range of the functions in parts b and c

each congruence statement Explain your reasoning A E DBC B D LCDB

3 On Sunday Tiana runs on a straight path to the park located at 8 12 on the grid and from there she runs on a straight path to her friend s house located at 10 6 on the grid From there she runs on a straight path back to her house Ronald runs on a straight path to the library located at 12 0 From there he runs on a straight path to the store located at 10 6 From the store he runs on a straight path directly back home Draw the routes on the coordinate plane 4 Demonstrate that the two triangles formed by their routes are congruent Include a triangle congruence statement Then determine a series of transformations that maps one triangle onto the other

2 Tiana and Ronald like to run as part of their exercise routines on the weekend They each go on runs from their house Tiana s house is located at point T and Ronald s house is located at point R on the coordinate plane shown LI V 20 12 R 10 12 14 1 On Saturday Tiana runs 3 miles north then 4 miles east and then back to her house via the shortest route Ronald runs 3 miles west then 4 miles south and then back to his house via the shortest route Draw the routes on the coordinate plane Demonstrate that the two triangles formed by their routes are congruent Include a triangle congruence statement Then determine a series of transformations that maps one triangle onto the other

a sin 0 b cos 8 c tan 0 d cos 20 e tan 20 cot 20 g sec 20 h CSC 28 12

Use a double angle formula to rewrite the expression Use a graphing utility to graph both expressions to verify that both forms are the same 8 sin x 4

Solve for the variables and find missing values Classify the triangle by the sides and angles 5 DE E 5x12 3x 4 F 6 3x 2 z 5 y 3 2x 5

Determine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle a 11 b 13 c 8 Law of Sines O Law of Cosines Then solve the triangle Round your answers to two decimal places A B C Mond 11 n O

Find the slope of the curve below at the given points Sketch the curve along with its tangent lines at these points R r 9 9 cos 0 0 2 T The slope at the point 0 2 Simplify your answer is www

Sketch the region defined by the inequalities 3 r 5 and Choose the correct graph below O A O B ses IN 2 O C X G D tio

an 2 given tan 7 3 with 180 B 270

148 A 2x 15 8 C

HQ Four Quadrant Ordered Pairs B C 3 3 G E C Z 4 3 2 4 S Write the ordered pair for each given point 8 4 9 W 11 I 10 12 Z 2 2 2 1 1 2 4 4 5 8 Tell what point is located at each ordered pair 1 3 7 3 6 4 2 8 7 4 9 7 8 9 5 8 9 6 3 8 13 G 14 T Plot the following points on the coordinate grid 17 O 7 4 19 V 2 5 18 F 3 6 20 A 2 9 W X messa 21 Y 1 6 22 U 2 5 1 2 6 1 D 7 4 4 8 1 3 15 D 8 6 16 J 3 1 23 M 1 5 24 N 8 8

Chapter b The report also gave data on the percentage of children who were not covered by health insurance for four groups Hispanic children with both parents foreign born Hispanic children with at 1Q least one U S born parent Non Hispanic White children and Non Hispanic Black children Those data were used to create the time series plots for these four groups shown below The data for all children are also included in the plot Uninsured 25 20 15 10 5 0 2010 2012 2014 Year Non Hispanic White children Non Hispanic Black children Hispanic children with foreign born parents Hispanic children with at least one U S born parent All Children Hispanic Foreign Born Parents Hispanic At Least One U S Born Parent Based on this the title of the report Select and the group showing the lowest rates is Select Non Hispanic White Non Hispanic Black 2016 2018 Write a paragraph based on this plot that comments on the similarities and differences of these groups Also explain whether the title of the report is or is not supported by these time series plots Bb Over time the percent of Hispanic children with foreign born parents who are uninsured appears to be Select who are uninsured appears to be Select 8 the percent of Hispanic children with at least one U S born parent e the percent of Non Hispanic White children who are uninsured appears to be Select B and the percent of Non Hispanic Black children who are uninsured appears to be Select B However if we look only at the last three years the percent of uninsured children in the following groups appear to be increasing Select all that apply G to be supported Additionally the group showing the highest rates of uninsured children is Select B