2D Geometry Questions and Answers

In a direct variation y 20 when x 10 Write a direct variation equation that shows the relationship between x and y y 20x 280 y 2x Dy y 28 2

Which of the following graphs shows a direct variation proportion a y 18 16 14 12 A 10 b YA B 15 10 20 20 w S

5 Find the length of DE E D

Find the value of each variable x and y 32 I 300 y

Use the reference angle to find all six trigonometric functions of the angle t Hint Enter the exact answer Type sqrt 5 for 5 3 sint sqrt 2 2 cost type your answer tant type your answer csct type your answer type your answer cott type your answer

The quantity z varies directly with y and inversely with x When y 8 and x 4 z 1 What is the value of k the constant of variation Write your answer in the form A or where A and B are constants or variable expressions

In a certain city E Street W Street C Street and D Street are parallel streets that intersect K Street and M Street How long is K Street between C Street and D Street The length of K Street between C Street and D Street is 50 Park E S W St K St SPOON 600 ft M St C St 310 f D St ft

5 Use the dimensions given in the diagram below Find h the height of the kite off the ground to the nearest tenth of a foot 2 pts H tan 300 40 2 7 300 ft 40

8 Use the dimensions given in the diagram below What is the value of y 3 pts 45 14 30

and 60 gle If they or obtuse 4 Given AWXY is a right triangle WX 25 WXY Solve for XY Round to the nearest tenth 2 pts W 25 mm X 58 X sin 213583 XY 41 7 Y m below Find h the height of the kite off the ground to the

The graph of y f x is shown 10 9 8 7 6 5 4 3 2 1 12 4 5 6 7 8 9 10 a Remember this is the graph of y f x and not the graph of y f x At 7 the graph of y a straight line concave up concave down f z is At 4 the graph of y f x is concave down a straight line concave up

vertices of a triangle a find the DISTANCE BETWEEN TWO POINTS 1 Given three points which serve as Determine whether the given points are collinear or non collinear 11 perimeter of each triangle and b 1 P 3 3 Q 0 1 R 9 7 determine the kind of triangle according to sides and angles 2 S 3 1 T 1 3 U 10 8 1 A 0 0 B 5 2 C 3 3 2 D 3 8 E 5 5 F 6 0 3 G 2 3 H 4 3 1 3 4 4 V 3 1 W 2 3 2 X 2 3 4 5 M 1 1 N 6 2 0 4 3 3 V 2 2 W 5 2 X 11 2 III If point M x 4 is equidistant from A 5 2 and B 3 4 find the value of x IV If point N 3 y is equidistant from P 2 6 and Q 7 2 find the value of y

Using the given diagram solve for x DO 8 6 X 3

A triangle is formed by the building s height and shadow Another triangle is formed by the flagpole s height and shadow Using the following diagram find the height of the building 46 ft 40 ft 2 ft

To the nearest millimeter a cell phone is 117 mm long and 48 mm wide What is the ratio of the wid to the length The ratio of the width to the length is Type the ratio as a simplified fraction

TRAP EZYD Use the diagram on the right to find the scale factor of TRAP to EZYD The scale factor of TRAR to EZYD is T 14 R E 43 14 14 P 28 Z 16

9 If LO 15x 19 and QN 10x 2 find PN 12 1 L P N 2X1

ind the length of the altitude to the hypotenuse of a right triangle whose sides have engths 6 8 and 10 The altitude to the hypotenuse separates the hypotenuse into wo parts The smaller part is 3 8 Round your answer to the nearest tenth

Find the value of x 3 6

Find all roots of g x g x 3x x 3x 1 Write your answer as a list of simplified values separated by commas if there is more th one value

Find all rational roots of g x g x 11x 54x 16x 1 Write your answer as a list of simplified values separated by commas if there is more one value

In the diagram to the right GKNM VRPT Find the value of x Give the scale factor M of the left polygon to the right polygon Type an integer or a decimal The scale factor of GKNM to VRPT is Simplify your apcworn Tupo X G N 8 4 3x 1 K R x 5 The figures are not to scale 63 P V 3

Identify the altitude in ARST shown to the right The altitude of ARST is RT ST R P

The unit circle below shows 125 and 125 Find the values below rounded to three decimal places if necessary 0 574 0 819 0 574 0 819 125 125 sin 125 I sin 125 sin 125

The unit circle below shows 35 and 35 Find the values below rounded to three decimal places if necessary 35 35 0 819 0 574 0 819 0 574 Next cos 35 cos 35 cos 35

The point P 3 y lies on the unit circle shown below What is the value of y in simplest form P x y 1 0

A polynomial function f x with integer coefficients has a leading coefficient of 3 and a constant term of 4 According to the Rational Root Theorem which of the following are possible roots of f x 4 314 2 4

A polynomial function g x with integer coefficients has leading coefficient of 1 and a constant term of 18 According to the Rational Root Theorem which of the following are possible roots of g x 18 9 1 1

Complete the following derivation using the basic rules and the following selection of derived rules DNE DNI Comm CommV DeM DSL DSR MT Trans HS Def E and Def I 1 P Q S Premise 2 P Q S Premise 3 P Q PVQ Premise n S Goal

15 10

Classify each polynomial based on the the degree of the polynomial DRAG DROP THE ANSWER T 9 3 7y 12y 3y 17 X T 12r 6r 6 32 92 12 x 9 42 16 Quadratic Linear Cubic Constant

For each polynomial expression in the table below classify the expression as a difference of squares difference of cubes sum of cubes or none of these by placing a check mark in all appropriate boxes Expression a 2 2 y b 82 24y C x 1 Difference of Squares Difference of Cubes Sum of Cubes None of these B 5000

Factor the polynomial expression completely 8x 27 A 4x 3 4x 3 B 2x 3 4x 6x 9 2x 3 4x 6x 9 D 2x 3 4x 6x 9

Factor the polynomial expression completely 27x 125 A 3x 5 9x 25 B 3x 5 9x 15x 25 3x 5 9x 15x 25 D 3x 5 9x 15x 25

The graphs below represent functions defined by polynomials For which function are the zeros of the polynomials 2 and 3 1 2 X X 3 X X

Factor By Grouping 3n 12n 2n 8

a b Consider the expression 15n m 25n m Part A What is the GCF of the polynomial A 5 B 5nm c 5n m D 5n m Part B Factor

Solve the equation by factoring x 11x 30 A x 5 x 6 B x 5 x 6 C x 5 x 6 x 5 x 6 D X

Factor By Grouping 6n 10n 3n 5 3

Factor completely 3 y 6y 5y

Select all of the statements that are true about the following expression 4x 3x A The polynomial is a cubic trinomial B The polynomial is not in standard form C The degree of the polynomial is 3 The leading coefficient is 4 E The polynomial has 3 terms The leading coefficient is 4 1

Factor the polynomial if possible If the polynomial cannot be factored write prime x 3x 4x 12

For which function defined by a polynomial are the zeros of the polynomial 4 and E Ay x 10x 24 By x 10x 24 y x 10x 24 y x 10x 24

7 Factoring 3bc 2b 10 15c by grouping results in b 5 3c 2 A True B False

Factor completely Note You will need to use more than one factoring method 4x 4x 24 A 4 x x 6 B 4 x 3 x 2 c 4 x 3 x 2 D 4x 12 x 2

For the polynomials in the first column determine the degree of each polynomial and tick the correct option Polynomial 884 686 8 12s 24s s s 25 584 8 78 586 28 6 3

Completely factor this polynomial Do NOT use the space bar when typing your answers 3x 27x Factored Form

Factoring the following polynomial expression completely 2x x 8x 4

A can only display numerical da O A univariate OB list O C histogram O D bar graph

UT 5 6 O 7 9 10 11 12 13 men completing the square you will need to undo a squared term at some point How is is accomplished subtract the number under the radical from both sides squaring both sides take the square root of both sides 15 it cannot be done Your answer is already simplified as much as possible FRE Clanl