Sample | LEAP 2025 Geometry Sample 1st Edition

Page 1



Leap 2025 geometry Better Scores in ONE Day

Our Louisiana LEAP 2025 Geometry Boot Camp is designed specifically to increase the number of students scoring Basic and Mastery on the LEAP 2025 Geometry assessment.

In just one day, students will learn: • Core skills for success in algebra • Pacing and time management • Test-taking and guessing strategies that really work • How to overcome test anxiety and put their best foot forward on test day

Why schedule a LEAP Geometry Boot Camp? • Authentic, up-to-date practice questions • Students review exactly what they need in the “final hours” before the test. • Improves student confidence • Easy to schedule, during the school day or on the weekend • Makes test prep fun and less overwhelming for students

Implementation Models • Full-day workshop during school hours • After-school or Saturday programming • Virtual and in-person programs available


Table of Contents

Table of Contents Chapter 1: LEAP 2025 GEomEtry ovErviEw ..................................................7 Chapter 2: ConGruEnCE trAnsformAtions And simiLArity................13 CongruenCe TransformaTions and similariTy overview............................. 14 whaT are BooT Camp mini-TesTs?...................................................................... 15 mini-TesT one................................................................................................................ 16 dilaTions........................................................................................................................... 18 refleCTions and roTaTions........................................................................................ 19 mini-TesT one explanaTions....................................................................................21

Chapter 3: simiLArity in triGonomEtry And modELinG & APPLyinG.......23 similariTy in TrigonomeTry and modeling & applying overview............. 24 mini-TesT Two...............................................................................................................25 sohCahToa.............................................................................................................28 assume values.............................................................................................................. 30 mini-TesT Two explanaTions...................................................................................32 Chapter 4: AdditionAL & suPPortinG ContEnt...............................................33 addiTional & supporTing ConTenT overview..................................................34 mini-TesT Three............................................................................................................ 35 arCs and angles......................................................................................................... 38 geomeTry definiTions.................................................................................................40 mini-TesT Three explanaTions.................................................................................41


Table of Contents

Chapter 5: ExPrEssinG mAthEmAtiCAL rEAsoninG..........................................43 expressing maThemaTiCal reasoning overview.............................................. 44 mini-TesT four..............................................................................................................45 mulTi-sTep paniC......................................................................................................... 46 ComponenTs and parTs: how The TesT is sCored......................................... 48 mini-TesT four explanaTions..................................................................................49 Chapter 6: modELinG & APPLiCAtion.........................................................................51 modeling & appliCaTion overview........................................................................52 mini-TesT five................................................................................................................ 53 word proBlem TranslaTion.....................................................................................55 hidden similar Triangles...........................................................................................56 mini-TesT five explanaTions....................................................................................58 Chapter 7: mixEd PrACtiCE.............................................................................................59 mini-TesT six..................................................................................................................60 angle rules....................................................................................................................63 mini-TesT six explanaTions.......................................................................................64 Chapter 8: Wrap-Up...........................................................................................................65


Chapter One: LEAP 2025 Geometry Overview

Chapter 1 LEAP 2025 Geometry Overview


LEAP 2025 GEOMETRY OVERVIEW

Chapter One: LEAP 2025 Geometry Overview LEAP 2025 GEomEtry ovErviEw

What Is End-of-Course Testing? End-of-Course (EOC) testing measures your aptitude in a given subject after you have finished a course. Consider it a subject understanding checkup. Teachers use it to identify both your strengths and areas for improvement. This helps ensure you are on track in developing the knowledge and skills needed for the next grade and, eventually, college and a career. In this Boot Camp, we’ll focus on the major concepts tested on the LEAP 2025 Geometry test.

Why Should You Care? •

Many schools require the EOC as part of your final grade in the course.

If your school uses the EOC as a final exam for the course, then doing well on this test can boost your GPA.

A good EOC score is a positive indicator that you are on track for college.

Mastering the foundational skills taught in this Boot Camp will help you succeed in more difficult math courses in the future.

Put in the effort now and save yourself from repeating a course or taking summer school.

NOTES:

8 |

leap 2025 geomeTry BooT Camp


LEAP 2025 GEomEtry ovErviEw

Orientation The five conceptual categories tested on the LEAP 2025 Geometry test are Congruence Transformations, Similarity in Trigonometry, Additional & Supporting Content, Expressing Mathematical Reasoning, and Modeling & Application. The test is timed. All sessions except the first one allow you to use a calculator. To do well on this test, it is important to be comfortable performing mathematical operations with and without a calculator. Here is a breakdown of possible ways the LEAP 2025 Geometry assessment will test you in each of its main content categories. Each test session features questions from each category. Congruence Transformations and Similarity ask you to use similarity and congruence criteria to determine the nature of transformed figures, to prove theorems and geometric relationships, and to solve problems related to congruence. Similarity in Trigonometry and Modeling & Applying measure your ability to understand and use trigonometric functions and the Pythagorean Theorem. You are also asked to apply geometric concepts in modeling situations, on the coordinate plane, and with equations to solve problems. Additional & Supporting Content includes problems related to understanding geometric definitions, transforming figures, and the geometry of circles and solids. Expressing Mathematical Reasoning asks you to construct mathematical justifications, arguments, and critiques. Modeling & Application assesses how well you solve real-world problems by practicing modeling.

NOTES:

leap 2025 geomeTry BooT Camp

| 9

LEAP 2025 GEOMETRY OVERVIEW

Chapter One: LEAP 2025 Geometry Overview


LEAP 2025 GEOMETRY OVERVIEW

Chapter One: LEAP 2025 Geometry Overview LEAP 2025 GEomEtry ovErviEw

Orientation In Louisiana, the LEAP 2025 test score counts as a percentage of your final grade for your Geometry course. The percentage is always between 15 and 30 percent of your grade, depending on your school district. The table below gives the approximate contribution of each conceptual category to your score. This is just an estimate and can vary greatly from one test to another. If you know what areas you struggle in, compare them to the most important skills needed for the test. Category

Total Points

Percentage of Points

Congruence Transformation and Similarity

14

20%

Similarity in Trigonometry

15

20%

Additional & Supporting Content

19

30%

Expressing Mathematical Reasoning

8

10%

Modeling & Application

12

20%

Total

68

100%

The test is administered in four sessions. The sessions are timed, so it is important to manage your minutes and avoid spending too much time on any one question. Usually, each single-part question is worth one point, and each multi-part question is worth one point per part. Questions that require you to show work or justify your answers are typically worth 2, 3, or even 4 points each. Each test session may include multiple choice, multiple select, constructed response, fill-in-the-blank, and a variety of technology-assisted answering methods. For example, you might have to actually draw a graph on your computer. We provide practice for all of these different question types during the boot camp.

10 |

Test Session

Calculator?

Number of Points

Time Limit

Session 1a

No

9

25 minutes

Session 1b

Yes

13

55 minutes

Session 2

Yes

23

80 minutes

Session 3

Yes

23

80 minutes

Total

68

240 minutes

leap 2025 geomeTry BooT Camp


Chapter Two: Congruence Transformations and Similarity

Chapter 2 Congruence Transformations and Similarity


Chapter Two: Congruence Transformations and Similarity CongrUenCe transformations and similarity:

overview

Congruence Transformations and Similarity Overview CONGRUENCE TRANSFORMATIONS

The Congruence Transformations and Similarity conceptual category tests your proficiency over a broad range of geometry skills. The skills that will be tested on your exam include but are not limited to the following:

Dilations •

Dilate a figure given a center and a scale factor

Congruence and Similarity •

Determine if two figures are similar

Use congruence and similarity criteria to solve problems and prove relationships

Transformations •

Transform figures using geometric descriptions of rigid motions

Geometric Theorems •

Prove geometric theorems

NOTES:

14 |

leap 2025 geomeTry BooT Camp


Chapter Two: Congruence Transformations and Similarity CongrUenCe transformations and similarity: whaT are mini-TesTs?

What Are Boot Camp Mini-Tests? During this Boot Camp you will take several mini-tests, which are small segments of a Geometry test. While taking these mini-tests, it’s important to imagine that you are in an actual testing environment. The time limits assigned as you complete the mini-tests. In the mini-tests, we are focusing on only one category of question at a time, but on the real assessment each test session will include questions from several conceptual categories. For these mini-tests, you have 10 to 15 minutes to answer several questions. Your instructor will signal when you are out of time. Try to get through all the questions within the time limit. Unless your instructor has provided you with an answer sheet, circle your answers directly in this book. The real test does not allow the use of cell phones, watches, or computers, so you shouldn’t use them on the mini-tests, either.

NOTES:

leap 2025 geomeTry BooT Camp

| 15

CONGRUENCE TRANSFORMATIONS

match the pace that you should try to keep during the actual test. Practice all of the skills that you have learned


Chapter Two: Congruence Transformations and Similarity

Mini-Test One 1.

2.

In the coordinate plane, line q has slope 6 and y-intercept (0, 8). Line p is the result of dilating line q by a factor of 4 with center (0, 4). What is the y-intercept and slope of line p? A.

Line p has slope 2 and y-intercept (0, 4).

B.

Line p has slope 6 and y-intercept (0, 8).

C.

Line p has slope 6 and y-intercept (0, 20).

D.

Line p has slope 10 and y-intercept (0, 12).

The figure gives rhombus ABCD on the coordinate plane. Diagonals AC and BD intersect at point E.

PART A Find the coordinates of point A in terms of r, s, and t. Write your answer in the box provided below. Write only your answer in the box.

'

Mini-Test One

16

GO ON TO THE NEXT PAGE.


Chapter Two: Congruence Transformations and Similarity

PART B Since ABCD is a rhombus, AC and BD bisect one another. Use the coordinates of the rhombus to prove that AC and BD bisect one another. Enter your justification in the space provided below.

3.

Vertices X(2, 3), Y(5, 7), and Z(5, 3) form triangle XYZ on the coordinate plane. The triangle is reflected across the y-axis and then rotated 90 degrees counterclockwise about the origin to form triangle X'Y'Z'. What is the sum of the x values of the vertices of triangle X'Y'Z'? A.

–13

B.

–12

C.

–11

D.

12

STOP! END OF TEST. Mini-Test One

17

YOU MAY GO BACK AND CHECK YOUR WORK.


Chapter Two: Congruence Transformations and Similarity CongrUenCe transformations and similarity:

dilaTions

Dilations In the Congruence Transformations and Similarity category, dilations are the most important topic. A dilation is a transformation that produces an image that is the same shape, but a different size.

CONGRUENCE TRANSFORMATIONS

1.

In the coordinate plane, line q has slope 6 and y-intercept (0, 8). Line p is the result of dilating line q by a factor of 4 with center (0, 4). What is the y-intercept and slope of line p? A.

Line p has slope 2 and y-intercept (0, 4).

B.

Line p has slope 6 and y-intercept (0, 8).

C.

Line p has slope 6 and y-intercept (0, 20).

D.

Line p has slope 10 and y-intercept (0, 12).

There are a few rules that need to be memorized about dilations. When a line or line segment is dilated, no matter where the center of dilation is, the slope remains the same. In the above question, since line q has a slope of 6, line p must also have a slope of 6. We can eliminate choices A and D. Every point on the line, line segment, or shape being dilated has a distance from the center of the dilation. The dilation factor gives you what to multiply that distance by to determine the distance of the new points on the dilated image. Each new point is always along the line formed by the center and the original point. For example, if point Z is part of a dilation and it has a distance of 2 from center, then a dilation factor of 3 would mean that Z’ should have a distance of 6 from center. If the dilation factor is 0.5, Z’ would be 1 from center. A dilation factor of 1 means that you end up with the same image. In the above question, the y-intercept of q has a distance of 4 from the center. Since the dilation factor is 4, the new corresponding point should have a distance of 16 from center. Since the center is on the y-axis, the new point has coordinates of (0, 20), which gives us line p’s y-intercept. Thus, the correct answer is C. A line that that passes through the center of a dilation remains unchanged. A line segment is shortened or lengthened by the dilation factor, regardless of where the center is. For example, a line segment with a length of 6 that gets dilated by a factor of 2 has a new length of 12. If the dilation factor is 0.5, the new length is 3. To dilate a shape, use the dilation factor and the location of the center to determine the location of each vertex in the new image.

18 |

leap 2025 geomeTry BooT Camp


Chapter Two: Congruence Transformations and Similarity CongrUenCe transformations and similarity: refleCTions and roTaTions

Reflections and Rotations

Some questions will ask you to reflect or rotate figures in the coordinate plane. With items of this type, it's important to take one step at a time, to make sure you are following instructions about clockwise or counterclockwise

3.

Vertices X(2, 3), Y(5, 7), and Z(5, 3) form triangle XYZ on the coordinate plane. The triangle is reflected across the y-axis and then rotated 90 degrees counterclockwise about the origin to form triangle X'Y'Z'. What is the sum of the x values of the vertices of triangle X'Y'Z'? A.

–13

B.

–12

C.

–11

B.

12

In this question, we are first asked to make a reflection across the y-axis. Here are the rules for reflections: • When reflecting across the x-axis, multiply all y-coordinates by –1. • When reflecting across the y-axis, multiply all x-coordinates by –1. With a reflection, you multiply by –1 the coordinates that don't belong to the reflection axis (x-axis means y, y-axis means x). After the reflection, our new triangle is X(–2, 3), Y(–5, 7), Z(–5, 3). Next, we must rotate the triangle 90° counterclockwise about the origin. • The rule for rotating 90° counterclockwise is to multiply the y-coordinate by –1, then swap the x- and y-coordinates. You can memorize this table if you want to be very fast with rotations around the origin: Counterclockwise Rotation

Clockwise Rotation

New Coordinates

90°

270°

(–y, x)

180°

180°

(–x, –y)

270°

90°

(y, –x)

However, if all you remember is the 90° counterclockwise rotation rule, you can slowly figure out everything on the table. If you are given a clockwise rotation, convert it to counterclockwise. (90° CW = 270° CCW, 270° CW = 90° CCW). Then do one 90° rotation at a time until you've reached the correct number of degrees.

leap 2025 geomeTry BooT Camp

| 19

CONGRUENCE TRANSFORMATIONS

direction, and to keep some essential rules in mind.


Chapter Two: Congruence Transformations and Similarity CongrUenCe transformations and similarity: mini-TesT explanaTions

Mini-Test Explanations 1. The correct answer is C. When a line is dilated with center not on the line, the resulting line is parallel (same slope). Line p must therefore have a slope of 6. Since the center of the dilation is on the y-axis and the distance from the y-intercept of line q to the center is 8 – 4 = 4, then the distance from the center to the y-intercept of line p must be 4 · 4 = 16. Add 16 to the y value of the center to find the y-intercept of line p. 16 + 4 = 20. The slope of line p is 6 and its y-intercept is (0, 20).

Since the shape is a rhombus, and the base of the shape runs along the x-axis, AB must also be parallel to the x-axis. Therefore, the y value for A must be the same as the y value for B: 2t. A rhombus has four side lengths that are the same. Since the distance from C to D is 2r, then the distance from A to B must also be 2r. The x-coordinate of B is 4s, so the x-coordinate of A must be 4s + 2r. The coordinates of point A are (4s + 2r, 2t). Part B: Sample correct response: (One point for stating that the midpoint of AC must be the same as the midpoint of BD. One point for providing reasoning to verify that AC and BD bisect one another.) AC bisects BD because AC has the same midpoint as BD. I know this because I can use the midpoint formula on the given coordinates.  4 s + 2 r + 0 2t + 0  , The midpoint of AC =   = (2s + r, t) 2 2    4 s + 2 r 2t + 0  , The midpoint of BD =   = (2s + r, t) 2 2   Since both line segments have the same midpoint, they bisect one another. 3. The correct answer is A. When a point is reflected across the y-axis, the y-coordinate stays the same and the x-coordinate is multiplied by –1. The reflected points are X(–2, 3), Y(–5, 7), and Z(–5, 3). To rotate counterclockwise 90 degrees, multiply the y-coordinate by –1 and then swap the x- and y-coordinates. The transformed vertices are thus X'(–3, –2), Y'(–7, –5), and Z'(–3, –5). Add the x-coordinates together. –3 + – 7 + – 3 = –13.

leap 2025 geomeTry BooT Camp

| 21

CONGRUENCE TRANSFORMATIONS

2. Part A: The correct answer is (4s + 2r, 2t).


Chapter Three: Similarity in Trigonometry and Modeling & Applying

Chapter 3 Similarity in Trigonometry and Modeling & Applying


Chapter Three: Similarity in Trigonometry and Modeling & Applying similarity in trigonometry:

overview

Similarity in Trigonometry and Modeling & Applying Overview SIMILARITY IN TRIGONOMETRY

The Similarity in Trigonometry conceptual category tests your proficiency over a broad range of trigonometry and geometry skills. The skills that will be tested on your exam include but are not limited to the following:

Solving Right Triangles •

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles

Line Segment Ratios •

Find a point on a line segment that splits the segment in a given ratio

Similarity and Trigonometric Ratios •

Use similarity, side ratios, and the properties of special right triangles to solve problems

Understand and apply the definitions of trigonometric ratios for acute angles

NOTES:

24 |

leap 2025 geomeTry BooT Camp


Chapter Three: Similarity in Trigonometry and Modeling & Applying

Mini-Test Two 1.

Point A, with coordinate 1.6, point B, with coordinate 3.4, and point C are on a number line. Point B partitions AC into two parts such that the ratio of the length of AB to BC is 6:5. What is the coordinate of point C? Write your answer in the box provided below.

2.

Right triangles LMN and QRS are similar to one another.

Which ratios are equal to cos S? Select all that apply. A.

QR SQ

B.

SR SQ

C.

QR SR

D.

LM NL

E.

NM NL

F.

NM LM

Mini-Test Two

25

GO ON TO THE NEXT PAGE.


Chapter Three: Similarity in Trigonometry and Modeling & Applying

3.

Use the triangle depicted below to answer the question.

In right triangle XYZ, m∠X ≠ m∠Y . Let cos X = 2a and sin X = 3b. What is cos Y – sin Y? A.

3b – 2a

B.

2a – 3b

C.

2a + 3b

D.

3b 2a

Mini-Test Two

26

GO ON TO THE NEXT PAGE.


Chapter Three: Similarity in Trigonometry and Modeling & Applying

4.

A projector screen is mounted from the ceiling at point A. The bottom of the screen is connected to a motorized hook at point B, which can move up and down a pole running between points C and D. The angle θ is the angle created as the hook moves between points C and D.

PART A When the screen is extended to a distance of 11.4 meters, what is the value of θ to the nearest tenth of a degree? A.

72.1°

B.

69.5°

C.

60.0°

D.

20.5°

PART B When θ = 47°, what is the distance from point B to point A to the nearest tenth of a meter? Write your answer in the box provided below. meters

STOP! END OF TEST. Mini-Test Two

27

YOU MAY GO BACK AND CHECK YOUR WORK.


Chapter Three: Similarity in Trigonometry and Modeling & Applying similarity in trigonometry:

mini-TesT explanaTions

Mini-Test Explanations 1. The correct answer is 4.9. The length of AB is 3.4 – 1.6 = 1.8. Use the ratio 6:5 to set up a proportion to find the length of BC. x 5 = 1.8 6

SIMILARITY IN TRIGONOMETRY

6x = 9 x = 1.5 Add the length to the coordinate of B to find the coordinate of C. 3.4 + 1.5 = 4.9. 2. The correct answers are B and E. The cosine of an angle is defined as the length ratio between the adjacent side and the hypotenuse. The adjacent side is SR, and the hypotenuse is SQ. cos S =

SR SQ

Therefore, B is correct. NM Since LMN is similar to QRS, m∠N = m∠S. It follows that cos N = cos S. Thus, is also equal to cos S. NL Choice E is correct. 3. The correct answer is A. sin X = cos Y, and cos X = sin Y. Since cos X = 2a, sin Y = 2a. Likewise, sin X = 3b, so cos Y = 3b. Therefore, cos Y – sin Y = 3b – 2a. 4. Part A: The correct answer is B. Since AB is 11.4 and AC is 4, the adjacent side and the hypotenuse have known lengths. Set up an equation using cosine and solve for θ. cos θ =

4 11.4

θ = cos–1

θ ≈ 69.5°

4 11.4

Part B: The correct answer is 5.9. AC is 4 and the measure of θ is 47°. Set up an equation using cosine and solve for the length of AB. cos 47° = x=

4 x

4 cos 47

x ≈ 5.9

32 |

leap 2025 geomeTry BooT Camp


Chapter Four: Additional & Supporting Content

Chapter 4 Additional & Supporting Content


Chapter Four: Additional & Supporting Content additional & sUpporting Content:

overview

Additional & Supporting Content Overview The Additional & Supporting Content item category tests your proficiency over a broad range of geometry skills.

ADDITIONAL & SUPPORTING CONTENT

The skills that will be tested on your exam include but are not limited to the following:

Definitions •

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment

Rotations and Transformations •

Given a shape, such as a parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that map it unto itself

Perform rotations, reflections, and translations on geometric figures

Circles, Angles, Radii, and Chords •

Find the center and radius of a circle using the equation of a circle and derive the equation of a circle using the Pythagorean Theorem

Solve problems involving inscribed angles, radii, and chords

Shapes and Solids •

Solve for the volume of cylinders, pyramids, cones, and spheres

Identify cross-sections of three-dimensional objects and determine 3-D objects created from rotations of 2-D objects

NOTES:

34 |

leap 2025 geomeTry BooT Camp


Chapter Four: Additional & Supporting Content

Mini-Test Three 1.

 is congruent to ST  is equal to  . Five times the measure of QR Points Q, R, S, and T lie on circle A. QR . four times the measure of QT R Q A S

T

Part A Select from the choices near the box to complete the statement: four-ninths

five-ninths

equal to

The measure of angle ∠RST is

the measure of ∠QRS . four times

five times

nine times

Part B Select from the choices near the box to complete the statement. four-ninths

five-ninths

equal to the measure of ∠QRS .

The measure of ∠QSR is four times

Mini-Test Three

five times

35

nine times

GO ON TO THE NEXT PAGE.


Chapter Four: Additional & Supporting Content

2.

Select from the choices near the boxes to complete each sentence. A shape formed by two rays diverging from a common endpoint is called a(n) triangle

tangent .

angle

perpendicular line

The common endpoint is called the center

vertex .

axis

3.

radius

Regular hexagon ABCDEF is given below with center at point G. D

C

G E

B

F

A

Which tranformations will map hexagon ABCDEF onto itself? Select each correct transformation. A.

reflecting over CF

B.

reflecting over BF

C.

reflecting over AD

D.

rotating 120° clockwise around point G

E.

rotating 90° clockwise around point G

F.

rotating 240° counterclockwise around point G

Mini-Test Three

36

GO ON TO THE NEXT PAGE.


Chapter Five: Expressing Mathematical Reasoning

Chapter 5 Expressing Mathematical Reasoning


Chapter Five: Expressing Mathematical Reasoning expressing mathematiCal reasoning:

overview

Expressing Mathematical Reasoning Overview The Expressing Mathematical Reasoning task category tests your proficiency over a broad range of geometry

EXPRESSING MATH REASONING

skills. The skills that will be tested on your exam include but are not limited to the following:

Coordinate Reasoning •

Apply geometric reasoning in the coordinate plane and use coordinates to draw geometric conclusions

Geometric Propositions and Conjectures •

Construct chains of reasoning to justify or refute geometric propositions and conjectures

Multi-Step Problems •

Solve multi-step geometry problems, or identify and correct solutions for multi-step problems, and explain your reasoning

Algebra and Geometry •

Use a combination of algebraic and geometric reasoning to justify or refute statements about geometric figures

NOTES:

44 |

leap 2025 geomeTry BooT Camp


Chapter Six: Modeling & Application

Chapter 6 Modeling & Application


Chapter Six: Modeling & Application modeling & appliCation:

word proBlem TranslaTion

Word Problem Translation The secret to solving a word problem is translating it into math. When translating word problems to algebraic equations, it is important to know which words translate to which

MODELING & APPLICATION

operations. is, equal to, is the same as → =

times, product, each, per, of → ·

minus, without, less, difference, change → –

plus, together, and, combined, both, more → +

divided into, split between or among, divvied up → ÷

Let’s take a look at how word problem translation can help you solve a problem on your exam. 1.

A company offers blankets in two sizes: twin and double. The twin blanket is 24 inches longer than it is wide. The double blanket has the same length as the twin blanket, but it is 14 inches wider. The area of the twin blanket is 1,260 square inches less than the area of the double. PART A Write and equation that can be used to determine the area of the double blanket. Define all variables used. Write your equation in the space provided below.

The area of the blanket is length times width. To find the equation of the blanket's area, you must first find its dimensions. You will need to translate the sentence the double blanket has the same length as the twin blanket, but it is 14 inches wider into an algebraic equation. Let x represent the width of the twin blanket and A represent the area of the double blanket. The length of the twin blanket, and thus the length of the double blanket, is x + 24, since the twin is 24 inches longer than it is wide. The width of the double blanket is x + 14 because it is 14 inches wider than the twin blanket. We use the plus operand in both cases because we are dealing with the concept of more: more width and more length. Area is determined by multiplying width by height, so we can create this final equation to answer Part A: A = (x + 14)(x + 24) Be sure to define the variables you use when the question asks for it. Otherwise you will not receive points!

leap 2025 geomeTry BooT Camp

| 55


Chapter Seven: Mixed Practice

Chapter 7 Mixed Practice


Chapter Seven: Mixed Practice

Mini-Test Six 1.







In the figure shown below, GH intersects AB and CF at points E and D, respectively. G

A E B C D

F H

PART A Given: ∠CDH ≅ ∠AED Prove: ∠EDF ≅ ∠AED Fill in the blanks using the following options: • • • • • •

Transitive Property of Congruence Symmetric Property of Congruence Reflexive Property of Congruence Definition of Congruent Angles Vertical Angles are Congruent Given

Statement: ∠CDH ≅ ∠AED . Reason:

Statement: ∠EDF ≅ ∠CDH . Reason:

Statement: ∠EDF ≅ ∠AED . Reason:

Mini-Test Six

60

GO ON TO THE NEXT PAGE.


LEAP 2025 Geometry: Wrap-Up

Chapter 8 Wrap-Up


LEAP 2025 Geometry: Wrap-Up

WORKKEYS OVERVIEW

Wrap-Up

Wrap-Up Remember These Key Tips •

Dilations

Reflections and Rotations

SOHCAHTOA

Assume Values

Arcs and Angles

Geometry Definitions

How the Test is Scored

Multi-Step Panic

Word Problem Translation

Hidden Similar Triangles

NOTES:

66 |

leap 2025 geomeTry BooT Camp


LEAP 2025 Geometry: Wrap-Up

WORKKEYS OVERVIEW

Wrap-Up

Study Plan •

7 Days Before Test: Review Chapter 2, Congruence Transformations and Similarity.

6 Days Before Test: Review Chapter 3, Similarity in Trigonometry and Modeling & Applying.

5 Days Before Test: Review Chapter 4, Additional & Supporting Content.

4 Days Before Test: Review Chapter 5, Expressing Mathematical Reasoning.

3 Days Before Test: Review Chapter 6, Modeling & Application.

2 Days Before Test: Quickly review the entire boot camp book, paying special attention to the strategies you learned.

1 Day Before Test: Be sure to get a good night’s rest and line up a nutritious breakfast in the morning.

NOTES:

leap 2025 geomeTry BooT Camp

| 67


LEAP 2025 Geometry: Wrap-Up

WORKKEYS OVERVIEW

Wrap-Up

Before Your Test Date •

Get enough sleep the entire week before the test.

Eat well, especially on the day of the test.

Bring a snack with you on test day. Fruit and/or protein bars work wonders. Avoid sugar and junk food. A bottle of water is a good suggestion.

If you can’t do without caffeine, allow about one month before test time to minimize your intake. Being jittery during the test can affect your test performance.

It is important to feel as healthy as possible both mentally and physically on the day of the exam.

Reduce distractions! Stay away from social media for 12–24 hours before the test starts.

NOTES:

68 |

leap 2025 geomeTry BooT Camp


Want to learn more about what MasteryPrep can do for your school? Check out our other college-readiness solutions and find the one that best suits your school’s needs. Click here to download the full MasteryPrep Catalog!

Professional Development: • Decoding the ACT • Mastering the SAT • ACT/SAT Mastery Certification Course Comprehensive training where teachers become ACT and SAT experts. Integrate college readiness in the classroom with tips, strategies, and content insights.

Practice Tests: • TruScore ACT Practice Testing Deep insights into ACT performance with 24-hour turnaround. No-hassle, pencil and paper practice testing and analysis.

Boot Camps: • • • • • •

ACT Boot Camp SAT Boot Camp WorkKeys Boot Camp EOC Boot Camps TSIA2 Boot Camp AccuPrep Better scores in one day. Engaging experts help students become prepared and confident with time management and testtaking strategies.

Curricula: • • • • • •

ACT Mastery ACT Snap Course SAT Mastery SAT Snap Course TSIA2 Snap Course ACT Essentials Online The first and only mastery-based ACT and SAT curricula. Fit any schedule with zero teacher prep time.

• ACT Elements Authentic daily reinforcement of ACT essential skills. Scaffolded approach builds confidence and competence.

• MasteryKeys The most comprehensive and successful WorkKeys prep program for earning a Silver NCRC™.


Turn static files into dynamic content formats.

Create a flipbook
Issuu converts static files into: digital portfolios, online yearbooks, online catalogs, digital photo albums and more. Sign up and create your flipbook.