GEOMETRY HONORSmylwa.lawrencewoodmere.academy/.../Geometry-Honors.pdf · 2017-06-12 · Welcome to Geometry Honors!! Complete the following assignment in the attached packet. This

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GEOMETRY HONORS

SUMMER ASSIGNMENT 2017

Welcome to Geometry Honors!! Complete the following assignment in the attached packet. This is due the first day of school. Bring in a copy of your answers including ALL WORK SHOWN, to hand in for a grade, This will count as your first test grade (10 points will be taken off for each day late). It will be graded on completeness rather than correctness. This assignment will be reviewed at the beginning of the school year and you will be tested on this material again after it is reviewed. These skills will be needed throughout the year. This is your ticket to Geometry Honors. Make sure that you start the year off well and have your assignment ready upon your return. Please answer all questions in the packet and clearly label your answers by boxing them in. You must show work where appropriate. If you need additional space to complete problems, please do your work on a separate sheet of paper, clearly label your work, and staple your additional pages to the back of the packet.

1. SOLVING LINEAR EQUATIONS: Solve the equation for the indicated variable. Write your

solution in the box to the right. YOU MUST SHOW ALL WORK!

1. Which value of p is the solution of ?

2. What is the solution of the equation ?

3. Which value of x is the solution of the equation ?

4. What is the value of x in the equation ?

5. Solve for x:

6. If and , what is the product of x and m?

7. If and , find the value of y.

8. What is the value of x in the equation ?

9. If , what is the value of x ?

10. Solve algebraically for x:

11. What is the value of x in the equation ?

12. Which value of x is the solution of the equation ?

13. What is the value of w in the equation ?

14. In the equation , what is n is equal to?

15. Which value of x is the solution of the equation ?

16. Solve for m:

17. Solve:

18. The number of people on the school board is represented by x. Two

subcommittees with an equal number of members are formed, one with

members and the other with members. How many people are on the school

board?

2. OPERATIONS WITH POLYNOMIALS: Simplify each of the following according to the given

instructions.

1. The sum of and can be expressed as

2. What is the sum of and ?

3. The expression is equivalent to

4. The expression is equivalent to

5. When is subtracted from , the result is

6. What is the result when is subtracted from ?

7. Find the perimeter of the triangle:

8. What is the product of and ?

9. What is the product of and ?

23 2x 22 6 3x x

8 5x

10. What is the product of and ?

11. What is the product of and ?

12. The expression is equivalent to

13. The expression is equivalent to

14. What is the product of (x + 4) and ( x – 4)?

15. If h represents a number, write an equation that is a correct translation of "Sixty more than 9 times a number is 375".

16. The width of a rectangle is 4 less than half the length. a. If represents the length, write an equation that could be used to find the width, w.

If the area of the rectangle is 40, write an equation that could be used to find the area of the rectangle in terms of l.

3. FACTORING COMPLETELY: Factor each of the following expressions completely. Remember to look for your factoring methods in the following order:

i. Greatest Common Factor ii. Trinomial A/M iii. Factoring by Grouping (“Tricky” Trinomial) iv. Difference of Two Perfect Squares

1. 22 32x

8. 3 27 10x x x

2. 3x x

9. 2 24 6 4x x

3. 25 10 15x x

10. 4 1y

4. 2 22 2a b

11. 25 20 20x x

5. 24 4a

12. 3b2 - 15b + 12

6. 2 2ba by

13. 5 4 34 21z z z

7. 24 4 48y y

14. 3x 2 + x -2

4. SOLVING QUADRATIC EQUATIONS BY FACTORING: Solve each of the following quadratic equations. YOU MUST SHOW ALL WORK.

Remember: i. Set the equation equal to 0. ii. Factor the non-zero side of the equation completely iii. Set each factor equal to 0. iv. Solve each equation.

1. What is the solution set of the equation 3x2 = 48?

2. What is the solution set of the equation x2 – 5x = 0?

3. 2 4 3x x

4. 3 + x(x – 1) = 5

5.

5 3

2

x

x

6. 2x x

7.

3

8 3

x x

x

8. 3 22 12 80y y y

9. 25 6 1b b

10. 22 5 3y y

11. The length of a rectangular window is 5 feet more than its width, w. The area of the window is 36 square feet. Find the dimensions of the window.

12. The length of a rectangle is 2 feet less than twice the width. The area of the rectangle is 84 square feet. Find the dimensions of the rectangle.

5. GRAPHING ON THE COORDINATE PLANE:

1. What is an equation of the line that passes through the points and ?

2. What is the slope of the line represented by the equation ?

3. What is the solution to the system of equations? (Where do the two graphs intersect?)

4. The lines represented by the equations and are

i. Parallel, but not the same line ii. Perpendicular iii. Intersecting but not perpendicular iv. The same line

5. Write an equation of a line that is parallel to the line whose equation is and that

passes through the point .

6. Write an equation of a line that is perpendicular to the line whose equation is and

that passes through the point .

7. The slope of is and the slope of is . If , determine and state the value of

x.

8. Write an equation that represents the line that passes through the points and .

9. What is the slope of a line passing through points and ?

10. Write an equation of a line that represents a VERTICAL line.

11. Write an equation of a line that represents a HORIZONTAL line.

12. Graph the following two functions and determine the points where they intersect.

13. Point lies on the line whose equation is . What is the value of k?

14. Sketch the graph of y = 4 and x = -3 on the same set of axes. Make sure to label each equation.

6. SQUARE ROOTS: Please show all work in the space provided. Box in your answer.

1. What is expressed in simplest radical form?

2. Express in simplest radical form.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

7. INDUCTIVE REASONING

VOCABULARY:

• A conjecture is an unproven statement that is based on observations

• Inductive reasoning is a process that involves looking for patterns and making conjectures.

• A counterexample is an example that shows a conjecture is false.

1.

2. Fill in the blank:

3. Show the conjecture is false by finding a counter example:

8. POINTS, LINES, PLANES

VOCAULARY:

• A point has no dimension.

• A line extends in one dimension.

• A plane extends in two dimensions.

• Collinear points are points that lie on the same line.

• Coplanar points are points that lie on the same plane.

• On a line passing through points A and B, segment AB consists of all points between A and B and endpoints A and B

• On a line passing through points A and B, then ray AB consists of the initial point A and all the points on the same side of A as point B.

• If point C is between A and B, then ray CA and ray CB are opposite rays.

• Two or more geometric figures intersect if they have one or more points in common. The intersection of the figures is the set of points the figures have in common.

1.

9. DISTANCE AND LINE SEGMENTS

1.

2. Using the distance formula, find the length of the segment joining the points whose coordinates are:

a. (6, 4), ( - 8, 11)

b. (- 5, 8), ( - 10, 14)

c. (- 4, - 20), ( - 10, 15)

d. (40, 32), ( 36, 20)

e. (5, - 8), ( 0, 0)

f. (A, B), ( - A, - B)

10. ANGLES

1.

2. Plot the given points and classify the given angles as acute, right, obtuse or straight.

3. Plot the given points and classify the given angles as acute, right, obtuse or straight.

4. For the following exervises, use the diagram below:

a.

b.

c.

d.

11. BISECTORS

1.

2.

3.

4.

5.

12. PAIRS OF ANGLES

1.

2.

3.Solve for x:

4. Solve for y :

5.

6. In the following exercises, find the values of x and y in each diagram.

7.

13. AREA AND PERIMETER

1. Find the perimeter (or circumference) and area of the given figure:

a.

b.

c.

d.

e.

f.

g.

h.