HW: Algebra Skills Name: ___________________________ Date: ________________ Period: _____ SHOW YOUR WORK!! Use this homework to recall your algebra skills. Additional help can be found in the textbook starting on page 753. You will be quizzed over algebra skills on the second day of class, so that any needs may be addressed as soon as possible. Solve for the variable in each equation using any method. 1. 3x + 6 = 24 _______

2. ¾ (d – 3) = 6 _______

3. 8r 5 3r 10

4+ −

=

_______

4. 0 = x2 + x _______

5. 28 = 7(y – 7) _______

6. x2 – 7x + 12 = 0 _______

7. 9x2 = 16 _______

8. x2 = 2x + 24 _______

9. Evaluate: f(a,b) = ab2 + ½ a – 3ac for a = 12, b = -6, c = -4. _______

10. Simplify: ( )265 −y ____________

Combine any like terms to simplify each of the following expressions. 11. 2(4 15 16) (2 20)x x x− + + − __________

12. 3 3(2 11 2) ( 2 7)x x x x+ + − − + __________

Word Problems: 13. A car rental agency charges a fee of $35 per day plus $.20 for each mile driven. Write an equation that can be used to find F, the fee of renting a car for d days and driving m miles.

____________________ How much will it cost to rent the car for 4 days and drive 730 miles? _______

14. Mark has $4.95 in quarters and dimes. He has 3 times as many dimes as quarters. Write a system of equations which can be used to find q, the number of quarters, and d, the number of dimes, that Mark has.

____________________

____________________

15. A rectangular rug has an area of 270 square feet. The length of the rug is 3 feet longer than its width. Write an equation that can be used to find w, the width of the rug.

____________________

16. Paige has started saving for a new television. She saved $75 last month. She plans to add $50 each month until she has saved at least $400. Write an inequality which can be used to find m, the number of months it will take Paige to save for her television.

____________________ 17. The area of a rectangular piece of paper is described by the equation w(w − 3) = 108 where w is the width of the paper in inches. What is the width of the piece of paper?

__________

18. A chef cooks 1 ½ potatoes for each serving of mashed potatoes. How many servings can he make from 18 potatoes?

__________ 19. The new parking lot has spaces for 450 cars. The ratio of spaces for full sized cars to compact cars is 11 to 4. How many spaces are for full-sized cars? How many spaces are for compact cars?

_____ full-sized cards, _____ compact cars

20. Suppose a video store charges non-member $4 to rent a video. A membership costs $21 and then videos cost only $2.50 to rent. How many videos would you need to rent in order to justify a membership?

__________ You may use a graphing calculator to answer all questions.

22. The table shows a set of values for x and y.

Write an equation that best represents this set of data.

____________________

21. Write a function (in y= form) that includes all of the ordered pairs in the table.

____________________

23. What is the y-intercept of the function 3x + 4y = 24 ?

__________

24. Mark and his brother went on a canoe trip. The graph shows the relationship between the distance traveled and the time of day.

What was the brothers’ average speed in miles per hour from 9 A.M. to 11 A.M.?

__________ 25. Write an equation (in slope-intercept form) of the function in the graph shown below.

____________________

26. Write an inequality that describes the graph below.

____________________ 27. Graph the inequality x + y > 3

28. Graph the equation 2x + 6 = 3y

29. The quadratic function f(x) is evaluated for different values of x, as shown on the table.

The graph of f(x) has a line of symmetry at x = 6.

For which other value of x is f(x) equal to 0?

__________

30. Between which 2 positive integers will the graph of

cross the x-axis?

Between _____ and _____

Find the solution to each system of equations using either substitution or elimination. 31. x + y = 7

x – y = 9 _______

32. 2x + 3y = -1 3x + 5y = -2 _______

Simplify the following radical expressions. 33. 40 _______

34. 4 24 _______

35. 2 28 63+ _______

36. 2 10 3 6• _______

Use the Pythagorean Theorem to find n. Express n as a radical in simplest form. Show your work. 37. __________

38. __________

39. __________

59

n2 7

8

n

3

5 n

WS – Simplifying Radicals and the Pythagorean Thm Name: ___________________________ Geometry textbook 8-1; Table of Squares and Square Roots on pg 768. Date: ________________ Period: _____ Simplify each radical expression.

Use the Pythagorean Theorem to find n. Express n as a radical in simplest form.

Answer yes if the given measures are measures of the sides of a right triangle. If the triple is a Pythagorean triple and belongs to one of these families, also give that letter. A. 3, 4, 5 B. 5, 12, 13 C. 8, 15, 17 D. 7, 24, 25 E. 9, 40, 41

HW: Distance and Midpoint (1-8) Name: ___________________________ (From McDougal Littell 1.2 Practice C and 1.3 Practice C) Date: ________________ Period: _____

Geometry Name________________________ Notes – Points, Lines, and Planes (extended) Date______________ Period _____ Decide whether each of these “things” is best modeled by a point, line or plane. 1. a star in the sky ____________ 2. an ice skating rink ____________ 3. a telephone wire between ____________ 4. a taut piece of thread ____________ two poles 5. a knot in a piece of string ____________ 6. a piece of cloth ____________ 7. the corner of a room ____________ 8. your desktop ____________ 9. the lines on notebook paper ____________ 10. A fold in paper ____________ Use the figure at the right to answer each of the following questions. 11. Name a line containing point A. ____________ 12. Name a line passing through B. ____________ 13. Name two points collinear with point D. ____________ 14. Name two points coplanar with point B. ____________ 15. Name a plane containing pts. B, C, and E. ____________ 16. Name a plane containing lines p and q ____________

A

B

CD

E

F

R

q

p

r

Draw and label a figure for each relationship. 17. Point S lies on line PR. 18. Points A and B are collinear but points F, A, B,

and C are noncollinear.

19. Line m contains A and B, but doesn’t contain C. 20. Lines a, b, and c are coplanar, but do not intersect.

4 4 4 4 4 4

Use the diagram below for problems 23-25.

thDetermine if the 4

Use the diagram on the right for problems 26 – 33. __________26. Name another point in plane ICD. __________27. Name another point in plane ABJ. __________28. Name a plane parallel to plane DCI. __________29. Name two lines parallel to line AB. __________ __________30. If planes EJD and DCI intersect, name their intersection. __________31. Name 2 intersecting lines in plane ABC __________ that are both skew to line KJ. __________32. Lines FE and HI can best be described as _________ lines. __________33. Lines DC and LG can best be described as _________ lines. Answer “always,” “sometimes,” or “never” for problems 35 -40. ______________34. Two lines that do not intersect are _________ skew. ______________35. Skew lines are __________ parallel. ______________36. Two lines parallel to a plane are __________intersecting. ______________37. Parallel lines are ___________ coplanar. ______________38. Rays JK and JL are _______________ the same ray. ______________39. Two rays that share an endpoint are __________ opposite rays. ______________40. In space, two lines perpendicular to the same line are __________ perpendicular.

A B

C

D E

F

G

H

I

J K

L

●B

●S

●T

●E

● H

● W ●C

point is coplanar with the first 3 points. Answer coplanar or noncoplanar. __________________ 23. C, B, W, T __________________ 24. C, H, S, B __________________ 25. Name the intersection of planes CBW and CHS. __________________ 25b. Are points E, W, T coplanar? Why?

4 4 4 4 4 4

HW: Segment Addition Postulate & Midpoint (1-5) Name: ___________________________ (From McDougal Littell 1.2 Practice C and 1.3 Practice C) Date: ________________ Period: _____ Odd #s only!

, and explain why the segments are congruent or not congruent.

WS – Explaining and Solving Angles # 2 Name: ___________________________ Geometry sections 1-6 and 2-5 Date: ________________ Period: _____ First, write 1 sentence explaining the relationship between the angles in each problem. (Hints:

A linear pair adds to _____. Supplementary angles add to _____. Complementary angles add to _____. Right angles are _____. Vertical angles are __________. The sum of adjacent angles _______ the whole. A bisector divides into two __________ parts.)

Next, set up an algebraic equation explained by this angle relationship. Finally, solve for x or the unknown angle. Show your work, and write your answer in the space provided.

3w

w =____________

Pre-AP Test Review 1-1: PLP, PDM, and Algebra Name: ___________________________ Geometry textbook 1-3, 1-4, 1-5, 1-6, 1-7, 1-8, 2-5 and vocabulary Date: ________________ Period: _____ 1. Create your own review: Finish all homework from this unit. Look over old quizzes and tests. If there is a question you don’t know how to do, make sure you know it before the test! (Tutorials, study groups, search online) Additional questions for practice: Show all work. Give answers in simplest form.

3. 4. B is the midpoint of AC. AB = 5 36x + AC = 2 11x x−

2.

5. Below is a park in the shape of a right triangle. a) Find the missing side length. b) A square garden will be built along the hypotenuse. What is its area?

3 x

9 2 6. In the figure below, OA bisects ∠DOE. 7. (This is a separate problem from #5). In the figure

uuur

m∠DOA = –2(5 – 3x), m∠AOE = 8x – 29. below, ∠EOB is a right angle. m∠DOA = 13 (11 18)y − ,

Find the value of x and m∠DOC. m∠AOE= 4(y + 1), m∠BOC= . Find y and w. ( )27 1w− +

O

E

D C

A B

3

a) Find AB (in simplest radical form). a) Find MN (hint: the radical cannot be simplified). b) Find the coordinates of C, b) Find the coordinates of L, the midpoint of MN. where B is the midpoint of AC. c) Find AC. c) Let J be the midpoint of ML. Find the value of x if

JL = x2 and MN = 384.

J

L

F

C

A

E

G

H

I

K

B

D

P

q

F

D

G

E

B C

A

H

Refer to the figure at the right to answer questions 10 through 13.

10. Name a point that is not coplanar with points A, B and C.

11. Name a line that is skew to DE

12. Name three pairs of parallel lines.

13. Name the intersection of plane P and line q.

Use the diagram to the right for problems #14-18.

14. Name a point that is non-coplanar with points C, D, and E.

15. Name the ray that is opposite EH .

16. Name ray EH in another way.

17. Name a line parallel to FB .

18. Name plane HIK another way.

Points, Lines & Planes, Oh My!

_____ 19. Write another name for line r .

_____ 20. Write another name for plane C.

_____ 21. What is the intersection of plane D and line t ?

_____ 22. What is the intersection of plane C and line r ?

_____ 23. What is the intersection of plane ABG and plane C ?

_____ 24. What is the intersection of lines p and s?

Textbook Review (Optional) Work these problems on a separate sheet of paper. Many are odd-numbered exercises in the Geometry textbook, whose answers can be checked in the back of the textbook. (Selected Answers start at page 831.) 1-3 Points, Lines, and Planes: Pg 19 # 1, 3, 17, 27, 34, 37, 39, 40, 74. 1-4 Segments, Rays, Parallel Lines and Planes: Pg 26 # 17, 19, 21, 23. 1-5 Measuring Segments: Pg 34 # 34, 37. 1-6 Measuring Angles: Pg 40 # 23, 45, 47. 1-7 Basic Constructions: Pg 48 # 12. 1-8 The Coordinate Plane: Pg 56 # 31, 38, 48. 2-5 Proving Angles Congruent: Pg 113 # 13, 32. Answers to the Textbook Review:

1-3: Pg 19 answers: 1) no. 3) yes; line n. 17) line RS . 27) see back of book. 34) X. 37) no. 39) coplanar. 40) noncoplanar. 74) infinitely many planes can intersect in one line.

1-4: Pg 26 answers: 17) false; they are skew. 19) false; they intersect above CG . 21) false; they intersect above point A. 23) false; they are parallel.

1-5: Pg 34 answers: 34) y = 15, AC = 24, DC = 12. 37a) 5x; b) GH = 9, JK = 15. 1-6: Pg 40 answers: 23) 30. 45) x = 7; m∠AOB = 31, m∠BOC = 49, m∠AOD = 111. 47a) 19.5; b) 43; 137;

c) answers may vary; sample: The sum of the angle measures should be 180. 1-7: Pg 48 answers: 12) x = 11; m∠ABC = 56. 1-8: Pg 56 answers: 31) (4, -11). 38a) 53 ≈ 6.7; b) (-2.5, -2). 48) Z; 145 or about 12 units. 2-5: Pg 113 answers: 13) x = 14, y = 15; 50, 50, 130. 32) x = 50, y = 20; 80, 100, 80. And study all the vocabulary for the PLP (Points, Lines, Planes, Angles) and PDM (Pythagorean Theorem, Distance, Midpoint) units!!!

●

●

t p r D

C●

● G

A BE

s