GEOMETRY (and Honors)

Welcome to Geometry! Geometry will be challenging but rewarding!! This full year course requires that everyone work hard and study for the entirety of the class. You will need a large binder or notebook and a graphing calculator for the course.

Student expectations:

General • keep an organized notebook • take good notes • complete homework every night • be active learners • ask questions and participate in class • seek help outside of class if needed • work with others • work with and without a calculator Specific Math Skills

1) Number Sense a. Know the order of operations b. Know and apply the distributive property c. Perform operations on rational numbers

2) Algebra a. Manipulate with ease fractions, decimals and variables in a variety of settings

including in equations, expressions, and rational functions b. Be comfortable with all forms of factoring quadratics, including factoring by

grouping c. Demonstrate mastery of multiplying binomials d. Solve equations and inequalities, including but not limited to

i. Linear ii. Quadratic

iii. Absolute value iv. Systems of Equations

e. Manipulate equations to solve for a single variable f. Know the Pythagorean Theorem g. Demonstrate mastery of simplifying radical expressions

3) Radical Functions and Rational Exponents a. Add, subtract, multiply and divide radical expressions b. Rationalize denominators c. Simplify expressions with rational exponents

4) Geometric Solids a. Find the volume of a geometric solid b. Find the surface area of a geometric solid

5) Graphing a. Be familiar with the graphs of linear, absolute value, quadratic, and exponential

(growth and decay) functions b. Linear Graphs

i. Be able to find the slope and y-intercept of a line from both a graph and an equation

ii. Be able to determine whether two lines are perpendicular, parallel or neither

c. Know and apply the distance formula to find the distance between two points on the coordinate plane

d. Be able to reflect images and write coordinates of reflected images on the coordinate plane

e. Determine whether a scatterplot has a negative or positive correlation Vocabulary Students should be able to properly name, describe, and provide examples of the following vocabulary:

• Point • Line • Line segment • Ray • Plane

*NOTE: Show all of your work. Your teacher will give a quiz on this material at the beginning of the year. You should “Google” the topic if you are unsure how to complete the examples. Useful resources are also linked at the end of this document.

Review Problems

I. Order of Operations and Radical Expressions Calculate: Solutions:

Solutions Answers for checking your work

II. Factoring

Factor each of the following completely or state that it is prime.

VI. Manipulating Equations

For problems 1 – 4, solve the Linear Equation for the indicated variable.

1) 2(g − h) + 3 = 2h; solve for h

2) 3m − 2n2 = 4; solve for n

3) ab2 + c = k; solve for b

4) 3rt − 2mn = 4ab; solve for r

Question5.

Question 6.

Theprecedingformulagivesthemonthlypayment m neededtopayoffaloanof P dollarsat r percentannualinterestover N months.Give P intermsof m, r,and N?

Answer:

V. Simplifying Expressions and Solving Equations

Answersforcheckingyourwork

Solve each system. Then explain how the solutions would appear on a coordinate grid. 5) 6) Solve each of the following equations by the method of your choice and check your solutions below. 13. x2 + 4 = 0 14. x2 + x = −1 15. 9y2 + 6y – 8 = 0 16. y2 − 25 = 0 Answers:

Answers

Simplify.

1. 9t + 7z – 7t + 7 – 10t

2. –4b2 + 8b – 5 – 2b2 – 9

3. –k5 m3

–5k4 m4

4 . m · 3 · m · m · 4

5. –3(–3x + 10) + 5(5 + 2x)

6. 4 + 2s – 4s2 + 2s + 4 + 3s2

Answers

1 . –8t + 7z + 7

2. –6b2 + 8b – 14

3. k

5m

4. 12m3

5. 19x – 5

6. –s2 + 4s + 8

VI. Graphing

Sketch the graph of each function & state the domain and range of each. Then, choose the name of the function from the word bank below. A) y = x B) y = x2

VII. Linear Functions

Graph each of the following equations, then identify the slope and y-intercept. 1) y = 3x + 4 2) 8x + 2y = 32 3) y =7 4) x = 9

5) Write an equation that creates a line parallel to the function y = ¼ x – 20.

6) Write an equation that creates a line perpendicular to the function y = ¼ x – 20.

Answers

• Use the Pythagorean Theorem to find the distance between the points in graphs 1 and 3. • Use the distance formula to find the distance between the points in graphs 2 and 4.

Answers

Identify the data sets as having a positive, a negative, or no correlation.

7) The number of hours a person has driven and the number of miles driven

8) The number of siblings a student has and the grade they have in math class

9) The age of a car and the value of the car

10) The number of weeks a CD has been out and the total sales

VIII. Geometric Solids

Answers

Answers

Online Instructional Resources

www.virtualnerd.com (Short 5-10 minute videos for classes through Algebra 2) www.math.com (Good for basic math, algebra, and geometry) www.purplemath.com (Click “Lessons” on the homepage) www.intmath.com (Great math lessons and practice problems with solutions) http://www.wtamu.edu/academic/anns/mps/math/mathlab/ (Or search “West Texas A&M Virtual Math Lab” on yahoo) www.khanacademy.org (Videos on just about any topic) www.youtube.com (Short videos on just about any topic. View the ratings and/or user comments first.) https://learnzillion.com/resources/99913-math-instructional-videos/ (collection of short videos/tutorials for all classes; many topics found under the Algebra link) https://www.mathisfun.com/ (simple explanations and examples for sophisticated topics)