AQR General Specific Math Skills

Transcription

1 AQR Welcome to AQR! AQR 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. 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. Be able to perform operations on fractions (for example: a fraction divided by a whole number) c. Be able to simplify radicals d. Read and interpret word problems to provide mathematical expressions to represent written expressions e. Know and use laws of exponents and properties of logarithms 2) Data and Statistics a. Be familiar with dependent and independent events b. Read and interpret scatterplots; find a trend line 3) Algebra a. Can manipulate with ease fractions, decimals and variables in a variety of settings including in equations, expressions, and rational functions b. Comfortable with all forms of factoring including quadratics, sum and difference of cubes, quartics and factoring by grouping c. Solve equations and inequalities, including but not limited to i. Polynomial ii. Logarithmic iii. Rational iv. Radical v. Exponential d. Manipulate equations to solve for a single variable e. Know the Pythagorean Theorem 4) Graphing a. Be familiar with the graphs of linear, absolute value, quadratic, cubic, quartic, logarithmic 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

2 c. Recognize end behaviors of graphs d. Be familiar with transformations of graphs 5) Trigonometry a. Understand and use angles of elevation and angles of depression to solve problems b. Work with three basic trig functions c. Know common values of the six basic trig functions using at least one of the following methods: i. Memorizing the trig table of values (link for practice) ii. Memorizing the unit circle iii. Finding the values from special right triangles *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. Some answers are given for particular problems for you to check your work. Review Problems I. Order of Operations and Operations on Fractions Calculate: Solutions:

3 Answers for checking work

4 Translate each of the following into an algebraic expression. 1) Two-fifths of w is subtracted from 7 2) Add one-third to 2 times y 3) 5 minus m 4) Three-fifths of the sum of 7 and h 5) s squared plus the product of 3 and g plus 6 II. 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. Not every word is used, some words are used more than once. Cubic Linear Radical Exponential (Growth) Logarithmic (log) Rational Exponential (Decay) Quadratic Trigonometric (Trig) A) y = x B) y = x 2

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

7 IV. 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 2n 2 = 4; solve for n 3) ab 2 + c = k; solve for b 4) 3rt 2mn = 4ab; solve for r Question 5. Question 6. The preceding formula gives the monthly payment m needed to pay off a loan of P dollars at r percent annual interest over N months. Give P in terms of m, r, and N?

8 Answer: V. Simplifying Expressions and Solving Equations Solutions

9 Solve each equation. Then state which values make the functions undefined. 3) 4) 5) 6) VI. 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.

10 Write the formula for each transformation. VII. Transformations A) y = x! translate right four units and up 3 units B) y = x a reflection about the x-axis and a vertical stretch to 3 times its height C) 2 x a reflection about the y-axis and then translate right 3 units D) y = x translation 3 units left and a horizontal shrink to ¼ its usual size VIII. Trigonometry Draw your own picture and then use SOHCAHTOA to solve for the missing information. 1. From a point 80 m from the base of a tower, the angle of elevation to the top of the tower is 28. How tall is the tower? 2. A ladder that is 20 ft. long is leaning against the side of a building. If the angle formed between the ladder and the ground is 75, how far is the bottom of the ladder from the base of the building? 3. When the sun is 62 above the horizon, a building casts a shadow 18 m long. How tall is the building? 4. A kite is flying at an angle of elevation of about 55. Ignoring the sag in the string, find the height of the kite if 85 m of string have been let out.

11 Trig Facts: You will need to know these as you know your multiplication tables. The values for sin, cos, and tan in Quadrant I should be memorized cold. The other Quadrants values should not take you more than a few seconds to find when quizzed. Fill in the blank: Every trig function takes an angle as input and returns a ratio as output. So, every inverse trig function takes a ratio as input and returns as output. Fill out the following 16-point unit circle by finding the following: 1) The measures for each angle in radians and in degrees. 2) The coordinate pair for each angle.

12 Finding Trigonometric (Trig) Values Find cos θ and tan θ. Find sin θ and tan θ. Find sin θ and tan θ. Find sin θ and tan θ. IX. Data and Statistics Describe the relationship (linear, exponential, etc.) between the variables in the following scatterplots.

13 Determine whether each event is dependent (D) or independent (I). 1. You have a jar with 24 pieces of chocolate candy and 14 pieces of orange candy. We take one piece of candy at random from the jar, put it back, and then take a second piece of candy at random from the jar. 2. Amy plays card games. He picks a card at random. Then without putting the first card back, he picks a second card at random. 3. Juan has 14 coins. He takes 3 of them at random and puts them back. He then picks 2 more coins at random. 4. Jeff has 3 children. His first 2 children are boys. His last child is a girl. 5. A tree that has 4 red flowers and 2 blue flowers. Brandy plucks 1 flower from the tree. After some time her sister plucks a flower from the same tree. Online Instructional Resources (Short 5-10 minute videos for classes through Algebra 2) (Good for basic math, algebra, and geometry) (Click Lessons on the homepage) (Great math lessons and practice problems with solutions) (Or search West Texas A&M Virtual Math Lab on yahoo) (Videos on just about any topic) (Short videos on just about any topic. View the ratings and/or user comments first.) (collection of short videos/tutorials for all classes; many topics found under the Algebra link) (simple explanations and examples for sophisticated topics)