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Semantics and logic honors

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Semantics and logic honors

Mr. Torres

- The SAT Math section covers math from basic number properties through mid-level Geometry, but does not include Trigonometry or Pre-Calculus.
- To ensure the highest possible score on your SAT Math section, focus on laying a strong foundation and building upon it early and often.
- Understand how numbers work and how they interact with one another to guarantee fewer silly mistakes on Test Day.

- Integer
- Even and Odd
- Positive and Negative
- Number Line
- Square and Square Root
- Fraction
- Reciprocal
- Decimal
- Scientific Notation
- PEMDAS
- Equation
- Cardinal Rule of Equations

- Integers – are whole numbers that can be positive or negative and include zero.
- Properties of Integers:
- Integer ± Integer = Integer
- Integer x Integer = Integer
- Integer ÷ Integer – Not Necessarily an Integer (e.g. 7 ÷ 3)

- Even/Odd Integers:
- Even ± Even = Even
- Odd ± Odd = Even
- Even ± Odd = Odd

- Even/Odd Integers (cont’d):
- Even x/ ÷ Even = Even
- Odd x/÷ Odd = Odd
- Odd x/÷ Even = Even

- Positive/Negative Integers
- Positive x/ ÷ Positive = Positive
- Negative x/ ÷ Negative = Positive
- Negative x/ ÷ Positive = Negative
- Subtracting a negative number is the same as adding a positive number.

- Number Lines and How They Work
- Number lines are a visual representation of a range of numbers.
- Most number lines have 0 in the middle, with positives on the right of zero, and negatives on the left of 0.
- The further to the right you move, the greater the value becomes.
- The further to the left you move, the smaller the value becomes.

- Squares and Square Roots
- Squaring a number simply means that you multiply it by itself.
- The number in the exponent tells you how many of the number that serves as the base are involved in the multiplication.
- E.g. – = 4 x 4 x 4 = 64
- Square Roots ask you to find how many times a number was multiplied by itself to reach the number inside the radical. The number of times a number must be multiplied by itself can be found on the outside of the radical. No number means 2, or square root.
- E.g. – = = 3

- Fractions and Decimals
- Fractions are numbers that have a numerator and a denominator and a line of division between them. E.g. = .
- The reciprocal of a fraction inverts the numerator and denominator so that the fraction is upside-down compared to the first fraction.
- Decimals have the same value as their equivalent fraction, but are represented instead by numbers after a decimal point that shows how many times past the number you started with you would have to divide another number to get an even number. E.g. = 0.75.
- Decimals that have no repeating pattern after the decimal point are said to be irrational.
- Scientific Notation – special decimals that are followed by “ x ” and is used to abbreviate long numbers with high values. E.g. 12546 = 1.2546 x .

- What is PEMDAS?
- Parentheses
- Exponents
- Multiplication/Division (in order, Left to Right)
- Addition/Subtraction (in order, Left to Right)
- Also known as “Please Excuse My Dear Aunt Sally” or “Push Eddie Murphy Down A Staircase”

- When should I use PEMDAS?
- ALWAYS!!!!!!!!!!!!!!!!!!!

- What makes an equation unique?
- The = sign makes it unmistakable. The values on either side of the = sign must be equal.

- When I change something on one side of the equation, what should I do to balance it?
- If you add, subtract, multiply, divide, raise to an exponent, or take a root of one side of the equation, you MUST do it to the other side as well.
- This is known as the Cardinal Rule of Equations.

- Always follow these four steps to answer your SAT Math questions:
- Identify what the question is.
- It is not always clear what the question is asking for, so circle, underline, or rewrite what the question is actually asking for so that you do not get confused on the exam.

- Identify the information in the question stem.
- SAT questions are always full of useful information. Circle, underline, or rewrite relevant information from the question stem so that you can use it to answer the question quickly and effectively.

- Choose the appropriate action.
- Choosing Numbers – remember, they must be allowed by the question AND easy to work with!
- Backsolving – the answers are already there, so just plug them in!
- Regular Math – if you cannot take a shortcut, just use your math skills!

- Check your work.

- Identify what the question is.

- Turn to page 423 in your blue SAT book and do questions 1-16 in section 9 of the practice test.
- Do not write on the book. Show all your work and highlight your answers on a separate sheet of paper with your name, the date, and your period number on it.
- You will have the rest of this class period to work on this assignment. Work quickly and efficiently.
- After you’ve completed this classwork assignment, turn it in to the teacher.
- ***Remember*** - Your Home Learning assignment will be available after class on Mr. Torres’s webpage. Please download and complete it for the next class period.