SEMANTICS AND LOGIC HONORS MR. TORRES

BELL RINGER

HOMEWORK REVIEW Which questions from the homework gave you the most trouble? Why? Remember that the SAT Math and Writing sections are presented in order of increasing difficulty, placing the easier questions at the beginning of the section and the harder questions at the end. If you find yourself having trouble with easy problems, skip them to tackle more difficult ones, but make sure to answer as many questions CORRECTLY as possible. You lose ¼ point for every wrong answer.

THE SAT MATH SECTION: KEY VOCABULARY Factor Multiple Remainder Greatest Common Factor (GCF) Least Common Multiple (LCM) Prime Number and Prime Factorization Ratio Proportion Average (arithmetic mean) Percent Cross-Multiplication Sequences Geometric Arithmetic Set Notation Median, Mode, Arithmetic Mean Elements Union of Sets Intersection of Sets Fundamental Counting Principle Factorial Notation Permutation Combination

SAT MATH: ELEMENTARY NUMBER THEORY Factors are positive integers that can be evenly divided into another number WITHOUT a remainder. 2 is a factor of every even number, because it can divide evenly into each one. E.g. – What are the factors of 24? Divisible by means that a number can be evenly divided by another without a remainder. E.g. – 15 is divisible by 5 because 15 divided by 5 yields no remainder. 15 is not divisible by 10 because the remainder would be 5. When numbers have common factors, they have one or more factors that divide evenly into both. The largest factor that two numbers share is called the Greatest Common Factor, or GCF. E.g. – the Greatest Common Factor of 24 and 40 is 8. Multiples of any given number are those numbers that can be divided by that number WITHOUT a remainder. 10 is a multiple of 5, but 5 is not a multiple of 10 because it cannot be divided evenly (without remainder) by 10. What are the first seven multiples of 3? The multiples of any number will also be multiples of any of its factors. E.g. – since 12 is a multiple of 2, 3, 4, and 6, all of its multiples (12, 24, 36, 48, 60, etc…) will be multiples of each of its factors! When numbers have common multiples, they have one or more multiples that those numbers all divide into evenly. The smallest multiple that is common to two (or more) numbers is known as the Least Common Multiple, or LCM. E.g. – the Least Common Multiple of 6 and 8 is 24.

SAT MATH: ELEMENTARY NUMBER THEORY EXAMPLES Example 1: Which is the least positive integer divisible by the numbers 2, 3, 4, and 5? Example 2: Which of the following could be the remainders when four consecutive positive integers are each divided by 3? a)1, 2, 3, 1 b)1, 2, 3, 4 c)0, 1, 2, 3 d)0, 1, 2, 0 e)0, 2, 3, 0

SAT MATH: ELEMENTARY NUMBER THEORY (CONT.) Prime Numbers Prime Numbers are positive integers greater than 1 whose only two factors are 1 and itself. What are the first 10 prime numbers? Is there anything that all prime numbers have in common besides the number of factors they have? Prime Factorization is a process by which you identify all of the prime factors of a number. It is also called a Factor Tree. Breaking down any number into its prime factors allows you to find square roots easily. Be wary of sneaky composite numbers that look prime. Make sure a number is prime before you stop factoring. A composite number is any number that is not prime. It is known as the product of two distinct integers.

SAT MATH: RATIOS, PERCENTS, AND AVERAGES

SAT MATH: SEQUENCES Arithmetic Sequences Geometric Sequences Sequences are ordered lists of numbers. There are two kinds of sequences.

SAT MATH: SETS

SAT MATH: FUNDAMENTAL COUNTING PRINCIPLE

SAT MATH: PERMUTATIONS AND COMBINATIONS Permutations Combinations

SAT MATH: CLASSWORK Open your textbooks to page 423. You will have the rest of the class period to work on this section. Please show your work for each problem on a separate sheet of paper with your name, the date, and your period number on it. When you have finished, please turn it in and sit quietly until you are dismissed. Remember to check the school website for Mr. Torres for your homework.