1. PSAT MATHEMATICS 9-A Basic Arithmetic Concepts

2. Set A collection of “things” that have been grouped together in some way. “things” – elements or members

3. Example  If A is the set of states in the United States, then _____________ is an element of A.  If B is the set of letters in the English alphabet, then _____ is a member of B.  If C is the set of even integers, then ___ is in C.

4. Union The union of two sets, A and B, is the set consisting of all the elements that are in A or B or both. A U B

5. Intersection The intersection of two sets, A and B, is the set consisting of only the elements that are in both A and B. A B U

6. Example A = {2, 3, 5, 7} B = {2, 4, 6, 8} Find the union and intersection of sets A and B.

7. Solution Set The set of all numbers that satisfy the equation.

8. Example If C={-2, -1, 0, 1, 2} and D is the set that consists of the squares of each of the elements of C, how many numbers are elements of D?

9. Signed Numbers  Draw a number line from -5 to 5.  Mark the following points.  -3 ½  0.25  π  - ¾  |-4|

10. Example How many integers are solutions of the inequality |x|<5? A. 0 B. 4 C. 8 D. 9 E. infinitely many

11. Example What is the sum of the product and quotient of 8 and 8?

12. Example What is the product of all the integers from -5 to 5, inclusive?

13. Example Which of the following are equal to (-1) 25 ? I. (-1) 100 II.-(1) 100 III. - (-1) 100 A. I only B. II only C. III only D. II and III only E. I, II, and III

14. Integers  Integers  Positive integers  Negative integers  Consecutive integers  Consecutive odd integers  Consecutive even integers  Prime numbers

15. Example If 0<x<3 and 2<y<8, what is the largest integer value of x+y?

16. Example If the remainder when a is divided by 7 is 2 and the remainder when b is divided by 7 is 4, what is the remainder when ab is divided by 7?

17. Example What is the sum of the largest prime factor of 26 and the largest prime factor of 28?

18. Exponents and Roots  Repeated addition of the same number is indicated by multiplication.  Repeated multiplication of the same number is indicated by an exponent.

19. Laws of Exponents  5 4 x 5 3  5 6 / 5 4  (5 2 ) 3  5 3 x 6 3

20. Example If 5 a x 5 b = 5 50, what is the average (arithmetic mean) of a and b?

21. Example What is the value of 16 ¾ ?

22. Perfect Squares  List the squares of 0 to 15.

23. Example What is the circumference of a circle whose area is 10 π ? A. 5 π B. 10 π C. π √10 D. 2 π √10 E. π √20

24. Order of Operations  Parentheses  Exponents  Multiplication & Division  Addition & Subtraction

25. Practice 1. 10 + 4 x 2 2. (10 + 4) x 2 3. 16 ÷ 2 x 4 4. 16 ÷ (2 x 4) 5. 10 + 15 ÷ (2 + 3) 6. 100 – 2 2 (3 + 4 x 5)

26. Example Which of the following is equivalent to for all nonzero numbers x? A. x + 1 B. x 5 C. x 5 + 1 D. x + x 4 E. x 16

27. Practice Problems