1. Numbers, Symbols, & Variables SAT/ACT MATH UNIT 1

2. Definitions Real numbers – different types of numbers, both positive & negative, you encounter during arithmetic & beginning algebra Variable – a symbol that serves as a placeholder for an unknown number

3. Types of Numbers NameExample Whole Numbers Integers Rational Numbers Irrational Numbers 0, 1, 2, 3… -3, -2, -1, 0, 1, 2, 3 (Neg.) (Pos.) *Fractions w/ integers on top & bottom *Terminating decimal such as 0.75 *Ongoing, repeating decimals such as 0.333333….. Numbers that do not have exact decimal equivalents such as π and

4. Comparison Symbols SymbolTranslationExample = Is equal to 5 = 5 ≠ Is not equal to 5 ≠ 3 > ≥ Is greater than or equal to X ≥ 5 X can be 5 or any number greater < ≤ Is less than or equal to X ≤ 3 X can be 3 or any number smaller

5. Multiplication Product – the answer when two or more numbers are multiplied Ways to Write Multiplication 1. 4∙y 2. 4(y) 3. 4y Factor – numbers that are multiplied together to get a product

6. Like Terms Coefficient – the variable; when a number and variable are written next to each other Like terms – product such as 3n and 2n that differ only in their numerical coefficients *like terms may include more than 1 variable: 4ab and 7ab are like terms* 5n - n is the coefficient Are 2ab and 3ac like terms?

7. Find Like Terms 1. 3y + 4y = 2. 9p + 3p + 2p = 3. 5x – x = 7y 14p 4x

8. Laws of Arithmetic LAWDefinition Commutative3 + 4 = 4 + 3 3 x 4 = 4 x 3 Associative2 x (3 x 4) = (2 x 3) x4 2 + (3 + 4) = (2 + 3) + 4 Distributive3 x (2 + 4) = 3(2) + 3(4)

9. Applying Laws of Arithmetic 1. Use the distributive law to simplify: 3(2x + 5) 2. Use the reverse of the distributive law (factoring) to rewrite: 4x + 5x 6x + 30 x(4 + 5)

10. Examples If a = 9 x 23 and b = 9 x 124, what is the value of b – a? (A) 901 (B) 903 (C) 906 (D) 909 (E) 911 D

11. Examples If the current odometer reading of a car is 31,983 miles, what is the LEAST number of miles that the car must travel before the odometer displays four digits that are the same? (A) 17 (B) 239 (C) 350 (D) 650 (E) 1350 B

12. Examples In store A a scarf costs $12, and in store B the same scarf is on sale for $8. How many scarves can be bought in store B with the amount of money, excluding sales tax, needed to buy 10 scarves in store A. (A) 4 (B) 12 (C) 15 (D) 18 (E) 21 C

13. Examples Let * represent one of the four basic arithmetic operations such that, for any nonzero real number r: r * 0 = r and r * r = 0 Which arithmetic operation(s) does the symbol * represent? (A) + only (B) - only (C) + and - (D) x only (E) +, -, or x B

14. Examples If the present time is exactly 1:oo P.M., what was the time exactly 39 hours ago? (A) 4:00 P.M. (B) 4:00 A.M. (C) 9:00 P.M. (D) 9:00 A.M. (E) 10:00 P.M. E

15. Examples If w = (6)(6)(6), x = (5)(6)(7), and y = (4)(6)(8), which inequality statement is true? (A) x < y < w (B) w < x < y (C) y < w < x (D) y < x < w (E) w < y < x D

16. Examples If 1 kilobyte of computer memory is equivalent to 1024 bytes and 1 byte is equivalent to 8 bits, how many kilobytes are equivalent to 40,960 bits? 5

17. Examples If 13 ≤ k ≤ 21, 9 ≤ p ≤ 19, 2 < m < 6, and k, p, and m are integers, what is the largest possible value of k – p ? m 4

18. Examples If x and y are positive integers, and 3x + 2y = 21, what is the sum of all possible values of x? 9