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Name_______________________Period_______Date_______Algebra 3 Review 1 --- 1.2 – 1.7 represents. 1 2) Given the set 11, , 2, 7,8.34 list the 2 numbers in each set they belong: a. Natural numbers:________________________ b. Whole numbers:_________________________ c. Integers:_______________________________ d. Rational numbers:________________________ e. Irrational numbers:_______________________ f. Real numbers:___________________________ a. Natural numbers:________________________ b. Whole numbers:_________________________ c. Integers:_______________________________ d. Rational numbers:________________________ e. Irrational numbers:_______________________ f. Real numbers:___________________________ 1) For each of the following, list the set it best 15 3) Given the set 4, , 2.3, 0, 6, ,3 list the numbers in each set they belong: 2 a. Natural numbers:________________________ b. Whole numbers:_________________________ c. Integers:_______________________________ d. Rational numbers:________________________ e. Irrational numbers:_______________________ f. Real numbers:___________________________ ****Determine if the following statements are True (T) or False (F). a. Every natural number is also a whole number. b. Every negative number is also an integer. c. A number can be both rational and irrational. d. Every irrational number is also a real number. 4) Insert >, < or = to make the statement true. a. 22 _____ 11 b. 6 _____ 6 c. 16 _____ 8 2 d. 0.52 _____ 0.55 e. 3 ______ 7 5) Write each sentence as a mathematical statement. Use the symbols >, < , ≤ , ≥ , ≠ and =. a. Five is greater than or equal to three___________ b. Negative two is less than zero____________ c. Six is less than or equal to nine_______________ d. One-half is equal to four-eighths__________ e. Absolute value of negative one is not equal to negative one_______________ 6) Simplify the following. a. |-2| = _________ b. |4| = _________ c. |-5.6| =__________ d. |0.25| = __________ 7 ) Find the product of primes of the following. a. 81 = ____________ b. 45 = _____________ c. 40 = ____________ d. 70 = ___________ 8) Write each fraction in lowest terms. a. 15 =_____ 10 b. 32 =______ 44 c. 56 =______ 42 d. 39 =_____ 9 9) Perform the indicated operation. Write your answer in lowest terms. a. 1 6 =______ 2 7 b. 16 21 =______ 9 8 c. 5 15 =______ 11 44 d. 36 9 =______ 25 10 e. 3 10 =______ 5 3 f. 4 1 =______ 15 15 g. 7 3 =______ 15 10 h. 9 2 =_______ 7 7 1 5 i. 3 =_______ 4 6 1 j. 4 2 =_______ 5 3 m. 2 1 =_______ 4 n. 2 2 2 =_______ 3 3 1 3 k. 5 2 =______ 3 4 o. 4 2 2 =______ 3 3 2 l. 6 3 =______ 3 1 1 p. 1 3 =______ 4 8 10) List the order of operations: 11) Simplify the following. a. 5 6 2 c. 6 2 2 25 b. 4 8 6 2 d. 3 22 4 6 e. 3 6 8 5 f. 42 2 16 13 5 32 17 5 12) Find the opposite or additive inverse of the following. b. a. 9 1 3 c. 2 d. 4 3 13) Find the reciprocal or multiplicative inverse of the following. a. 1 8 b. 4 14) Perform the indicated operation of real numbers: 4 1 a. b. 8.3 0.62 7 7 e. 2 25 15 6 f. 4 ( 6) c. 3 2 c. 5 c. 4 5 1 1 d. 2 4 1 g. 5 4 h. 16 8 27 45 15) Evaluate the following for x = 1, y = -4, and z = 2 b. x y 2 a. x y c. x2 y x z z3 y 16) Write an algebraic expression or equation for each of the following. a. b. c. d. e. f. g. h. The sum of three times a number and two.___________________ The difference of four and a number._______________________ The product of five and a number._________________________ The quotient of sixteen and a number.______________________ Nine decreased by twice a number is the same as four plus the number.________________________ Seven less than a number equals the quotient of the number and two.__________________________ Eight times a number increased by four is three.___________________________________________ The ratio of two and a number is the same as five less than the number.________________________ 17) Determine if x = 3 is a solution to the following equations. a. 7 x 6 9x b. 2 x 5 x 2 1 c. x 4 2 2 x 5 d. x2 x 10 9 18) For the equation x 2 2 11, determine if the following numbers are solutions. a. 2 b. 3 c. 1 d. -3