Review for Final Exam

Final Exam Review MATD 0330 Austin Community College Page 1 of 12 Review for Basic Math Skills Final Exam In order to be prepared for the final exam, students should be able to do all of the following problems and related problems as well. Students are expected to know: • Perimeter and area formulas for triangles, rectangles, and squares • Simple interest • Mean, median, and mode for a set of numbers • Relationship between the radius and the diameter of a circle • Relationships in similar figures, including similar triangles • Relationships involving angles: complementary, supplementary, vertical • Relationships involving angles formed by parallel lines and a transversal Be sure to include proper units. Simplify all fractions, if possible. Unless otherwise instructed in a problem, you may represent an answer as either an improper fraction or a mixed number. Neither is “simpler.” 1. Round to the indicated place. a. 19,384 to the nearest hundred b. to the nearest ten thousand 264,980 c. to the nearest thousandth 7834.0629 d. 9.548 to the nearest tenth e. 0.395 to the nearest hundredth 2. Place the appropriate symbol < , > , or = between the two numbers. a. 18 81 b. 0 − 0 5 c. 3 5 − − d. 4.058 4.06 e. 0.07 0.007 − − f. 6 6 − g. 3 7 − 3. a. Express 42 as a product of prime factors. b. Express 60 as a product of prime factors. c. Find the LCM of 42 x and 60 x 3 .

Final Exam Review MATD 0330 Basic Math Skills Austin Community College Page 2 of 12 4. Perform the indicated operations. Simplify your answer, if possible. a. 17 17 10 5 + b. 5 7 12 15 − c. 1 5 8 4 6 9 − d. 16 5 27 12 + e. 2 5 35 12 − ⋅ f. 3 12 5 ÷ g. 1 5 4 2 3 6 ÷ h. 2 3 2 5 5 ⎛ ⎞ 3 4 − ÷ ⎜ ⎟ ⎝ ⎠ i. ( ) ( ) ( ) 2 4 4 6 2 3 2 − − − − − j. 2 4 1 7 3 ⋅ − k. 3 25 5 x x 5. Evaluate each of the following expressions. Simplify your answer, if possible. a. 2 2 9 for 6 9 3 x x − = b. 2 for 7 x x = − c. 2 for 7 x x − = d. 2 2 for 6 and 8 2 x y x y − = − = − e. 2 2 for 1 and 4 7 x y x y + = − = − − 6. Write in decimal notation: Seven thousand nine and one hundred twenty-eight thousandths 7. Translate the following into mathematical symbols. a. The square of eight b. Seven cubed c. A number increased by six d. Six greater than a number e. Six is greater than a number f. Nine more than double a number g. Two times the sum of a number and ten h. The sum of two times a number and ten i. The difference of five and a number j. Five decreased by a number k. Five subtracted from a number l. Five less than a number m. Five is less than a number n. Triple a number minus one o. Twice a number decreased by three p. Seven less than four times a number q. The product of six and a number r. The quotient of a number and nine s. A number divided by nine t. A number divided into nine

Final Exam Review MATD 0330 Basic Math Skills Austin Community College Page 3 of 12 8. Perform the indicated operations. a. 6 3 8 − − + b. ( ) 9 11 7 2 − − − − − + 4 c. ( ) 4 5 1 − − − d. ) 2 3 4( 3 − + − e. ( ) 9 5 4 8 − − f. ( )( )( )( )( )( ) 5 2 3 1 5 4 − − − − − g. 24 6 2 − ÷ ⋅ h. 4 0 ÷ i. 0 12 j. 8 0 k. 0 13 ÷ l. ( )( ) 2 35 15 5 3 4 − ÷ − − + m. 2 2 3400 17 400 5 3 + ⋅ ÷ − n. ) ( ) ( 3 5 6 3 12 3 − + − ÷ 9. Solve. a. 45 13 x − = − b. 32 160 x − = − c. ( ) 9 5 x x + − = − 52 d. 1 3 6 2 x − = − e. 0.5 1.45 2.1 x − = f. 9 5 34 x = 1 10. Perform the indicated operations. a. 2.73 25 0.048 + + b. ( ) 11.59 3.6 − − − c. 14 3.1 2.7 0.3 − + − × d. ( ) 26 2.3 3 3.5 1.25 − + ÷ e. ( ) 3 0.4 − 11. Perform the operations indicated. a. ( ) 4 7 a b. 2 5 − c. 3 8 5 24 16 x y x y d. ( )( )( ) 4 3 6 x y x − − e. ( ) 3 5 x − ⋅ f. ( )( ) ( ) ( ) 2 2 4 2 2 3 4 x x x x − − − g. ( ) 10 0 x h. ( ) 7 3 y i. 8 2 5 5 5 ⋅ ⋅

Final Exam Review MATD 0330 Austin Community College Page 4 of 12 12. Place the appropriate symbol < , > , or = between the two numbers. a. 0.0803 0.803 b. 0.03 0.3 − c. ( 2) 2 − − − 13. Perform the operations indicated. a. (9 3) (4 15) x x − + + b. (3 4 5) ( 4 9) a b b − − − − + c. 2 2 (6 2 7) ( 3 ) x x x − + − − x d. ) 8 2( 4 z z − − 14. Simplify. a. 4( 7) a − b. 3 (2 5 1) x x y − − + c. 5 2 (5 3)( 2 ) y y − − d. ( ) 7 5 6 8 x x x + − 15. Solve. a. 2 3 5 7 y y − = − b. 3(2 8) 7 30 x x + − = c. 1 2 2 4 3 y − + = d. 8 ( ) ( ) 4 1 6 2 x x − = − + + e. 14 2 16 x x = − + f. 2 2 (4 1) (4 2) 3 x x x − − − + = − g. 3 4 4 x − = 4 16. Complete the table of equivalent notations. Fraction Decimal Percent 8 9 0.189 64.05% 3 8 4