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Chicago High School for the Arts Algebra 1 (Honors) Name ______________________________________________________________ Date _____________________________ Unit 1 Exam – The Language of Algebra **Please remember to SHOW ALL WORK in order to receive full credit, and circle or box your final answer. Focus Standard C.4.1 Description Solve routine two-step or three-step arithmetic problems involving concepts such as rate and proportion, tax added, percentage off, and computing with a given average Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, pattern identification, absolute value, primes and greatest common factor Evaluate algebraic expressions by substituting integers for unknown quantities Compute the area and perimeter of triangles and rectangles in simple problems Find and use least common multiple C.4.2 Order fractions 3 C.5.1 Apply number properties involving prime factorization 3 C.5.2 Apply number properties involving even/odd numbers and factors/multiples C.5.3 2 Apply number properties involving positive/negative numbers A.3.1 REVIEW C.3.1 D.3.1 G.3.1 PRIMARY SECONDARY Points Percent # Correct # of Points 13 6 4 3 5 Grade 38 Solve routine two-step or three-step arithmetic problems… [A.3.1] _______________________________ **Please show EACH STEP in order to receive full credit! 1. A 5-pound bag of onions costs $1.95 at Grocery Garden. A 2-pound bag of the same type of onions costs $0.88 at Food Fair. How much cheaper, per pound, are the Grocery Garden onions than the Food Fair onions? a. $0.05 b. $0.15 c. $0.21 d. $0.54 e. $1.07 2. Simplify the following: 52 +12 ¸[4 - (4 + 6)] a. 7 b. 17 c. 22 d. 26 e. 30 Chicago High School for the Arts Algebra 1 (Honors) 3. (16 4) 3 7 2 5 ? a. – 1 b. 0 c. 1 d. 4 e. 45 Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, pattern identification, absolute value, primes and greatest common factor [C.3.1] 4. (Patterns) The second term of an arithmetic sequence is –11, and the third term is –38. What is the first term? (Note: In an arithmetic sequence, consecutive terms differ by the same amount.) a. – 27 b. 1 11 c. d. e. 11 16 27 5. (Patterns) The decimal representation of 6/7 repeats and can be written as 0.857142857142… what is the 100th digit to the right of the decimal point in the decimal representation? a. b. c. d. e. 1 2 4 5 8 5. (Primes) Which of the following lists gives the 3 largest prime numbers that are less than 60? a. b. c. d. e. 2, 3, and 5 3, 5, and 7 37, 47, and 59 47, 51, and 57 47, 53, and 59 6. (GCF) What is the greatest common factor of 45, 60, and 90? a. b. c. d. e. 3 5 15 30 180 Chicago High School for the Arts Algebra 1 (Honors) Evaluate algebraic expressions by substituting integers for unknown quantities [D.3.1] _______ 7. Evaluate ac bc for a 2 , b 6 and c 3 . a. – 24 b. – 12 c. 3 d. 12 e. 24 8. The book Fahrenheit 451 by Ray Bradbury is about a society in which all books are banned and burned. The title of the book gives the approximate temperature at which paper starts to burn. Since Fahrenheit, F, and Celsius, C, temperatures are related by the formula C 5 ( F 32) , which of the following would make an equivalent title for the book? 9 a. b. c. d. e. Celsius 219 Celsius 233 Celsius 268 Celsius 754 Celsius 844 Compute the area and perimeter of triangles and rectangles in simple problems [G.3.1] _______ 9. The perimeter of a square is 16 centimeters. What is the area in square centimeters? a. b. c. d. e. 16 20 28 32 64 10. What is the area of a triangle where the length of the base is 9 inches, and the height is 14 inches? a. 23 inches b. 37 inches c. 45 inches d. 63 inches e. 126 inches Find and use least common multiple [C.4.1] ___________________________________________________________ 11. What is the least common multiple of 5, 24, and 36? a. 4,320 b. 360 c. 180 d. 120 e. 60 Chicago High School for the Arts Algebra 1 (Honors) 12. Dena ran 2 4 1 miles on Monday and 3 miles on Tuesday. The total distance, in miles, Dena 5 3 ran during those 2 days is within which of the following ranges? 1 2 and less than 5 2 3 2 b. At least 5 and less than 6 3 1 c. At least 6 and less than 6 3 1 1 d. At least 6 and less than 6 3 2 1 2 e. At least 6 and less than 6 2 3 a. At least 5 Order fractions [C.4.2] _____________________________________________________________________________________ 13. What fraction lies exactly halfway between a. b. c. d. e. 2 3 and ? 3 4 3 5 5 6 7 12 9 16 17 24 14. Write the following fractions in order from smallest to largest. 0 2 3 a. 3 1 1 2 5 , , , 0, , 4 3 8 3 6 b. 1 1 3 2 5 , , , 0, , 8 3 4 3 6 c. 5 2 1 1 3 , ,0, , , 6 3 8 3 4 d. 0 , e. 3 1 1 2 5 , , , , 4 3 8 3 6 3 1 1 5 2 , , , 0, , 4 3 8 6 3 1 8 5 6 3 4 1 3 Chicago High School for the Arts Algebra 1 (Honors) Apply number properties involving prime factorization [C.5.1] _____________________________________ 15. If z = (5)(11)(28)(38), what is the greatest prime factor of z? a. 5 b. 7 c. 11 d. 13 e. 19 16. If a is the greatest prime factor of 52 and b is the greatest prime factor of 72, what is the value of ab? a. 6 b. 16 c. 26 d. 39 e. 117 Apply number properties involving even/odd numbers and factors/multiples [C.5.2] and Apply number properties involving positive/negative numbers [C.5.3] ___________________________ 17. The product of a positive odd number, a negative even number, and a negative odd number will be: a. a negative even number b. a negative odd number c. a positive prime number d. a positive even number e. a positive odd number 18. The sum of a negative even number and a negative odd number will be: a. a negative even number b. a negative odd number c. a negative prime number d. a positive even number e. a positive odd number Almost done… Please go through the checklist below before submitting your exam. Take a deep breath. Retry and double check the problems that you had trouble with. Carefully check EVERY problem on your test. Try to show all your work. Keep an eye out for careless mistakes. Reset and close your calculator. Raise your hand to let me know you are done! Chicago High School for the Arts Algebra 1 (Honors) Answer Key: 1. A 2. C 3. D 4. A 5. B 6. E 7. C 8. A 9. B 10. A 11. B 12. B 13. C 14. A 15. E 16. E 17. B 18. E