Clifton High School Mathematics Summer Workbook

Transcription

1 Clifton High School Mathematics Summer Workbook Algebra II-H: 9 th grade Completion of this summer work is required on the first day of the school year. Date Received: Date Completed: Student Signature: Parent Signature:

2 Dear Parents and Guardians, Attached is the mathematics workbook that your child is required to work on over the summer. Our goal is that your child will continue to work on appropriate math skills and concepts to maintain the progress made during the previous grade. This work will help prepare your child for the net level. Summer workbooks can be accessed online through the Clifton web site: click on: mathematics summer workbooks Please sign to indicate the date the workbook was received and the date it was completed. Encourage your child to work through the booklet a section at a time during July and August. Your child s math teacher will collect the booklet during the first week of school. Giving time and thought to this work will help to maimize your child s grade on the test given in September. The test will be based on the work shown and will count as the first test of the school year. The grade will be determined as follows: Completion of the workbook on time will count as 0% of the grade. Performance on the test will count as 80% of the grade. Thank you for your anticipated cooperation. Sincerely, Jimmie Warren Mary Campbell CHS Principal Supervisor of Mathematics 9-1

3 Name: Date: Algebra II-H:9 th grade SUMMER WORKBOOK Directions: Part I Vocabulary Match the given words to the correct definition Directions: Part II - Multiple Choice NOTA ( stands for None Of The Above ) For questions #1-50 show all work on a separate sheet of white lined paper. Your work should be numbered and neat. Please use pencil and put the letter that corresponds to your answer in a circle net to the work for each problem. Directions: Part III - Open-Ended For questions #1-1 show all work on a separate sheet of white lined paper. Your work should be numbered and neat. Please use pencil and circle your final answer for each problem.

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5 Part I-VOCABULARY Match the given words to the correct definition. absolute value equation GCF prime number sum base eponent integers product variable composite numbers epression LCM quotient < difference factors ordered pair rational number > root reciprocal solution set monomial conjugates quadrant origin slope of a line term coefficient function 1) a mathematical sentence that contains an equal sign ) made up of quantities and the operations performed on them does not contain =,, <,, >, ) a symbol that is used to represent a number ) used to locate points (, y) in the coordinate plane 5) the solution to an addition problem 6) the solution to a subtraction problem 7) the solution to a multiplication problem 8) the solution to a division problem 9) whole numbers and their opposites { -,-,-1,0,1,,, } (symbol is Z) 10) a number that can be epressed in the form a/b, in which a and b are integers and b 0 (symbol is Q) 11) a number s distance from zero on the number line 1) the quantities that are multiplied in a multiplication epression 1) a whole number greater than one, with eactly factors, 1 and itself 1) a whole number greater than 1 that has more than factors 15) the greatest number that is a factor of two or more integers 16) the least positive integer that is divisible by each of or more integers 17) the in an epression of the form n 18) the n in an epression of the form n 19) the symbol for less than ( ) 0) the symbol for greater than ( )

6 1) When a term is the product of a number and a power of a variable (also the numerical factor of a monomial). ) a relation with eactly one output for each input. ) An epression that is a number, a variable, or the product of a number and variables. ) the point (0,0) where the -ais and y-ais intersect on a coordinate plane. 5) the reciprocal, or multiplicative inverse, of any nonzero real number a is 1 a. 6) a number that, when substituted for the variable, makes the equation a true statement. 7) the ratio of vertical change (the rise) to horizontal change (the run) for a nonvertical line. 8) the four regions into which two perpendicular number lines separate the plane. 9) A solution of an equation. 0) each number in a sequence. 1) the sum and the difference of the same two terms.

7 Part II: Multiple Choice (50 Questions) For questions #1-50 show all work on a separate sheet of white lined paper. Your work should be numbered and neat. Please use pencil and put the letter that corresponds to your answer in a circle net to the work for each problem. Use the answer NOTA for None Of The Above 1. Solve: + 5 = 0, B. 1, C.,1 1,. If + y = 10 then y = y = 1 1 B. C. 7 1 E. 1. Solve: = 1 (6+ ) B. C. 0. Simplify: 6 ( cd ) ( cd ) c d B c d E c d C. 7 7c d 7 9c d 5. Which of the following is the least? 0.7 B. 1 C One Factor of 5 is E. 11% 5 + B. 5 C E. 5 1

8 7. Find a possible middle term to make this polynomial factorable: B. 1 C. 7 E Factor: 8a 17a+ (a )(a 1) B. a(8a 17) + C. (8a )( a 1) (8a+ 1)( a ) E. (8a 1)( a ) 9. Find the -coordinate of the system: + y = y = B. 1 C. 1 5 E Find the slope and y-intercept of the line whose equation is: y = + Slope =, y-int = B. Slope =, y-int = C. Slope =, y-int = Slope =, y-int = E. Slope =, y-int = 11. Find the slope of the line that passes through (,7) and (1,) B. C. E.

9 1. The solution to + 1= 1are: 0, B., 6 C. 6, 1, 1. Find the equation of the line containing the point (,5) and having slope: y = 7 B. y = C. y = y = Solve: B. 1 C. E = 5 5 B. 5 C. 5 5 E Which pair of lines represent graphs that are perpendicular? y = + 7 y = + B. y = 5+ 5 y = C. y = 16 y = 8 y = 9 y = E. = 5 y = 17. The graph of y+ 8= 0 crosses the y-ais at 8 B. C. 0 E What is the first step to solve this problem: 10= ( + ) Add 10 to both sides of the equation. B. Subtract from both sides of the equation. C. Distribute the on the right side. Divide by on both sides of the equation E. NOT

10 19. Solve: y + = 11 B. 11 C A boy is mowing a rectangular lawn 0 ft. long and 0 ft. wide. He has cut all of it ecept for a rectangle that is 0 ft. long and 15 ft. wide. What fractional part of the lawn remains uncut? 1 B. 5 C Evaluate mn m+ n when m = 8 and n = B C Simplify: 675 (6 + 9 ) 15 B. 9 C E. 15. ( y ) = 5 8 y B y C. 6 y 16 y. ( )(+ 1) = 1 8 B C

11 5. ( y ) = y B. 6 y 1 C. 6 6 y y 6 6. ( )( + ) = 16 B C Factor: y y B. 5(5 y) (5 ) C. (5 + y)(5 y) (5 + y)(5 8 y) 8. Solve the system of equations: + y = 11 y = = 1, y = B. = 1, y = C. =, y = = 1, y = 9. Which one of the following equals a negative number? ( 5) + 9 B. ( 9) + 5 C ( 9) + E. 9 ( 5) 0. Factor: (6+ 5)( 1) B. (+ 1)( 5) C. (6 1)( + 5) ( 1)(+ 5) 1. Find the equation that best represents the following word problem: In a certain freshman class, the number of girls is 8 less than twice the number of boys (b). The total number of students in that freshman class is 59. How many boys and girls are in That class? b+ b= 59 8 B. b+ b 8 = 59 C. b+ 8 b= 59 b+ b= 59

12 . ( + ) = B C E. 5. You and three friends are eating a pizza with 1 pieces. Each person eats the same number of pieces. Let represent the number of pieces each person eats. Which of the following equations is an algebraic model for the situation? = 1 B. 1 = 1 C. 1 = 1 = 1. Solve: ( )(+ 5) = 0, 5 B. 5,,, 0 C. 5,, 0, 5, 0 5. One of the solutions of the equation: 11 + = is 0 B. 11 C Simplify: (c + 1) (7c ) + (c + 5 c ) 6c c + B. 6c c + C. 6c c c c E. c + 7. The number ten is raised to a power between 0 and 1. The answer has to be between which two numbers? 0 and 1 B. 1 and 10 C. 10 and 100 but not 5 0 and 100 but not 50 E. 10 and 0

13 8. If = and y = then y = 6 B. 18 C. 1 1 E Define p q by the equation p q p q q =. Then = 108 B. 7 C E If 7 + = , then 1 equals. B. C Which of the following best describes the rectangle part of the statement? = 0 Coefficient B. Variable C. Term Epression E. Solution. Solve for : 5 10 = + 10( ) 6 B. C. 1. Solve for r : A = p+ prt 1 A + tp B. ta ( p) C. A p pt pt A p. Write the answer in proper scientific notation: 5 (7 10 ) ( 10 ) B C

14 5. yz y 6 = y B. y z C. z yz E. 6 y z 6. ( y y ) (y 5y ) + = y 9y+ 5 B. y 9y + 1 C. + y y 5 y + y 5 E. + y 7y 1 7. The solutions of the equation = are : and 1 B.. and 1 C. and 1 1 and E. 1 and 8. Solve 6 = 10 8 B. {,8 } C. {, 8} 9. Simplify: ( 6)( 8) ( ) ( ) B. C Simplify: 1 ( ) 1 1 B. 9 C. 9 1

15 Part III Open-Ended For questions #1-1 show all work on a separate sheet of white lined paper. Your work should be numbered and neat. Please use pencil and circle your final answer for each problem. In order to receive credit for the following, you must show all work. Final answers should be circled. 1. Find all values of such that = 1 +. Simplify ( ) ( 5 1). Simplify the following: a) ( 1)( 1) b) ( a b) c) ( 1)( ) + +. Simplify the following: 6m + m a) b) ( y ) c) ( a b c )( a b c ) m d) + 0 e) 7ab c a b c Factor the following: a bc + a b + a bc + 5 a) 6 b) 9 c) 5 6. Simplify the following: y y a) b) c) y y y y 7. Simplify 1 1 z 1 z If 7 y = 16 + y, then y =? 9. If 5( + ) ( + ) = 0, then =? 10. If a + b = and a 0, then =? a 11. If H =, then =? 6b

16 If =, then =? 1. Solve the following: a) p > p+ 1 b) 1 5< c) + > Find the slope of the line that contains the points (-,) and (0,0) 15. Given y = 8 a) solve for y b) find the slope c) find the -intercept d) find the y-intercept e) graph this line on graph paper 16. Find the equation of a line that contains the point (-,1) and has a slope of Given + y = 7 a) find the equation of a parallel line that contains the point (,6) b) find the equation of a perpendicular line that contains the origin. 18. Graph the following inequalities simultaneously on graph paper: y and Solve the following system of equations: + 5y = 7 + y = 1 0. Find the roots of the following: a) ( + 1)( ) = 0 b) = 0 1. If st ( ) = t t 1, then find s( 1)