CHAPTER 5, NUMBER THEORY AND THE REAL NUMBERS

Transcription

1 TEST A CHAPTER, NUMBER THEORY AND THE REAL NUMBERS 1. Find a rational number with a denominator of 28 and equal to Find the reciprocal of: a d Perform the indicated operations: a. (- 4 9 ) ( ) ( ) 4. Write as decimals: a Write in simplest form as the quotient of two Integers: a Write: a in expanded form in decimal form.

2 . Do the following calculation and write the answer in scientific notation: (9 10 ) ( ) 8. Which of the following numbers is (are) irrational? 36, 42, 144, , a. Find a rational number between 0.2 _ and Find an irrational number between 0.2 _ and The diameter of a circle is 4 inches. To the nearest tenth of an inch what is the circumference of this circle? (Use π 3.14.) 11. Tell whether the underlined item is used as a cardinal number, an ordinal number, or for identification. a. Joe came third in the election. Susan's lottery ticket won five dollars. Bill's auto license number was What properties of the system of natural numbers are used in the following equations a. ( + 6) + 3 = ( + 3) + 6 9(10 + 3) = (2 39) = (2 ) Write 286 as a product of primes. 14. Write the prime numbers between 40 and 0.

3 1. Is 123 prime or composite? 16. Consider the numbers 634, 18, 849, 160 Identify the numbers divisible by: a Find the GCF of 13, and 22 and reduce the fraction 13 to lowest terms Find the LCM of 90, 13 and 22 and perform the indicated operations: What fractional part of Julian's budget goes for entertainment if 3 of his budget is for school expenses, 1 is for gasoline, 1 20 is for savings and the remainder is for entertainment? 20. Evaluate: (-8 + 4) Perform the indicated operations: a d The three sides of a triangle are measured as 18.4, 6.68, and cm, respectively. What is the perimeter of this triangle? (Give the answer to the correct number of places.)

4 23. The dimensions of a rectangular court are measured as 83.6 by 0. feet. What is the area of this court? (Give the answer to the correct number of places.) 24. The circumference of a ball is measured as 11. inches. What is the diameter of this ball? (Use π 3.14 and give the answer to the correct number of places.) 2. Write as a decimal: a. 23%.% 0.34% 26. Write as a percent: a d. (Answer to one decimal place.) 9 2. A 2-liter bottle of soda sells for 69 cents and costs the store 49 cents. Find the percent of profit, correct to two decimal places of the employees of Company A make between $2,000 and $0,000 annually. If this represents 20% of the company's employees, how many employees does Company A have? 29. Simplify as much as possible: a d

5 30. Perform the indicated operations and simplify: a d For a right triangle with sides of length a, b and hypotenuse c, c 2 = a 2 + b 2. If the sides of a right triangle are 6 and 9 inches long, what is the length of the hypotenuse? Simplify your answer. 32. Classify the given numbers by making a check mark in the appropriate row: Number Set Natural Integers Rational Irrational Real. 33. Classify as an arithmetic or a geometric sequence: a. 3, 6, 12, 24,... 4,, 10, 13, For the sequence 6, 9, 12, 1,..., find: a. The first term The common difference The sum of the first ten terms d. The sum of the first n terms

6 3. For the sequence 4, -2, 1, - 1 2,..., find: a. a 1 r The sum of the first five terms. d. The sum of the first n terms 36. Use the sum of an infinite geometric sequence to write the following repeating decimals as fractions in lowest terms: a

7 TEST B CHAPTER, NUMBER THEORY AND THE REAL NUMBERS 1. A rational number between 0.2 _ and 0.2 is a d e The diameter of a circle is 4 inches. To the nearest tenth of an inch, what is the circumference of this circle? (Use π 3.14.) a in in. 12. in. d. 12 in. e. None of these = a d e The three sides of a triangle are measured as 18.4, 6.68, and centimeters long, respectively. What is the perimeter of the triangle? a. 4 cm 44.8 cm 44.4 cm d cm e. 44. cm. The dimensions of a rectangular court are measured to be 83.6 by 0. feet. What is the area of this court? a sq ft 4222 sq ft sq ft d sq ft e sq ft 6. The circumference of a ball is measured as 11. in. What is the diameter of this ball? (Use π 3.14.) a in. 3. in in. d in. e. None of these. Written as a decimal,.% is a d.. e. None of these 8. Written as a percent, correct to one decimal place, 9 a. 0.6%.6% 6% d..6% e. None of these is 9. A 2-liter bottle of soda sells for 69 cents and costs the store 49 cents. Find the percent of profit, correct to two decimal places. a. 28% 40.82% 28.99% d % e. None of these

8 10. 0 of the employees of Company A make between $2,000 and $0,000 annually. If this represents 20% of all the employees, how many employees does Company A have? a d. 400 e. None of these 11. In simplified form, 648 = a d e. None of these 12. In simplified form, = a d e In simplified form, 1 = a. 3 3 d. 20 e. None of these = a d e. None of these 1. Which one of the following is an arithmetic sequence? a. 2, 3,, 8,... 4, 8, 16, 32,... 2,, 8, 11,... d. 1, 0, 1, 0,... e. 0, 2, 3,, The sum of the first ten terms of the sequence 2,, 8, 11,... is a d. 30 e. None of these

9 1. For the sequence 1, - 1 2, 1 4, - 1,..., which of the following is 8 correct? (Note: S 6 means the sum of the first six terms.) a. r = - 1 2, S 6 = - 21 r = , S 6 = 63 r = , S 6 = d. S 6 = - 3. e. None of these The repeating decimal = a d e. None of these The underlined word in the sentence "This is the fifth test." is used as: a. a cardinal number b. an ordinal number identification d. a natural number e. None of these 20. What addition properties of the system of natural numbers are used in the equation: = = ( + 3) + 6? a. Associativity only Commutativity only The distributive property only d. The associative and the distributive properties only e. Commutativity and associativity only 21. Written as a product of primes, 286 = a b d e. None of these 22. All the prime numbers between 0 and 60 are: a. 1, 3 and 3 and 9 1, and 9 d. 3 and e. None of these 23. The number 123 is: a. a prime number b. a composite number an even number d. neither prime nor composite e. None of these 24. The number 4 is divisible by: a. only b. 1, 3, and only 1, 3 and 1 only d. 1, 3,, 9, and 1 only e. 1, 3,, 9, 1 and 4 only

10 2. The GCF of 13 and 22 is a. 3 1 d. 4 e When written in simplest reduced form = a. d. e. None of these The LCM of 12, 24 and 30 is a d. 3 0 e When written in simplest reduced form, a d e = 29. A pattern for a wedding outfit calls for yards of lace trim for t h e dress and 6 1 yards of lace trim for the veil. How many yards of lace 2 trim does the pattern call for? a. 1 yd 10 yd 23 yd d yd e. None of these (-12) = a d. -8 e. None of these = a d e. None of these 32. The reciprocal of - is: a. - d. - (- ) e. None of these

11 33. (- 4 9 ) (11 18 ) = a d e. None of these Written as a decimal, = 6 a d e. None of these 3 3. Written as the quotient of two integers 0.63 = 63 a d e. None of these _ Written in standard decimal notation, 3.86 x 10 6 = a. 3,860, , ,000 d ,000 e. None of these 3. In scientific notation, (9 10 ) ( ) = a d e. None of these 38. Which one of the following numbers is irrational? a d e