Assignment: Summer Assignment Part 1 of 8 Real Numbers and Their Properties. Student: Date:

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1 Student: Date: Assignment: Summer Assignment Part of 8 Real Numbers and Their Properties. Identify to which number groups (natural numbers, whole numbers, integers, rational numbers, real numbers, and irrational numbers) does each of the following numbers belong. (a) 0 (b) 22 (c) 5 2 (d) 4 (e) 3 (f) 4.49 (a) Choose the correct answer below. A. Rational numbers B. Irrational numbers C. Whole numbers D. Integers E. Natural numbers F. Real numbers (b) Choose the correct answer below. A. Whole numbers B. Irrational numbers C. Integers D. Real numbers E. Rational numbers F. Natural numbers (c) Choose the correct answer below. A. Integers B. Irrational numbers C. Rational numbers D. Natural numbers E. Real numbers F. Whole numbers (d) Choose the correct answer below. A. Whole numbers B. Irrational numbers C. Integers D. Rational numbers E. Natural numbers F. Real numbers (e) Choose the correct answer below. A. Irrational numbers B. Whole numbers C. Integers D. Real numbers

2 E. Rational numbers F. Natural numbers (f) Choose the correct answer below. A. Irrational numbers B. Whole numbers C. Real numbers D. Integers E. Rational numbers F. Natural numbers 2. Which of the following are rational numbers? 4, 25, 0.2, 7, 3 3, 5 2,, 3 7, The rational numbers in the list are. (Use a comma to separate answers as needed.) 3. Evaluate = Evaluate the expression. ( 3) 2 Evaluate the expression ( 3) 2 = (Simplify your answer. Type an integer.) = 6. Evaluate the expression. 5(8 7) + ( 4)(2) 2 5(8 7) + ( 4)(2) 2 = 7. Evaluate the expression for p = 7, q = 8, and r =. 2 2 p 4q + r The answer is. 8. Evaluate the expression if p = 2, q = 4, and r = 7. q + r q p q + r q p = (Type an integer or a simplified fraction.)

3 9. Evaluate the expression for p = 4 and r = 2. 3p + 2(4 + p) 3 r + 9 The answer is. (Type an integer or a simplified fraction.) 0. Name the property illustrated by the following sentence. w w = Choose the property that is illustrated by the sentence. A. Multiplicative Inverse Property B. Distributive Property C. Associative Property D. Commutative Property. Evaluate the absolute value expression = 2. Find the value of 8. The value is. 3. Let x = 6 and y = 5. Evaluate the expression. 7x + 2y If x = 6 and y = 5, then 7x + 2y =. 4. In the Golf Tournament, Zach won the final round with a score that was 2 under par, while the previous year's tournament winner, John, finished with a finalround score that was 4 over par. Using 2 to represent 2 under par and + 4 to represent 4 over par, find the difference between these scores (in either order) and take the absolute value of this difference. The absolute value of the difference between scores 2 under par and 4 over par is. 5. The Blood Alcohol Concentration (BAC) of a person who has been drinking is given by the following expression. number of oz % alcohol body wt in lb hr of drinking 0.05 In 8 hours, a 40-lb person has drunk 4 6-oz beers ( 64 oz), each having a 5.5% alcohol content. Find this person's BAC. The person's BAC is. (Round to the nearest thousandth.)

4 Student: Date: Assignment: Summer Assignment Part 2 of 8 Laws of Exponents. 2. Use the product rule to simplify. ( 5x 2 )( 4x 5 ) 3 6 c c c 3 6 c c c = (Type exponential notation with positive exponents.) ( 5x 2 )( 4x 5 ) = (Simplify the coefficient. Type using an exponent.) x 5 y 7x 4 y = (Simplify your answer. Type exponential notation with positive exponents.) 7x 5 y 7x 4 y 3 = Simplify. y 5 7 z = (Simplify your answer. Type exponential notation with positive exponents.) y 5 7 z 7 = (Simplify your answer. Use positive exponents only.) 7. Assume the denominator does not equal 0. 3x 7 4y 6 3 3x 7 4y 6 3 = 8. Simplify each expression. Assume variables represent nonzero real numbers. x2 y 6 z 0 x2 y 6 z 0 =

5 9. Match each expression in Column I with its equivalent in Column II. (a) Which of the following expressions is equivalent to 7 0? I II ( 7) 0 ( 7) A. 7 B. 0 C. D. E. 7 (b) Which of the following expressions is equivalent to 7 0? A. B. 7 C. 7 D. 0 E. (c) Which of the following expressions is equivalent to ( 7) 0? A. B. 0 C. 7 D. E. 7 (d) Which of the following expressions is equivalent to ( 7) 0? A. B. 7 C. 0 D. E Explain why x + x is not equivalent to x 4. Choose the correct answer below. A. m n m n The product rule states that a a = a. B. m n m + n The product rule states that a a = a. C. m n m n The product rule states that a + a = a. D. m n m + n The product rule states that a + a = a.

6 Student: Date: Assignment: Summer Assignment Part 3 of 8 Polynomials. Identify the expression as a polynomial or not a polynomial. For a polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these. 5x 3 A. The expression is a polynomial. Its degree is and it is a monomial. B. The expression is a polynomial. Its degree is and it is a trinomial. C. The expression is a polynomial. Its degree is and it is a binomial. D. The expression is a polynomial. Its degree is and it is none of these. E. The expression is not a polynomial. 2. Identify the expression as a polynomial or not a polynomial. For a polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these z 7z + 8 A. The expression is a polynomial. Its degree is and it is a monomial. B. The expression is a polynomial. Its degree is and it is a binomial. C. The expression is a polynomial. Its degree is and it is a trinomial. D. The expression is a polynomial. Its degree is and it is none of these. E. The expression is not a polynomial. 3. Add. ( 6x 2 2 x + 0 ) + ( 5x 2 + 9x 53) The answer is. 4. Find the difference y 8y y 5y y 8y y 5y + 8 = 5. Find the sum or difference m 8m + m 9m + 7m + 4m + m m m 8m + m 9m + 7m + 4m + m m =

7 6. Find the product. (3v 5)(4v + 7) (3v 5)(4v + 7) = 7. Find the product x 2x + 6x 2x x 2x + 6x 2x + 9 =. 8. Use the distributive property to find the product. (y 6)( 7y y + 4) (y 6)( 7y y + 4 ) = 9. Use the formula for a binomial squared to multiply. (2x + 9y) 2 (2x + 9y) 2 = 0. Find the product. 9t 3r 2 2 9t 3r 2 2 =. Find the product. (k + 2) 3 (k + 2) 3 = 2. Multiply. ( p 2) 4 ( p 2) 4 = 3. Multiply. (5b + 7)(5b 7) (5b + 7)(5b 7) =

4. Perform the division. 36x 9 96x 6 + 32x 5 84x 3 2x 3 36x 9 96x 6 + 32x 5 84x 3 2x 3 =. 5. An amazing formula from ancient mathematics was used by the Egyptians to find the volume of the frustum of a square pyramid, as shown in the figure.

8 4. Perform the division. 36x 9 96x x 5 84x 3 2x 3 36x 9 96x x 5 84x 3 2x 3 =. 5. An amazing formula from ancient mathematics was used by the Egyptians to find the volume of the frustum of a square pyramid, as shown in the figure. Its volume is given by V = h 3 a 2 + ab + b 2 where b is the length of the base, a is the length of the top, and h is the height., a. When a pyramid was partially completed to a height h of 204 ft, b was 760 ft, and a was 36 ft. Calculate its volume at this stage of construction. The volume is ft 3. (Round to the nearest integer as needed.) b. Try to visualize the figure if a = b. What is the resulting shape? Find its volume. The resulting shape is () The volume of the obtained figure is V =. c. Let a = b in the Egyptian formula and simplify. Are the results the same? No Yes () rectangular box with a square base. cube. sphere.

9 Student: Date: Assignment: Summer Assignment Part 4 of 8 Factoring Polynomials. Factor out the greatest common factor from the polynomial. 7x + 4 7x + 4 = 2. Factor out the greatest common factor from the polynomial. 9xy 7xy 5 9xy 7xy 5 = 3. Factor out the greatest common factor from the polynomial p q 2p q p q 2p q = 4. Factor the polynomial using the greatest common factor. If there is no common factor other than and the polynomial cannot be factored, so state x y 6xy Select the correct choice below and fill in any answer boxes in your choice. A x y 6xy = (Type your answer in factored form.) B. The expression is not factorable. 5. Factor the polynomial by grouping x + 2 ax 3a 5 5 4x + 2 ax 3a = 6. Factor the polynomial by grouping p q 24 3q + 8p p q 24 3q + 8p = 7. Factor the trinomial, if possible. 2 6v 23v + 0 Select the correct choice below and fill in any answer boxes within your choice. A. 2 6v 23v + 0 = (Type your answer in factored form.) B. The polynomial is prime.

10 8. Factor the polynomial, if possible. 2 3r + 0r + 8 Select the correct choice below and fill in any answer boxes within your choice. A. 2 3r + 0r + 8 = (Type your answer in factored form.) B. The polynomial is prime. 9. Match each polynomial in Column I with its factored form in Column II. I II 2 2 x + 2xy + 36y (x + 6y)(x 6y) 2 2 x 2xy + 36y (x + 6y) x 36y (x 6y) y x (6y + x)(6y x) 2 2 Choose the correct factoring of x + 2xy + 36y below. A. (x + 6y)(x 6y) B. (x + 6y) 2 C. (6y + x)(6y x) D. (x 6y) Choose the correct factoring of x 2xy + 36y below. A. (x 6y) 2 B. (6y + x)(6y x) C. (x + 6y)(x 6y) D. (x + 6y) Choose the correct factoring of x 36y below. A. (x + 6y) 2 B. (x + 6y)(x 6y) C. (x 6y) 2 D. (6y + x)(6y x) 2 2 Choose the correct factoring of 36y x below. A. (x 6y) 2 B. (x + 6y) 2 C. (6y + x)(6y x) D. (x + 6y)(x 6y)

11 0. Factor the polynomial. 36r 2 25 Select the correct choice below and fill in any answer boxes within your choice. A. 36r 2 25 = (Type your answer in factored form.) B. The polynomial is prime.. Factor the polynomial s 8t A s 8t = (Type your answer in factored form. Factor completely.) B. The polynomial is prime. 2. Factor the polynomial. (y + 8) 3 52 A. (y + 8) 3 52 = (Simplify your answer. Type your answer in factored form.) B. The polynomial is prime. 3. Factor the polynomial by substitution. t 4 + 8t A. t 4 + 8t = B. The polynomial is prime. 4. Factor the following binomial completely. 2 4x A. 4x + 25 = B. 2 4x + 25 is prime.

12 5. Find all values of b that will make the polynomial a perfect square trinomial. 2 25z + bz + 6 b = (Use a comma to separate answers as needed.)

13 Student: Date: Assignment: Summer Assignment Part 5 of 8 Rational Expressions. Find the domain of the rational expression. x + 5 x 7 A. The domain is x x. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. ) B. The domain is the set of all real numbers. 2. Find the domain of the rational expression. 7x + 8 (2x + 6)(x 7) What is the domain? x x (Use a comma to separate answers. Type an integer or a fraction.) 3. Find the domain of the rational expression. y 2 2 y + 7 A. { y y } (Use a comma to separate answers as needed. Type the integers or a simplified fractions.) B. Set of all real numbers 4. Write the rational expression in lowest terms. 8x x 2x 2 What is the expression in lowest terms? Write the rational expression in lowest terms. 2y 4 5y 0 Write the rational expression in lowest terms. 2y 4 5y 0 = x 2 9x + 20 x 2 + x 30 x 2 9x + 20 x 2 = + x 30

14 7. Write the rational expression in lowest terms. 2x 2 7x x 2 5x 25 2x 2 7x x 2 = 5x Perform the subtraction. 2 9b a a 2 2 9b a a 2 = 9. Perform the subtraction. 5 8x 2 y 6xy 5 8x 2 = y 6xy 0. Perform the addition x + y x y x + y x y =. Perform the subtraction. x + y 4x y 5x y 4x x + y 4x y 5x y 4x = 2. Perform the subtraction. 7x x 2 + 2x 24 x x x x 2 + 2x 24 x x 2 = 36

15 3. x + 8 x x x + 8 x x = b 4 + b + 4 b 4 + b = 5. w 3 z 3 w 2 2wz + z 2 w 3 z 3 = w 2 2wz + z 2 (Use positive exponents only. Use integers or fractions for any numbers in the expression.)

16 Student: Date: Assignment: Summer Assignment Part 6 of 8 Rational Exponents. Identify the set as finite or infinite. Then determine whether 2 is an element of the set. { 5, 6, 7,..., 6} Identify the set as finite or infinite. finite infinite Is 2 an element of the set? No Yes 2. Match each expression in Column I with its equivalent expression in Column II. Choices may be used once, more than once, or not at all. I (a) 3 2 A. 9 II (b) 3 2 B. 9 (c) ( 3) 2 C. 9 (d) ( 3) 2 D. 9 Match expression (a) in Column I with its equivalent expression in Column II. (Type A, B, C, or D. Use a comma to separate answers as needed.) Match expression (b) in Column I with its equivalent expression in Column II. (Type A, B, C, or D. Use a comma to separate answers as needed.) Match expression (c) in Column I with its equivalent expression in Column II. (Type A, B, C, or D. Use a comma to separate answers as needed.) Match expression (d) in Column I with its equivalent expression in Column II. (Type A, B, C, or D. Use a comma to separate answers as needed.) Evaluate this expression. ( 3) 3 = ( 3) 3 Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. (5x) 2 (5x) 2 = (Simplify your answer. Use integers or fractions for any numbers in the expression)

17 5. Use the quotient rule to simplify = 2 3 (Give your answer using positive exponents. Leave your answer in exponential notation.) 6. Divide and simplify. x 20 x 7 x 20 x 7 = (Simplify your answer. Type exponential notation with positive exponents.) 7. Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent nonzero real numbers. 2r 8 2r 8 5r 5r = (Simplify your answer. Use integers or fractions for any numbers in the expression) 8. Perform the indicated operation. Assume all variables represent nonzero real numbers. 6a 4 a 2 5 a 2 6a 4 a 2 5 a 2 = (Simplify your answer. Type exponential notation with positive exponents.) 9. Perform the indicated operation. Assume all variables represent nonzero real numbers. (0x) 3 0x x 2 2 (0x) 3 0x x 2 2 = (Simplify your answer. Use positive exponents only. Use integers or fractions for any numbers in the expression.) 0. 6 / 2 6 / 2 = (Simplify your answer. Type an integer or a fraction.)

18 . 6 / 4 6 / 4 = / 3 / = 8 (Simplify your answer. Type an integer or an improper fraction.) 3. Evaluate the expression. ( 4) / 2 Choose the correct choice below and, if necessary, fill in the answer box to complete your choice. A. ( 4) / 2 = B. This expression is not a real number 4. Perform the indicated operation. Assume all variables represent positive real numbers / / 2 = (Simplify your answer. Type an integer or a fraction.) 5. Perform the indicated operations. / 3 5 / / 3 5 / =

19 Student: Date: Assignment: Summer Assignment Part 7 of 8 Radical Expressions. Identify the set as finite or infinite. Then determine whether 0 is an element of the set. { 3, 4, 5,..., 4} Identify the set as finite or infinite. infinite finite Is 0 an element of the set? Yes No 2. 3 Write 343 using exponents and evaluate using exponents is written as. (Use positive exponents only. Do not simplify. Use integers or fractions for any numbers in the expression.) Evaluate Select the correct choice below and, if necessary, fill in the answer box within your choice. A = B. The root is not a real number Write 024 using exponents and evaluate using exponents is written as. (Use positive exponents only. Do not simplify. Use integers or fractions for any numbers in the expression.) Evaluate Select the correct choice below and, if necessary, fill in the answer box within your choice. A = B. The root is not a real number. 4. Write in radical form. Assume all variables represent positive real numbers. 2 3 m 2 3 m = 5. Write in exponential form. Assume all variables represent positive real numbers. 6 x 7 6 x 7 = (Simplify your answer. Type exponential notation with positive exponents.)

20 6. Write in exponential form. Assume all variables represent positive real numbers. 8 2p 3 8 2p 3 = (Simplify your answer. Type your answer using exponential notation. Use integers or fractions for any numbers in the expression.) 7. Assume all variables represent positive real numbers. x 9 y 7 z 2 Select the correct choice below and fill in any answer boxes in your choice. A. x 9 y 7 z 2 = (Simplify your answer. Type an exact answer, using radicals as needed.) B. The expression cannot be simplified. 8. Assume all variables represent positive real numbers. 4 gh 9 25r 4 Select the correct choice below and fill in any answer boxes in your choice. A. 4 gh 9 25r 4 = (Simplify your answer. Type an exact answer, using radicals as needed.) B. The expression cannot be simplified. 9. Assume all variables represent positive real numbers x y 6x y Select the correct choice below and fill in any answer boxes in your choice. A. The simplified form is. (Simplify your answer. Type an exact answer, using radicals as needed.) B. The expression cannot be simplified.

21 Select the correct choice below and fill in any answer boxes in your choice. A = (Simplify your answer. Type an exact answer, using radicals as needed.) B. The expression cannot be simplified Select the correct choice below and fill in any answer boxes in your choice. A = (Simplify your answer. Type an exact answer, using radicals as needed.) B. The expression cannot be simplified = = =

22 The Hindu mathematician Bhaskara used as an approximation for π circa A.D In which decimal place does this value first differ from π? Use your calculator to answer this question. Assume π = It first differs in the () decimal place. () fourth third fifth

23 Student: Date: Assignment: Summer Assignment Part 8 of 8 Solving Equations and Inequalities. Solve the equation. 3x 5 = 7 x + The solution set is. 2. Solve the equation. 8( 4 x + 6 ) = (x + 7) The solution set is. (Simplify your answer. Type an integer or a fraction.) 3. Solve the equation for x. 3(x a) + b = 4x + a x = 4. A driver averaged 44 miles per hour and took 7 hours to travel between two cities. What is the distance between the two cities? The distance between the two cities is miles. 5. A rectangle has a width of 57 centimeters and a perimeter of 230 centimeters. What is the rectangle's length? The length is cm Solve the equation by the zero factor property. r 2 7r + 2 = 0 Find all solutions by factoring. 3c 2 22c = 6 Solve the equation by using the square root property. 20 t 2 = 0 The solution set is. (Use a comma to separate answers as needed.) The solution set is. (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.) The solution set is. (Simplify your answer. Type exact answers, using radicals as needed. Use a comma to separate answers as needed.) 9. The area of a rectangular wall of a barn is 208 square feet. Its length is 0 feet longer than twice its width. Find the length and width of the wall of the barn. width = feet length = feet

24 0. Cynthia Besch wants to buy a rug for a room that is 5 ft wide and 20 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 76 square feet of carpeting. What dimensions should the rug have? 76 5 ft 20 ft The dimensions of the rug should be (Use a comma to separate answers as needed.) ft.. Sales of SUVs (sport utility vehicles) in the United States (in millions) for the years can be modeled by the quadratic equation shown below. 2 y = 0.06x x Here x = 0 represents 990, x = represents 99, and so on. Use the model to approximate sales in 999. Sales in 999 were approximately million SUVs. (Round to the nearest tenth as needed.) 2. Solve the equation. 4x + 5 5x = x 4 x 3 A. The solution set is. (Simplify your answer. Use a comma to separate answers as needed.) B. The solution is the empty set. 3. Solve the equation. x 7 = + 8 x 7 x 7 A. The solution set is. (Simplify your answer. Use a comma to separate answers as needed.) B. The solution is the empty set. 4. Solve the equation. 2x 7 x = x 2 5 A. The solution set is. (Simplify your answer. Use a comma to separate answers as needed.) B. The solution is the empty set.

25 5. At a dairy plant, a milk tank can be filled in 4 hours (using the in valve). Using the out valve, the tank can be emptied in 8 hours. If both valves are open and milk is being pumped into the tank, how long will it take to fill the tank? It will take hours to fill the tank. 6. Solve the equation. x = 5 x + 4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is. (Simplify your answer. Use a comma to separate answers as needed.) B. There is no solution. 7. Write the inequality in interval notation. 9 < x 2 Write the solution in interval notation. 8. Solve the inequality. Write the solution set in interval notation. 7 2 y The inequality in interval notation is. 9. Solve the quadratic inequality. Write the solution set in interval notation. 2 x 9x 20 2 A. The solution set is. (Use integers or fractions for any numbers in the expression.) B. The solution set is the empty set. 20. Solve the quadratic inequality. Write the solution set in interval notation. 2 x + 5x + 8 < 0 The solution set is. (Use integers or fractions for any numbers in the expression.) The solution set is the empty set.

Remember, you may not use a calculator when you take the assessment test.

Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation.