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Honor's Pre-Algebra Chapter 4 Test Review Short Answer Write the expression using exponents. 1. 2. 3. 4. Evaluate 5. Evaluate if x = 8 and y = 7. if b = –3. Write the prime factorization of the number. Show your factor tree or division steps. 6. 90 7. 100 Factor the monomial. Show your work (factor Trees or division steps) 8. 9. Find the GCF of the set of numbers or monomials. (at least show the prime factorization) 10. 44, 48 11. , Factor the expression. 12. 13. Simplify the fraction. If the fraction is already in simplest form, choose simplified. 14. 15. Find the product or quotient. Express using exponents. 16. 17. 18. 19. Write the fraction as an expression using a negative exponent other than –1. 20. 21. 22. Evaluate 23. Evaluate if if 24. Express and . . in standard form. 25. Express 0.0000983 in scientific notation. 26. The table shows the land area in square miles of the three largest states in the USA. Rank the states in order from smallest to largest. State Land Area Area (sq mi) Texas California Alaska 27. The table shows the populations of the world’s most populous countries. Rank the countries in order from most populous to least populous. Country 2003 Population Population USA China India 28. Is the value of prime or composite if 29. Determine the value of for ? . Is the value prime or composite? Honor's Pre-Algebra Chapter 4 Test Review Answer Section SHORT ANSWER 1. ANS: Since the base is multiplied by itself five times, use an exponent of 5. PTS: OBJ: STA: KEY: 2. ANS: 1 DIF: Basic REF: Lesson 4-1 4-1.1 Write expressions using exponents. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 PFA 7 TOP: Write expressions using exponents. Exponents | Write Expressions Use an exponent of 2 for the first base, an exponent of 3 for the second, and an exponent of 2 for the third base. PTS: OBJ: STA: KEY: 3. ANS: 1 DIF: Average REF: Lesson 4-1 4-1.1 Write expressions using exponents. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 PFA 7 TOP: Write expressions using exponents. Exponents | Write Expressions Use an exponent of 2 for the first base, an exponent of 3 for the second, and an exponent of 2 for the third base. PTS: 1 DIF: Average REF: Lesson 4-1 OBJ: 4-1.1 Write expressions using exponents. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: PFA 7 TOP: Write expressions using exponents. KEY: Exponents | Write Expressions 4. ANS: 511 Multiply the x value by itself three times and subtract 1. (Remember that any number to the zero power is one.) PTS: 1 DIF: Average REF: Lesson 4-1 OBJ: 4-1.2 Evaluate expressions containing exponents. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NNSO 3 | PFA 7 | PFA 8 TOP: Evaluate expressions containing exponents. KEY: Exponents | Evaluate Expressions 5. ANS: –500 First evaluate the expression in parentheses, then raise that to the third power, then multiply the result by 4. PTS: 1 DIF: Average REF: Lesson 4-1 OBJ: 4-1.2 Evaluate expressions containing exponents. NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 STA: NNSO 3 | PFA 7 | PFA 8 TOP: Evaluate expressions containing exponents. KEY: Exponents | Evaluate Expressions 6. ANS: Write the number as a product of prime factors. PTS: OBJ: NAT: TOP: KEY: 7. ANS: 1 DIF: Basic REF: Lesson 4-2 4-2.1 Write the prime factorizations of composite numbers. NA 1 | NA 6 | NA 8 | NA 10 | NA 2 Write the prime factorizations of composite numbers. Prime Factorization | Composite Numbers Write the number as a product of prime factors. PTS: OBJ: NAT: TOP: KEY: 8. ANS: 1 DIF: Average REF: Lesson 4-2 4-2.1 Write the prime factorizations of composite numbers. NA 1 | NA 6 | NA 8 | NA 10 | NA 2 Write the prime factorizations of composite numbers. Prime Factorization | Composite Numbers Write the monomial as a product of prime numbers and variables with no exponent greater than one. PTS: 1 DIF: Average REF: Lesson 4-2 NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 2 KEY: Factor | Monomials 9. ANS: OBJ: 4-2.2 Factor monomials. TOP: Factor monomials. Write the monomial as a product of prime numbers and variables with no exponent greater than one. PTS: 1 DIF: Average REF: Lesson 4-2 OBJ: 4-2.2 Factor monomials. NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 2 TOP: Factor monomials. KEY: Factor | Monomials 10. ANS: 4 List all of the factors of each number and circle the factors in both lists. The greatest number circled is the GCF. PTS: OBJ: TOP: KEY: 11. ANS: 1 DIF: Basic REF: Lesson 4-3 4-3.1 Find the greatest common factor of two or more numbers or monomials. Find the greatest common factor of two or more numbers or monomials. Greatest Common Factor Completely factor each monomial and circle the common factors. The GCF is the product of the common factors. PTS: 1 DIF: Average REF: Lesson 4-3 OBJ: 4-3.1 Find the greatest common factor of two or more numbers or monomials. TOP: Find the greatest common factor of two or more numbers or monomials. KEY: Greatest Common Factor 12. ANS: Find the GCF of both terms, then rewrite the expression as a product of the GCF and its remaining factors. PTS: OBJ: NAT: TOP: KEY: 13. ANS: 1 DIF: Average REF: Lesson 4-3 4-3.2 Use the Distributive Property to factor algebraic expressions. NA 1 | NA 6 | NA 9 | NA 10 | NA 2 Use the Distributive Property to factor algebraic expressions. Distributive Property | Factor Expressions Find the GCF of both terms, then rewrite the expression as a product of the GCF and its remaining factors. PTS: OBJ: NAT: TOP: KEY: 14. ANS: 1 DIF: Average REF: Lesson 4-3 4-3.2 Use the Distributive Property to factor algebraic expressions. NA 1 | NA 6 | NA 9 | NA 10 | NA 2 Use the Distributive Property to factor algebraic expressions. Distributive Property | Factor Expressions Divide the numerator and the denominator by the GCF. PTS: 1 DIF: Average REF: Lesson 4-4 NAT: NA 1 | NA 4 | NA 6 | NA 10 | NA 2 KEY: Simplify Fractions | Fractions 15. ANS: OBJ: 4-4.2 Simplify algebraic fractions. TOP: Simplify algebraic fractions. Divide the numerator and the denominator by the GCF. PTS: 1 DIF: Average REF: Lesson 4-4 NAT: NA 1 | NA 4 | NA 6 | NA 10 | NA 2 KEY: Simplify Fractions | Fractions 16. ANS: OBJ: 4-4.2 Simplify algebraic fractions. TOP: Simplify algebraic fractions. Multiply powers with the same base by adding their exponents. PTS: 1 DIF: Basic NAT: NA 1 | NA 3 | NA 6 | NA 7 | NA 2 KEY: Monomials | Multiply Monomials 17. ANS: REF: Lesson 4-5 STA: PFA 5 OBJ: 4-5.1 Multiply monomials. TOP: Multiply monomials. Multiply powers with the same base by adding their exponents. PTS: 1 DIF: Average NAT: NA 1 | NA 3 | NA 6 | NA 7 | NA 2 REF: Lesson 4-5 STA: PFA 5 OBJ: 4-5.1 Multiply monomials. TOP: Multiply monomials. KEY: Monomials | Multiply Monomials 18. ANS: Divide powers with the same base by subtracting their exponents. PTS: 1 DIF: Basic NAT: NA 1 | NA 3 | NA 6 | NA 7 | NA 2 KEY: Monomials | Divide Monomials 19. ANS: REF: Lesson 4-5 OBJ: 4-5.2 Divide monomials. TOP: Divide monomials. Divide powers with the same base by subtracting their exponents. PTS: 1 DIF: Average NAT: NA 1 | NA 3 | NA 6 | NA 7 | NA 2 KEY: Monomials | Divide Monomials 20. ANS: The definition of a negative exponent is PTS: OBJ: STA: KEY: 21. ANS: . 1 DIF: Basic REF: Lesson 4-6 4-6.1 Write expressions using negative exponents. NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2 NNSO 3 | PFA 7 TOP: Write expressions using negative exponents. Exponents | Negative Exponents | Write Expressions The definition of a negative exponent is PTS: OBJ: STA: KEY: 22. ANS: REF: Lesson 4-5 OBJ: 4-5.2 Divide monomials. TOP: Divide monomials. . 1 DIF: Average REF: Lesson 4-6 4-6.1 Write expressions using negative exponents. NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2 NNSO 3 | PFA 7 TOP: Write expressions using negative exponents. Exponents | Negative Exponents | Write Expressions Replace the variables with the given values and evaluate using the definition of negative exponents. PTS: OBJ: NAT: TOP: KEY: 23. ANS: 1 DIF: Average REF: Lesson 4-6 4-6.2 Evaluate numerical expressions containing negative exponents. NA 1 | NA 6 | NA 7 | NA 9 | NA 2 STA: NNSO 3 | PFA 7 | PFA 8 Evaluate numerical expressions containing negative exponents. Exponents | Negative Exponents | Evaluate Expressions Replace the variable with the given value and evaluate using the definition of negative exponents. PTS: 1 DIF: Average REF: Lesson 4-6 OBJ: 4-6.2 Evaluate numerical expressions containing negative exponents. NAT: NA 1 | NA 6 | NA 7 | NA 9 | NA 2 STA: NNSO 3 | PFA 7 | PFA 8 TOP: Evaluate numerical expressions containing negative exponents. KEY: Exponents | Negative Exponents | Evaluate Expressions 24. ANS: 9370 If the exponent of 10 is positive, move the decimal point that many places to the right. If it is negative, move the decimal point that many places to the left. PTS: OBJ: NAT: TOP: KEY: 25. ANS: 1 DIF: Average REF: Lesson 4-7 4-7.1 Express numbers in standard form and in scientific notation. NA 1 | NA 4 | NA 7 | NA 9 | NA 2 STA: NNSO 1 Express numbers in standard form and in scientific notation. Standard Form | Scientific Notation Put the decimal point after the first nonzero digit. The number of places the decimal point moved will be the exponent. If the decimal point moved to the left, use a positive exponent; if it moved to the right, use a negative exponent. PTS: 1 DIF: Average REF: Lesson 4-7 OBJ: 4-7.1 Express numbers in standard form and in scientific notation. NAT: NA 1 | NA 4 | NA 7 | NA 9 | NA 2 STA: NNSO 1 TOP: Express numbers in standard form and in scientific notation. KEY: Standard Form | Scientific Notation 26. ANS: California, Texas, Alaska Using the areas written in scientific notation, list the states in order from smallest to largest. PTS: 1 DIF: Average REF: Lesson 4-7 OBJ: 4-7.2 Compare and order numbers written in scientific notation. NAT: NA 1 | NA 4 | NA 7 | NA 9 | NA 2 STA: NNSO 8 TOP: Compare and order numbers written in scientific notation. KEY: Compare Numbers | Order Numbers | Scientific Notation 27. ANS: China, India, USA Using the populations written in scientific notation, list the countries in order from most populous to least populous. PTS: OBJ: NAT: TOP: KEY: 28. ANS: prime 1 DIF: Average REF: Lesson 4-7 4-7.2 Compare and order numbers written in scientific notation. NA 1 | NA 4 | NA 7 | NA 9 | NA 2 STA: NNSO 8 Compare and order numbers written in scientific notation. Compare Numbers | Order Numbers | Scientific Notation Evaluate the value of the given expression by replacing the variable with the given value. Find the factors of the value obtained. If the number has exactly two factors, 1 and itself then the number is prime. Otherwise, it is composite. PTS: 1 DIF: Basic TOP: Solve multi-step problems. 29. ANS: composite REF: Lesson 4-2 OBJ: 4-2.3 Solve multi-step problems. KEY: Multi-step | Problem Solving Evaluate the value of the given expression by replacing the variable with the given value. Find the factors of the value obtained. If the number has exactly two factors, 1 and itself, then the number is prime. Otherwise, it is composite. PTS: 1 DIF: Advanced TOP: Solve multi-step problems. REF: Lesson 4-2 OBJ: 4-2.3 Solve multi-step problems. KEY: Multi-step | Problem Solving