Download Honor`s Pre-Algebra Chapter 4 Test Review Short Answer Write the

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