Download Singapore Chapter 1 Test Review Enriched Pre

Singapore Chapter 1 Test Review (Enriched Pre-Algebra 8)
Short Answer
1. What is
written in exponential notation?
2. What is the expanded form of
?
3. What is the prime factorization of 72 in exponential notation?
4. It takes 120 drops of water to fill a teaspoon. Write the prime factorization of 120 using exponents.
5. Multiply. Write the product as one power.
6. Simplify
.
7. What is
written in simplified form?
8. Divide. Write the quotient as one power.
9. Simplify
.
10. What is
written in simplified form?
11. What is the simplified form of
12. Simplify
.
13. Simplify
14. Simplify
?
.
.
15. What is the simplified form of
?
16. What is the simplified form of
?
17. What is
written with one base and one exponent?
18. What is
written with one base and one exponent?
19. Simplify
20. Simplify
.
.
21. Simplify
.
22. What is
written with one base and one exponent?
23. Simplify
.
24. Evaluate
for
and
.
25. Simplify the expression. Express your answer using a positive exponent.
26. Simplify the expression. Express your answer using a positive exponent.
27. Find the two square roots of the number 144.
28. Find the cube root of 125.
29. What is the value of x in
30. What is the value of x in
? Show your algebraic work.
? Show you algebraic work.
31. Carl is enclosing a square garden with a fence. The area of the garden is 237.16 square feet. How long, in feet,
is each side of the garden? Show your algebraic work.
32. If a sticker is
inches thick and you stick
stickers be? Show your work.
stickers on top of one another, how thick will your stack of
33. If it requires
silkworms to produce enough silk to make a scarf in a given amount of time but it requires
silkworms to produce enough silk to make a sheet in the same amount of time, how many times more
silkworms are needed for the sheet than for the scarf? Show your work.
Singapore Chapter 1 Test Review (Enriched Pre-Algebra 8)
Answer Section
SHORT ANSWER
1. ANS:
In exponential notation, the number being multiplied is the base, and the number of times it is being
multiplied is the exponent. So the base is 4 and the exponent is 5. The expression in exponential notation is
.
PTS: 1
DIF: Average
OBJ: 1-1.1 Understand Exponential Notation
NAT: 8.EE.1
TOP: 1-1 Exponential Notation
KEY: exponential notation | exponent | base
2. ANS:
The expanded form shows the repeated multiplication of a number times itself. In exponential notation, it is
the base that is multiplied by itself the number of times indicated by the exponent. So the base
multiplied by itself 3 times. The expanded form is
is
.
PTS: 1
DIF: Average
OBJ: 1-1.1 Understand Exponential Notation
NAT: 8.EE.1
TOP: 1-1 Exponential Notation
KEY: exponential notation | exponent | base | expanded form
3. ANS:
When finding prime factors of a number, you can begin with just two factors of the number. Continue
factoring until there are only prime factors. Then use exponents to represent multiple identical factors.
So, the prime factorization of 72 is
PTS:
OBJ:
NAT:
KEY:
4. ANS:
.
1
DIF: Average
1-1.2 Use Exponents to Write the Prime Factorization of a Number
8.EE.1
TOP: 1-1 Exponential Notation
prime factorization | exponent | prime
PTS: 1
DIF: Average
OBJ: 1-1.2 Use Exponents to Write the Prime Factorization of a Number
NAT: 8.EE.1
TOP: 1-1 Exponential Notation
KEY: prime factorization | exponent
5. ANS:
To multiply powers with the same base, keep the base and add the exponents.
PTS: 1
DIF: Average
OBJ: 1-2.1 Understand the Product of Powers Property
NAT: 8.EE.1
TOP: 1-2 The Product and the Quotient of Powers
KEY: exponent | power | multiplication | base
6. ANS:
When simplifying an expression that is a product of terms, you can separate the factors of the terms, then
recombine like terms with the same base. Remember, when multiplying like variable terms, keep the common
base and add the exponents.
So, the simplified expression is
PTS:
OBJ:
NAT:
KEY:
7. ANS:
.
1
DIF: Average
1-2.2 Use the Product of Powers Property with Algebraic Expressions
8.EE.1
TOP: 1-2 The Product and the Quotient of Powers
base | exponent | power | product | property
When simplifying an expression that is a product of terms, you can separate the factors of the terms, then
recombine like terms with the same base. Remember, when multiplying like variable terms, keep the common
base and add the exponents.
So, the simplified expression is
PTS:
OBJ:
NAT:
KEY:
8. ANS:
.
1
DIF: Average
1-2.2 Use the Product of Powers Property with Algebraic Expressions
8.EE.1
TOP: 1-2 The Product and the Quotient of Powers
base | exponent | power | product | property
To divide powers with the same base, keep the base and subtract the exponents.
PTS: 1
DIF: Average
OBJ: 1-2.3 Understand the Quotient of Powers Property
NAT: 8.EE.1
TOP: 1-2 The Product and the Quotient of Powers
KEY: exponent | power | division | base
9. ANS:
To simplify an expression that is a quotient of terms, you can first write the expression as a fraction. Then,
separate the fraction into individual factors whose numerator and denominator are like terms. Use the quotient
of powers property to simplify each factor. Be sure to subtract exponents when dividing terms with the same
base.
.
So, the simplified expression is
PTS:
OBJ:
NAT:
KEY:
10. ANS:
.
1
DIF: Average
1-2.4 Use the Quotient of Powers Property with Algebraic Expressions
8.EE.1
TOP: 1-2 The Product and the Quotient of Powers
base | exponent | power | quotient | property
To simplify an expression that is a quotient of terms, you can first write the expression as a fraction. Then,
separate the fraction into individual factors whose numerator and denominator are like terms. Use the quotient
of powers property to simplify each factor. Be sure to subtract exponents when dividing terms with the same
base.
So, the simplified expression is
PTS:
OBJ:
NAT:
KEY:
11. ANS:
.
1
DIF: Average
1-2.4 Use the Quotient of Powers Property with Algebraic Expressions
8.EE.1
TOP: 1-2 The Product and the Quotient of Powers
base | exponent | power | quotient | property
To simplify an expression involving the product and the quotient of powers, use the properties of exponents to
simplify. Be sure add exponents when multiplying powers with the same base, and subtract exponents when
dividing powers with the same base.
So, the simplified expression is
PTS:
OBJ:
NAT:
KEY:
12. ANS:
.
1
DIF: Average
1-2.5 Multiply and Divide Expressions in Exponential Notation
8.EE.1
TOP: 1-2 The Product and the Quotient of Powers
base | exponent | power | product | quotient | property
=
=
PTS: 1
Multiply the exponents.
DIF: Average
OBJ: 1-3.1 Understand Raising a Power to a Power
NAT: 8.EE.1
13. ANS:
TOP: 1-3 The Power of a Power
KEY: exponent | simplify | power
Multiply the exponents.
=
=
PTS: 1
NAT: 8.EE.1
14. ANS:
DIF: Average
OBJ: 1-3.1 Understand Raising a Power to a Power
TOP: 1-3 The Power of a Power
KEY: exponent | simplify | power
Multiply the exponents.
=
=
PTS: 1
NAT: 8.EE.1
15. ANS:
DIF: Average
OBJ: 1-3.1 Understand Raising a Power to a Power
TOP: 1-3 The Power of a Power
KEY: exponent | simplify | power
To simplify, add exponents when multiplying powers with the same base and multiply exponents when
raising a power to a power.
So, the simplified expression is
PTS:
OBJ:
NAT:
KEY:
16. ANS:
.
1
DIF: Average
1-3.2 Use Properties of Exponents to Simplify Expressions
8.EE.1
TOP: 1-3 The Power of a Power
base | exponent | power | product | property
When simplifying an expression with exponents, apply the correct property of exponents to each operation.
Add exponents when multiplying powers with the same base. Subtract exponents when dividing powers with
the same base. And multiply exponents when raising a power to a power.
So, the simplified expression is
PTS:
OBJ:
NAT:
KEY:
17. ANS:
.
1
DIF: Difficult
1-3.2 Use Properties of Exponents to Simplify Expressions
8.EE.1
TOP: 1-3 The Power of a Power
base | exponent | power | product | quotient | property
When you multiply numbers with the same exponent, you can multiply the numbers and the exponent remains
the same.
The expression written with one base and one exponent is
.
PTS: 1
DIF: Average
OBJ: 1-4.1 Understand the Power of a Product Property
NAT: 8.EE.1
TOP: 1-4 The Power of a Product and the Power of a Quotient
KEY: base | exponent | power | product | property
18. ANS:
When you multiply numbers with the same exponent, you can multiply the numbers and the exponent remains
the same.
The expression written with one base and one exponent is
.
PTS: 1
DIF: Average
OBJ: 1-4.1 Understand the Power of a Product Property
NAT: 8.EE.1
TOP: 1-4 The Power of a Product and the Power of a Quotient
KEY: base | exponent | power | product | property
19. ANS:
When dividing numerical expressions with the same exponent, you can divide the numbers and keep the
common exponent.
The simplified expression is
.
PTS: 1
DIF: Average
OBJ: 1-4.2 Understand the Power of a Quotient Property
NAT: 8.EE.1
TOP: 1-4 The Power of a Product and the Power of a Quotient
KEY: base | exponent | power | product | property
20. ANS:
When dividing expressions with the same exponent, you can divide the bases and keep the common exponent.
The simplified expression is
.
PTS: 1
DIF: Average
OBJ: 1-4.2 Understand the Power of a Quotient Property
NAT: 8.EE.1
TOP: 1-4 The Power of a Product and the Power of a Quotient
KEY: base | exponent | power | quotient | property
21. ANS:
When dividing expressions with the same exponent, you can divide the bases and keep the common exponent.
The simplified expression is
.
PTS: 1
DIF: Average
OBJ: 1-4.2 Understand the Power of a Quotient Property
NAT: 8.EE.1
TOP: 1-4 The Power of a Product and the Power of a Quotient
KEY: base | exponent | power | quotient | property
22. ANS:
When simplifying exponential expressions, use the appropriate property of exponents for each operation. To
multiply expressions with the same base, keep the base and add the exponent. To divide expressions with the
same exponent, divide the bases and keep the common exponent.
The expression written with one base and one exponent is
PTS:
OBJ:
NAT:
KEY:
23. ANS:
.
1
DIF: Average
1-4.3 Use Properties of Exponents to Simplify Expressions
8.EE.1
TOP: 1-4 The Power of a Product and the Power of a Quotient
base | exponent | power | product | quotient | property
Rewrite
=
without zero exponents.
=
PTS: 1
DIF: Average
OBJ: 1-5.1 Understand the Zero Exponent
NAT: 8.EE.1
TOP: 1-5 Zero and Negative Exponents
KEY: zero exponent | zero power | simplify | power | exponent
24. ANS:
1
9
Substitute –3 for a and –3 for b.
1
( 9 )(1)
Evaluate expressions with exponents.
1
9
Simplify.
PTS: 1
DIF: Difficult
OBJ: 1-5.1 Understand the Zero Exponent
NAT: 8.EE.1
TOP: 1-5 Zero and Negative Exponents
KEY: zero exponent | zero power | evaluate | power | exponent
25. ANS:
Use the Product of Powers property, and simplify.
PTS: 1
NAT: 8.EE.1
26. ANS:
DIF: Average
OBJ: 1-5.2 Understand Negative Exponents
TOP: 1-5 Zero and Negative Exponents KEY: negative exponent | simplify
Rewrite using a positive exponent, and simplify.
PTS: 1
DIF: Average
OBJ: 1-5.2 Understand Negative Exponents
NAT: 8.EE.1
TOP: 1-5 Zero and Negative Exponents KEY: negative exponent | simplify
27. ANS:
12, –12
The square root of a number is another number that, when multiplied by itself, equals the first number.
12 is a square root, since
= 144.
–12 is also a square root, since
= 144.
PTS: 1
DIF: Average
OBJ: 1-6.1 Evaluate Square Roots of Positive Real Numbers
NAT: 8.EE.2
TOP: 1-6 Real-World Problems: Squares and Cubes
KEY: square | square root | positive | negative
28. ANS:
5
The cube root of a number is a number that, when multiplied by itself 3 times, results in the original number.
The cube root of 125 is 5.
PTS: 1
NAT: 8.EE.2
DIF: Average
OBJ: 1-6.2 Evaluate Cube Roots of Positive Real Numbers
TOP: 1-6 Real-World Problems: Squares and Cubes
KEY: cube root | real number
29. ANS:
3.2 or –3.2
To solve for x, take the square root of both sides of the equation. The square root of a number is a number
that, when multiplied by itself, results in the original number. Remember that square roots can be both
positive and negative numbers.
The value of x is 3.2 or –3.2.
PTS: 1
DIF: Average
OBJ: 1-6.3 Solve Equations Involving Squares and Cubes of Variables
NAT: 8.EE.2
TOP: 1-6 Real-World Problems: Squares and Cubes
KEY: square root | equation
30. ANS:
8
To solve for x, take the cube root of both sides of the equation. The cube root of a number is a number that,
when multiplied by itself 3 times, results in the original number.
The cube root of 512 is 8.
PTS: 1
DIF: Average
OBJ: 1-6.3 Solve Equations Involving Squares and Cubes of Variables
NAT: 8.EE.2
TOP: 1-6 Real-World Problems: Squares and Cubes
KEY: equation | cube root
31. ANS:
15.4
The area of a square is side length times side length, or side squared. To solve this problem, write an equation
using x as the side length. Then solve the equation for x by taking the square root of both sides. Since you are
looking for a side length, negative values will not apply.
The length of each side of the garden is 15.4 feet.
PTS: 1
DIF: Average
OBJ: 1-6.4 Solve Real-World Problems Involving Squares and Cubes
NAT: 8.EE.2
TOP: 1-6 Real-World Problems: Squares and Cubes
KEY: square | cube
32. ANS:
It will be 2 inches thick.
The bases are the same, so add the exponents.
PTS: 1
DIF: Average
OBJ: 1-2.1 Understand the Product of Powers Property
NAT: 8.EE.1
TOP: 1-2 The Product and the Quotient of Powers
KEY: exponent | power | multiplication | base
33. ANS:
It requires
times more silkworms for the sheet than for the scarf.
“
times some number x equals
Divide both sides by
.”
.
Since the bases are the same, subtract the exponents.
PTS: 1
DIF: Difficult
OBJ: 1-2.3 Understand the Quotient of Powers Property
NAT: 8.EE.1
TOP: 1-2 The Product and the Quotient of Powers
KEY: exponent | power | division | base