Unit 1 Test chp1-3(3rd/4th period)

Unit 1 Test chp1-3 enr

Multiple Choice

Identify the letter of the choice that best completes the statement or answers the question.

Use the four-step plan to solve each problem.

____ 1. Michelle sold 62 coupon books for a school trip fundraiser, and Lorenzo sold 97 coupon books. About how many more coupon books did Lorenzo sell than Michelle?

100

Evaluate each expression.

____ 2. 9 – 30 · 6

–126

–171

____ 3. |3|

(–3)

–3

____ 4. |28| + |20|

–8

–48

Evaluate each expression if a = 3, b = 5, and c = 9.

____ 5. 6a – 4b – 6c

–56

–12

Name the property shown by each statement.

____ 6. (3 + 8)6 = 3(6) + 8(6)

a.	Associative Property of Addition
b.	Distributive Property
c.	Commutative Property of Multiplication
d.	Additive Identity Property

____ 7.

a.	Commutative Property of Multiplication
b.	Distributive Property
c.	Multiplicative Identity Property
d.	Associative Property of Addition

____ 8. 25 + (4 + 16) = (25 + 4) + 16

a.	Commutative Property of Addition	c.	Additive Identity Property
b.	Distributive Property	d.	Associative Property of Addition

____ 9. 8 + 0 = 8

a.	Multiplicative Identity Property	c.	Commutative Property of Addition
b.	Distributive Property	d.	Additive Identity Property

Graph each set of integers on a number line.

____ 10. {–8, –1, 3, 4, –6}

a.
b.
c.
d.

Order the integers in each set from least to greatest.

____ 11. {–63, 90, –7, 10, –53}

a.	{7, 10, 53, 63, 90}	c.	{–7, –53, 90, –63, 10}
b.	{90, 10, –7, –53, –63}	d.	{–63, –53, –7, 10, 90}

Add.

____ 12. –31 + 54

–85

Subtract.

____ 13. –5 – 6

–11

–1

Multiply.

____ 14. –3(–3)

–9

–6

Divide.

____ 15. 35 ÷ (–5)

–7

–8

____ 16.

–30

–9

Write each verbal phrase as an algebraic expression.

____ 17. 7 points less than the class average

x + 7

7 – x

x – 7

____ 18. 75 decreased by a

a – 75

75 + a

75 – a

75a

Write each verbal sentence as an algebraic equation.

____ 19. 9 more than a number is equal to 30.

n – 9 = 30

n + 9 = 30

9 – n = 30

9n = 30

____ 20. –2 is three times a number.

–2 = 3n

–2 = n ÷ 3

–2 = 3 + n

–2n = 3

Solve each equation. Check your solution.

____ 21. b + 7 = –17

–24

–10

____ 22. –252 = 18p

–14

____ 23.

–77

____ 24.

a.	0.93	c.	–0.93
b.	5.57	d.	–5.57

____ 25. x – =

a.		c.
b.		d.

____ 26.

a.		c.	3
b.	–5.48	d.	–2.74

Write each fraction as a decimal.

____ 27.

a.	0.16	c.	6
b.		d.

____ 28. –

a.	–0.625	c.	– 0.58
b.	0.625	d.	–1.6

Write each mixed number as a decimal.

____ 29.

a.		c.	–1.5
b.	1.5	d.	0.32

____ 30. –

a.		c.	–0.53
b.		d.	–0.6

Write each decimal as a fraction in simplest form.

____ 31. 0.2

a.		c.
b.		d.

____ 32. –0.25

a.		c.
b.		d.

Write each decimal as a mixed number in simplest form.

____ 33.

a.		c.
b.		d.

____ 34.

a.		c.
b.		d.

Replace eachwith <, >, or =.

____ 35. –0.5

a.	<
b.	=
c.	>

____ 36.

a.	<
b.	=
c.	>

____ 37. Order this set of rational numbers from least to greatest.

–2.7, , ,

a.	, , , –2.7	c.	, , –2.7,
b.	, , , –2.7	d.	, , –2.7,

Find each product. Write in simplest form.

____ 38. ´

a.		c.
b.		d.

____ 39. ´

a.		c.
b.		d.

Find each quotient. Write in simplest form.

____ 40. ¸

a.		c.
b.		d.

____ 41. ¸

a.		c.
b.		d.

Find each sum or difference. Write in simplest form.

____ 42. +

a.		c.
b.		d.

____ 43. -

a.		c.
b.		d.

____ 44. -

a.		c.
b.		d.

____ 45. +

a.		c.
b.		d.

____ 46. +

a.		c.
b.		d.

____ 47. +

a.		c.
b.		d.

____ 48. +

a.		c.
b.		d.

Write each expression using exponents.

____ 49. 2 · 2 · 2 · 2 · 2

a.		c.
b.		d.

____ 50. a · a · a · a

a.		c.
b.		d.

____ 51. 8 · 3 · 3 · 3 · 3 · 8 · 8 · 8 · 3

a.		c.
b.		d.

Write each number in scientific notation.

____ 52. 2,825

a.		c.
b.		d.

____ 53. 0.2447

a.		c.
b.		d.

Find each square root.

____ 54.

a.		c.
b.		d.

Estimate to the nearest whole number.

____ 55.

a.	8	c.	7
b.	6	d.	3

Name all sets of numbers to which each real number belongs.

____ 56.

a.	Real and irrational
b.	Real and rational.
c.	Real, rational, and integer
d.	Real, rational, integer, and whole

____ 57.

a.	Real, rational, integer, and whole	c.	Real and irrational
b.	Real, rational, and integer	d.	Real and rational

____ 58. Write an equation you could use to find the length of the missing side of each right triangle. Then find the missing length. Round to the nearest tenth if necessary.

a.	16 cm	c.	256 cm
b.	45.34 cm	d.	4 cm

____ 59. Write an equation you could use to find the length of the missing side of each right triangle. Then find the missing length. Round to the nearest tenth if necessary.

a.	2 ft	c.	4 ft
b.	16 ft	d.	5.83 ft

____ 60. Find the distance between each pair of points whose coordinates are given. Round to the nearest tenth if necessary.

a.	2.8	c.	1.8
b.	3.8	d.	5.7

Unit 1 Test chp1-3 enr

Answer Section

MULTIPLE CHOICE

1. ANS: D

Round each number of coupon books sold to the nearest ten and find the difference.

100 – 60 = 40

DIF: Basic OBJ: 1-1.1 Solve problems by using the four-step plan.

TOP: Solve problems by using the four-step plan.

KEY: Four-step plan, Problem solving

NOT: /a/ This is the approximate number of coupon books sold by Michelle. How does this number compare with the approximate number sold by Lorenzo? /b/ Use the four-step plan to set up a subtraction problem. /c/ This is the approximate number of coupon books sold by Lorenzo. How does this number compare with the approximate number sold by Michelle? /d/ Correct!

2. ANS: D

Use the order of operations to simplify the expression.

Sample:

6 – 10 ÷ 5

6 – 2

DIF: Basic OBJ: 1-2.1 Evaluate expressions.

STO: 8.1.1.i, 8.1.2.d, 8.2.2.c, 8.2.2.f TOP: Evaluate expressions.

KEY: Evaluating expressions, Expressions

NOT: /A/ Apply the order of operations to simplify the expression./B/ Apply the order of operations to simplify the expression. /C/ In the order of operations, multiplication and division are performed before addition and subtraction. /D/ Correct!

3. ANS: D

The absolute value of a number is that number’s distance from zero on the number line.

Sample:

|–15| = 15

DIF: Basic OBJ: 1-3.3 Find absolute value. TOP: Find absolute value.

KEY: Absolute value, Distance

NOT: /A/ The absolute value of a number is always positive. /B/ The absolute value of a number is the distance from the number to 0 on the number line./C/ The absolute value of a number is always positive. /D/ Correct!

4. ANS: B

Take the absolute value of both numbers before performing the addition or subtraction

Sample:

|–11| – |–8|

11 – 8

DIF: Average OBJ: 1-3.3 Find absolute value. TOP: Find absolute value.

KEY: Absolute value, Distance

NOT: /A/ Take the absolute value of both numbers before performing the addition or subtraction./B/ Correct! /C/ Take the absolute value of both numbers before performing the addition or subtraction. /D/ Be careful with your signs and try again.

5. ANS: B

Substitute the appropriate values and simplify.

Sample:

DIF: Basic OBJ: 1-2.2 Evaluate algebraic expressions.

STO: 8.1.1.i, 8.1.2.d, 8.2.2.c, 8.2.2.f TOP: Evaluate algebraic expressions.

KEY: Evaluating expressions, Algebraic expressions

NOT: /A/ Check your signs and try again. /B/ Correct! /C/ Substitute for each unknown and use the order of operations to simplify the expression. /D/ Be sure to substitute the correct values for a, b, and c.

6. ANS: B

The 6 is distributed over the sum of 3 + 8.

DIF: Average OBJ: 1-2.3 Identify properties. TOP: Identify properties.

KEY: Identifying properties, Properties

NOT: /a/ The Associative Property of Addition shows that the order of the terms does not affect the sum. /b/ Correct! /c/ The factors in the product do not change order. /d/ The Additive Identity Property shows that when 0 is added to a term, the result of the addition is the original term.

7. ANS: A

The order of the factors in the multiplication is changed.

DIF: Average OBJ: 1-2.3 Identify properties. TOP: Identify properties.

KEY: Identifying properties, Properties

NOT: /a/ Correct! /b/ The Distributive Property involves a multiplication where one of the factors is a sum. /c/ The Multiplicative Identity Property shows that the product of a factor and 1 is simply the factor. /d/ There is no addition in the problem.

8. ANS: D

The order of the terms does not change, only the position of the grouping symbols changes.

DIF: Average OBJ: 1-2.3 Identify properties. TOP: Identify properties.

KEY: Identifying properties, Properties

NOT: /a/ The order of the terms does not change, only the position of the grouping symbols changes. /b/ The Distributive Property involves a multiplication where one of the factors is a sum. /c/ The Additive Identity Property shows that the sum of 0 and a term is simply the term. /d/ Correct!

9. ANS: D

When 0 is added to a term, the result of the addition is the original term.

DIF: Basic OBJ: 1-2.3 Identify properties. TOP: Identify properties.

KEY: Identifying properties, Properties

NOT: /a/ There is no multiplication in the problem. /b/ The Distributive Property involves multiplication over a sum. /c/ The terms of the sum do not change order. /d/ Correct!

10. ANS: C

DIF: Average OBJ: 1-3.1 Graph integers on a number line.

STO: 8.1.1.g, 8.1.1.l, 8.1.1.n TOP: Graph integers on a number line.

KEY: Graphing integers, Number line

NOT: /A/ Carefully double check each point and try again. /B/ Check your signs and try again. /C/ Correct! /D/ Check your signs and try again.

11. ANS: D

The smallest integer is the negative integer with the largest absolute value. The greatest integer is the positive integer with the largest absolute value.

{–63, –53, –7, 10, 90}

DIF: Average OBJ: 1-3.2 Order integers from least to greatest.

STO: 8.1.1.g, 8.1.1.l, 8.1.1.n TOP: Order integers from least to greatest.

KEY: Integers, Ordering integers

NOT: /A/ The instructions do not ask you to order the absolute values of the integers. Try again. /B/ The instructions are to order the integers from least to greatest./C/ The smallest integer is the negative integer with the largest absolute value. The greatest integer is the positive integer with the largest absolute value. /D/ Correct!

12. ANS: C

To add integers with different signs, subtract their absolute values. Keep the sign of the integers with the greatest absolute value.

Sample:

–43 + 59

DIF: Basic OBJ: 1-4.1 Add integers. STO: 8.1.3.b

TOP: Add integers. KEY: Addition, Integers

NOT: /A/ To add integers with different signs, subtract their absolute values. /B/ To add integers with different signs, subtract their absolute values./C/ Correct! /D/ To add integers with different signs, subtract their absolute values.

13. ANS: A

To subtract an integer, add its additive inverse.

Sample:

4 – 9

4 + (–9)

–5

DIF: Basic OBJ: 1-5.1 Subtract integers. STO: 8.1.1.l, 8.1.3.b

TOP: Subtract integers. KEY: Subtraction, Integers

NOT: /A/ Correct! /B/ Check your sign and try again. /C/ To subtract an integer, add its additive inverse./D/ To subtract an integer, add its additive inverse.

14. ANS: B

The product of two integers with the same sign is positive. The product of two integers with different signs is negative.

Sample:

2(11)

DIF: Average OBJ: 1-6.1 Multiply integers. STO: 8.1.1.l, 8.1.3.b

TOP: Multiply integers. KEY: Multiplication, Integers

NOT: /A/ Double check your product. Remember, multiplication is simply repeated addition. /B/ Correct! /C/ The product of two integers with the same sign is positive. The product of two integers with different signs is negative. /D/ The instructions are to multiply the integers, not to add them.

15. ANS: C

The quotient of two integers with the same sign is positive. The quotient of two integers with different signs is negative.

Sample:

45 ÷ (–5)

–9

DIF: Average OBJ: 1-6.2 Divide integers. STO: 8.1.1.l, 8.1.3.b

TOP: Divide integers. KEY: Division, Integers

NOT: /A/ The quotient of two integers with the same sign is positive. The quotient of two integers with different signs is negative. /B/ The instructions say to divide the integers, not to add them. /C/ Correct! /D/ Be careful with your division. You can check your work by multiplying your quotient by the second integer. The result should be the first integer.

16. ANS: B

The quotient of two integers with the same sign is positive. The quotient of two integers with different signs is negative.

Sample:

DIF: Average OBJ: 1-6.2 Divide integers. STO: 8.1.1.l, 8.1.3.b

TOP: Divide integers. KEY: Division, Integers

NOT: /A/ Divide the integer in the numerator by the integer in the denominator./B/ Correct! /C/ Be careful with your division. You can check your work by multiplying your quotient by the second integer. The result should be the first integer. /D/ The quotient of two integers with the same sign is positive. The quotient of two integers with different signs is negative.

17. ANS: D

The phrase “less than” indicates subtraction.

x – 7

DIF: Average OBJ: 1-7.1 Write algebraic expressions from verbal phrases and sentences.

TOP: Write algebraic expressions from verbal phrases and sentences.

KEY: Write expressions, Algebraic expressions

NOT: /a/ What operation is indicated by the phrase “less than”? /b/ Should you subtract from the class average or from 7? /c/ What operation is indicated by the phrase “less than”? /d/ Correct!

18. ANS: C

The phrase “decreased by” indicates subtraction.

75 – a

DIF: Average OBJ: 1-7.1 Write algebraic expressions from verbal phrases and sentences.

TOP: Write algebraic expressions from verbal phrases and sentences.

KEY: Write expressions, Algebraic expressions

NOT: /a/ Is this “75 decreased by a” or “a decreased by 75″? /b/ What operation is indicated by the phrase “decreased by”? /c/ Correct! /d/ What operation is indicated by the phrase “decreased by”?

19. ANS: B

The phrase “more than” indicates addition.

n + 9 = 30

DIF: Basic OBJ: 1-7.2 Write algebraic equations from verbal phrases and sentences.

TOP: Write algebraic equations from verbal phrases and sentences.

KEY: Write equations, Algebraic equations

NOT: /a/ What operation is indicated by the phrase “more than”? /b/ Correct! /c/ What operation is indicated by the phrase “more than”? /d/ What operation is indicated by the phrase “more than”?

20. ANS: A

The keyword “times” indicates multiplication.

–2 = 3n

DIF: Average OBJ: 1-7.2 Write algebraic equations from verbal phrases and sentences.

TOP: Write algebraic equations from verbal phrases and sentences.

KEY: Write equations, Algebraic equations

NOT: /a/ Correct! /b/ What operation is indicated by the keyword “times”? /c/ What operation is indicated by the keyword “times”? /d/ The keyword “is” indicates equality. Note its position in the sentence.

21. ANS: A

Use the Subtraction Property of Equality.

Sample:

DIF: Basic OBJ: 1-8.1 Solve equations using the Subtraction Property of Equality.

TOP: Solve equations using the Subtraction Property of Equality.

KEY: Subtraction property, Solving equations

NOT: /A/ Correct! /B/ Use subtraction to undo the addition on the left hand side of the equation./C/ Be careful with your signs! /D/ Use subtraction to undo the addition on the left hand side of the equation.

22. ANS: C

Use the Division Property of Equality.

Sample:

DIF: Average OBJ: 1-9.1 Solve equations using the Division Property of Equality.

TOP: Solve equations using the Division Property of Equality.

KEY: Division property, Solving equations

NOT: /A/ Use the Division Property of Equality to undo the multiplication on the right hand side of the equation. /B/ Be careful with your signs!/C/ Correct! /D/ Use the Division Property of Equality to undo the multiplication on the right hand side of the equation.

23. ANS: D

Use the Multiplication Property of Equality.

Sample:

DIF: Average OBJ: 1-9.2 Solve equations using the Multiplication Property of Equality.

TOP: Solve equations using the Multiplication Property of Equality.

KEY: Multiplication property, Solving equations

NOT: /A/ Be careful with your signs!/B/ Use the Multiplication Property of Equality to undo the division on the right hand side of the equation. /C/ Use the Multiplication Property of Equality to undo the division on the right hand side of the equation. /D/ Correct!

24. ANS: B

To solve equations involving rational numbers with addition and subtraction, use the addition and subtraction properties of equality to obtain an equivalent equation with the variable alone on one side.

DIF: Basic

OBJ: 2-7.1 Solve equations involving rational numbers with addition and subtraction.

STO: 8.1.3.e, 8.1.3.g

TOP: Solve equations involving rational numbers with addition and subtraction.

KEY: Rational numbers, Solving equations

NOT: /A/ Should you add or subtract from both sides? /B/ Correct! /C/ Did you check your solution?/D/ Were you careful with sign rules?

25. ANS: A

DIF: Average

OBJ: 2-7.1 Solve equations involving rational numbers with addition and subtraction.

STO: 8.1.3.e, 8.1.3.g

TOP: Solve equations involving rational numbers with addition and subtraction.

KEY: Rational numbers, Solving equations

NOT: /A/ Correct! /B/ Did you check your solution?/C/ Should you add or subtract from both sides? /D/ Did you rename your fractions with a common denominator?

26. ANS: C

To solve equations involving rational numbers with multiplication and division, use the multiplication and division properties of equality to obtain the variable alone on one side.

DIF: Average

OBJ: 2-7.2 Solve equations involving rational numbers with multiplication and division.

STO: 8.1.3.e, 8.1.3.g

TOP: Solve equations involving rational numbers with multiplication and division.

KEY: Rational numbers, Solving equations

NOT: /A/ Are you sure you divided by the correct number? /B/ How should you undo the multiplication?/C/ Correct! /D/ Did you use multiplication or division?

27. ANS: D

Any fraction can be expressed as a decimal by dividing the numerator by the denominator. You can use bar notation to indicate repeating digits.

DIF: Average OBJ: 2-1.1 Express fractions as decimals.

STO: 8.1.1.e TOP: Express fractions as decimals. KEY: Fractions, Decimals

NOT: /A/ Did you use a math operation? /B/ Should the value of the fraction be less than or greater than one-half?/C/ Is that answer reasonable? /D/ Correct!

28. ANS: A

Any fraction can be expressed as a decimal by dividing the numerator by the denominator. You can use bar notation to indicate repeating digits.

DIF: Average OBJ: 2-1.1 Express fractions as decimals.

STO: 8.1.1.e TOP: Express fractions as decimals. KEY: Fractions, Decimals

NOT: /A/ Correct! /B/ Are you remembering the rules for dividing signed numbers?/C/ Did you use a math operation? /D/ Is that answer reasonable?

29. ANS: B

Any mixed number can be expressed as a decimal by first converting the mixed number to an improper fraction, and then dividing the numerator by the denominator. You can use bar notation to indicate repeating digits.

DIF: Average OBJ: 2-1.2 Express mixed numbers as decimals.

STO: 8.1.1.e TOP: Express mixed numbers as decimals.

KEY: Mixed numbers, Decimals

NOT: /A/ Is that answer reasonable? /B/ Correct! /C/ Are you remembering the rules for dividing signed numbers?/D/ Did you use a math operation?

30. ANS: B

DIF: Average OBJ: 2-1.2 Express mixed numbers as decimals.

STO: 8.1.1.e TOP: Express mixed numbers as decimals.

KEY: Mixed numbers, Decimals

NOT: /A/ Are you remembering the rules for dividing signed numbers? /B/ Correct! /C/ Did you use a math operation?/D/ Is that answer reasonable?

31. ANS: A

To express a decimal as a fraction, write the decimal as a fraction with a denominator that is a power of ten. Simplify. If it is a repeating decimal, use the method in your book.

DIF: Basic OBJ: 2-1.3 Express decimals as fractions.

STO: 8.1.1.e TOP: Express decimals as fractions. KEY: Decimals, Fractions

NOT: /A/ Correct! /B/ Be careful with sign rules. /C/ Did you express the decimal as a fraction and simplify?/D/ Did you express the decimal as a fraction and simplify?

32. ANS: A

To express a decimal as a fraction, write the decimal as a fraction with a denominator that is a power of ten. Simplify. If it is a repeating decimal, use the method in your book.

DIF: Basic OBJ: 2-1.3 Express decimals as fractions.

STO: 8.1.1.e TOP: Express decimals as fractions. KEY: Decimals, Fractions

NOT: /A/ Correct! /B/ Be careful with sign rules. /C/ Did you express the decimal as a fraction and simplify?/D/ Did you express the decimal as a fraction and simplify?

33. ANS: D

To write a decimal as a mixed number, keep the digits left of the decimal, and convert the decimal part to a fraction. Unless it is repeating, you can write it as a fraction with the denominator being a power of 10. If it is repeating, use the method in your textbook.

DIF: Average OBJ: 2-1.4 Express mixed numbers as fractions.

STO: 8.1.1.e TOP: Express mixed numbers as fractions.

KEY: Mixed numbers, Fractions

NOT: /A/ Should the answer be less than one? /B/ Does the fraction part of this answer equal the decimal part of the question?/C/ Can you convert to a mixed number? /D/ Correct!

34. ANS: B

DIF: Average OBJ: 2-1.4 Express mixed numbers as fractions.

STO: 8.1.1.e TOP: Express mixed numbers as fractions.

KEY: Mixed numbers, Fractions

NOT: /A/ Does the fraction part of this answer equal the decimal part of the question?/B/ Correct! /C/ Can you convert to a mixed number? /D/ If the decimal repeats, how do you eiliminate the repeating part? If the decimal terminates, try saying the number and writing what you hear in fractional form. Then reduce.

35. ANS: C

Express both fractions as decimals and compare the decimals.

DIF: Average OBJ: 2-2.1 Compare rational numbers. STO: 8.1.1.e

TOP: Compare rational numbers. KEY: Rational numbers, Comparing rational numbers

NOT: /A/ Did you compare them as decimals? /B/ Did you compare them as decimals?/C/ Correct!

36. ANS: A

Express the fractions with common denominators or as decimals, then compare.

DIF: Average OBJ: 2-2.1 Compare rational numbers. STO: 8.1.1.e

TOP: Compare rational numbers. KEY: Rational numbers, Comparing rational numbers

NOT: /A/ Correct! /B/ Did you compare them as decimals or with common denominators? /C/ Did you compare them as decimals or with common denominators?

37. ANS: B

To order rational numbers written as decimals, compare the decimals to the same number of places.

DIF: Average OBJ: 2-2.2 Order rational numbers. STO: 8.1.1.e

TOP: Order rational numbers. KEY: Rational numbers, Ordering rational numbers

NOT: /A/ Write all numbers as decimals and then compare./B/ Correct! /C/ Would that be the order on a number line? /D/ Compare the decimals carefully.

38. ANS: A

To multiply fractions, multiply the numerators and multiply the denominators. Use the rules for multiplying integers. Write your answer in simplest form.

DIF: Basic OBJ: 2-3.1 Multiply fractions. STO: 8.1.3.b, 8.1.3.e, 8.1.3.f

TOP: Multiply fractions. KEY: Multiplication, Fractions

NOT: /a/ Correct! /b /What are the rules for multiplying fractions? /c/ Did you multiply the second fraction by the reciprocal of the first? /d/ Did you multiply the first fraction by the reciprocal of the second?

39. ANS: C

To multiply mixed numbers, convert both factors to improper fractions. Then multiply the numerators and denominators. Simplify.

DIF: Average OBJ: 2-3.2 Multiply mixed numbers. STO: 8.1.3.b, 8.1.3.e, 8.1.3.f

TOP: Multiply mixed numbers. KEY: Multiplication, Mixed numbers

NOT: /A/ Did you multiply the reciprocals after converting to improper fractions? /B/ Did you multiply the second fraction by the reciprocal of the first?/C/ Correct! /D/ Is that the product or the quotient?

40. ANS: D

To divide by a fraction, multiply by its multiplicative inverse.

DIF: Basic OBJ: 2-4.1 Divide fractions.

STO: 8.1.3.b, 8.1.3.e, 8.1.3.f TOP: Divide fractions.

KEY: Division, Fractions

NOT: /A/ Is this the quotient or the product?/B/ Did you divide the second fraction by the first? /C/ Is this the sum of the two fractions? /D/ Correct!

41. ANS: B

To divide mixed numbers, change both of them to fractions. Then multiply the first by the multiplicative inverse of the second.

DIF: Average OBJ: 2-4.2 Divide mixed numbers. STO: 8.1.3.b, 8.1.3.e, 8.1.3.f

TOP: Divide mixed numbers. KEY: Division, Mixed numbers

NOT: /A/ You multiplied the second fraction by the multiplicative inverse of the first./B/ Correct! /C/ Did you add instead of divide? /D/ Is that the product or the quotient?

42. ANS: C

To add fractions with like denominators, add the numerators.

DIF: Basic OBJ: 2-5.1 Add fractions with like denominators.

STO: 8.1.3.b, 8.1.3.e, 8.1.3.f TOP: Add fractions with like denominators.

KEY: Fractions, Like denominators

NOT: /A/ Did you add the denominators? /B/ Is that the product?/C/ Correct! /D/ That is the difference.

43. ANS: A

To subtract mixed numbers with like denominators, subtract the whole numbers and subtract the fractions. Use the rules for subtracting signed numbers. Simplify.

DIF: Average OBJ: 2-5.4 Subtract mixed numbers with like denominators.

STO: 8.1.3.b, 8.1.3.e, 8.1.3.f

TOP: Subtract mixed numbers with like denominators.

KEY: Mixed numbers, Like denominators

NOT: /A/ Correct! /B/ Did you divide? Watch your sign rules./C/ Did you multiply? Watch your sign rules. /D/ Did you add? Watch your sign rules.

44. ANS: D

To subtract mixed numbers with like denominators, subtract the whole numbers and subtract the fractions. Use the rules for subtracting signed numbers. Simplify.

DIF: Average OBJ: 2-5.4 Subtract mixed numbers with like denominators.

STO: 8.1.3.b, 8.1.3.e, 8.1.3.f

TOP: Subtract mixed numbers with like denominators.

KEY: Mixed numbers, Like denominators

NOT: /A/ Did you add? Watch your sign rules. /B/ Did you divide? Watch your sign rules./C/ Did you multiply? Watch your sign rules. /D/ Correct!

45. ANS: C

To find the sum of two fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify, if necessary.

DIF: Basic OBJ: 2-6.1 Add fractions with unlike denominators.

STO: 8.1.3.b, 8.1.3.e, 8.1.3.f TOP: Add fractions with unlike denominators.

KEY: Fractions, Unlike denominators

NOT: /A/ Did you add the numerators and add the denominators? /B/ That is the product. /C/ Correct! /D/ Did you rename the fractions with a common denominator?

46. ANS: B

To find the sum of two fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify, if necessary.

DIF: Average OBJ: 2-6.1 Add fractions with unlike denominators.

STO: 8.1.3.b, 8.1.3.e, 8.1.3.f TOP: Add fractions with unlike denominators.

KEY: Fractions, Unlike denominators

NOT: /A/ Is that the product. Be careful with rules for signed numbers. /B/ Correct! /C/ Did you rename the fractions with a common denominator?/D/ Did you add the numerators and add the denominators?

47. ANS: C

To find the sum of two mixed numbers with unlike denominators, rename the fractions with a common denominator. Then add the whole numbers and add the fractions. Observe rules for adding signed numbers. Simplify.

DIF: Average OBJ: 2-6.2 Add mixed numbers with unlike denominators.

STO: 8.1.3.b, 8.1.3.e, 8.1.3.f TOP: Add mixed numbers with unlike denominators.

KEY: Mixed numbers, Unlike denominators

NOT: /A/ When adding fractions do you need to add the denominators?/B/ That is the product. /C/ Correct! /D/ Is that the sum?

48. ANS: A

DIF: Average OBJ: 2-6.2 Add mixed numbers with unlike denominators.

STO: 8.1.3.b, 8.1.3.e, 8.1.3.f TOP: Add mixed numbers with unlike denominators.

KEY: Mixed numbers, Unlike denominators

NOT: /A/ Correct! /B/ When adding fractions do you need to add the denominators?/C/ That is the product. /D/ Is that the sum?

49. ANS: D

The common factor is the base. The exponent is the number of times the common factor is used as a factor.

DIF: Basic OBJ: 2-8.1 Use powers in expressions. STO: 8.1.1.b, 8.1.1.k

TOP: Use powers in expressions. KEY: Powers, Exponents

NOT: /A/ Which is the base and which is the exponent? /B/ That would be one over the product of factors./C/ Count the number of factors. /D/ Correct!

50. ANS: A

The common factor is the base. The exponent is the number of times the common factor is used as a factor.

DIF: Basic OBJ: 2-8.1 Use powers in expressions. STO: 8.1.1.b, 8.1.1.k

TOP: Use powers in expressions. KEY: Powers, Exponents

NOT: /A/ Correct! /B/ Count the number of factors. /C/ Which is the base and which is the exponent? /D/ That would be one over the product of factors.

51. ANS: B

The common factor is the base. The exponent is the number of times the common factor is used as a factor.

DIF: Average OBJ: 2-8.2 Use exponents in expressions.

STO: 8.1.1.b, 8.1.1.k TOP: Use exponents in expressions.

KEY: Powers, Exponents

NOT: /A/ Which are the bases and which are the exponents? /B/ Correct! /C/ Count the number of factors. /D/ This would be one over the product of the factors.

52. ANS: D

When a number is expressed in scientific notation, it is written as a product of a factor and a power of 10. The factor must be greater than or equal to 1 and less than 10. Multiplying by a positive power of 10 moves the decimal point to the right the same number of places as the exponent.

DIF: Average OBJ: 2-9.1 Express numbers in scientific notation.

STO: 8.1.1.b, 8.1.1.k TOP: Express numbers in scientific notation.

KEY: Scientific notation, Numbers

NOT: /A/ Be careful counting places./B/ Be careful counting places. /C/ Did you move the decimal right or left? /D/ Correct!

53. ANS: B

When a number is expressed in scientific notation, it is written as a product of a factor and a power of 10. The factor must be greater than or equal to 1 and less than 10. Multiplying by a negative power of 10 moves the decimal point to the left the same number of places as the absolute value of the exponent.

DIF: Average OBJ: 2-9.1 Express numbers in scientific notation.

STO: 8.1.1.b, 8.1.1.k TOP: Express numbers in scientific notation.

KEY: Scientific notation, Numbers

NOT: /A/ Count decimal places carefully./B/ Correct! /C/ Count places carefully. /D/ Did you move the decimal right or left?

54. ANS: B

If x² = y then x is a square root of y. You must do this for the numerator and the denominator.

DIF: Average OBJ: 3-1.1 Find square roots of perfect squares.

STO: 8.1.1.c, 8.1.2.e TOP: Find square roots of perfect squares.

KEY: Square roots, Perfect squares

NOT: /A/ Finding the square root of a number is the inverse of squaring a number. /B/ Correct! /C/ Finding the square root of a number is the inverse of squaring a number./D/ You must take the square root of the numerator and the denominator.

55. ANS: C

Use the perfect squares above and below. Choose the perfect square that is closest to the given square root. You may want to use a number line to illustrate proximity.

DIF: Basic OBJ: 3-2.1 Estimate square roots. TOP: Estimate square roots.

KEY: Estimate square roots, Square roots

NOT: /A/ Your estimate is too high. /B/ Your estimate is too low. /C/ Correct! /D/ Remember a square is a number multiplied by itself.

56. ANS: C

Rational numbers are numbers that can be expressed as the quotient of two integers. As decimals, rational numbers will either repeat or terminate. Irrational numbers as decimals will not repeat or terminate.

DIF: Average OBJ: 3-3.1 Identify numbers in the real number system.

STO: 8.1.1.d, 8.1.1.g TOP: Identify numbers in the real number system.

KEY: Real numbers, Identify numbers

NOT: /A/ Irrational numbers will not terminate or repeat as decimals. /B/ Integers are of the set {…-2, -1, 0, 1, 2, …}/C/ Correct! /D/ Whole numbers are of the set {0, 1, 2, …}

57. ANS: B

Real numbers are all rational and irrational numbers. Rational numbers are any number that can be expressed as the quotient of two integers. Integers are the numbers {…-3, -2, -1, 0, 1, 2, 3, …}. Whole numbers are the integer values greater than or equal to zero. Therefore a negative number cannot be a whole number.

DIF: Average OBJ: 3-3.1 Identify numbers in the real number system.

STO: 8.1.1.d, 8.1.1.g TOP: Identify numbers in the real number system.

KEY: Real numbers, Identify numbers

NOT: /A/ Whole numbers are of the set {0, 1, 2, …} /B/ Correct! /C/ Irrational numbers cannot be expressed as the quotient of two integers./D/ Integers are of the set {…-2, -1, 0, 1, 2, …}

58. ANS: A

The Pythagorean Theorem is a² + b² = c². If you are solving for either a or b, solve the theorem for that variable: c² – b² = a² or c² – a² = b².

DIF: Average OBJ: 3-4.1 Use the Pythagorean Theorem.

STO: 8.3.1.g, 8.4.2.i TOP: Use the Pythagorean Theorem.

KEY: Pythagorean Theorem, Triangles

NOT: /A/ Correct! /B/ Which side of the triangle are you solving for? /C/ Did you remember to take the square root to get your final answer? /D/ Check over the Pythagorean Theorem.

59. ANS: C

The Pythagorean Theorem is a² + b² = c². If you are solving for either a or b, solve the theorem for that variable: c² – b² = a² or c² – a² = b².

DIF: Average OBJ: 3-4.1 Use the Pythagorean Theorem.

STO: 8.3.1.g, 8.4.2.i TOP: Use the Pythagorean Theorem.

KEY: Pythagorean Theorem, Triangles

NOT: /A/ Check over the Pythagorean Theorem./B/ Did you remember to take the square root to get your final answer? /C/ Correct! /D/ Which side of the triangle are you solving for?

60. ANS: A

For example, let’s assume the points are (2, 0) and (5, -4). Draw the right triangle with the line segment connecting these two points as the hypotenuse in the right triangle. Then use the Pythagorean Theorem to find the length of this segment. 4² + 3² = c². You will find that c = 5 in this case.

DIF: Basic OBJ: 3-6.1 Find the distance between points on the coordinate plane.

STO: 8.3.2 TOP: Find the distance between points on the coordinate plane.

KEY: Distance, Pythagorean Theorem

NOT: /A/ Correct! /B/ Remember that you have to square each of your values. /C/ Remember that you have to take the square root of your answer. /D/ The lengths of the sides that you used are not correct.

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Unit 1 Test chp1-3(3rd/4th period)

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