Standards of Learning Test Preparation Workbook Teacher’s ...

virginia

Standards of Learning Test Preparation Workbook

Teacher’s Guide

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Copyright © by Houghton Mifflin Harcourt Publishing Company

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ISBN 978-0-547-48198-2

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iii

To the TeacherIncluded in this booklet are answer keys for the following books:

• Virginia End of Course Assessment Grade 6



Grade 6 answers 1

Grade 7 answers 25

Grade 8 answers 47

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Answer Key 1Grade 6 Virginia

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Test Prep Doctor for Virginia Grade 6 Pre Test

1 To compare and order decimals, it helps to add additional zeros so that all decimals have the same number of digits following the decimal point. So, 13.5 can be written as 13.50 so it can be more easily compared with 13.05 and 13.55.

The answer is B: 13.55, 13.50, 13.05.

Students who chose C may have misread the instructions and ordered the decimals from least to greatest.

2 The Identity Property of Addition states that the sum of any real number and zero is equal to the real number. This property is sometimes called the Additive Identity Property.

A real number is any number whose position can be shown on a number line. Some examples of real numbers are: 4, 212, 3/5, 5.86, and Ï

}

25 .

Since 1,003 is a real number, the equation is an example of the Identity Property of Addition.

0 1 1,003 5 1,003

zero 1 real number 5 real number

Answer B is correct.

3 The circumference of a circle is the distance around, or perimeter.

A diameter of a circle is a line segment that connects opposite sides of a circle by passing through the center of the circle.

Answer A: A radius is a line segment that connects the center to the circle.

Answer B: Pi (symbol p) is the ratio of the circumference of a circle to its diameter. This ratio is

constant for all circles. For general purposes, 3.14 or 22

} 7 are used as approximations for pi.

Answer C: The area of a circle is the number of square units needed to fill the circle.

Answer D: Volume relates to 3-dimensional objects, not to circles. It is the number of cubic units needed to fill the space inside the object.

The answer is B, pi.

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Grade 6 I VirginiaAnswer Key 2

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Test Prep Doctor for Virginia Grade 6 Pre Test (continued)

4 The mean is the average number for a set of data. To find the mean, first add the numbers in the data set. Then divide the sum by the total number of addends.

The mean is a good way to represent the average if the numbers in a data set are close in value. Look at the numbers in this data set. The value $100 is far lower than the other values. This causes the mean to be lower than every value except $100.

$100 $472.50 $495 $520 $525 $590 $605

An average that is lower than 5 out of 6 numbers in a data set is misleading.

Answer J is correct. In this situation, the mean is not the best measure of central tendency.

Answer F is incorrect. When the values in a data set are not fairly evenly distributed, the average value can be misleading.

Answer G is incorrect. The data do not cluster around $470.

Answer H is incorrect. The range of the data is not the problem. The problem is the large gap between $100 and the cluster of the other values in the data set.

5 A length is being divided into equal segments. Therefore, this is a division problem.

4 4 2 }

3 5

4 }

1 3

3 }

2 5

12 }

2 5 6

The answer is A, 6 pieces.

Students who chose C may have added: 4 1 2 }

3 5 4

2 }

3 , or 4 whole pieces.

Students who chose D may have subtracted: 4 2 2 }

3 5 3

1 }

3 , or 3 whole pieces.

6 A quadrilateral is a closed, 2-dimentional figure with four sides. One way to find the correct answer is to decide which answer choices cannot be correct.

Given Information The figure cannot be a . . .

no right angles rectangle or a square because they each have 4 right angles.

no congruent sides parallelogram because it has opposite sides congruent.

one pair of parallel sides rectangle, square, or parallelogram because they each have two pairs of parallel sides.

This leaves the trapezoid. The definition of a trapezoid is a quadrilateral with exactly one pair of sides parallel.

Another way to find the answer is to draw a figure that matches the description. Since the quadrilateral has no congruent sides, the figure will be an irregular trapezoid, not an isosceles trapezoid.

Answer J is correct.

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Grade 6 I Virginia Answer Key 3

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7 Percent means “per 100” or how many “out of 100.” A percent can be written as a ratio in notation form, as a fraction with denominator of 100, and as a decimal.

The answer is B because the fraction is 20

} 100

.

8 At the start, there were 6 gallons. Some of that amount was removed by people at the party and some was removed by the brother and friends.

6 2 3 1 }

2 2 1

1 }

4

First, combine the two amounts of punch that were removed.

3 1 }

2 1 1

1 }

4 5 3

2 }

4 1 1

1 }

4 5

14 }

4 1

5 }

4 5

19 }

4 5 4

3 }

4

Then subtract.

6 2 4 3 }

4 5 5

4 }

4 2 4

3 }

4 5 1

1 }

4

The answer is G, 1 1 }

4 .

Students who chose H may have subtracted the first amount but failed to subtract the second

amount. 6 2 3 1 }

2 5 5

2 }

2 2 3

1 }

2 5 2

1 }

2

Students who chose J may have found the amount removed from the punch but didn’t understand that they were to find the amount of punch that remained from the original amount.

9 Probability (P) is the ratio of the number of desired outcomes to the total number of possible outcomes. In this situation, the two events—rolling the cube and spinning the spinner—are independent events because the outcome of one does not affect the outcome of the other.

First find the probability of each event.

P of rolling an even number 5 3 even numbers

}} 6 total number

5 3 }

6 5

1 }

2

P of spinner landing on 5 5 1 five

} 5 numbers

5 1 } 5

Then multiply the two probabilities.

1 }

2 3

1 } 5 5

1 }

10

Answer A is correct.

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Answer Key Grade 6 Virginia4

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10 Each side of a cube is the same with the same dimensions. Each side of this cube is 6.5 inches. To find the volume of a cube, use the formula V 5 lwh.

V 5 lwh

5 6.5 3 6.5 3 6.5

5 274.625

The volume of the cube is 274.63 cubic inches to the nearest hundredth. The answer is J.

Students who chose F may not have understood the difference between area and volume, and found the area of one face. 6.5 3 6.5 5 42.25

Students who chose H may have confused surface area with volume.

(6.5 3 6.5) 3 6 faces 5 253.5

11 This question asks you to make a prediction based on information displayed on a circle graph. The graph shows that 20% of the 60 teenagers surveyed say red is their favorite color.

Assume that this percent will be about right for a group of 50 students, especially if they are in the same age range as the first group.

20% of 50 5 0.2 3 50 5 10

Answer G is correct.

12 Negative numbers decrease in value the farther away they are from zero on a number line. Therefore, the coldest temperature in the table is 2368 and the warmest is 2248.

The answer is G, Day 2, with a temperature of 2248.

Students who chose J may have reasoned that since the digits are greater than the other numbers, the temperature is greater.

13 A coordinate plane is made up of a horizontal number line (x-axis) and a vertical number line ( y-axis). The two number lines cross at a point called the origin. An ordered pair of numbers is used to name a point’s coordinates, or location, on a coordinate plane. For example, the coordinates of the origin are (0, 0).

Identify the point located at (22, 5).

The first coordinate, 22, tells the location of the point on the x-axis to the left or the right of the origin. Find the origin. Count two places to the left.

The second coordinate, 5, tells the location of the point above or below the x-axis. Count up five places. This takes you to point W. Point W represents the ordered pair (22, 5).


Answer B is incorrect. The coordinates for point X are (2, 2).

Answer C is incorrect. The coordinates for point Y are (25, 22).

Answer D is incorrect. The coordinates for point Z are (2, 22).

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14 One way to solve this problem is to share the cubes out equally between the two cylinders.

cylinder - cube, cube, cube, cube, cubecylinder - cube, cube, cube, cube, cube

There are 5 cubes for every 1 cylinder. To balance the scale, place 5 cubes on the right side.

Another way to solve the problem is to divide: 10 cubes 4 2 cylinders 5 5 cubes per 1 cylinder.

Answer F is correct.

15 A power of a number represents repeated multiplication of the number by itself.

12 3 means to multiply 12 by itself three times, or 12 3 12 3 12. Therefore, the answer is D.

16 The corner rectangle is enclosed within the larger rectangle. To find the area that does not need to be replaced (the corner rectangle), subtract the area of the corner rectangle from the total area of the patio.

Find the areas of the corner rectangle and the total patio.

corner rectangle total patio rectangle

A 5 lw A 5 lw

5 4 3 3 5 15 3 10

5 12 5 150

150 2 12 5 138

The area of the patio that does not need to be replaced is 138 ft 2 . The answer is F.

Students who chose H may have simply found the area of the entire patio. 15 3 10 5 150

Students who chose J may have completed the first step of finding the areas of the two rectangles, but then found the sum of the areas instead of the difference. 12 1 150 5 162

17 The mean of the set of data is 6, so 6 is the balance point of the data set.

The value plotted at 1 is 5 points to the left of the mean, so it is 5 less than the mean.The value plotted at 4 is 2 points to the left of the mean, so it is 2 less than the mean.

Since 5 1 2 5 7, the fourth point must be 7 greater than the mean. 6 1 7 5 13, the location of the fourth point.

Answer C is correct.

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18 The Inverse Property of Multiplication states that the product of a number and its reciprocal is

equal to one. For example, 5 3 1 } 5 5 1, as shown below.

5 3 1 } 5

5 1 5

} 1 1

3 1 1

} 1 5

5 1 } 1

5 1


19 Use order of operations to find the value. For this expression, begin by finding the value within the parentheses. Then compute that value with the power. Finally, multiply from left to right.

2 3 (20 2 14) 2

2 3 (6) 2

2 3 36

72

The value of the expression is 72. The answer is B.

Students who chose A may have ignored the parentheses and computed straight through from left to right.

2 3 20 2 14 2

40 2 14 2

40 2 196

2156

Students who chose C may have computed:

2 3 (20 2 14) 2

(2 3 6) 2

12 2

144

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20 Percent means “per 100.” The percentage 75% can be written as 75

} 100

and simplified to 3 }

4 .

In answer H, midway between 1 }

2 and 1 1 or

3 }

4 2 is shaded, which is 75%. So, the answer is H.

In answer F, about 1 }

4 , or 25%, of the rectangle is shaded. Students who chose F may have

confused the white area with the shaded area.

In answer G, 1 }

2 , or 50%, is shaded.

In answer J, closer to 100%, or about 85%, is shaded.

21 A event is dependent if its probability is affected by a prior event.

Suppose you have a deck of 12 animal cards—4 mammals, 4 birds, and 4 reptiles. You want to choose a bird card. You choose a card and do not return it to the deck.

The probability for the first draw is 4 }

12 5

1 }

3 .

The probability of the second draw is different.

• If the first card drawn is NOT a mammal card, the probability is 4 }

11 .

• If the first card drawn is a mammal card, the probability is 3 }

11 .


In answers A, C, and D, the probability of the second event does not depend on what happens in the first event.

22 A circle graph is used to display the parts of a whole. All of the equipment sold is equal to 100%. Think about the relationship between percents and fractions.

55% is a little over 50%, and 50% 5 1 }

2 . The section that represents “Football” should be a little

over half the circle.

25% 5 1 }

4 . The section that represents “Baseball” should be one-fourth of the circle.

10% 5 1 }

10 . The sections that represent “Basketball” and “Hockey” should each be one-tenth of

the circle.

Answer H is correct.

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23 The distance from the center of the garden to the edge describes the radius. To find the area, use the formula A 5 p r 2 . Use 3.14 as an approximation for pi.

A 5 p r 2

A 5 3.14 3 15 2

5 3.14 3 225

5 706.5

The area of the garden is 706.5 square feet. So, the answer is C.

Student who chose A may have confused the formula for the circumference with the formula for the area.

C 5 2pr

5 2 3 3.14 3 15

5 94.2

24 The number line shows negative numbers to the left of 0 and positive numbers to the right of 0. Find the point to the left of 0 that represents 226.

The answer is F.

Students who chose G may have counted from 220 to the right to find an “increasing” value. Point Q would seem to be at 224, which would seem fairly close to 226. Point Q is at 216.

Students who chose answer H might have misread the number line. Point R is at 6.

Students who chose J may have ignored the negative sign and located the point at positive 26. Point S is at 26.

25 Examine the numbers in the sequence and determine the rule for the way they change.

One way to do this is to find the difference between the numbers in the sequence.

6 2 3 5 3

10 2 6 5 4

15 2 10 5 5

The differences are increasing by 1. Since subtraction is the opposite of addition, the numbers added to the terms increase by 1.

3 1 3 5 6

6 1 4 5 10

10 1 5 5 15

15 1 6 5 21

Answer C is correct.

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26 Since the question asks for a total, this is an addition problem. It requires adding a zero and aligning the decimal points.

806.3 1439.0 1,245.3

The answer is H.

Students who chose F may have added zero and aligned the decimal points correctly but subtracted instead of adding.

Students who chose J may have ignored the decimal points and simply added the numbers.

27 The Zero Property of Multiplication states that the product of a number multiplied by zero is zero.

Think of it as taking a number zero, or no, times. If you take the number 5 zero times you have zero.

This property is also called the Multiplicative Property of Zero or the Property of Zero for Multiplication.

Answer D is correct.

Answer choices A, B, and C are equations that represent other properties of numbers.

28 First, determine what operation is appropriate.

The farmer has plowed part of his whole field and then planted part of that part of his whole field.

He planted corn in 2 }

3 of the

5 }

8 part. The word “of ” indicates multiplication.

2 }

3 3

5 }

8 5

2 3 5 }

3 3 8 5

10 }

24 5

5 }

12

Or this can be simplified first and then solved.

2 }

3 3

5 }

8 5

1 }

3 3

5 }

4 5

5 }

12

So, the farmer planted corn in 5 }

12 of his field.

The answer is H.

Students who chose J may have divided instead of multiplying.

5 }

8 4

2 }

3 5

5 }

8 3

3 }

2 5

15 }

16

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29 Congruent figures have exactly the same size and shape. Corresponding angles and correspond-ing sides of congruent figures have the same measure.

The given information says the trapezoids are isosceles. Identify the corresponding sides and angles of the trapezoids.

• All four nonparallel sides are congruent.

• The bases are congruent.

• The top sides are congruent.

• The base angles are congruent acute angles.

• The top angles are congruent obtuse angles.


Answer A is incorrect because angle A is an obtuse angle and angle P is an acute angle.

Answer B is incorrect because angle D is an acute angle and angle N is an obtuse angle.

Answer C is incorrect because the opposite parallel sides of an isosceles trapezoid are not equal in length.

30 The notation | 24| represents the absolute value of 24. The absolute value of a number is the distance of the number from zero on the number line regardless of direction.

The number 24 is 4 units from 0, or 4. The answer is F.

Students who chose G may not have understood that the absolute value of a negative number is the number without the negative sign.

31 Read each statement and look at the graphs. Decide if the statement is accurate. A bar graph is best used for categorical data such as days of the week. Circle graphs are used to show the relationship of the parts of the data to the whole.

Answer D is correct. If you look at the circle graph it is easy to see that almost one-half of the people thought the performance was good.

Answer A is incorrect because both graphs are easy to read.

Answer B is incorrect because the bar graph does not show the numbers as part of a whole.

Answer C is incorrect because the key for the circle graph shows the categories clearly.

32 A percentage can be written as a fraction whose denominator is 100 and then simplified, if possible.

48% 5 48

} 100

5 12

} 25

The answer is F.

Students who chose J may have confused the positions of the numerator and denominator.

100

} 48 5 25

} 12

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33 A coordinate plane is made up of a horizontal number line (x-axis) and a vertical number line ( y-axis). The two number lines cross at a point called the origin, with coordinates (0, 0). These coordinates name a point’s location on the coordinate plane.

The first coordinate names a distance along the horizontal axis. Start at the origin. Count left to point P. Point P is 3 places to the left of the origin, so the first coordinate is 23.

The second coordinate names a distance above or below the horizontal axis. Count down 1 place to point P. Point P is 1 place below the horizontal axis, so the second coordinate is 21.

The coordinates for point P are (23, 21).


34 There are 12 boys for every 15 girls. So, the ratio is 12 to 15, 12

} 15

, or 12:15. In simplest

form, 12

} 15

5 4 } 5 . The ratio is

4 } 5 , or 4:5. Therefore, the answer is F.

Students who chose H found the ratio of boys (12) to the total number of students, 12 1 15 5 27.

Students who chose J found the ratio of girls (15) to the total number of students, 12 1 15 5 27.

35 An inequality is a mathematical statement that two quantities are not equal in value. In this inequality the value of x is greater than 2.

Since x . 2, 2 is not included in the solution. The point at 2 should be open, not solid.

Since x . 2, the arrow points to the right.

Answer A is correct. This number line shows that all numbers . 2 are solutions to the inequality.

Answer B is incorrect because the point at 2 is solid. It shows the solutions for x $ 2.

Answer C is incorrect because the arrow points to the left. It shows the solutions for x , 2.

Answer D is incorrect because the point is solid and the arrow points to the left. It shows the solutions for x # 2.

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36 Use the formula 9 } 5 C 8 1 32. Substitute the temperature in the sign for C.

9 } 5 (24) 1 32

9 } 5 3

24 }

1 1 32

216

} 5 1 32

43 1 } 5 1 32 5 75

1 } 5

75 1 } 5 8 is very close to 758 F. The answer is H.

Students who chose F may have computed 9 } 5 (24) 5 43

1 } 5 and forgotten to add 32. Or they may

have not understood how to set up the expression, ignoring the fraction and simply adding 32 and 24 to get 56. The closest answer in either case is 508 F.

37 First find the cost of the two shirts and the cost of the four pairs of socks.

2 3 12.85 5 25.7 and 4 3 3.49 5 13.96

Then add the two sums to find the total amount of money needed.

25.7113.96

Add a zero in the top number to make aligning the digits clearer.

25.7113.96 39.66

The answer is D, $39.66.

Students who chose A may have found the difference between the two sums.

25.70 213.96 11.74

Students who chose C may have applied adding a zero incorrectly when aligning the two sums.

25.07 113.96 39.03

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38 The marks on the figure show that the quadrilateral has two pairs of parallel sides equal. This means that the opposite sides are also parallel.

The figure cannot be a trapezoid because a trapezoid has only one pair of opposite sides parallel.

The figure cannot be classified as a rhombus because the sides of the figure are not known to be equal in length.

Visual inspection shows that the figure has no right angles. The figure is not a rectangle.

The figure has the attributes of a parallelogram–two pairs of parallel sides.


39 The Identity Property of Multiplication states that the product of any real number and one is equal to the real number. This property is sometimes called the Multiplicative Identity Property.

A real number is any number whose position can be shown on a number line. 3 is a real number. The equation 3 3 1 5 3 is an example of the Identity Property of Multiplication.


Answers A, C, and D are examples of other properties of numbers.

40 The symbol . means “is greater than.” The symbol , means “is less than.” Negative numbers are less than positive numbers. Negative numbers decrease in value the farther away they are from zero on a number line.

The answer is J; 273 is farther away from zero than 269.

A negative number cannot be greater than a positive number. Therefore, answers F and H are not true.

In answer G, 231 is farther away from zero than 229. Answer G is not true.

Students who chose G or H may have reversed the meanings of the . and , symbols.

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41 To find the circumference of a hockey puck, first find the diameter of a puck. The pucks are arranged such that they each touch another puck, so there is no space between the diameters of circles. The dimensions of the rectangle are given, so the diameter of a puck can be found.

Count the number of pucks along one or both sides and divide.

9 4 3 5 3 and 15 4 5 5 3

So, the diameter of each puck must be 3 inches.

Use the formula for circumference.

C 5 pd

5 3.14 3 3 5 9.42

The circumference of one hockey puck is 9.42 inches. The answer is D.

Students who chose C may have confused the radius with the diameter and used the formula

C 5 2pr

5 2 3 3.14 3 3 5 18.84

42 There are 18 marbles and 6 of them are white. Eric pulls one marble but does not return it. to the box. Assume that this marble is white because the questions asks, “If both marbles are white . . . ”

These are dependent events because the probability of the second event depends on the outcome of the first event.

First draw: P 5 6 desired outcomes

}} 18 possible outcomes

5 1 }

3

After the first draw there are 17 marbles in the box and 5 of them are white.

Second draw (white): P 5 5 }

17

P of drawing two white marbles in this situation: P 5 1 }

3 3

5 }

17 5

5 }

51


Students who chose G may have only solved for the probability of pulling one white marble.

43 An inequality is a mathematical statement that two quantities are not equal in value.

There is a solid point at 3. This means that 3 is included in the solution. x can be equal to 3.

The arrow points to the left. This means all numbers less that 3 are part of the solution. x can also be equal to any value less than 3.

The value of x is equal to or less than 3. Use the symbol #, which means “is equal to or less than.”


Answer A is incorrect because it says that x is greater than 3.

Answers B is incorrect because it says that x is less than 3. If this were true, the point would be open, not solid.

Answer C is incorrect because it says that x is equal to or greater than 3. If this were true, the line would point to the right.

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44 You could fit 1 1 }

2 flower gardens inside the vegetable garden, so divide the area of the vegetable

garden by 1 1 }

2 to find the area of the flower garden.

Write the mixed numbers as fractions. 5 3 }

4 4 1

1 }

2 5

23 }

4 4

3 }

2

To divide, write the reciprocal of 3 }

2 and multiply.

23

} 4 3

2 }

3 5

23 }

2 3

1 }

3 5

23 }

6 5 3

5 }

6

The flower garden is 3 5 }

6 square meters. The answer is F.

Students who chose G may have subtracted instead of divided. 5 3 }

4 2 1

1 }

2 5 5

3 }

4 2 1

2 }

4 5 4

1 }

4

Students who chose H may have added instead of divided. 5 3 }

4 1 1

1 }

2 5 5

3 }

4 1 1

2 }

4 5 6

5 }

4 5 7

1 }

4

Students who chose J may have reasoned that the operation should be multiplication. Or they

may have reasoned that the operation should be division but failed to write the reciprocal of 1 1 }

2

before multiplying. 23

} 4 3

3 }

2 5

69 }

8 5 8

5 }

8

45 A coordinate plane is made up of a horizontal number line (x-axis) and a vertical number line (y-axis). The two number lines cross at a point called the origin.

A point’s coordinates tell its location on the coordinate plane. For example, the coordinates of the origin are (0, 0).

Identify the point located at (2, 24).

The first coordinate, 2, tells the location of the point on the x-axis to the left or the right of the origin. Find the origin. Count two places to the right.

The second coordinate, 24, tells the location of the point above or below the x-axis. Count down four places. This takes you to point M. Point M has the coordinates (2, 24).


46 Think of the problem as: 2 3 what number (t) is equal to 36?

Use division to find the value of t.

36 4 2 5 18


Answers G, H, and J reflect using the wrong operation to find the value of t.

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47 Since there are no parentheses or powers in this expression, first multiply or divide from left to right. Then add or subtract from left to right.

22 2 6 4 2 1 3

22 2 3 1 3

19 1 3

22

The answer is D.

Students who chose B may have computed straight across from left to right.

22 2 6 4 2 1 3

16 4 2 1 3

8 1 3

11

48 Congruent figures have exactly the same size and exactly the same shape.

Look at the dimensions given for each answer choice. Find the figure in which the corresponding sides have the same dimensions as quadrilateral ABCD.

Answer G is correct. If you flip this figure up, you can see that it is exactly like quadrilateral ABCD.

Answers F, H, and J are incorrect. Each of these figures has two sides that are congruent with quadrilateral ABCD but the figures themselves are not congruent.

49 Examine the numbers in the sequence and determine the rule for the way they change.

One way to do this is to decide what operation will give the next number in the pattern.

3 1 6 5 93 3 3 5 9

The operation is most likely addition or multiplication.

9 1 3 5 12 The operation is not addition.9 3 3 5 27 The operation may be multiplication.

27 3 3 5 8181 3 3 5 243

The rule is multiply by 3, so the numbers are tripling.


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50 A coordinate plane is made up of a horizontal number line (x-axis) and a vertical number line (y-axis). The two number lines cross at a point called the origin, with coordinates (0, 0). These coordinates name a point’s location on the coordinate plane.

The first coordinate names a distance along the horizontal axis. Start at the origin. Count left to point J. Point J is 2 places to the left of the origin, so the first coordinate is 22.

The second coordinate names a distance above or below the horizontal axis. Count up 4 places to point J. Point J is 4 places above the horizontal axis, so the second coordinate is 4.

The coordinates for point J are (22, 4).


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Pre Test pp. 1-15

Item Answer Standard

1 B 6.2d

2 G 6.19a

3 B 6.10a

4 J 6.15b

5 A 6.4

6 J 6.13

7 B 6.2a

8 G 6.6b

9 A 6.16b

10 J 6.10d

11 B 6.14b

12 G 6.3b

13 A 6.11b

14 F 6.18

15 D 6.5

16 F 6.10c

17 C 6.15A

18 J 6.19c

19 B 6.8

20 H 6.2b

21 B 6.16a

22 H 6.14a

23 C 6.10b

24 F 6.3a

25 B 6.17


26 H 6.7

27 D 6.19b

28 H 6.6a

29 D 6.12

30 F 6.3c

31 D 6.14c

32 F 6.2c

33 A 6.11a

34 F 6.1

35 A 6.20

36 H 6.9

37 D 6.7

38 F 6.13

39 B 6.19a

40 J 6.3b

41 D 6.10b

42 J 6.16b

43 D 6.20

44 F 6.6a

45 D 6.11b

46 F 6.18

47 D 6.8

48 G 6.12

49 A 6.17

50 H 6.11a

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Standards Review 6.1 pp. 17–18


1 B 6.1

2 G 6.1

3 B 6.1

4 J 6.1

5 C 6.1

6 H 6.1

7 D 6.1

8 J 6.1

Standards Review 6.2a pp. 19–20


1 D 6.2a

2 F 6.2a

3 C 6.2a

4 G 6.2a

5 A 6.2a

6 J 6.2a

Standards Review 6.2b pp. 21–22


1 D 6.2b

2 H 6.2b

3 B 6.2b

4 H 6.2b

5 D 6.2b

6 H 6.2b

7 A 6.2b

8 H 6.2b

Standards Review 6.2c pp. 23–24


1 C 6.2c

2 F 6.2c

3 B 6.2c

4 J 6.2c

5 C 6.2c

6 G 6.2c

7 B 6.2c

8 H 6.2c

Standards Review 6.2d pp. 25–26


1 B 6.2d

2 H 6.2d

3 C 6.2d

4 F 6.2d

5 C 6.2d

6 G 6.2d

7 C 6.2d

8 G 6.2d



1 C 6.3a

2 H 6.3a

3 A 6.3a

4 J 6.3a

5 C 6.3a

6 G 6.3a



1 C 6.3b

2 G 6.3b

3 B 6.3b

4 G 6.3b

5 D 6.3b

6 G 6.3b

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1 C 6.3c

2 H 6.3c

3 B 6.3c

4 F 6.3c

5 C 6.3c

6 J 6.3c



1 C 6.4

2 J 6.4

3 D 6.4

4 F 6.4

5 A 6.4

6 G 6.4

7 C 6.4



1 D 6.5

2 J 6.5

3 A 6.5

4 H 6.5

5 C 6.5

6 H 6.5

7 C 6.5

8 H 6.5



1 C 6.6a

2 H 6.6a

3 A 6.6a

4 H 6.6a

5 B 6.6a

6 G 6.6a

7 D 6.6a

8 G 6.6a



1 A 6.6b

2 G 6.6b

3 C 6.6b

4 G 6.6b

5 A 6.6b

6 G 6.6b

7 C 6.6b

8 F 6.6b



1 D 6.7

2 G 6.7

3 B 6.7

4 J 6.7

5 B 6.7

6 H 6.7

7 D 6.7

8 H 6.7

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1 D 6.8

2 G 6.8

3 C 6.8

4 F 6.8

5 B 6.8

6 J 6.8

7 C 6.8

8 F 6.8



1 C 6.9

2 H 6.9

3 A 6.9

4 H 6.9

5 B 6.9

6 G 6.9

7 A 6.9

8 G 6.9



1 B 6.10a

2 H 6.10a

3 C 6.10a

4 J 6.10a

5 D 6.10a

6 F 6.10a



1 C 6.10b

2 H 6.10b

3 D 6.10b

4 H 6.10b

5 C 6.10b

6 H 6.10b

7 A 6.10b



1 D 6.10c

2 J 6.10c

3 D 6.10c

4 G 6.10c

5 A 6.10c

6 H 6.10c



1 B 6.10d

2 J 6.10d

3 C 6.10d

4 J 6.10d

5 C 6.10d

6 J 6.10d

7 A 6.10d

8 H 6.10d



1 B 6.11a

2 G 6.11a

3 D 6.11a

4 F 6.11a

5 A 6.11a

6 G 6.11a

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1 B 6.11b

2 G 6.11b

3 C 6.11b

4 F 6.11b

5 C 6.11b

6 G 6.11b



1 B 6.12

2 J 6.12

3 C 6.12

4 G 6.12

5 C 6.12



1 G 6.13

2 F 6.13

3 D 6.13

4 H 6.13

5 D 6.13

6 J 6.13

7 D 6.13

8 G 6.13



1 B 6.14a

2 G 6.14a

3 C 6.14a

4 J 6.14a

5 C 6.14a

6 H 6.14a



1 A 6.14b

2 F 6.14b

3 C 6.14b

4 J 6.14b

5 A 6.14b

6 G 6.14b

7 C 6.14b

8 G 6.14b



1 C 6.14c

2 J 6.14c



1 C 6.15a

2 G 6.15a

3 D 6.15a

4 J 6.15a

5 C 6.15a

6 G 6.15a

7 D 6.15a

8 G 6.15a



1 B 6.15b

2 F 6.15b

3 B 6.15b

4 G 6.15b

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1 C 6.16a

2 H 6.16a

3 B 6.16a

4 F 6.16a

5 B 6.16a

6 G 6.16a



1 B 6.16b

2 F 6.16b

3 C 6.16b

4 F 6.16b

5 A 6.16b

6 J 6.16b

7 D 6.16b

8 J 6.16b



1 D 6.17

2 F 6.17

3 B 6.17

4 H 6.17

5 B 6.17

6 G 6.17

7 B 6.17

8 F 6.17



1 B 6.18

2 F 6.18

3 D 6.18

4 G 6.18

5 A 6.18

6 G 6.18

7 B 6.18

8 F 6.18



1 B 6.19a

2 H 6.19a

3 D 6.19a

4 H 6.19a

5 B 6.19a

6 J 6.19a

7 B 6.19a

8 G 6.19a



1 C 6.19b

2 J 6.19b

3 A 6.19b

4 H 6.19b

5 D 6.19b

6 J 6.19b

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1 C 6.19c

2 J 6.19c

3 C 6.19c

4 H 6.19c

5 B 6.19c

6 H 6.19c



1 C 6.20

2 G 6.20

3 A 6.20

4 G 6.20

5 B 6.20

6 H 6.20

7 A 6.20

8 H 6.20

Post Test pp. 89-103


1 C 6.14a

2 H 6.10a

3 B 6.4

4 J 6.16b

5 A 6.2d

6 G 6.15a

7 B 6.6b

8 J 6.2b

9 A 6.16a

10 H 6.7

11 B 6.19b

12 H 6.10a

13 D 6.3b

14 H 6.12

15 C 6.18

16 G 6.8


17 D 6.1

18 F 6.11a

19 D 6.14c

20 H 6.5

21 B 6.15b

22 F 6.13

23 B 6.10c

24 F 6.17

25 D 6.3a

26 J 6.14b

27 C 6.2c

28 H 6.19a

29 A 6.9

30 J 6.3c

31 B 6.19c

32 J 6.6a

33 D 6.2a

34 J 6.10d

35 B 6.11b

36 F 6.20

37 D 6.3b

38 B 6.8

39 C 6.11b

40 J 6.13

41 A 6.18

42 F 6.16b

43 D 6.7

44 H 6.10b

45 B 6.12

46 H 6.19a

47 A 6.6a

48 J 6.11a

49 C 6.17

50 H 6.20

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1 Apply the rule to the values of n that indicate the position in the sequence:

n 3n 1 1

1 4

2 7

3 10

4 13

5 16

The correct answer is A.

Students who answered B and C gave formulas that worked for n 5 1, but did not work for the rest of the numbers of the sequence.

Students who answered D interpreted n to be a value representing each term of the sequence to which 3 was added to get the next term.

2 To solve 75 5 7s 2 5s 1 15, first combine the like terms, then isolate the variable on one side and solve for s.

75 5 7s 2 5s 1 15

75 2 15 5 2s 1 15 2 15

60 5 2s

30 5 s

The answer is H.

Students who chose F multiplied each side by 2.

Students who chose G added 15 to each side.

Students who chose J combined 7s and 5s by adding these terms together.

3 The volume of a cylinder is equal to the area of the base times the height. Round the height to 25 in. The area of the base, 8, times 25 is 200, so the volume of the cylinder is about 200 in3.

The answer is A.

Students who answered B rounded 8 to 10 and 24 to 30 and multiplied.

Students who answered C squared 8 and rounded that result to 60, then rounded 24 to 25 and multiplied 25 and 60.

Students who answered D rounded 8 to 10 and 24 to 20. Then, the student squared 10 to get 100, then multiplied by 20.

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4 To solve 3 # d 2 3, students should first add 3 to both sides: 3 1 3 # d 2 3 1 3 → 6 # d.

6 # d can be rewritten as d $ 6. The graph of d $ 6 has a solid dot at x 5 6 and a solid line shaded to the right of 6 on the number line.

The answer is J.

Students who chose F and H most likely did not solve the inequality correctly.

Students who chose G most likely solved the inequality correctly, but did not chose the correct graph because 6 # d is not in the form in which the variable appears on the left hand side of the inequality. If students did rewrite 6 # d so that the variable appeared on the left hand side, they must remember to flip the sign.

5 Set up a proportion comparing the longest sides and the shortest sides.

4 }

6 5

2 } x

4x 5 12

x 5 3

The correct answer is C.

Students who answered A and B set up the proportion incorrectly.

Students who answered D probably thought that the two shortest sides should be equal.

6 The multiplicative inverse property states that the product of a number and its multiplicative

inverse (or reciprocal) always equals one. Since 6 3 1 }

6 5 1,

1 }

6 is the multiplicative inverse of 6.

The answer is G.

Students who chose F, H, or J did not use the multiplicative inverse property correctly.

7 Rewrite all fractions so that they have a common denominator:

4 }

16 ,

8 }

16 ,

5 }

16 ,

6 }

16 ,

12 }

16 ,

7 }

16

Rearrange so that they are ordered from least to greatest:

4 }

16 ,

5 }

16 ,

6 }

16 ,

7 }

16 ,

8 }

16 ,

12 }

16


Students who answered A or B may not have changed the fractions to a common denominator.

Students who answered D arranged the fractions so that the denominators were ordered from least to greatest.

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8 A histogram is most appropriate for data that can be characterized using consecutive intervals and should be used when a student wants to show the frequency of the data elements as they fall into each interval. A histogram is just one example of a type of graph that can be used to display data visually. Other examples include circle graphs, line plots and stem and leaf plots. A circle graph best displays data as percents of a whole.

The answer is F.

Students who chose answer G may not have realized that a histogram is better for comparing frequencies of data that are grouped in equal intervals.

Students who chose answer H may not have realized that a line graph is more appropriate for representing data over time.

Students who chose answer J may not have realized that a stem and leaf plot is better for comparing ordered data.

9 Use the order of operations:

252 1 3(12 2 5) 5 225 1 3(7)

5 225 1 21

5 24

The correct answer is B.

Students who answered A added 3 to 225 before multiplying 3 by 7.

Students who answered C did not multiply 3 by 25.

Students who answered D found the square of 25 instead of finding the opposite of the square of 5.

10 The distributive property states that the product of a number and the difference of two other numbers equals the difference of the products of the number and each other number. Therefore 6(3x 2 1) 5 18x 2 6

The answer is F.

Students who chose G, H, or J did not identify the correct property.

11 Triangle ABC is slid down to the left and therefore the transformation is a translation.

The correct answer is D.

Students who answered A, B, or C do not understand the definitions of dilation, reflection, rotation, and translation.

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12 The equation that represents the relationship between x and y given the table of values is y 5 25x.

The answer is G.

Students who chose F interchanged x and y.

Students who chose H found an equation that represents the relationship in the first pair of x and y in the table, but did not verify this relationship holds true for all other pairs.

Students who chose J did not find an equation that represents the relationship between x and y.

13 The square root of 225 is 15 because 15 3 15 5 225.


Students who answered A and D factored 225 into 9 3 25 and chose one of the factors to be the answer.

14 The equation that represents how many bananas Ken bought: 0.5b 1 4.25 5 5.50

0.5b 1 4.25 2 4.25 5 5.50 2 4.25

0.5b 5 1.25

b 5 2.5

The answer is G.

Students who chose F multiplied each side by 0.5.

Students who chose H added 4.25 to each side and multiplied each side by 0.5.

Students who chose J added 4.25 to each side.

15 To find the volume, multiply the length times the width times the height: V = lwh. Tripling each dimension gives a new volume of (3l)(3w)(3h) = 27lwh, or 27 times the original volume. So the new volume is 27(200) = 5400 ft3.


Students who answered A tripled the volume.

Students who answered C tripled only two of the dimensions.

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16 Add the exponents when multiplying numbers with the same base.

4 1 (24) 5 0

Substitute: 100 5 1.

The correct answer is J.

Students who answered F multiplied the exponents.

Students who answered G multiplied the exponents and used the wrong sign.

Students who answered H added the exponents incorrectly.

17 To evaluate 6q 1 4x 2 y for q 5 5, x 5 24, and y 5 2, plug in the values for q, x, and y and perform the correct order of operations:

6(5) 1 4(24) 2 (2) 5 30 2 16 2 2 5 12

The answer is C.

Students who chose A, B, or D evaluated the equation incorrectly.

18 Set up a proportion to represent the number of ounces of pizza sauce to the number of pizzas.

8 }

2 5

x }

8

2x 5 64

x 5 32

The correct answer is H.

Students who answered F added 8 and 2.

Students who answered G multiplied 8 by 2.

Students who answered J squared the 8 ounces.

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19 To solve 26x $ 12, students should divide each side by 26, remembering to reverse the inequality symbol:

26x

} 26

$ 12

} 26

→ x # 22

The answer is D.

Students who chose A did not change the sign and did not reverse the inequality symbol.

Students who chose B did not reverse the inequality symbol.

Students who chose C did not change the sign.

20 The arrow from 0 to 4 represents 14. From that position, the arrow to the left represents 26.

The correct answer is G.

Students who answered F used 0 rather than 4 as the starting point for the second arrow.

Students who answered H or J did not understand how to model successive operations using a number line.

21 The commutative property of multiplication states that changing the order of the factors does not change the product. Therefore 4 ? 6 5 6 ? 4.

The answer is D.

Students who chose A, B, or C did not identify the correct property.

22 A quadrilateral with 4 congruent sides is a rhombus.


Answers F and G are incorrect because the figure does not have a right angle.

Answer J is incorrect because the figure has two sets of parallel sides.

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23 When writing an algebraic expression from a verbal expression, the word “sum” refers to addition and the phrase “twice a number” refers to a number multiplied by 2. The sum of twice a number and 7 is translated into the following algebraic expression: 2n 1 7.

The answer is C.

Students who chose A did not recognize “twice a number” to mean a number multiplied by 2.

Students who chose B multiplied the 7 by 2, not the variable. Students mistook “a number” to mean the specific number given in the problem, the 7, not any number as represented by a variable.

Students who chose D did not recognize “the sum of ” to mean addition.

24 The absolute value of a number is the value of the number without the sign.

The correct answer is J.

Students who answered F found the opposite of the number.

Students who answered G or H found the square root of the number or its opposite.

25 When analyzing the data presented in the histogram, students should recognize that the height of each bar represents the number of runners that completed a mile in that particular time interval.

The only statement that cannot be supported by the data shown in the histogram is, “The fastest student ran the mile in 7 minutes and 30 seconds.” The histogram shows that two runners completed the mile somewhere between 7 minutes, 0 seconds and 7 minutes, 59 seconds, but does not give the actual result time of any individual runner.

The answer is B.

Students who chose A read the histogram incorrectly. The bar labeled 12:00–12:59 has a height of 1. This means one runner completed the mile within this time interval; therefore, statement A is supported by the data in the histogram.

Students who chose C read the histogram incorrectly. The bar labeled 7:00–7:59 has a height of 2. This means two runners completed the mile in less than 8 minutes; therefore, statement C is supported by the data in the histogram.

Students who chose D read the histogram incorrectly. The height of the first four bars are 2, 5, 7 and 8 respectively. This means 22 students completed the mile in less than 11 minutes. Twenty-two students is a majority of the runners; therefore, statement D is supported by the data in the histogram.

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26 A number written in scientific notation is written as a number between 1 and 10 multiplied by a power of 10. The exponent is equal to the number of places the decimal point is moved.


Students who answered F did not count the number of places the decimal point moved correctly.

Students who answered G and J did not move the decimal point the correct number of spaces.

27 The multiplicative property of zero states that the product of a number and zero is zero. The equation 4 3 0 5 0 demonstrates the multiplicative property of zero.

The answer is A.

Students who chose B, C, or D did not identify the multiplicative property of zero correctly.

28 The depths of the cube and prism are the same, so the cubes will fit exactly one deep. Three cubes will fit along the length, and two along the height, so the total number of cubes that will fit is 3 ? 2 5 6.

The correct answer is F.

Students who answered H divided the volume of the rectangular prism, 750 by 5.

Students who answered J found the volume of the rectangular prism.

29 Rolling the number cube and spinning the spinner are independent events, so the probability of the compound event (even number and 5) is the product of the probabilities of each simple event.

1st simple event (cube will land on an even number): The number of favorable outcomes is 3 and the

number of total possible outcomes is 6. The probability the cube will land on an even number is 3 }

6 .

2nd simple event (spinner will land on 5): The number of favorable outcomes is 1 and the number

of total possible outcomes is 5. The probability that the spinner will land on 5 is 1 } 5 .

Therefore, the probability that the compound event will occur is the product of 3 }

6 and

1 } 5 .

3 }

6 3

1 } 5 5

3 }

30 5

1 }

10

The answer is A.

Students who chose B may have calculated 2 as the number of favorable outcomes in the first

event. P(cube lands on even number) 5 2 }

6 5

1 }

3 , P(compound event) 5

1 }

3 3

1 } 5 5

1 }

15 .

Students who chose C may have added the probabilities of the simple events.

3 }

6 1

1 } 5 5

15 }

30 1

6 }

30 5

21 }

30 5

7 }

10 .

Students who chose D may have calculated 3 }

6 3

1 } 5 incorrectly:

3 }

6 3

1 } 5 Þ

(3 1 1) }

(6 1 5) .

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30 The multiplicative identity property states that the product of any real number and one is equal

to the given real number. In Step 3, 1 2 1 }

2 (1) simplifies to 1 2

1 }

2 . This is an example of the

identity property of multiplication.

The answer is H.

Students who chose F or G gave properties used in other steps.

31 The probability of the arrow stopping on blue is 2 }

8 . The probability of the arrow stopping on

green is 2 }

8 . The probability of the arrow stopping on blue or green is

2 }

8 1

2 }

8 5

4 }

8 5

1 }

2 .


Students who answered A chose this because there is no section on the spinner labeled “blue or green.”

Students who answered B did not combine the individual probabilities.

Students who answered D wrote the probability as whole to part.

32 Apply the rule to the values of n that indicate the position in the sequence:

n 3 } 2 n 1 5 }

2

1 4

2 11

} 2

3 7

4 17

} 2

5 10

The correct answer is F.

Students who answered G added the fractions before substituting values of n.

Students who answered H substituted 1 through 5 for n but did not add 5 }

2 .

Students who answered J continued the sequence for the numerators, 3, 5, 7, 9, …, and kept the denominator the same.

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33 To find the missing y-values in the chart, students should plug the corresponding x-value listed in the chart into the equation y 5 2x 2 5. For x 5 3, y 5 2(3) 2 5 5 6 2 5 5 1. For x 5 4, y 5 2(4) 2 5 5 8 2 5 5 3.

The answer is D.

Students who chose A calculated the y-values correctly, but listed them in reverse.

Students who chose B found negative y-values.

Students who chose C calculated the y-values incorrectly (found negative y-values) and also listed them in reverse.

34 The distributive property states that the product of a number and the sum of two other num-bers equals the sum of the products of the number and each other number. Therefore 4(x 1 y) is equivalent to 4x 1 4y.

The answer is H.

Students who chose F did not use the distributive property.

Students who chose G distributed the 4 only to the first term of the sum.

Students who chose J distributed the 4 only to the last term of the sum.

35 The area of the smaller square is 4 because 2 3 2 5 4. The area of the larger square is 6 3 6 5 36.


Students who answered A added the two values.

Students who answered B multiplied the two values.

Students who answered C multiplied the two values then multiplied by 2.

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36 The phrase “3 more than the number of girls g” can be written as g 1 3. This is the number of boys b in Kyle’s class, so g 1 3 can be set equal to b. The correct algebraic equation that matches the statement is b 5 g 1 3.

The answer is H.

Students who chose F set up an equation that states there are 3 total students in the class.

Students who chose G set up an equation that states there are more girls than boys in the class.

Students who chose J set up an equation that states there are an equal number of girls and boys in the class.

37 The square root of 100 is 10 because 10 3 10 5 100. The negative square root of 100 is 210.


Students who answered B or C found the incorrect square root.

Students who answered D did not take into account the negative.

38 To solve 22x 1 8 5 10, first isolate the term with the variable by subtracting 8 from both sides of the equation. Next, x should be isolated by dividing each side of the equation by 22.

22x 1 8 5 10

22x 1 8 2 8 5 10 2 8

22x 5 2

x 5 21

The answer is J.

Students who chose F, G, or H solved the equation incorrectly.

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39 The solution graphed is z # 22.

The answer is B.

Students who chose A, C, or D solved the inequality incorrectly or read the graph of the given solution incorrectly.

40 Point A(22, 21) becomes A´(2, 21), therefore, (2x, 2y) becomes (x, 2y).

The correct answer is G.

Answer F is incorrect because the rule works only for point A.

Answer H is incorrect because the new points would have to be in quadrant I for the rule to work.

Answer J is incorrect because the rule works only for point D.

41 Let x represent the original price. Then use the percent proportion equation to find the value of x.


Students who answered B, C, or D did not represent 60% as 60

} 100

. They did not understand how a proportion can be used to solve a percent problem.

42 To solve 2s 2 5 5 13, first add 5 to each side, then divide each side by 2.

The answer is G.

Students who chose F subtracted 5 from each side and then divided by 2.

Students who chose H subtracted 2 from each side instead of dividing each side by 2 and then added 5.

Students who chose J added 5 but then multiplied each side by 2.

43 The associative property of addition states that regrouping the addends does not change the sum. Therefore (4 1 3) 1 7 5 4 1 (3 1 7).

The answer is C.

Students who chose A, B, or D did not identify the correct property.

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44 The volume of a cylinder is equal to the area of the base times the height. The area of the base equals the radius, 3, squared times pi.

32 3 3 10 so the volume of the cylinder is about 9 3 3.14 3 10, which equals about 280 in3.


Students who answered F squared the radius and multiplied by 10.

Students who answered G squared the radius, multiplied by 10, then added the values together.

Students who answered J multiplied 3 3 10 3 10.

45 The absolute value of a number is the value of the number without the sign.


Students who answered A found the opposite of the number.

Students who answered B found the reciprocal of the number.

Students who answered D squared the number.

46 When analyzing the data presented in the histogram, students should recognize that the height of each bar represents the number of students in that particular height interval. To find the total number of students, add the numbers in each interval: 2 1 5 1 7 1 8 1 4 1 1 5 27. To find the number of students who are less than 160 cm tall, add the numbers in the first three bars: 2 1 5 1 7 5 14.

The answer is F.

Students who chose answer G calculated a median value, but an exact median value cannot be determined in a histogram.

Students who chose answer H did not tabulate the numbers correctly. The correct value is 14, which is the majority of the 27 students.

Students who chose answer J mistook the tallest bar in the histogram to represent the majority of the students.

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47 Use the order of operations:

28 1 (23) 2 (6 2 9) 5 28 1 (23) 2 (23)

5 28 1 23 1 3

5 211 1 3

5 28

The correct answer is B.

Students who answered A ignored any parentheses and just added the values.

Students who answered C added 28 and 23 as 5 and 6 2 9 as 23 giving a final value of 2.

Students who answered D ignored the parentheses and made a calculation error.

48 The solutions to the inequalities are:

y . 8

9 . w (or w , 9)

x . 9

n . 8

The only inequality that includes 8 as a solution is 9 . w (or w , 9).

The answer is G.

Students who chose F, H, or J solved the inequality incorrectly.

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49 Use the formula SA 5 2(r2) 1 2rh to find the surface area of a cylinder.

SA 5 2(r2) 1 2rh

5 2(3.14)(22) 1 2(3.14)(2)(9)

5 25.12 1 113.04

5 138.16


Students who answered A only used the first part of the formula.

Students who answered B only used the second part of the formula.

Students who answered D not only squared the radius in the first part of the equation, but also squared the 2.

50 To evaluate r(3s 1 7y) for r 5 5, s 5 24, and y 5 2, plug in the values for r, s, and y and perform the correct order of operations:

5[3(24) 1 7(2)] 5 5[212 1 14] 5 5[2] 5 10

The answer is H.

Students who chose F did not perform the order of operations correctly: 5[3(24) 1 7(2)] Þ 5(212) 1 14

Students who chose G most likely made the following arithmetic error: (212 1 14) 5 22, 5(22) 5 210.

Students who chose J evaluated the equation incorrectly.

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Pre Test pp. 1–15


1 A 7.2

2 H 7.14a

3 A 7.5a

4 J 7.15b

5 C 7.6

6 G 7.16d

7 C 7.1c

8 F 7.11b

9 B 7.3b

10 F 7.16b

11 D 7.8

12 G 7.12

13 C 7.1d

14 G 7.14b

15 D 7.5c

16 J 7.1a

17 C 7.13b

18 H 7.4

19 D 7.15a

20 G 7.3a

21 D 7.16a

22 H 7.7

23 C 7.13a

24 J 7.1e

25 B 7.11a


26 H 7.1b

27 A 7.16e

28 F 7.5b

29 A 7.10

30 H 7.16c

31 C 7.9

32 F 7.2

33 D 7.12

34 H 7.16b

35 D 7.6

36 H 7.13a

37 A 7.1d

38 J 7.14a

39 B 7.15b

40 G 7.8

41 F 7.4

42 H 7.14b

43 C 7.16a

44 H 7.5a

45 C 7.1e

46 F 7.11a

47 B 7.3b

48 G 7.15a

49 C 7.5b

50 H 7.13b

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1 A 7.1a

2 F 7.1a

3 B 7.1a

4 G 7.1a

5 C 7.1a

6 H 7.1a

7 B 7.1a

8 J 7.1a



1 C 7.1b

2 G 7.1b

3 A 7.1b

4 G 7.1b

5 C 7.1b

6 H 7.1b

7 C 7.1b

8 H 7.1b



1 B 7.1c

2 D 7.1c

3 C 7.1c

4 H 7.1c

5 A 7.1c

6 F 7.1c

7 C 7.1c

8 J 7.1c



1 B 7.1d

2 F 7.1d

3 B 7.1d

4 G 7.1d

5 B 7.1d

6 H 7.1d

7 B 7.1d

8 G 7.1d

Standards Review 7.1e pp. 25–26


1 D 7.1e

2 H 7.1e

3 B 7.1e

4 H 7.1e

5 D 7.1e

6 H 7.1e

7 C 7.1e

8 H 7.1e



1 C 7.2

2 F 7.2

3 A 7.2

4 G 7.2

5 C 7.2

6 G 7.2

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1 B 7.3a

2 G 7.3a

3 B 7.3a

4 H 7.3a

5 C 7.3a

6 H 7.3a



1 A 7.3b

2 J 7.3b

3 B 7.3b

4 J 7.3b

5 B 7.3b

6 F 7.3b



1 D 7.4

2 J 7.4

3 D 7.4

4 H 7.4

5 D 7.4

6 H 7.4

7 B 7.4

8 G 7.4



1 A 7.5a

2 H 7.5a

3 C 7.5a

4 J 7.5a



1 D 7.5b

2 F 7.5b

3 D 7.5b

4 G 7.5b

5 B 7.5b

6 G 7.5b



1 C 7.5c

2 H 7.5c

3 C 7.5c

4 F 7.5c

5 B 7.5c

6 F 7.5c



1 D 7.6

2 H 7.6

3 F 7.6

4 J 7.6

5 D 7.6

6 J 7.6



1 C 7.7

2 F 7.7

3 D 7.7

4 J 7.7

5 A 7.7

6 F 7.7

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1 C 7.8

2 F 7.8

3 C 7.8

4 G 7.8



1 D 7.9

2 H 7.9

3 D 7.9

4 G 7.9

5 C 7.9

6 G 7.9



1 C 7.10

2 H 7.10

3 A 7.10

4 G 7.10

5 A 7.10

6 F 7.10

7 C 7.10



1 B 7.11a

2 H 7.11a

3 C 7.11a

4 F 7.11a



1 A 7.11b

2 F 7.11b

3 C 7.11b

4 J 7.11b



1 B 7.12

2 G 7.12

3 C 7.12

4 H 7.12

5 C 7.12

6 F 7.12



1 A 7.13a

2 G 7.13a

3 C 7.13a

4 J 7.13a

5 D 7.13a

6 G 7.13a

7 C 7.13a

8 J 7.13a

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1 A 7.13b

2 F 7.13b

3 A 7.13b

4 G 7.13b

5 C 7.13b

6 H 7.13b

7 D 7.13b

8 G 7.13b



1 D 7.14a

2 G 7.14a

3 D 7.14a

4 J 7.14a

5 D 7.14a

6 F 7.14a

7 D 7.14a

8 F 7.14a



1 C 7.14b

2 J 7.14b

3 C 7.14b

4 H 7.14b

5 A 7.14b

6 H 7.14b

7 C 7.14b

8 G 7.14b



1 A 7.15a

2 F 7.15a

3 B 7.15a

4 H 7.15a

5 B 7.15a

6 J 7.15a

7 C 7.15a

8 G 7.15a



1 A 7.15b

2 G 7.15b

3 A 7.15b

4 F 7.15b

5 D 7.15b

6 F 7.15b

7 C 7.15b

8 F 7.15b



1 D 7.16a

2 F 7.16a

3 C 7.16a

4 F 7.16a

5 C 7.16a

6 H 7.16a

7 C 7.16a

8 H 7.16a

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1 A 7.16b

2 H 7.16b

3 A 7.16b

4 F 7.16b

5 B 7.16b

6 G 7.16b

7 C 7.16b

8 F 7.16b



1 C 7.16c

2 J 7.16c

3 B 7.16c

4 G 7.16c

5 B 7.16c

6 J 7.16c

7 A 7.16c

8 G 7.16c



1 A 7.16d

2 F 7.16d

3 D 7.16d

4 G 7.16d

5 D 7.16d

6 H 7.16d

7 B 7.16d

8 G 7.16d

Standards Review 7.16e pp. 77–78


1 B 7.16e

2 F 7.16e

3 B 7.16e

4 J 7.16e

5 A 7.16e

6 H 7.16e

7 D 7.16e

8 H 7.16e

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Post Test pp. 79−93


1 B 7.1b

2 H 7.5a

3 C 7.11a

4 F 7.15b

5 B 7.3b

6 G 7.13b

7 C 7.2

8 F 7.12

9 B 7.6

10 H 7.16c

11 C 7.5c

12 J 7.15a

13 D 7.3a

14 G 7.11b

15 C 7.1c

16 G 7.16e

17 A 7.8

18 H 7.5b

19 D 7.10

20 G 7.1a

21 A 7.7

22 G 7.14b

23 C 7.9

24 J 7.16a

25 A 7.13a


26 G 7.4

27 B 7.14a

28 F 7.1e

29 D 7.16b

30 G 7.1d

31 D 7.16d

32 H 7.11a

33 A 7.14b

34 H 7.5b

35 B 7.1e

36 J 7.14a

37 C 7.4

38 J 7.8

39 A 7.15b

40 J 7.12

41 C 7.6

42 J 7.2

43 A 7.15a

44 H 7.13a

45 B 7.5a

46 H 7.1d

47 A 7.16b

48 H 7.13b

49 C 7.3b

50 F 7.16a

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1 All of the answer choices are examples of real numbers.

Answer C is correct. The set of natural numbers is a subset of the whole numbers.

Answer A is incorrect because the set of irrational numbers is a subset only of the real numbers.

Answer B is incorrect because the set of integers includes the opposite of the whole numbers.

Answer D is incorrect because the set of rational numbers is a subset only of the real numbers.

2 When a transversal intersects two parallel lines, the corresponding angles formed by the intersection are equal in measure. To find the measure of /3, use the measure of /8 to find the measure of /7, because /7 and /3 are corresponding angles.

/8 and /7 are supplementary angles. The measure of /7 is found by subtracting the measure of /8 from 180°.

The measure of /7 is 180° 2 135° or 45°. Thus, the measure of /3 is 45°.


Students who chose G regrouped incorrectly when subtracting 135° from 180°.

Students who chose H may have assumed that /7 and /8 are complementary angles.

Answer J is incorrect because 135° is the measure of the angle that is supplementary to /3.

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3 The area of a composite figure is the sum of the areas of each individual figure. To find the area of the square, you will need to know the length of one side. To find the area of the right isosceles triangle, you will need to know the measure of its height (vertical leg) and base (horizontal leg).

Each side of the square measures s centimeters. The height h of the triangle is also a side of the square. So, h 5 s. The triangle is isosceles, so base b 5 s as well.

Find s:

2s 5 16

s 5 16

} 2

s 5 8

Find the area of the composite figure:

Acomposite 5 Atriangle 1 Asquare

5 1 __ 2 bh 1 s2

5 1 } 2 (s ? s) 1 s2

5 3

} 2 s2

5 3

} 2 (82)

5 96

The answer is C.

Students who chose answer A may have calculated only the area of the triangle.

Students who chose answer B may have calculated only the area of the square.

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4 One form of the equation of a line is y 5 mx 1 b, where m is the slope of the line and b is the y-intercept.

The slope m is the ratio of vertical distance (rise) to horizontal distance (run) between any two points (x1, y1) and (x2, y2) on the line. For example, choose (22, 1) and (0, 3) on the given line. The slope is:

m 5 y2 2 y1

} x2 2 x1

5 3 2 1

} 0 2 (22)

5 2 } 2

5 1

The y-intercept b is the value of the y-coordinate of the intersection of the given line and the y-axis. The line intersects the y-axis at (0, 3), so the y-intercept b is 3.

The answer is F.

Students who chose answer G may have incorrectly calculated slope.

Students who chose answer J may have used the x-intercept instead of the y-intercept.

5 A reflection produces a mirror-image of a figure on the opposite side of a line called the line of reflection. Polygon PQRSTU is in Quadrant II of the coordinate plane. Since the polygon is to be reflected across the horizontal or x-axis, it will appear in Quadrant III after the reflection.

The answer is D.

Answer A is incorrect because it shows a translation of six units to the right.

Answer B is incorrect because it shows a translation of five units down.

Answer C is incorrect because it shows a reflection across the vertical or y-axis.

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6 An increase from $3.00 to $3.75 is an increase of $0.75. To solve the problem, translate the question “$0.75 is what percent of $3.00?” to an equation.

$0.75 is what percent of $3.00?

□ □ □ □

0.75 5 (x) (3)

Divide both sides of the equation by 3 to find that x 5 0.25.

Change 0.25 to a percent: 0.25 3 100 5 25%.


Answer G is incorrect because the cost increased by 1 }

4 , not

1 }

3 .

Students who chose answer H subtracted the quotient 3 4 3.75 from 1 and changed the difference to a percent.

Students who chose answer J changed the quotient 3 4 3.75 to a percent.

7 The Distributive Property states that for real numbers a, b, and c:

a(b 1 c) 5 ab 1 ac

Substitute a 5 12, b 5 8, and c 5 5. Simplify.

a(b 1 c) 5 ab 1 ac

12(8 1 5) 5 12 ? 8 1 12 ? 5

5 96 1 60

5 156

The answer is A.

Students who chose answer B may have tried to distribute 8 instead of 12.

Students who chose answer D may have tried to multiply the products instead of adding them.

8 Since Ï}

25 5 5, the correct answer will be the square root closest to Ï}

25 .


Answers F, G, and J are incorrect because Ï}

27 is closer to Ï}

25 .

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9 A front view, side view, or top view is a way to show a three-dimensional object in two dimensions.

To picture the front view of the tower of blocks, imagine that the tower has no depth. The front of the tower would be four rows of blocks. The bottom row would be four blocks wide, and the three upper rows would be three blocks wide.

To picture the right side view of the tower, imagine that the tower has no width. The side of the tower would be four rows of blocks. The bottom row would be four blocks across. The middle two rows would be three blocks across. The top row would be one block.

The answer is C.

Students who chose A may have reversed the front and side views.

10 Use division to change 3 }

4 and

4 } 5 to decimals.

3 4 4 5 0.75 4 4 5 5 0.80

Then change each answer to a decimal, and find the decimal that is greater than 0.75 but less than 0.80.

Answer F is incorrect because 5 }

8 5 0.625.

Answer G is incorrect because 9 }

10 5 0.9.

Answer H is incorrect because 2 }

3 5 0.

} 6 .

Answer J is correct because 7 }

9 5 0. } 7 .

11 In the line plot, each x represents one employee. For example, there are two x’s above 24 on the number line. This means that Charlene found two employees who are 24 years old.

The total number of x’s equals the total number of employees. There are 20 x’s on the line plot, so the company has 20 employees.

The answer is C.

Students who chose answer A may have noticed that the midpoint of the number line is 30.5.

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12 One way to find the effect of doubling one dimension is to solve a simpler problem. For example, suppose the rectangular prism measures 2 3 3 3 4. Use the formula V 5 lwh to find that the volume of the prism is 24 cubic units.

Now double one of the dimensions and suppose the prism measures 2 3 3 3 8 (instead of 2 3 3 3 4). Again use the formula V 5 lwh to find that the new volume is 48 cubic units.

So, doubling a dimension doubles the volume of a rectangular prism.


Answers F, H, and J are not correct.


The y-intercept of y 5 1 }

2 x 2 3 is 23. The only graph that intersects the y-axis at (0, 23) is graph A.

The answer is A.

Students who chose answer D may have calculated the slope as the ratio of run to rise instead of rise to run.

14 A perfect square is any number that can be written as the product of an integer and itself. For example:

1 is an integer and 12 5 1, so 1 is a perfect square.




5 is an integer and 52 5 25, so 25 is a perfect square. And so on.


Answers F, H, and J are not perfect squares.

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15 The Pythagorean Theorem states that, for a right triangle, the square of the hypotenuse c is the sum of the squares of sides a and b. Substitute the values given for a and b and solve the equation for c.

a2 1 b2 5 c2

62 1 62 5 c2

Ï}

36 1 36 5 c

Ï}

36 ? 2 5 c

6 Ï}

2 5 c

The answer is B.

Students who chose A may have thought one of the legs was the hypotenuse.

Students who chose D may have used the equation 2a 1 2b 5 2c.

16 To find the value of the expression, substitute 10 for a, and then simplify by following the Order of Operations.

(2a 1 5)2 2 2a Given.

(2(10) 1 5)2 2 2(10) Substitute 10 for a.

(2(10) 1 5)2 2 2(10) Work inside ( ). Multiply first.

(20 1 5)2 2 2(10) Work inside ( ). Add.

(25)2 2 2(10) Simplify (25)2.

625 2 2(10) Multiply.

625 2 20 Subtract.

605


Answer F represents a process error.

Students who chose answer H did not subtract 20.

Students who chose answer J changed the subtraction to an addition.

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17 Let a be the cost of one angelfish. The amount Joshua started with ($40) minus the cost of 5 angelfish (5a) gives the amount Joshua has left ($10). Translate this into algebraic symbols.

starting minus cost of is amountamount 5 fish left

□ □ □ □ □

40 2 5a 5 10

Isolate the variable on one side of the equation to solve for a. Subtract 40 from both sides of the equation. Then divide both sides by 25.

40 2 5a 5 10

40 2 40 2 5a 5 10 2 40

25a 5 230

25a

} 25 5

230 }

25

a 5 6

One angelfish costs $6.

The answer is B.

Students who chose answer A may have divided the amount Joshua has left ($10) by 5 fish.

Students who chose answer C may have divided the amount Joshua started with ($40) by 5 fish.

18 The amount of money spent will be repaid in 48 equal payments. First find the amount of money that was spent.

$32,610 1 $18,512 5 $51,122

Then divide the amount by 48.

$51,122 4 48 < $1065.04

You can use estimation to check your work. Round $51,122 to $50,000 and round 48 to 50. Then divide. Since $50,000 4 50 5 $1000, it is reasonable to expect that the payments will be around $1000 per month.


Answers G, H, and J represent process or computation errors.

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19 The general trend shown in the scatter plot is that as distance from the city increases, the price of gasoline decreases. Draw a best-fit line through the plot. The cost per gallon c at a distance of 12 miles from the city will be the value of c at the intersection of the best-fit line and the vertical line d 5 12.

The answer is B.

Students who chose answer C may have drawn the best-fit line too high.

20 An oblique angle means that the intersection is not a right angle. The diagram below represents the problem, and shows transversal t intersecting parallel lines l and m at an oblique angle.

4 3

21

8 7

65

l

t

m

Vertical angles are congruent. The diagram shows that the intersection creates four acute vertical angles (/1 and /3, /5 and /7), and four obtuse vertical angles (/2 and /4, /6 and /8.)


Answers F, G, and J are not correct because the intersection of a transversal and two parallel lines creates two pairs of acute vertical angles and two pairs of obtuse vertical angles, or eight vertical angles altogether.

21 Because Heather replaces the straw, choosing the first straw has no effect on choosing the second straw. The events “choose a red straw” and “choose a blue straw” are independent.

The probability of two independent events A and B is the product of their individual probabilities: P(A and B) 5 P(A) ? P(B)

So,

P(red and blue) 5 P(red) ? P(blue)

5 2 } 16 ?

4 }

16

5 1 } 8 ?

1 }

4

5 1 } 32

The answer is A.

Students who chose answer D may have added the probabilities instead of multiplying them.

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22 An equilateral triangle has three vertices, and it will appear as if it has not moved if it is rotated in multiples of 360° 4 3 or 120°. So, rotations of 120°, 240°, 360°, and so on, will make an equilateral triangle appear as if it has not moved.

Another way to think about the problem is that a 360° rotation is the same as a full turn. Any plane figure that is rotated a full turn will appear as if it has not moved.


Answers F, G, and H are not correct because rotations of 90°, 180°, and 270° will change the orientation of an equilateral triangle.

23 The domain of the function is the set of all values of x for which the function is defined. Because division by 0 is undefined,

x 2 1 Þ 0

x Þ 1

The answer is C.

Students who chose answer A may have set the numerator equal to 0 instead of the denominator.

Students who chose answer B may have subtracted 1 from the right side of x 2 1 Þ 0 instead of adding 1.

24 According to the Pythagorean Theorem, the relationship a2 1 b2 5 c2 is always true for a right triangle where sides a and b (the legs) form the right angle and side c (the hypotenuse) is opposite the right angle.

The answer is F.

Students who chose G may have switched the hypotenuse with one leg of the triangle.

Students who chose H may have overlooked the fact that the Pythagorean Theorem only applies to right triangles.

Students who chose J may have mistaken the altitude of the triangle for a leg of the triangle.

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25 To simplify the expression, follow the Order of Operations.

1 25 ? 1 }

8 1 16 2 2 Work inside the parentheses. Simplify 25.

1 32 ? 1 }

8 1 16 2 2 Work inside the parentheses. Multiply.

(4 1 16)2 Work inside the parentheses. Add.

(20)2 Simplify the exponent.

400


Students who chose answer B simplified 202 as 40.

Students who chose answer D simplified 25 as 16.

Students who chose answer C simplified 25 as 64.

26 The graph starts with a closed circle at 24 and points to the right. The graph represents values of t greater than or equal to 24: t $ 24.

Since the inequality must have an “or equal to” symbol, answers A and B cannot be correct.

Solve the inequality in answer C by isolating the variable. Subtract 3 from both sides of the inequality.

24t 1 3 # 19

24t # 16

Next, divide both sides by 24. When dividing an inequality by a negative number, remember to reverse the inequality sign.

24t # 16

24t

} 24

$ 16

} 24

t $ 24

The answer is H.

Students who chose answer F may have forgotten that a closed circle on the graph of an inequality means “or equal to”.

Students who chose answer J may have forgotten to reverse the inequality when dividing by a negative number.

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27 In the given formula, substitute one dimension of the prism for l, substitute another dimension for w, and substitute the remaining dimension for h. (The order of the substitutions does not matter because multiplication is a commutative operation.)

SA 5 2(3.0 ? 2.5) 1 2(2.5 ? 2.5) 1 2(3.0 ? 2.5) Work inside ( ) first.

SA 5 2(7.5) 1 2(6.25) 1 2(7.5) Multiply.

SA 5 15 1 12.5 1 15 Add.

SA 5 42.5

The surface area of the box is 42.5 square feet.


Answers A, B, and D represent process or computation errors.

28 I 5 prt is the formula for finding simple interest. In the formula, t represents time in years. Since the problem states that the time is 6 months (or

1 }

2 of a year), use 0.5 for t.

Substitute $150 for the principal p, 3% for the rate r, and 0.5 for the time t.

I 5 (150)(3%)(0.5) Substitute.

I 5 (150)(0.03)(0.5) Change 3% to its decimal equivalent.

I 5 2.25 Multiply.

Rachel’s deposit will earn $2.25.


Students who chose answer G substituted 1 for t.

Students who chose answer H misplaced the decimal point in the product.

Students who chose answer J found the amount of interest for 6 years.

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29 The area of the composite figure is the sum of the areas of each individual figure. Notice that for each semicircle the diameter is the same length as a side of the square: s 5 d 5 4 meters.

Find the area of the composite figure:

Acomposite 5 Asquare 1 3Asemicircle

5 s2 1 3pr2

5 s2 1 3p 1 d } 2 2 2

5 42 1 3p 1 4 } 2 2 2

5 16 1 3p 1 16 } 4 2

5 16 1 12p

The answer is B.

Students who chose answer A may have used the area of only 1 semicircle.

Students who chose answer C may have set radius equal to 4 meters instead of 2 meters.

30 If two angles are complementary, the sum of their measures is 90°. To find the measure of the unknown angle, subtract the measure of the known angle from 90°.

90 255 45

The measure of the angle is 45°. Answer F is correct.

Students who chose answer G did not rename correctly during the subtraction.

Students who chose answer H assumed that the sum of the measures of two complementary angles is 180°.

Students who chose answer J subtracted 55° from 360°.

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31 To solve the equation, isolate the variable on one side of the equal sign. First, subtract 45 from both sides of the equation.

15w 1 45 5 195

15w 1 45 2 45 5 195 2 45

15w 5 150

Next, divide each side of the equation by 15.

15w 5 150

15w

} 15

5 150

} 15

w 5 10

Eduardo will need 10 weeks to save up the cost of the bike.

The answer is C.

Students who chose answer D may have added three weeks to account for the initial $45.

32 In the formula, r represents the radius of the base. Note that the problem gives the diameter of the base. Since a radius is one-half of a diameter, divide the given diameter by 2 when you substitute for r.

V 5 pr2h Given. Substitute 2 for r and 2 for h.

V 5 p(2)2(2) Follow the Order of Operations. Simplify (2)2.

V 5 p(4)(2) Multiply.

V 5 p(8)

The answer in simplest form is V 5 8p. Answer F is correct.

Students who chose answer G substituted 4 for h.

Students who chose answer H did not substitute or simplify correctly.

Students who chose answer J substituted 4 for r.

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33 First, find the number of students who participated in the survey. Add the number of students who said they favored each candidate.

24 1 17 1 27 1 22 5 90

A total of 90 students participated in the survey.

Next, set up a proportion to compare the numbers of students choosing a candidate and the numbers of expected votes for Lo.

90 students

} 240 students

5 24 expected votes

}} x expected votes

90x 5 5760

x 5 5760

} 90

x 5 64

The answer is C.

Students who chose answer A may have used the value of Lo’s bar on the graph.

Students who chose answer D may have found the difference between the number of students who participated in the survey and the number of students who vote in the election.


The y-intercept of y 5 2x 2 2 is 22. The only graph that intersects the y-axis at (0, 22) is graph J.

The answer is J.

Students who chose answer G may have chosen a graph with the same slope (m 5 2) as y 5 2x 2 2.

35 Point Z is located at (24, 3). In a translation, every point of a figure moves the distance described by the translation. Since the problem states that the distance moved is 2 units to the right and 9 units down, add 2 to the x-coordinate of (24, 3), and subtract 9 from the y-coordinate.

The new location of Point Z is (24 1 2, 3 29), which simplifies to (22, 26).


Answers A, C, and D do not represent movements of 2 units to the right and 9 units down.

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36 Write 3 3 1022 and 3 3 1023 in standard form by shifting the decimal point in each factor of 3 the direction and number of decimal places indicated by the exponent. An exponent of 22 represents a shift of two decimal places to the left. An exponent of 23 represents a shift of three decimal places to the left. So 3 3 1022 5 0.03 and 3 3 1023 5 0.003.

Compare each of the decimal answers to 0.03 and 0.003 and choose the decimal that is greater than 0.003 and less than 0.03.

Answer G is correct because 0.005 is greater than 0.003 and less than 0.03.

Answer F is incorrect because 0.0005 less than 0.003.

Answer H is incorrect because 0.05 is greater than 0.03.

Answer J is incorrect because 333 is greater than 0.03.

37 Flipping the coin and rolling the cube are independent events. The probability of two independent events A and B is the product of their individual probabilities:

P(A and B) 5 P(A) ? P(B)

Having the coin land on heads and rolling the number 1 are independent events. The probability of both occurring is:

P(heads and 1) 5 P(heads) ? P(1)

5 1 } 2 ?

1 }

6

5 1 }

12

The answer is D.

Students who chose answer A may have only calculated the probability of the coin landing on heads.

Students who chose answer B may have only calculated the probability of rolling 1.

38 Substitute 22 for x, then simplify by following the Order of Operations.

2 1 x } 2 2 2 Substitute 22 for x.

2 1 22 }

2 2 2 Simplify inside parentheses first.

2(21)2 Simplify the exponent.

2(1) Multiply.

2

The expression simplifies to 2. Answer G is correct.

Students who chose answer F simplified the expression by working from left to right.

Students who chose answer H wrote the incorrect sign when finding the product of (21)2.

Answer J represents a computation error.

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39 Draw a best-fit line on the scatter plot, following the trend of the data. Extend the best-fit line until it intersects the vertical line x 5 8 (which corresponds to 8 years after 2000, or the year 2008). The expected average price in 2008 will be the value of y at this intersection, or about $675. The expected average price of a personal computer in 2008 will be $675.

The answer is C.

Students who chose answer A may have chosen the greatest average price shown on the plot.

40 One way to solve the problem is to write a pattern of the square roots of perfect squares. (Perfect squares are 1, 4, 9, 16, 25, 36, and so on.)

Ï}

1 5 1 Ï}

4 5 2 Ï}

9 5 3 Ï}

16 5 4 Ï}

25 5 5 Ï}

36 5 6 and so on.

Since Ï}

35 is greater than Ï}

25 and less than Ï}

36 , Ï}

35 is between 5 and 6.


Answers F, H, and J represent process errors.

41 The graph of the function f (x) 5 25 is a horizontal line that intersects the y-axis at (0, 25). The line includes all ordered pairs in the form (x, 25). No matter what the value of x is, f (x) will always be 25.

The answer is A.

Students who chose answer B may have chosen the domain of the function.

42 The ladder, the side of the house, and the ground form a right triangle with the ladder as the hypotenuse. Apply the Pythagorean Theorem.

a2 1 b2 5 c2

242 1 b2 5 262

b2 5 262 2 242

b 5 Ï}

676 2 576

b 5 Ï}

100

b 5 10

The answer is H.

Students who chose F may have incorrectly substituted 26 for b and solved the equation for c.

Students who chose G may have taken the average of the given lengths.

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43 A decrease from $5.00 to $4.80 is a decrease of $0.20. To solve the problem, translate the question “$0.20 is what percent of $5.00?” to an equation.

$0.20 is what percent of $5.00?

□ □ □ □

0.2 5 (x) (5)

Divide both sides of the equation by 5 to find that x 5 0.04.

Change 0.04 to a percent: 0.04 3 100 5 4%.


Answers A and C represent misplaced decimal points.

Students who chose answer D may have subtracted the percent of decrease from 100%.

44 One way to find the effect of doubling each dimension is to solve a simpler problem. For example, suppose a rectangular prism measures 1 unit by 2 units by 3 units. Use the formula V 5 lwh to find that the volume of the prism is 6 cubic units.

Now, double each of the dimensions. The prism now measures 2 units by 4 units by 6 units. Again, use the formula V 5 lwh to find the new volume, which is 48 cubic units.

So, doubling each dimension increases the volume of a rectangular prism by a factor of 8.


45 Each table contains three ordered pairs (x, y). If a graph and a table represent the same function, then all the ordered pairs from the table will be on the graphed line. The graphed line contains (1, 21), (2, 1), and (3, 3), all points from table C.

The answer is C.

Students who chose answer D may have noticed that the y-intercept of the line represented by table D (b 5 3) is the opposite of the y-intercept of the graphed line (b 5 23).

46 Pi is a decimal number that does not repeat and does not terminate. Non-repeating, non-terminating decimals belong to the set of irrational numbers.


47 Try using the process of elimination. The side views of a pyramid would be triangles, so answers A and D are not correct. The top view of a cone is a circle, so answer C is not correct.

The answer is B.

Students who chose A may have known that the front face of a pyramid is a triangle.

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48 Write 6.5 3 109 in standard form by shifting the decimal point in the factor 6.5 the direction and number of decimal places indicated by the exponent. An exponent of 9 represents a shift of nine decimal places to the right. So 6.5 3 109 5 6,500,000,000.


Answer F represents the standard form of 6.5 3 107.

Answer G represents the standard form of 6.5 3 108.

Answer J represents the standard form of 6.5 3 1010.

49 Solve the inequality for m by isolating m on one side of the inequality sign. First, subtract 1 from both sides.

3m 1 1 . 10

3m . 9

Then, divide both sides by 3.

3m . 9

3m

} 3 . 9 }

3

m . 3

The only value of m that is greater than 3 is 3 1 }

3 .

The answer is D.

Students who chose answer C may have thought m could be greater than or equal to 3.

50 Before the figure is reflected, the location of the point at the center of the figure is (5, 3), which means that the point is 5 units to the right of the y-axis. After the figure is reflected across the y-axis, the point will be 5 units to the left of the y-axis. So, the center of the figure will be located at (25, 3) after the reflection.

Another way to visualize this transformation is to recognize that the point at the center of the figure is in Quadrant I before the reflection. After the reflection, the point will be in Quadrant II.


Answer F is incorrect because the point (5, 3) is in Quadrant I.

Answer G is incorrect because the point (5, 23) is in Quadrant IV.

Answer J is incorrect because the point (25, 23) is in Quadrant III.

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Pre Test pp. 1–15


1 C 8.2

2 F 8.6b

3 C 8.11

4 F 8.14

5 D 8.8a

6 F 8.3b

7 A 8.15c

8 H 8.5b

9 C 8.9

10 J 8.1b

11 C 8.13a

12 G 8.7b

13 A 8.16

14 G 8.5a

15 B 8.10b

16 G 8.4

17 B 8.15a

18 F 8.3a

19 B 8.13b

20 H 8.6a

21 A 8.12

22 J 8.8b

23 C 8.17

24 F 8.10a

25 C 8.1a


26 H 8.15b

27 D 8.7a

28 F 8.3a

29 B 8.11

30 F 8.6a

31 C 8.15a

32 F 8.7a

33 C 8.13a

34 J 8.16

35 B 8.8a

36 G 8.1b

37 D 8.12

38 G 8.4

39 C 8.13b

40 G 8.5b

41 A 8.17

42 H 8.10b

43 B 8.3b

44 J 8.7b

45 C 8.14

46 H 8.2

47 B 8.9

48 H 8.1a

49 D 8.15b

50 H 8.8b

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1 A 8.1a

2 H 8.1a

3 B 8.1a

4 H 8.1a

5 A 8.1a

6 G 8.1a

7 C 8.1a

8 H 8.1a



1 D 8.1b

2 H 8.1b

3 C 8.1b

4 F 8.1b

5 C 8.1b

6 G 8.1b

7 D 8.1b

8 J 8.1b



1 B 8.2

2 F 8.2

3 D 8.2

4 G 8.2

5 D 8.2

6 H 8.2

7 B 8.2

8 F 8.2



1 B 8.3a

2 G 8.3a

3 D 8.3a

4 H 8.3a

5 B 8.3a



1 A 8.3b

2 G 8.3b

3 C 8.3b

4 G 8.3b

5 C 8.3b

6 G 8.3b

7 C 8.3b

8 H 8.3b



1 C 8.4

2 G 8.4

3 C 8.4

4 J 8.4

5 A 8.4

6 H 8.4

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1 B 8.5a

2 H 8.5a

3 D 8.5a

4 F 8.5a

5 C 8.5a

6 G 8.5a

7 A 8.5a

8 J 8.5a



1 C 8.5b

2 G 8.5b

3 B 8.5b

4 G 8.5b

5 A 8.5b

6 F 8.5b

7 D 8.5b

8 H 8.5b



1 D 8.6a

2 H 8.6a

3 B 8.6a

4 G 8.6a

5 B 8.6a

6 H 8.6a



1 C 8.6b

2 H 8.6b

3 C 8.6b

4 J 8.6b



1 C 8.7a

2 F 8.7a

3 B 8.7a

4 H 8.7a

5 B 8.7a



1 A 8.7b

2 G 8.7b

3 B 8.7b

4 G 8.7b

5 C 8.7b

6 H 8.7b

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1 D 8.8a

2 J 8.8a

3 A 8.8a

4 H 8.8a

5 B 8.8a

6 G 8.8a



1 B 8.8b

2 G 8.8b

3 C 8.8b

4 J 8.8b

5 A 8.8b

6 H 8.8b



1 C 8.9

2 F 8.9

3 A 8.9

4 H 8.9

5 A 8.9



1 D 8.10a

2 F 8.10a

3 A 8.10a

4 J 8.10a

5 A 8.10a

6 F 8.10a



1 B 8.10b

2 F 8.10b

3 B 8.10b

4 H 8.10b

5 A 8.10b

6 G 8.10b

7 B 8.10b



1 A 8.11

2 G 8.11

3 B 8.11

4 F 8.11

5 D 8.11

6 G 8.11

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1 A 8.12

2 J 8.12

3 B 8.12

4 G 8.12

5 C 8.12

6 J 8.12

7 B 8.12



1 A 8.13a

2 H 8.13a

3 D 8.13a

4 F 8.13a



1 C 8.13b

2 F 8.13b

3 B 8.13b

4 G 8.13b



1 D 8.14

2 G 8.14

3 B 8.14

4 J 8.14

5 D 8.14



1 C 8.15a

2 F 8.15a

3 D 8.15a

4 H 8.15a

5 A 8.15a

6 F 8.15a

7 D 8.15a

8 H 8.15a



1 B 8.15b

2 F 8.15b

3 A 8.15b

4 G 8.15b

5 A 8.15b

6 F 8.15b

7 C 8.15b

8 G 8.15b

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1 A 8.15c

2 H 8.15c

3 D 8.15c

4 F 8.15c

5 C 8.15c

6 J 8.15c

7 A 8.15c



1 B 8.16

2 G 8.16

3 A 8.16



1 C 8.17

2 F 8.17

3 C 8.17

4 J 8.17

5 B 8.17

6 H 8.17

7 A 8.17

8 J 8.17

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Post Test pp. 71–86


1 B 8.6a

2 G 8.7b

3 B 8.10b

4 F 8.13b

5 B 8.3b

6 G 8.16

7 B 8.2

8 F 8.9

9 A 8.15a

10 J 8.5b

11 C 8.12

12 G 8.1a

13 D 8.13a

14 G 8.15c

15 D 8.8b

16 F 8.3a

17 D 8.10a

18 G 8.7a

19 C 8.14

20 J 8.8a

21 B 8.17

22 J 8.1b

23 B 8.11

24 H 8.4

25 D 8.15b


26 J 8.6b

27 C 8.5a

28 H 8.9

29 C 8.13b

30 H 8.3a

31 C 8.16

32 H 8.8a

33 B 8.12

34 F 8.1b

35 A 8.10b

36 J 8.7a

37 A 8.14

38 F 8.7b

39 B 8.15a

40 J 8.8b

41 C 8.13a

42 H 8.2

43 C 8.6a

44 G 8.17

45 C 8.5b

46 G 8.11

47 A 8.1a

48 J 8.15b

49 D 8.3b

50 J 8.4

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