SOL Review Booklet

2015-2016

Math 7

Name: _____________

Block: ______________

SOL Date: ___________

SOL 7.1 The student will

a) Investigate and describe the concept of negative exponents for powers of ten; b) Determine scientific notation for numbers greater than zero;

c) Compare and order fractions, decimals, and percents and numbers written in scientific notation; d) Determine square roots; and

e) Identify and describe absolute value for rational numbers.

HINTS & NOTES To write a number in scientific notation:

o To write a number in scientific notation, you write the number as two factors: a decimal greater than or equal to 1 and less than 10, and a power of 10.

o Move the decimal to make a factor between 1 and 10 (so that there is only one number to the left of the decimal).

o The will be the number of places that you moved the decimal. Example: 25,000,000 = 2.5 x 107

0.0000045 = 4.5 x 10-6 * The exponent is positive for numbers greater than 1 and negative for numbers less than 1 (decimals)

To write a number in standard form, you move the decimal point as many places as the exponent (positive exponent right, negative exponent left). Put 0 in any space.

Example: 3.4 x 105 = 340,000 4.2 x 10-5= 0.000042

1. Which fraction and decimal are equivalent to 10-3? A. −1

103 and -0.003

B. 1103

and -0.003

C. −1103

and 0.001

D. 1103

and 0.001 2. What decimal and decimal are equivalent to 10-7?

3. Identify the numbers that are equivalent to 10-4.

110,000

0.004

-0.0001 0.0001

−1

10,000

140,000

PRACTICE

Steps for ordering numbers:

1. Change all of the numbers to decimals. 2. Line up the decimals. 3. Add on zeros until the numbers are the same length. (same number of digits) 4. Ignore the decimals and put them in order. **Remember to look for the order that the questions asks. (L →G or G→L)

SOL 7.1 The student will

a) Investigate and describe the concept of negative exponents for powers of ten; b) Determine scientific notation for numbers greater than zero;

c) Compare and order fractions, decimals, and percents and numbers written in scientific notation; d) Determine square roots; and

e) Identify and describe absolute value for rational numbers.

4. What is 0.000012 written in scientific notation? A. 1.2 x 10-5 B. 1.2 x 10-4 C. 1.2 x 104 D. 1.2 x 105

5. The number of water droplets in a specific body of water is 123,000,000,000,000. How can this number be written in scientific notation?

1.23 x 1012 12.3 x 1013 1.23 x 10-14

1.23 x 1014 123 x 10-12 1.23 x 10-12

6. Which list of numbers is arranged from least to greatest?

A. 0.25, 17%, 29

B. 0.25, 29, 17%

C. 17%, 0.25, 29

D. 17%, 29, 0.25

7. Arrange the three numbers shown in order from least to greatest.

4.7 x 105 3.9 x 108 5.2 x 105

8. Identify two values that have a value less than 3. 2.9 x 101 3.2 x 103

2.9 x 100 3.2 x 10-2

9. Which number would make the sentence true?

𝟐𝟐𝟏𝟏𝟏𝟏

< < 1.42

A. 1 23

B. 0.153 C. 22% D. 1.3 x 101

10. Which number is the square root of 400?

A. 400 B. 200 C. 40 D. 20

11. Which number is the square root of 1?

A. 14

B. 12

C. 1 D. 2

12. What is the absolute value of -8.2?

A. 8.2 B. 4.1 C. -4.1 D. -8.2

13. What is �−𝟏𝟏𝟏𝟏

𝟏𝟏𝟐𝟐�?

A. 1211

C. −1112

B. 1112

D. −1211

PRACTICE

Least

Greatest

HINTS & NOTES An arithmetic sequence you have to find the ____________________. This is what you would add or

subtract from each number to get the next. In geometric sequences you have to find the ____________________. This is what number you

would have to multiply to get the following number. To write the variable expression you pair the common difference or ratio and a variable.

o Examples: 3, 6, 9, 12… expression: m + 3 1, 5, 25, 125… expression: 5n

1. Let n represent any number in this sequence. 2, 24, 46, 68, …

Which of these can be used to determine the next number?

A. 𝑛𝑛12

B. 12𝑛𝑛 C. 𝑛𝑛 + 22 D. 𝑛𝑛 − 22

2. Which statement is true about the pattern shown?

5, 20, 80, 320, …

A. The common ratio is 4. B. The common ratio is 15. C. The common difference is 4. D. The common difference is 15.

3. Complete the table with an expression that describes each sequence.

Sequence Expression

3, 6, 9, 12, …

1, 5, 25, 125, …

2, 4, 8, 16, …

4, 8, 12, 16, …

𝑏𝑏 + 4 𝑤𝑤 ÷ 5

2𝑡𝑡 𝑘𝑘 ÷ 2

5𝑟𝑟 𝑎𝑎 − 4

𝑝𝑝 + 3 𝑧𝑧 − 3

PRACTICE

SOL 7.2 The student will describe and represent arithmetic and geometric sequences using variable expressions.

4. Look at the following variable expression: 𝒑𝒑 + 𝟖𝟖. Which sequence is described by the given variable expression?

A. 3, 24, 192, 1536, … B. 8, 16, 32, 64, … C. 17, 25, 33, 41, … D. 56, 63, 70, 77, …

5. Identify each sequence that has a common ratio of 𝟏𝟏

𝟒𝟒.

7, 28, 112, 448, …

512, 128, 32, 8, …

256, 64, 16, 4, …

12, 48, 192, 768, …

320, 80, 20, 5, …

768, 192, 48, 12, …

560, 140, 36, 9, …

1. Which number sentence is represented by this model?

A. −3 ∙ 5 = 15 B. −3 ∙ 5 = −15 C. −3 ∙ (−5) = 15 D. −3 ∙ (−5) = −15

2. Which number sentence is represented by this model?

A. −4 ∙ 7 = 28 B. −4 ∙ 7 = −28 C. 4 ∙ (−7) = 28 D. 4 ∙ (−7) = −28

3. Which model illustrates the division of integers?

SOL 7.3 The student will

a) Model addition, subtraction, multiplication, and division of integers; and b) Add, subtract, multiply, and divide integers.

HINTS & NOTES Adding integers –

o Example: (-4) +( -2)= -6 or (-4) + 2 = -2 Subtracting integers –

o Example: ( -4) – (-2) becomes (-4)+ 2 which = -2 Multiplying and Dividing Integers –

o positive • positive = ____ o negative • negative=____ o positive • negative = ____ o negative • positive = ____

PRACTICE

4. During a winter’s day, the low temperature was recorded at 21℉. The wind-chill temperature that same day was −𝟖𝟖℉. What was the difference between the wind-chill temperature and the low temperature?

A. 8℉ B. 13℉ C. 25℉ D. 29℉

5. The change in the number of students enrolled at a school over six months is shown in the following table.

The number of students enrolled at the end of September was 4,327. What was the number of students enrolled in the school at the end of March?

A. 4, 275 B. 4,300 C. 4,325 D. 4,352

6. Using the following key as a guide, what this the result of the operation in the model below?

A. -10 B. -2 C. 2 D. 10

7. Identify each statement that is equivalent to -2.

−6− (−12) ÷ 3

5 + (−6) ∙ 4 + 2

(−12 + 8) ÷ 2

−12— 4 + (−3) ∙ (−2)

−4 + 8 ∙ (−1) ÷ 2

8. A dolphin is 30 feet below the surface of the water. She rises 23 feet, sinks 17 feet, and finally rises another 27 feet. If there are no other changes, the dolphin is –

A. 3 feet above the surface of the water

B. 3 feet below the surface of the water

C. 63 feet above the surface of the water

D. 63 feet below the surface of the water

9. Identify each number that can be placed in the blank to make the value of this expression a negative number.

(−13)− _________

-20 -14 -12 -8 10

SOL 7.3 The student will

a) Model addition, subtraction, multiplication, and division of integers; and b) Add, subtract, multiply, and divide integers.

PRACTICE

1. Clarence made a scale drawing of a classroom. The scale in the drawing is 2 inches represents 9 feet. The actual length of the classroom is 36 feet. What is the length of the classroom on the scale drawing?

A. 4 inches B. 8 inches C. 27 inches D. 162 inches

2. Kelly received a 25% discount on the purchase of a $240 bicycle. What was the amount of the discount Kelly received?

A. $25 B. $60 C. $180 D. $215

3. The original price of a chair was $545.00. A store discounted the price of this chair by 25%. What is the exact price of the chair, not including tax, with this discount?

A. $136.25 B. $408.75 C. $520.00 D. $681.25

4. Max ran 5 miles on Thursday. One mile is equal to 5,280 feet. Which proportion can be used to determine how many feet, x, Max ran on Thursday?

A. 15,280

= 5𝑥𝑥

C. 15,280

= 𝑥𝑥5

B. 1

5= 𝑥𝑥

5,280 D. 1

𝑥𝑥= 5,280

5

5. The correct mixture of oil to gas in a weed eater is 𝟏𝟏𝟐𝟐

pint of oil to 𝟐𝟐 𝟏𝟏𝟐𝟐 gallons of gas. How many pints of oil are

needed for 10 gallons of gas? A. 1 B. 2 C. 5 D. 8

6. Philip’s meal costs $12.82 at a local restaurant. The server did their job very well and Philip would like to leave a 20% tip. What amount of money should he leave for the waitress?

A. $0.03 B. $1.28 C. $2.56 D. $10.26

7. Seventy-six is 80% of what number? 8. Thirty-two is what percent of 80? 9. What is 4.5% of 40?

SOL 7.4 The student will solve single-step and multistep practical problems, using proportional reasoning.

HINTS & NOTES When setting up a proportion – make sure that the numerators and __________match.

Example:

=

To solve a proportion –

Proportions can be used to convert between the measurement systems. For example: 2 𝑖𝑖𝑛𝑛𝑖𝑖ℎ𝑒𝑒𝑒𝑒

𝑥𝑥 = 5 𝑖𝑖𝑐𝑐

16 𝑖𝑖𝑐𝑐

Proportions can also be used to represent percent problems. For example: 𝑝𝑝𝑒𝑒𝑝𝑝𝑖𝑖𝑒𝑒𝑛𝑛𝑝𝑝100

= 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑤𝑤ℎ𝑜𝑜𝑜𝑜𝑒𝑒

PRACTICE

1. One way to determine the surface area of this cylinder is to –

A. Add the areas of both bases to the rectangular area around the cylinder

B. Add the areas of both bases C. Multiply the area of the base by the height D. Multiply the rectangular area around the cylinder

by pi. 2. A container in the shape of a cube will be completely filled with sand. The container has an edge length of 8 inches. What is the exact number of cubic inches of sand needed to completely fill the container? 3. The dimensions of 4 rectangular prisms are shown. Identify each of the prisms for which the maximum amount of sand the prism can hold is 30 cubic inches.

4. This table shows the dimensions of four rectangular prisms.

Which rectangular prism has the greatest volume?

A. Rectangular Prism Q B. Rectangular Prism R C. Rectangular Prism S D. Rectangular Prism T

5. The diameter and height of a cylindrical container are shown.

The container is filled completely with cheese sauce. Which of these represents the total number of cubic inches of cheese in the container?

A. 𝜋𝜋 ∙ 82 ∙ 7 B. 𝜋𝜋 ∙ 162 ∙ 7 C. 2𝜋𝜋 ∙ 82 + 2𝜋𝜋 ∙ 8 ∙ 7 D. 2𝜋𝜋 ∙ 162 + 2𝜋𝜋 ∙ 16 ∙ 7

SOL 7.5 The student will

a) Describe volume and surface area of cylinders; b) Solve practical problems involving the volume and surface area of rectangular prisms and cylinders;

c) Describe how changing one measured attribute of a rectangular prism affects its volume and surface area.

HINTS & NOTES **Use the formula sheet at all times**

Use the formulas exactly as they are on the sheet. Be sure to highlight the following information in the problem:

Don’t forget to check the units: Squared units for area and cubed units for volume. Surface area –

Volume –

PRACTICE

6. Trevor covered a cylindrical can with paper for a project. The can is 18 centimeters tall and has a 5-centimeter radius. Which is closest to the minimum amount of paper Trevor needed to cover the entire can?

A. 283 cm2 B. 644 cm2 C. 722 cm2 D. 1,413 cm2

7. Carl is covering the rectangular prism-shaped box with cloth.

What is the minimum amount of cloth Carl needs to cover the entire box?

A. 96 sq in. B. 136 sq in. C. 192 sq in. D. 272 sq in.

8. The length of Rectangular Prism A is shown.

The length of this prism is multiplied by a scale factor of 𝟏𝟏𝟐𝟐 to create Rectangular Prism B. The volume of

Rectangular Prism B is – A. 2 times the volume of Rectangular Prism A

B. 3 times the volume of Rectangular Prism A

C. 14 times the volume of Rectangular Prism A

D. 12 times the volume of Rectangular Prism A

9. A rectangular prism has a height of 3 inches and volume of 27 cubic inches. The height of this prism is changed to 6 inches, and the other dimensions stay the same. What is the volume of the prism with this change?

A. 30 cubic inches B. 54 cubic inches C. 81 cubic inches D. 162 cubic inches

10. Rectangular Prism A is shown.

Rectangular Prism B has the same height and width as Rectangular Prism A but its length is 8 inches. The volume of Prism B is –

A. Twice the volume of Prism A B. One-half of the volume of Prism A C. One-fourth the volume of Prism A D. Four times the volume of Prism A

11. A company has produced a cereal box with the following dimensions and needs to reduce the surface area due to cost of production.

• Width = 2.4 inches • Length = 7.8 inches • Height = 11.6 inches

Which situation will create the least surface area?

A. Multiply the length of a scale factor of 13

B. Multiply the width of a scale factor of 13

C. Multiply the height of a scale factor of 12

D. Multiply the length of a scale factor of 12

SOL 7.5 The student will

a) Describe volume and surface area of cylinders; b) Solve practical problems involving the volume and surface area of rectangular prisms and cylinders;

c) Describe how changing one measured attribute of a rectangular prism affects its volume and surface area.

PRACTICE

1. Triangle STV and triangle ZXY are similar. Which pair of segments are corresponding sides of these triangles?

2. Quadrilateral PQMN is similar to quadrilateral WXYZ.

What is the measure of angle Z?

A. 65⁰ B. 80⁰ C. 100⁰ D. 115⁰

3. What must the value of x be in order for the figures below to be similar?

A. 12 cm B. 24 cm C. 36 cm D. 48 cm

4. Triangle PQR is similar to triangle STU.

Which proportion can be used to find n?

A. 515

= 𝑛𝑛12

B. 155

= 𝑛𝑛12

C. 1315

= 1236

D. 13𝑛𝑛

= 3612

6. Are the two figures below similar?

A. No, the sides are not congruent. B. Yes, the sides are proportional. C. No, the sides are not proportional. D. Yes, the sides are congruent.

SOL 7.6 The student will determine whether plane figures – quadrilaterals and triangles – are similar and write

proportions to express the relationships between corresponding sides of similar figures.

HINTS & NOTES Similar figures – same shape but different . Their corresponding angles have the _____ measure

and their corresponding sides are _______. This means that the ratios of corresponding sides are equal.

Remember – to solve a proportion – cross multiply or use equivalent ratios. The symbol ~

PRACTICE

1. Which statement is false? A. All squares are rectangles. B. All squares are parallelograms. C. All rhombuses are squares. D. All rhombuses are parallelograms.

2. Every rhombus is also a –

A. Parallelogram B. Trapezoid C. Rectangle D. Square

3. Which classifications must describe the figure shown?

A. Square and parallelogram B. Trapezoid and parallelogram C. Square and quadrilateral D. Trapezoid and quadrilateral

4. Select each classification that does NOT describe this figure.

Parallelogram Rhombus Rectangle Trapezoid Square Quadrilateral

5. Identify each classification to which this figure belongs.

Parallelogram Rhombus Trapezoid Rectangle

Quadrilateral Square 6. Which is a parallelogram with four congruent sides whose diagonals bisect each other and intersect at four right angles?

A. Cube B. Trapezoid C. Rhombus D. Rectangle

SOL 7.7 The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle,

square, rhombus, and trapezoid.

HINTS & NOTES Quadrilateral – polygon w/ 4 sides Types of Quadrilaterals

Quadrilateral Properties Parallelogram • Both pairs of opposite sides are congruent.

• Both pairs of opposite sides are parallel. • Both pairs of opposite angles are congruent.

Rectangle • Both pairs of opposite sides are congruent. • Both pairs of opposite sides are parallel. • All four interior angles measure 90⁰ (right angles). • Diagonals are congruent and bisect each other.

Square • Both pairs of opposite sides are parallel. • All four sides are congruent. • All four interior angles measure 90⁰ (right angles). • Diagonals are perpendicular bisectors and are congruent.

Rhombus • Both pairs of opposite sides are parallel. • All four sides are congruent. • Diagonals are perpendicular bisectors.

Trapezoid • One pair of opposite sides are parallel.

PRACTICE

1. Quadrilateral KLMN is rotated 180⁰ clockwise about the origin. Which coordinates best represent the image of point K?

A. (6,8) B. (-4,2) C. (8, -6) D. (4, -2)

2. Which numbered triangle is a 90⁰ counterclockwise rotation about the origin of shaded triangle?

A. Triangle 1 B. Triangle 2 C. Triangle 3 D. Triangle 4

3. Figure LMNP will be reflected across the y-axis. Place the point on the graph that represents N’.

4. Translate the figure vertically 6 positive units.

Which best describes the location of the image of vertex V?

A. (5, -8) B. (5, 4) C. (-1, -2) D. (11, -2)

SOL 7.8 The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations,

rotations, and translations) by graphing in the coordinate plane.

HINTS & NOTES Translation = Slide Rotation = Turn Reflection = Flip Dilations

PRACTICE

Clockwise Counterclockwise Vertical Horizontal

1. A spinner has 5 sections of equal size labeled P, Q, R, S, and T. The arrow of this spinner was spun 15 times and landed 4 times on the section labeled Q.

Which statement best describes the experimental probability and theoretical probability of the arrow landing on the section labeled Q?

A. The experimental probability is 15, and the

theoretical probability is 15.

B. The experimental probability is 15, and the

theoretical probability is 415

.

C. The experimental probability is 415

, and the

theoretical probability is 15.

D. The experimental probability is 415

, and the

theoretical probability is 415

. 2. This spinner has six sections of equal size.

3. The table shows the results of 50 rolls of a fair number cube numbered 1 to 6.

4. Peter picks one bill at a time from a bag and replaces it. He repeats this process 100 times and records the results in the table.

Based on the table, which bill has an experimental probability of 𝟕𝟕

𝟐𝟐𝟐𝟐 for being drawn from the bag next?

A. $1 B. $5 C. $10 D. $20

SOL 7.9 The student will investigate and describe the difference between the experimental probability and theoretical

probability of an event.

HINTS & NOTES Always write probability as a fraction first, then change it to a decimal or percent if needed.

# 𝑜𝑜𝑜𝑜 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑎𝑎𝑛𝑛 𝑡𝑡𝑒𝑒𝑡𝑡𝑛𝑛𝑡𝑡 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑟𝑟𝑡𝑡𝑡𝑡𝑜𝑜𝑡𝑡𝑎𝑎𝑡𝑡 # 𝑜𝑜𝑜𝑜 𝑝𝑝𝑜𝑜𝑡𝑡𝑡𝑡𝑡𝑡𝑏𝑏𝑡𝑡𝑡𝑡 𝑜𝑜𝑜𝑜𝑡𝑡𝑜𝑜𝑜𝑜𝑡𝑡𝑡𝑡𝑡𝑡

Number cubes and dice are the same thing. Theoretical probability is what should happen in an experiment based on reason. Experimental probability is what actually happens during an experiment.

PRACTICE

The arrow of this spinner was spun 60 times. On 45 out of 60 times, the arrow landed on a section with a multiple of 4. What was the experimental probability of the arrow landing on a section labeled with a multiple of 4?

According to the data in the table, what was the experimental probability of rolling a 1?

A. 425

B. 16

C. 950

D. 15

1. This table shows the types of pizza and drink selections at a party.

Maya will randomly select one type of pizza and one drink from these choices. What is the probability that Maya will select pepperoni pizza and cola?

A. 112

C. 27

B. 17 D. 3

4

2. The digits 1, 2, 3, and 4 are used to make a 3-digit number. Each digit can be repeated. What is the total number of 3-digit numbers that can be made using these digits?

A. 12 B. 27 C. 64 D. 81

3. A spinner has sections labeled W, X, Y, and Z. The faces of a number cube are labeled 1, 2, 3, 4, 5, and 6. What is the total number of possible outcomes of 1 spin of the arrow on the spinner and 1 roll of the number cube?

A. 6 B. 10 C. 24 D. 48

4. A container has 2 red flags, 3 blue flags, and 3 green flags. If Ron chooses two flags to keep, what is the probability of choosing a red flag and then a green flag?

A. 58

B. 564

C. 332

D. 328

5. Sarah has been given two number cubes. One cube has one of the following letters, A, B, C, D, E, and F on each side. The other cube has one of the following numbers, 1, 2, 3, 4, 5, 6, 7, 8, on each side. If Sarah rolls both cubes, what is the probability of rolling the letter C and an even number?

A. 148

B. 27

C. 23

D. 112

6. The spinner consists of ten equal regions as shown.

SOL 7.10 The student will determine the probability of compound events, using the Fundamental (Basic) Counting

Principle.

HINTS & NOTES The Fundamental (Basic) Counting Principle is a procedure that helps you determine the number of possible

outcomes of several events. o For example: the possible outfits for 2 shirts, 3 pants, and 4 hats would be 2 ∙ 3 ∙ 4 = 24 different outfits.

PRACTICE

Jeff spins the spinner twice. What is the probability of spinning an odd number and then an 8?

1. The number of 8-ounce glass of water Shane drank each day for 12 days is represented in the histogram.

Based on this histogram, which statement must be true?

A. On exactly 2 of these days, Shane drank 1 to 2 glasses of water.

B. On exactly 3 of these days, Shane drank 7 to 8 glasses of water.

C. On exactly 25% of these days, Shane drank 3 to 4 glasses of water.

D. On exactly 60% of these days, Shane drank 5 to 6 glasses of water.

2. Scott recorded the low temperature in Richmond each day for 10 days. This list shows the temperatures in degrees Celsius.

8⁰, 12⁰, 11⁰, 9⁰, 9⁰, 12⁰, 10⁰, 14⁰, 13⁰, 12⁰ Create a histogram of this set of data.

3. This stem-and-leaf plot shows the high temperatures for a city over 20 days.

Which histogram represents the same set of data?

SOL 7.11 The student, given data for a practical situation, will

a) Construct and analyze histograms; and b) Compare and contrast histograms with other types of graphs presenting information from the same

data set.

HINTS & NOTES A histogram is a form of a bar graph where the categories are consecutive intervals. How tall the bars are, are

determined by how many times something falls into that interval. The bars DO touch in this type of graph because it is continuous data. In comparing different graphs, you could see how data are or are not related, find differences (make

comparisons), make predictions by look at trends, and decide “what could happen if”.

PRACTICE

1. Ethan earns $12 per hour to walk 2 dogs, plus an additional $7 for brushing the 2 dogs after their walk.

• Let x represent the hours Ethan works. • Let y represent the total he earns each day.

Which number sentence best represents this situation?

A. 12𝑥𝑥 + 2 + 7 = 𝑦𝑦 B. 12𝑥𝑥 ∙ 2 + 7 = 𝑦𝑦 C. 12𝑥𝑥 + 7 = 𝑦𝑦 D. 12𝑥𝑥 − 7 = 𝑦𝑦

2. Which table contains only points that lie on the line represented by 𝒚𝒚 = 𝟐𝟐

𝟒𝟒𝒙𝒙 − 𝟑𝟑?

3. Which is true for all values in the table below?

4. Which rule is best represented by this graph?

A. 𝑦𝑦 = 2𝑥𝑥 + 4 B. 𝑦𝑦 = 2𝑥𝑥 − 4 C. 𝑦𝑦 = −2𝑥𝑥 − 4 D. 𝑦𝑦 = −2𝑥𝑥 + 4

5. Larry charges a customer a one-time fee of $15 plus $40 each week. Which table has values that represent this situation?

SOL 7.12 The student will represent relationships with tables, graphs, rules, and words.

HINTS & NOTES

Relations are any set of ordered pairs. A function is a relation where there is only one y-value for each x-value. Remember the Rule of 5!

1. 2. 3. 4. 5.

PRACTICE

C

A. 𝑦𝑦 = −𝑥𝑥 + 3 B. 𝑦𝑦 = 2𝑥𝑥 + 3 C. 𝑦𝑦 = 𝑥𝑥 − 1 D. 𝑦𝑦 = 2𝑥𝑥 − 3

1. Which algebraic expression best represents the verbal expression shown?

“Eleven times the sum of a number and five” A. 11 + 5𝑥𝑥 B. 11 + 𝑥𝑥2 + 5 C. 11 + 5 + 𝑥𝑥 D. 11(𝑥𝑥 + 5)

2. Marjorie bought 24 bottles of juice. Each day she opens and drinks 2 of these bottles of juice. Which of the following best represents the number of unopened bottles of juice Marjorie has at the end of d days?

A. 2𝑑𝑑 − 24 B. 24𝑑𝑑 − 2 C. 24 + 2𝑑𝑑 D. 24 − 2𝑑𝑑

3. Which of the following is the algebraic form for the verbal statement shown?

“13 more than the product of 4 and a number, n”

A. 𝑛𝑛4

+ 13

B. 4𝑛𝑛 + 13

C. 4(𝑛𝑛 + 13)

D. 13(𝑛𝑛 + 4)

4. Select each of the following that is an expression.

2𝑥𝑥 − 7 −14

3𝑥𝑥 2𝑥𝑥 − 7 = 14

𝑥𝑥 = 1 2 + 7

5. If k = 2, what is the value of 𝒌𝒌𝟐𝟐 − (𝒌𝒌 − 𝟏𝟏𝟏𝟏) + 𝟒𝟒𝒌𝒌? A. 6 B. 8 C. 22 D. 24

6. What is the value of 𝒂𝒂+𝟒𝟒𝟒𝟒𝒂𝒂+𝟒𝟒

if 𝒂𝒂 = −𝟒𝟒 and 𝟒𝟒 = 𝟑𝟑?

A. -24 B. -8 C. 0 D. 8

7. What is the value of 𝒎𝒎(𝒉𝒉 + 𝒑𝒑) − 𝒑𝒑 ÷ 𝒉𝒉 + 𝒎𝒎 if 𝒉𝒉 =−𝟏𝟏,𝒎𝒎 = 𝟑𝟑, and 𝒑𝒑 = 𝟒𝟒?

A. 0 B. 2 C. 8 D. 16

8. What is the value of |𝒚𝒚| + 𝟒𝟒 − 𝒚𝒚 ∙ 𝒙𝒙 if 𝒙𝒙 = 𝟕𝟕 and 𝒚𝒚 =−𝟐𝟐?

A. -12 B. -8 C. 16 D. 20

9. If 𝒂𝒂 = 𝟑𝟑, what is the value of 𝟖𝟖𝒂𝒂

𝟐𝟐− 𝟐𝟐𝒂𝒂 ∙ 𝟐𝟐?

A. 0 B. 4 C. 14 D. 18

SOL 7.13 The student will

a) Write verbal expressions as algebraic expressions and sentences as equations and vice versa; and b) Evaluate algebraic expressions for given replacement values of the variables.

HINTS & NOTES

Addition words/phrases:

Subtraction words/phrases:

Multiplication words/phrases:

Division words/phrases:

REMEMBER: “7 less than a number” means n – 7, not 7 – n.

PRACTICE

1. What is the solution to 𝒙𝒙−𝟒𝟒

= 𝟏𝟏𝟏𝟏? A. -40 B. -6 C. 6 D. 40

2. What is the value of n that makes the following true?

𝒏𝒏 + (−𝟕𝟕) = −𝟕𝟕𝟕𝟕

A. -84 B. -70 C. 84 D. 70

3. Aidan’s age is 6 years less than half of Maggie’s age. Aidan’s age is 4 years. What is Maggie’s age?

A. 2 years B. 5 years C. 10 years D. 20 years

4. A server at a restaurant gets paid $10 an hour and also gets to keep any tips. The server’s tips average $7 per table. If in the last hour the server earned $45, which equation can be used to calculate the number of tables served?

A. 7𝑥𝑥 − 10 = 45 B. 7𝑥𝑥 + 10 = 45 C. 45 − 10𝑥𝑥 = 7 D. 10𝑥𝑥 + 7 = 45

5. Maria called her sister long distance on Wednesday. The first 5 minutes cost $3, and each minute after that costs $0.25. How much did it cost if they talked for 15 minutes?

A. $3.25 B. $5.50 C. $6.75 D. $9.00

6. What is the solution to –𝟐𝟐𝒙𝒙 + 𝟑𝟑 = 𝟏𝟏𝟐𝟐? 7. What is the solution to 𝒙𝒙

𝟒𝟒− 𝟕𝟕 = −𝟏𝟏𝟏𝟏?

8. What is the solution to 𝟑𝟑𝒙𝒙 + 𝟒𝟒 = −𝟐𝟐𝟏𝟏?

SOL 7.14 The student will

a) Solve one- and two-step linear equations in one variable; and b) Solve practical problems requiring the solution of one- and two-step linear equations.

HINTS & NOTES Remember to use your inverse operations to solve equations:

o Addition ↔ subtraction o Multiplication ↔ division

Always check your answer but substituting it back into the equation. If you get the same answer on both sides of the equals sign, you have the right answer!

PRACTICE

1. What is the solution to −𝟏𝟏𝟐𝟐𝒙𝒙 ≤ −𝟕𝟕𝟐𝟐?

A. 𝑥𝑥 ≥ 6 B. 𝑥𝑥 ≤ 6 C. 𝑥𝑥 ≥ −6 D. 𝑥𝑥 ≤ −6

2. Which graph represents the solution set to this inequality?

𝒙𝒙 + 𝟐𝟐 < 7

3. Which value of k makes −𝟐𝟐 > 𝑘𝑘 + 11 true?

A. 8 B. -4 C. -16 D. -22

4. What is the solution to 𝒄𝒄 − 𝟏𝟏𝟒𝟒 < 16?

A. 𝑜𝑜 < 2 B. 𝑜𝑜 > 2 C. 𝑜𝑜 < 30 D. 𝑜𝑜 > 30

5. What is the solution to −𝟒𝟒𝒏𝒏 < 16? 6. What is the solution to −𝟑𝟑𝟏𝟏 > 6𝒚𝒚? 7. Graph the solution set for #5.

8. Graph the solution set for #6.

SOL 7.15 The student will

a) Solve one-step inequalities in one variable; and b) Graph solutions to inequalities on the number line.

HINTS & NOTES Inequalities do not just have one solution. Remember when both sides of an inequality are multiplied or divided by a negative number, the

inequality symbol reverses. When graphing the solution to an inequality on a number line, use the following tips.

o Use an open circle for inequalities < and >. o Use a solid circle for the inequalities ≤ and ≥. o Pick a number to substitute into your inequality. If it works, then shade in that side of your

number line.

PRACTICE

1. Which property is illustrated by this number sentence?

(−1 ∙ 7) + 3 = 3 + (−1 ∙ 7)

Associative Property of

Addition

Commutative Property of

Addition

Distributive Property

Associative Property of

Multiplication

Commutative Property of

Multiplication

Multiplicative Identity Property

2. Identify each number sentence that illustrates the associative property of addition.

7 + (3 + 8) = (7 + 3) + 8

(4 ∙ 7) ∙ 1 + 6 = 4 ∙ (7 ∙ 1) + 6

2 + 6 + 7 = 2 + 7 + 6

�5 + (−1)� + 6 = 5 + (−1 + 6)

(4 + 1) + 3 − 7 = 4 + (1 + 3) − 7

1 − (5 + 2) = 1 − (2 + 5)

3. Which expression completes this equation using only the multiplicative property of zero?

(𝟐𝟐 + 𝟏𝟏) + (−𝟒𝟒+ 𝟒𝟒) − (𝟔𝟔 ∙ 𝟏𝟏) = _________

A. (𝟐𝟐) + (−𝟒𝟒 + 𝟒𝟒) − (𝟔𝟔 ∙ 𝟏𝟏) B. (𝟐𝟐 + 𝟏𝟏) + 𝟏𝟏 − (𝟔𝟔 ∙ 𝟏𝟏) C. (𝟐𝟐 + 𝟏𝟏) + (−𝟒𝟒 + 𝟒𝟒) − 𝟏𝟏 D. (𝟏𝟏 + 𝟐𝟐) + (−𝟒𝟒 + 𝟒𝟒) − (𝟔𝟔 ∙ 𝟏𝟏)

4. Which equation illustrates the multiplicative identity property?

A. (8 − 5) ∙ 0 = 0 B. �3

8∙ 12� ∙ 1 = �3

8∙ 12�

C. (8 + 0) ∙ 1 = 8 ∙ 1 D. �2

3∙ 32� ∙ 5 = 1 ∙ 5

5. Identify each number sentence that illustrates the distributive property.

(4 ∙ 7) ∙ 1 + 6 = 4 ∙ (7 ∙ 1) + 6

4(3 + 1) = 4(3) + 4(1)

5(3 + 7 ∙ 0) = 5(3 + 0)

7 + 5(4 + 2) = 7 + 5(4) + 5(2)

7(9 − 1) + 2 = 7(9) − 7(1) + 2

1(5 + 2) = 1(2 + 5)

SOL 7.16 The student will apply the following properties of operations with real numbers:

a) The commutative and associative properties for addition and multiplication; b) The distributive property;

c) The additive and multiplicative identity properties; d) The additive and multiplicative inverse properties; and

e) The multiplicative property of zero.

HINTS & NOTES Property Addition Multiplication

Commutative (Change Order) 𝑎𝑎 + 𝑏𝑏 = 𝑏𝑏 + 𝑎𝑎 𝑎𝑎 ∙ 𝑏𝑏 = 𝑏𝑏 ∙ 𝑎𝑎 Associative (Grouping changes) (𝑎𝑎 + 𝑏𝑏) + 𝑜𝑜 = 𝑎𝑎 + (𝑏𝑏 + 𝑜𝑜) (𝑎𝑎 ∙ 𝑏𝑏) ∙ 𝑜𝑜 = 𝑎𝑎 ∙ (𝑏𝑏 ∙ 𝑜𝑜) Identity 𝑎𝑎 + 0 = 𝑎𝑎 𝑎𝑎 ∙ 1 = 𝑎𝑎 Inverse 𝑎𝑎 + (−𝑎𝑎) = 0 𝑎𝑎 ∙

1𝑎𝑎

= 1

Property of zero 𝑎𝑎 ∙ 0 = 0 Distributive property uses addition and multiplication: 𝑎𝑎(𝑏𝑏 + 𝑜𝑜) = 𝑎𝑎𝑏𝑏 + 𝑎𝑎𝑜𝑜

PRACTICE