· Web viewTo 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. Move the decimal

SOL Review Booklet2016-2017

Math 7Sterling Middle School

Adapted from Spotsylvania County Schools

SOL 7.1The 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

PRACTICE

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

110,000

0.004

-0.0001 0.0001

−110,000

140,000

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

A.−1103

and -0.003

B.1103

and -0.003

C.−1103

and 0.001

D.1103

and 0.001

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 exponent 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




e) Identify and describe absolute value for rational numbers.

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)




4. Look at the following variable expression: p+8.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 14

.

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, …

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

PRACTICE

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.n12

B. 12nC. n+22D. n−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, …

b+4 w÷5

2 t k ÷2

5 r a−4

p+3 z−3

HINTS & NOTES An arithmetic sequence you have to find the common difference. This is what you would add or subtract from

each number to get the next. In geometric sequences you have to find the common ratio. 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


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

PRACTICE


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

PRACTICE

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

Example:heightshadow =

height 2shadow2

To solve a proportion – CROSS MULITPLY, THEN DIVIDE BY THE COEFFICIENT (THE NUMBER THAT IS WITH THE VARIABLE)

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

5cm16cm

Proportions can also be used to represent percent problems. For example: percent100 =

partwhole

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

5. The correct mixture of oil to gas in a weed eater is 12

pint of oil to 2 12 gallons of gas. How many pints of oil are

needed for 10 gallons of gas?A. 1B. 2C. 5D. 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. $0.03B. $1.28C. $2.56D. $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?

1. Mark 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 inchesB. 8 inchesC. 27 inchesD. 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. $25B. $60C. $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. $136.25B. $408.75C. $520.00D. $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.1

5,280=5x C.

15,280

= x5

B.15= x5,280 D.

1x=5,280

5


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.

9. A rectangular prism has a height of 3 inches and volume of 27 cubic inches. The height of this prism is

6. Trevor covered a cylindrical can with paper for a project. The can is 18 centimeters tall and has a 5-

PRACTICE


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.

4. Triangle PQR is similar to triangle STU.

Which proportion can be used to find n?

A.515

= n12

B.155

= n12

C.1315

=1236

D.13n

=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.

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. 65⁰B. 80⁰C. 100⁰D. 115⁰

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

A. 12 cmB. 24 cmC. 36 cmD. 48 cm

9. A rectangular prism has a height of 3 inches and volume of 27 cubic inches. The height of this prism is

6. Trevor covered a cylindrical can with paper for a project. The can is 18 centimeters tall and has a 5-

PRACTICE

HINTS & NOTES Similar figures – same shape but different SIZE. Their corresponding angles have EQUAL__ measure and their

corresponding sides are PROPORTIONAL __ . This means that the ratios of corresponding sides are equal. Remember – to solve a proportion – cross multiply or use equivalent ratios. The symbol ~ CONGRUENT

SOL 7.6The 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 Quadrilateral – polygon w/ 4 sides Types of Quadrilaterals

SOL 7.7The 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

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

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

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

Clockwise Counterclockwise Vertical Horizontal

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

PRACTICE

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

¿of×anevent occurstotal ¿

of possible outcomes¿

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.

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

probability of an event.

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?

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

PRACTICE

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.

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

Principle.

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

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

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?

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

PRACTICE

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”.

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

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

data set.

4. Which rule is best represented by this graph?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. 12 x+2+7= yB. 12 x ∙2+7= yC. 12 x+7= yD. 12 x−7= y

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

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

PRACTICE

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.

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

4. Which rule is best represented by this graph?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. 12 x+2+7= yB. 12 x ∙2+7= yC. 12 x+7= yD. 12 x−7= y

PRACTICE

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.


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

5. If k = 2, what is the value of k 2−(k−10 )+4 k?A. 6B. 8C. 22D. 24

6. What is the value of a+4ba+b if a=−4 and b=3?

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

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

“Eleven times the sum of a number and five”A. 11+5 xB. 11+x2+5C. 11+5+xD. 11 ( x+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?

5. If k = 2, what is the value of k 2−(k−10 )+4 k?A. 6B. 8C. 22D. 24

6. What is the value of a+4ba+b if a=−4 and b=3?

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

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

“Eleven times the sum of a number and five”A. 11+5 xB. 11+x2+5C. 11+5+xD. 11 ( x+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?

PRACTICE

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

o Addition ↔ subtractiono 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!


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

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

6. What is the solution to –2 x+3=15?

1. What is the solution to x

−4=10?

A. -40B. -6C. 6D. 40

2. What is the value of n that makes the following true?n+(−7 )=−77

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

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

5. What is the solution to −4n<16?

6. What is the solution to −30>6 y?

7. Graph the solution set for #5.

1. What is the solution to −12 x≤−72?

A. x≥6B. x≤6C. x≥−6D. x≤−6

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

x+5<7

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

6. What is the solution to –2 x+3=15?

1. What is the solution to x

−4=10?

A. -40B. -6C. 6D. 40

2. What is the value of n that makes the following true?n+(−7 )=−77

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

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

PRACTICE

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.


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

5. What is the solution to −4n<16?

6. What is the solution to −30>6 y?

7. Graph the solution set for #5.

1. What is the solution to −12 x≤−72?

A. x≥6B. x≤6C. x≥−6D. x≤−6

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

x+5<7

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

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

(5+0 )+ (−4+4 )−(6 ∙0 )=¿¿

A. (5 )+(−4+4 )−(6 ∙0 )B. (5+0 )+0−(6 ∙0 )C. (5+0 )+ (−4+4 )−0D. (0+5 )+ (−4+4 )−(6 ∙0 )

4. Which equation illustrates the multiplicative identity property?

A. (8−5 ) ∙0=0

B. ( 38 ∙ 12 )∙1=( 38 ∙ 12 )C. (8+0 ) ∙1=8 ∙1

SOL 7.16The 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 & NOTESProperty Addition Multiplication

Commutative (Change Order) a+b=b+a a ∙b=b ∙aAssociative (Grouping changes) (a+b )+c=a+(b+c ) (a ∙b ) ∙ c=a ∙ (b ∙c )Identity a+0=a a ∙1=aInverse a+ (−a )=0 a ∙ 1

a=1

Property of zero a ∙0=0

Distributive property uses addition and multiplication: a (b+c )=ab+ac

PRACTICE

Documents

· Web viewTo 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. Move the decimal