Loudoun County Public Schools / Overview



SOL Review Booklet2016-2017Math 7Sterling Middle SchoolAdapted from Spotsylvania County Schools-9525-85725SOL 7.1The student will Investigate and describe the concept of negative exponents for powers of ten;Determine scientific notation for numbers greater than zero;Compare and order fractions, decimals, and percents and numbers written in scientific notation;Determine square roots; and Identify and describe absolute value for rational numbers.HINTS & NOTESTo write a number in scientific notation: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.Move the decimal to make a factor between 1 and 10 (so that there is only one number to the left of the decimal).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 1. Which fraction and decimal are equivalent to 10-3?-1103 and -0.0031103 and -0.003-1103 and 0.0011103 and 0.0012. What decimal and decimal are equivalent to 10-7?3. Identify the numbers that are equivalent to 10-4. 110,0000.004-0.00010.0001-110,000140,000PRACTICE00SOL 7.1The student will Investigate and describe the concept of negative exponents for powers of ten;Determine scientific notation for numbers greater than zero;Compare and order fractions, decimals, and percents and numbers written in scientific notation;Determine square roots; and Identify and describe absolute value for rational numbers.HINTS & NOTESTo write a number in scientific notation: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.Move the decimal to make a factor between 1 and 10 (so that there is only one number to the left of the decimal).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 1. Which fraction and decimal are equivalent to 10-3?-1103 and -0.0031103 and -0.003-1103 and 0.0011103 and 0.0012. What decimal and decimal are equivalent to 10-7?3. Identify the numbers that are equivalent to 10-4. 110,0000.004-0.00010.0001-110,000140,000PRACTICE3457575203835Steps 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)00Steps 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)-57150-28575SOL 7.1The student will Investigate and describe the concept of negative exponents for powers of ten;Determine scientific notation for numbers greater than zero;Compare and order fractions, decimals, and percents and numbers written in scientific notation;Determine square roots; and Identify and describe absolute value for rational numbers.4. What is 0.000012 written in scientific notation?1.2 x 10-51.2 x 10-41.2 x 1041.2 x 1055. 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 101212.3 x 10131.23 x 10-141.23 x 1014123 x 10-121.23 x 10-126. Which list of numbers is arranged from least to greatest?0.25, 17%, 290.25, 29, 17%17%, 0.25, 2917%, 29, 0.257. Arrange the three numbers shown in order from least to greatest.4.7 x 1053.9 x 1085.2 x 1058. Identify two values that have a value less than 3.2.9 x 1013.2 x 1032.9 x 1003.2 x 10-29. Which number would make the sentence true?211< <1.421230.15322%1.3 x 10110. Which number is the square root of 400?400200402011. Which number is the square root of 1?14121212. What is the absolute value of -8.2?8.24.1-4.1-8.213. What is -1112?1211C. -11121112D. -1211PRACTICELeastGreatest00SOL 7.1The student will Investigate and describe the concept of negative exponents for powers of ten;Determine scientific notation for numbers greater than zero;Compare and order fractions, decimals, and percents and numbers written in scientific notation;Determine square roots; and Identify and describe absolute value for rational numbers.4. What is 0.000012 written in scientific notation?1.2 x 10-51.2 x 10-41.2 x 1041.2 x 1055. 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 101212.3 x 10131.23 x 10-141.23 x 1014123 x 10-121.23 x 10-126. Which list of numbers is arranged from least to greatest?0.25, 17%, 290.25, 29, 17%17%, 0.25, 2917%, 29, 0.257. Arrange the three numbers shown in order from least to greatest.4.7 x 1053.9 x 1085.2 x 1058. Identify two values that have a value less than 3.2.9 x 1013.2 x 1032.9 x 1003.2 x 10-29. Which number would make the sentence true?211< <1.421230.15322%1.3 x 10110. Which number is the square root of 400?400200402011. Which number is the square root of 1?14121212. What is the absolute value of -8.2?8.24.1-4.1-8.213. What is -1112?1211C. -11121112D. -1211PRACTICELeastGreatest-28575-171450HINTS & NOTESAn 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.Examples:3, 6, 9, 12… expression: m + 31, 5, 25, 125… expression: 5n1. Let n represent any number in this sequence.2, 24, 46, 68, …Which of these can be used to determine the next number?n1212nn+22n-222. Which statement is true about the pattern shown?5, 20, 80, 320, …The common ratio is 4.The common ratio is 15.The common difference is 4.The common difference is 15.3. Complete the table with an expression that describes each sequence.SequenceExpression3, 6, 9, 12, …1, 5, 25, 125, …2, 4, 8, 16, …4, 8, 12, 16, …b+4w÷52tk÷25ra-4p+3z-3PRACTICESOL 7.2The student will describe and represent arithmetic and geometric sequences using variable expressions.4. Look at the following variable expression: p+8.Which sequence is described by the given variable expression?3, 24, 192, 1536, …8, 16, 32, 64, …17, 25, 33, 41, …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, …00HINTS & NOTESAn 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.Examples:3, 6, 9, 12… expression: m + 31, 5, 25, 125… expression: 5n1. Let n represent any number in this sequence.2, 24, 46, 68, …Which of these can be used to determine the next number?n1212nn+22n-222. Which statement is true about the pattern shown?5, 20, 80, 320, …The common ratio is 4.The common ratio is 15.The common difference is 4.The common difference is 15.3. Complete the table with an expression that describes each sequence.SequenceExpression3, 6, 9, 12, …1, 5, 25, 125, …2, 4, 8, 16, …4, 8, 12, 16, …b+4w÷52tk÷25ra-4p+3z-3PRACTICESOL 7.2The student will describe and represent arithmetic and geometric sequences using variable expressions.4. Look at the following variable expression: p+8.Which sequence is described by the given variable expression?3, 24, 192, 1536, …8, 16, 32, 64, …17, 25, 33, 41, …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, …-123825-95251. Which number sentence is represented by this model?-3?5=15-3?5=-15-3?(-5)=15-3?-5=-152. Which number sentence is represented by this model?-4?7=28-4?7=-284?(-7)=284?-7=-28 3. Which model illustrates the division of integers?SOL 7.3The student will Model addition, subtraction, multiplication, and division of integers; andAdd, subtract, multiply, and divide integers.HINTS & NOTESAdding integers – Example: (-4) +( -2)= -6 or (-4) + 2 = -2Subtracting integers – Example: ( -4) – (-2) becomes (-4)+ 2 which = -2Multiplying and Dividing Integers –positive ? positive = __+__negative ? negative=_+___positive ? negative = __-__negative ? positive = __-__PRACTICE001. Which number sentence is represented by this model?-3?5=15-3?5=-15-3?(-5)=15-3?-5=-152. Which number sentence is represented by this model?-4?7=28-4?7=-284?(-7)=284?-7=-28 3. Which model illustrates the division of integers?SOL 7.3The student will Model addition, subtraction, multiplication, and division of integers; andAdd, subtract, multiply, and divide integers.HINTS & NOTESAdding integers – Example: (-4) +( -2)= -6 or (-4) + 2 = -2Subtracting integers – Example: ( -4) – (-2) becomes (-4)+ 2 which = -2Multiplying and Dividing Integers –positive ? positive = __+__negative ? negative=_+___positive ? negative = __-__negative ? positive = __-__PRACTICE-104775-857254. During a winter’s day, the low temperature was recorded at 21℉. The wind-chill temperature that same day was -8℉. What was the difference between the wind-chill temperature and the low temperature?8℉13℉25℉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?4, 2754,3004,3254,3526. Using the following key as a guide, what this the result of the operation in the model below? -10-2210 7. Identify each statement that is equivalent to -2.-6--12÷35+-6?4+2-12+8÷2-12—4+-3?(-2)-4+8?(-1)÷28. 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 –3 feet above the surface of the water3 feet below the surface of the water63 feet above the surface of the water63 feet below the surface of the water9. Identify each number that can be placed in the blank to make the value of this expression a negative number. -13-_________-20-14-12-810SOL 7.3The student will Model addition, subtraction, multiplication, and division of integers; andAdd, subtract, multiply, and divide integers.PRACTICE004. During a winter’s day, the low temperature was recorded at 21℉. The wind-chill temperature that same day was -8℉. What was the difference between the wind-chill temperature and the low temperature?8℉13℉25℉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?4, 2754,3004,3254,3526. Using the following key as a guide, what this the result of the operation in the model below? -10-2210 7. Identify each statement that is equivalent to -2.-6--12÷35+-6?4+2-12+8÷2-12—4+-3?(-2)-4+8?(-1)÷28. 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 –3 feet above the surface of the water3 feet below the surface of the water63 feet above the surface of the water63 feet below the surface of the water9. Identify each number that can be placed in the blank to make the value of this expression a negative number. -13-_________-20-14-12-810SOL 7.3The student will Model addition, subtraction, multiplication, and division of integers; andAdd, subtract, multiply, and divide integers.PRACTICE-90805-1238251. 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?4 inches8 inches27 inches162 inches2. Kelly received a 25% discount on the purchase of a $240 bicycle. What was the amount of the discount Kelly received?$25$60$180 $2153. 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?$136.25$408.75$520.00$681.254. 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?15,280=5xC. 15,280=x515=x5,280 D. 1x=5,28055. The correct mixture of oil to gas in a weed eater is 12 pint of oil to 212 gallons of gas. How many pints of oil are needed for 10 gallons of gas?12586. 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?$0.03$1.28$2.56$10.267. Seventy-six is 80% of what number?8. Thirty-two is what percent of 80?9. What is 4.5% of 40? SOL 7.4The student will solve single-step and multistep practical problems, using proportional reasoning. HINTS & NOTESWhen setting up a proportion – make sure that the numerators and __DENOMINATORS_____match.Example:= 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: 2 inchesx = 5 cm16 cmProportions can also be used to represent percent problems. For example: percent100 = partwholePRACTICE001. 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?4 inches8 inches27 inches162 inches2. Kelly received a 25% discount on the purchase of a $240 bicycle. What was the amount of the discount Kelly received?$25$60$180 $2153. 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?$136.25$408.75$520.00$681.254. 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?15,280=5xC. 15,280=x515=x5,280 D. 1x=5,28055. The correct mixture of oil to gas in a weed eater is 12 pint of oil to 212 gallons of gas. How many pints of oil are needed for 10 gallons of gas?12586. 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?$0.03$1.28$2.56$10.267. Seventy-six is 80% of what number?8. Thirty-two is what percent of 80?9. What is 4.5% of 40? SOL 7.4The student will solve single-step and multistep practical problems, using proportional reasoning. HINTS & NOTESWhen setting up a proportion – make sure that the numerators and __DENOMINATORS_____match.Example:= 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: 2 inchesx = 5 cm16 cmProportions can also be used to represent percent problems. For example: percent100 = partwholePRACTICE2095500267652500-90805-762001. One way to determine the surface area of this cylinder is to – Add the areas of both bases to the rectangular area around the cylinderAdd the areas of both basesMultiply the area of the base by the heightMultiply 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?Rectangular Prism QRectangular Prism RRectangular Prism SRectangular Prism T5. 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?π?82?7π?162?72π?82+2π?8?72π?162+2π?16?7SOL 7.5The student will Describe volume and surface area of cylinders; Solve practical problems involving the volume and surface area of rectangular prisms and cylinders; 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 – PRACTICE001. One way to determine the surface area of this cylinder is to – Add the areas of both bases to the rectangular area around the cylinderAdd the areas of both basesMultiply the area of the base by the heightMultiply 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?Rectangular Prism QRectangular Prism RRectangular Prism SRectangular Prism T5. 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?π?82?7π?162?72π?82+2π?8?72π?162+2π?16?7SOL 7.5The student will Describe volume and surface area of cylinders; Solve practical problems involving the volume and surface area of rectangular prisms and cylinders; 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-90805-762006. 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?283 cm2644 cm2722 cm21,413 cm27. Carl is covering the rectangular prism-shaped box with cloth.What is the minimum amount of cloth Carl needs to cover the entire box?96 sq in.136 sq in.192 sq in.272 sq in.8. The length of Rectangular Prism A is shown.The length of this prism is multiplied by a scale factor of 12 to create Rectangular Prism B. The volume of Rectangular Prism B is –2 times the volume of Rectangular Prism A3 times the volume of Rectangular Prism A14 times the volume of Rectangular Prism A12 times the volume of Rectangular Prism A9. 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?30 cubic inches54 cubic inches81 cubic inches162 cubic inches10. 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 –Twice the volume of Prism AOne-half of the volume of Prism AOne-fourth the volume of Prism AFour times the volume of Prism A11. 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 inchesLength = 7.8 inchesHeight = 11.6 inchesWhich situation will create the least surface area?Multiply the length of a scale factor of 13Multiply the width of a scale factor of 13Multiply the height of a scale factor of 12Multiply the length of a scale factor of 12SOL 7.5The student will Describe volume and surface area of cylinders; Solve practical problems involving the volume and surface area of rectangular prisms and cylinders; Describe how changing one measured attribute of a rectangular prism affects its volume and surface area. PRACTICE006. 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?283 cm2644 cm2722 cm21,413 cm27. Carl is covering the rectangular prism-shaped box with cloth.What is the minimum amount of cloth Carl needs to cover the entire box?96 sq in.136 sq in.192 sq in.272 sq in.8. The length of Rectangular Prism A is shown.The length of this prism is multiplied by a scale factor of 12 to create Rectangular Prism B. The volume of Rectangular Prism B is –2 times the volume of Rectangular Prism A3 times the volume of Rectangular Prism A14 times the volume of Rectangular Prism A12 times the volume of Rectangular Prism A9. 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?30 cubic inches54 cubic inches81 cubic inches162 cubic inches10. 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 –Twice the volume of Prism AOne-half of the volume of Prism AOne-fourth the volume of Prism AFour times the volume of Prism A11. 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 inchesLength = 7.8 inchesHeight = 11.6 inchesWhich situation will create the least surface area?Multiply the length of a scale factor of 13Multiply the width of a scale factor of 13Multiply the height of a scale factor of 12Multiply the length of a scale factor of 12SOL 7.5The student will Describe volume and surface area of cylinders; Solve practical problems involving the volume and surface area of rectangular prisms and cylinders; Describe how changing one measured attribute of a rectangular prism affects its volume and surface area. PRACTICE-100330-1524001. 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?65?80?100?115?3. What must the value of x be in order for the figures below to be similar?12 cm24 cm36 cm48 cm 4. Triangle PQR is similar to triangle STU.Which proportion can be used to find n?515=n12155=n121315=123613n=36126. Are the two figures below similar?No, the sides are not congruent.Yes, the sides are proportional.No, the sides are not proportional.Yes, the sides are 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 & NOTESSimilar figures – same shape but different SIZE. Their corresponding angles have EQUAL__ measure and their corresponding sides arePROPORTIONAL__. This means that the ratios of corresponding sides are equal. Remember – to solve a proportion – cross multiply or use equivalent ratios.The symbol ~ CONGRUENTPRACTICE001. 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?65?80?100?115?3. What must the value of x be in order for the figures below to be similar?12 cm24 cm36 cm48 cm 4. Triangle PQR is similar to triangle STU.Which proportion can be used to find n?515=n12155=n121315=123613n=36126. Are the two figures below similar?No, the sides are not congruent.Yes, the sides are proportional.No, the sides are not proportional.Yes, the sides are 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 & NOTESSimilar figures – same shape but different SIZE. Their corresponding angles have EQUAL__ measure and their corresponding sides arePROPORTIONAL__. This means that the ratios of corresponding sides are equal. Remember – to solve a proportion – cross multiply or use equivalent ratios.The symbol ~ CONGRUENTPRACTICE-90805-1524001. Which statement is false?All squares are rectangles.All squares are parallelograms.All rhombuses are squares.All rhombuses are parallelograms.2. Every rhombus is also a –ParallelogramTrapezoidRectangleSquare3. Which classifications must describe the figure shown?Square and parallelogramTrapezoid and parallelogramSquare and quadrilateralTrapezoid and quadrilateral 4. Select each classification that does NOT describe this figure.ParallelogramRhombusRectangleTrapezoidSquareQuadrilateral5. Identify each classification to which this figure belongs.ParallelogramRhombusTrapezoidRectangleQuadrilateralSquare6. Which is a parallelogram with four congruent sides whose diagonals bisect each other and intersect at four right angles?CubeTrapezoidRhombusRectangleSOL 7.7The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid.HINTS & NOTESQuadrilateral – polygon w/ 4 sidesTypes of QuadrilateralsQuadrilateralPropertiesParallelogram 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 90? (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 90? (right angles).Diagonals are perpendicular bisectors and are congruent.RhombusBoth pairs of opposite sides are parallel.All four sides are congruent.Diagonals are perpendicular bisectors.Trapezoid One pair of opposite sides are parallel.PRACTICE001. Which statement is false?All squares are rectangles.All squares are parallelograms.All rhombuses are squares.All rhombuses are parallelograms.2. Every rhombus is also a –ParallelogramTrapezoidRectangleSquare3. Which classifications must describe the figure shown?Square and parallelogramTrapezoid and parallelogramSquare and quadrilateralTrapezoid and quadrilateral 4. Select each classification that does NOT describe this figure.ParallelogramRhombusRectangleTrapezoidSquareQuadrilateral5. Identify each classification to which this figure belongs.ParallelogramRhombusTrapezoidRectangleQuadrilateralSquare6. Which is a parallelogram with four congruent sides whose diagonals bisect each other and intersect at four right angles?CubeTrapezoidRhombusRectangleSOL 7.7The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid.HINTS & NOTESQuadrilateral – polygon w/ 4 sidesTypes of QuadrilateralsQuadrilateralPropertiesParallelogram 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 90? (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 90? (right angles).Diagonals are perpendicular bisectors and are congruent.RhombusBoth pairs of opposite sides are parallel.All four sides are congruent.Diagonals are perpendicular bisectors.Trapezoid One pair of opposite sides are parallel.PRACTICE159067533718500149542516192500159067513335001657350306705001657350457200035528252095500-62230-571501. Quadrilateral KLMN is rotated 180? clockwise about the origin. Which coordinates best represent the image of point K?(6,8)(-4,2)(8, -6)(4, -2)2. Which numbered triangle is a 90? counterclockwise rotation about the origin of shaded triangle?Triangle 1Triangle 2Triangle 3Triangle 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?(5, -8)(5, 4)(-1, -2)(11, -2)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.HINTS & NOTESTranslation = SlideRotation = TurnReflection = FlipDilationsPRACTICE001. Quadrilateral KLMN is rotated 180? clockwise about the origin. Which coordinates best represent the image of point K?(6,8)(-4,2)(8, -6)(4, -2)2. Which numbered triangle is a 90? counterclockwise rotation about the origin of shaded triangle?Triangle 1Triangle 2Triangle 3Triangle 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?(5, -8)(5, 4)(-1, -2)(11, -2)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.HINTS & NOTESTranslation = SlideRotation = TurnReflection = FlipDilationsPRACTICE5657850272415Horizontal00Horizontal4514850272415Vertical 00Vertical 3181350272415Counterclockwise00Counterclockwise1847850272415Clockwise00Clockwise51530253238500335280028956000204787528956000576262519050050387252695575According to the data in the table, what was the experimental probability of rolling a 1?425169501500According to the data in the table, what was the experimental probability of rolling a 1?425169501516002007010400The 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?00The 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?-81280-857251. 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?The experimental probability is 15, and the theoretical probability is 15.The experimental probability is 15, and the theoretical probability is 415.The experimental probability is 415, and the theoretical probability is 15.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 725 for being drawn from the bag next?$1$5$10$20SOL 7.9The student will investigate and describe the difference between the experimental probability and theoretical probability of an event.HINTS & NOTESAlways write probability as a fraction first, then change it to a decimal or percent if needed.# of times an event occurstotal # of possible outcomesNumber 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.PRACTICE001. 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?The experimental probability is 15, and the theoretical probability is 15.The experimental probability is 15, and the theoretical probability is 415.The experimental probability is 415, and the theoretical probability is 15.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 725 for being drawn from the bag next?$1$5$10$20SOL 7.9The student will investigate and describe the difference between the experimental probability and theoretical probability of an event.HINTS & NOTESAlways write probability as a fraction first, then change it to a decimal or percent if needed.# of times an event occurstotal # of possible outcomesNumber 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-10033001. 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?112 C. 2717D. 342. 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?122764813. 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?61024484. 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?585643323285. 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?14827231126. The spinner consists of ten equal regions as shown.SOL 7.10The student will determine the probability of compound events, using the Fundamental (Basic) Counting Principle. HINTS & NOTESThe Fundamental (Basic) Counting Principle is a procedure that helps you determine the number of possible outcomes of several events.For example: the possible outfits for 2 shirts, 3 pants, and 4 hats would be 2?3?4 = 24 different outfits.PRACTICE001. 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?112 C. 2717D. 342. 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?122764813. 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?61024484. 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?585643323285. 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?14827231126. The spinner consists of ten equal regions as shown.SOL 7.10The student will determine the probability of compound events, using the Fundamental (Basic) Counting Principle. HINTS & NOTESThe Fundamental (Basic) Counting Principle is a procedure that helps you determine the number of possible outcomes of several events.For example: the possible outfits for 2 shirts, 3 pants, and 4 hats would be 2?3?4 = 24 different outfits.PRACTICE51816006884670Jeff spins the spinner twice. What is the probability of spinning an odd number and then an 8?00Jeff spins the spinner twice. What is the probability of spinning an odd number and then an 8?-81280-571501. 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?On exactly 2 of these days, Shane drank 1 to 2 glasses of water.On exactly 3 of these days, Shane drank 7 to 8 glasses of water.On exactly 25% of these days, Shane drank 3 to 4 glasses of water.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. 8?, 12?, 11?, 9?, 9?, 12?, 10?, 14?, 13?, 12?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 7.11The student, given data for a practical situation, willConstruct and analyze histograms; andCompare and contrast histograms with other types of graphs presenting information from the same data set.HINTS & NOTESA 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”.PRACTICE001. 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?On exactly 2 of these days, Shane drank 1 to 2 glasses of water.On exactly 3 of these days, Shane drank 7 to 8 glasses of water.On exactly 25% of these days, Shane drank 3 to 4 glasses of water.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. 8?, 12?, 11?, 9?, 9?, 12?, 10?, 14?, 13?, 12?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 7.11The student, given data for a practical situation, willConstruct and analyze histograms; andCompare and contrast histograms with other types of graphs presenting information from the same data set.HINTS & NOTESA 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-57150-762001. 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?12x+2+7=y12x?2+7=y12x+7=y12x-7=y2. Which table contains only points that lie on the line represented by y=54x-3?3. Which is true for all values in the table below?4. Which rule is best represented by this graph?y=2x+4y=2x-4y=-2x-4y=-2x+45. Larry charges a customer a one-time fee of $15 plus $40 each week. Which table has values that represent this situation?SOL 7.12The student will represent relationships with tables, graphs, rules, and words.HINTS & NOTESRelations are any set of ordered pairs.A function is a relation where there is only one y-value for each x-value.PRACTICECy=-x+3y=2x+3y=x-1y=2x-3001. 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?12x+2+7=y12x?2+7=y12x+7=y12x-7=y2. Which table contains only points that lie on the line represented by y=54x-3?3. Which is true for all values in the table below?4. Which rule is best represented by this graph?y=2x+4y=2x-4y=-2x-4y=-2x+45. Larry charges a customer a one-time fee of $15 plus $40 each week. Which table has values that represent this situation?SOL 7.12The student will represent relationships with tables, graphs, rules, and words.HINTS & NOTESRelations are any set of ordered pairs.A function is a relation where there is only one y-value for each x-value.PRACTICECy=-x+3y=2x+3y=x-1y=2x-3-119380-762001. Which algebraic expression best represents the verbal expression shown?“Eleven times the sum of a number and five”11+5x11+x2+511+5+x11x+52. 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?2d-2424d-224+2d24-2d3. Which of the following is the algebraic form for the verbal statement shown?“13 more than the product of 4 and a number, n”n4+134n+134n+1313n+44. Select each of the following that is an expression.2x-7-143x2x-7=14x=12+75. If k = 2, what is the value of k2-k-10+4k?6822246. What is the value of a+4ba+b if a=-4 and b=3?-24-8087. What is the value of mh+p-p÷h+m if h=-1, m=3, and p=4?028168. What is the value of y+4-y?x if x=7 and y=-2?-12-816209. If a=3, what is the value of 8a2-2a?2?041418SOL 7.13The student will Write verbal expressions as algebraic expressions and sentences as equations and vice versa; andEvaluate algebraic expressions for given replacement values of the variables.HINTS & NOTESAddition words/phrases: Subtraction words/phrases:Multiplication words/phrases:Division words/phrases:REMEMBER: “7 less than a number” means n – 7, not 7 – n. PRACTICE001. Which algebraic expression best represents the verbal expression shown?“Eleven times the sum of a number and five”11+5x11+x2+511+5+x11x+52. 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?2d-2424d-224+2d24-2d3. Which of the following is the algebraic form for the verbal statement shown?“13 more than the product of 4 and a number, n”n4+134n+134n+1313n+44. Select each of the following that is an expression.2x-7-143x2x-7=14x=12+75. If k = 2, what is the value of k2-k-10+4k?6822246. What is the value of a+4ba+b if a=-4 and b=3?-24-8087. What is the value of mh+p-p÷h+m if h=-1, m=3, and p=4?028168. What is the value of y+4-y?x if x=7 and y=-2?-12-816209. If a=3, what is the value of 8a2-2a?2?041418SOL 7.13The student will Write verbal expressions as algebraic expressions and sentences as equations and vice versa; andEvaluate algebraic expressions for given replacement values of the variables.HINTS & NOTESAddition words/phrases: Subtraction words/phrases:Multiplication words/phrases:Division words/phrases:REMEMBER: “7 less than a number” means n – 7, not 7 – n. PRACTICE50292006105525001390650504825000-138430-190501. What is the solution to x-4=10?-40-66402. What is the value of n that makes the following true?n+-7=-77-84-7084703. Aidan’s age is 6 years less than half of Maggie’s age. Aidan’s age is 4 years. What is Maggie’s age?2 years5 years10 years20 years4. 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?7x-10=457x+10=4545-10x=710x+7=455. 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?$3.25$5.50$6.75$9.006. What is the solution to –2x+3=15?7. What is the solution to x4-7=-11?8. What is the solution to 3x+4=-20?SOL 7.14The student will Solve one- and two-step linear equations in one variable; andSolve practical problems requiring the solution of one- and two-step linear equations.HINTS & NOTESRemember to use your inverse operations to solve equations:Addition ? subtractionMultiplication ? divisionAlways 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!PRACTICE001. What is the solution to x-4=10?-40-66402. What is the value of n that makes the following true?n+-7=-77-84-7084703. Aidan’s age is 6 years less than half of Maggie’s age. Aidan’s age is 4 years. What is Maggie’s age?2 years5 years10 years20 years4. 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?7x-10=457x+10=4545-10x=710x+7=455. 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?$3.25$5.50$6.75$9.006. What is the solution to –2x+3=15?7. What is the solution to x4-7=-11?8. What is the solution to 3x+4=-20?SOL 7.14The student will Solve one- and two-step linear equations in one variable; andSolve practical problems requiring the solution of one- and two-step linear equations.HINTS & NOTESRemember to use your inverse operations to solve equations:Addition ? subtractionMultiplication ? divisionAlways 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-128905-666751. What is the solution to -12x≤-72?x≥6x≤6x≥-6x≤-62. Which graph represents the solution set to this inequality?x+5<73. Which value of k makes -5>k+11 true?8-4-16-224. What is the solution to c-14<16?c<2c>2c<30c>305. What is the solution to -4n<16?6. What is the solution to -30>6y?7. Graph the solution set for #5.8. Graph the solution set for #6.SOL 7.15The student will Solve one-step inequalities in one variable; andGraph solutions to inequalities on the number line.HINTS & NOTESInequalities 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.Use an open circle for inequalities < and >.Use a solid circle for the inequalities ≤ and ≥.Pick a number to substitute into your inequality. If it works, then shade in that side of your number line. PRACTICE001. What is the solution to -12x≤-72?x≥6x≤6x≥-6x≤-62. Which graph represents the solution set to this inequality?x+5<73. Which value of k makes -5>k+11 true?8-4-16-224. What is the solution to c-14<16?c<2c>2c<30c>305. What is the solution to -4n<16?6. What is the solution to -30>6y?7. Graph the solution set for #5.8. Graph the solution set for #6.SOL 7.15The student will Solve one-step inequalities in one variable; andGraph solutions to inequalities on the number line.HINTS & NOTESInequalities 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.Use an open circle for inequalities < and >.Use a solid circle for the inequalities ≤ and ≥.Pick a number to substitute into your inequality. If it works, then shade in that side of your number line. PRACTICE20808953552825PRACTICE00PRACTICE-13843038481001. Which property is illustrated by this number sentence?-1?7+3=3+(-1?7)Associative Property of AdditionCommutative Property of AdditionDistributive PropertyAssociative Property of MultiplicationCommutative Property of MultiplicationMultiplicative Identity Property2. Identify each number sentence that illustrates the associative property of addition.7+3+8=7+3+84?7?1+6=4?7?1+62+6+7=2+7+65+-1+6=5+-1+64+1+3-7=4+1+3-71-5+2=1-(2+5)001. Which property is illustrated by this number sentence?-1?7+3=3+(-1?7)Associative Property of AdditionCommutative Property of AdditionDistributive PropertyAssociative Property of MultiplicationCommutative Property of MultiplicationMultiplicative Identity Property2. Identify each number sentence that illustrates the associative property of addition.7+3+8=7+3+84?7?1+6=4?7?1+62+6+7=2+7+65+-1+6=5+-1+64+1+3-7=4+1+3-71-5+2=1-(2+5)-1384301333500HINTS & NOTESPropertyAdditionMultiplicationCommutative (Change Order)a+b=b+aa?b=b?aAssociative (Grouping changes)a+b+c=a+b+ca?b?c=a?b?cIdentitya+0=aa?1=aInversea+-a=0a?1a=1Property of zeroa?0=0Distributive property uses addition and multiplication: ab+c=ab+ac00HINTS & NOTESPropertyAdditionMultiplicationCommutative (Change Order)a+b=b+aa?b=b?aAssociative (Grouping changes)a+b+c=a+b+ca?b?c=a?b?cIdentitya+0=aa?1=aInversea+-a=0a?1a=1Property of zeroa?0=0Distributive property uses addition and multiplication: ab+c=ab+ac332867038481003. Which expression completes this equation using only the multiplicative property of zero?5+0+-4+4-6?0=_________5+-4+4-6?05+0+0-6?05+0+-4+4-00+5+-4+4-6?04. Which equation illustrates the multiplicative identity property?8-5?0=038?12?1=38?128+0?1=8?123?32?5=1?55. Identify each number sentence that illustrates the distributive property.4?7?1+6=4?7?1+643+1=43+4153+7?0=53+07+54+2=7+54+5279-1+2=79-71+215+2=1(2+5)003. Which expression completes this equation using only the multiplicative property of zero?5+0+-4+4-6?0=_________5+-4+4-6?05+0+0-6?05+0+-4+4-00+5+-4+4-6?04. Which equation illustrates the multiplicative identity property?8-5?0=038?12?1=38?128+0?1=8?123?32?5=1?55. Identify each number sentence that illustrates the distributive property.4?7?1+6=4?7?1+643+1=43+4153+7?0=53+07+54+2=7+54+5279-1+2=79-71+215+2=1(2+5)-138430-85725SOL 7.16The student will apply the following properties of operations with real numbers:The commutative and associative properties for addition and multiplication;The distributive property;The additive and multiplicative identity properties; The additive and multiplicative inverse properties; andThe multiplicative property of zero.00SOL 7.16The student will apply the following properties of operations with real numbers:The commutative and associative properties for addition and multiplication;The distributive property;The additive and multiplicative identity properties; The additive and multiplicative inverse properties; andThe multiplicative property of zero. ................
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