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MATHBITSNOTEBOOK
Common Core On-Line Study Mathematical Resources for High School Students. CCSS Algebra 1, CCSS Geoemtry, other levels to follow. GEOMETRY AND DENSITY PRACTICE An older method of estimating body fat percentage was to measure a person's average density (total mass divided by total volume), and apply a formula to convert to a body fat percentage. Formula: BF = (4.57/ p - 4.142) x 100. where BF = body fat and p = density in g/cm3. A man weighs 175 pounds. GEOMETRY AND MODELING PRACTICE Geometry and Modeling Practice - MathBitsNotebook (Geo - CCSS Math) Directions: Read carefully and choose the best answer. You may access the following section of the PARCC reference sheet when solving these problems. Be sure to show your work. 1. A thermal insulating sleeve is used to cover the lateral surface of a hot water heater to help PRACTICE WITH VOLUME (C) A smaller cone of base radius 4 inches and height of 12 inches is cut off the top. The remaining bottom section of the original cone which is left behind is called a frustum. Not drawn to scale. a) Find the volume of the frustum. Leave answer in terms of π. Choose: 64π cu.in. 448π cu. in.
PRACTICE WITH ANGLES OUTSIDE THE CIRCLE Area of sector = 3.93/ (2 • pi • r) • area of circle. 2. Find the area of the sector shown at the right. The radius of the circle is 9 cm. and the central angle of the sector is 120º. Express the answer to the nearest tenth of a square centimeter. Hint: Find the fractional part of the circle by using 120/360.DILATION PRACTICE
Directions: Read carefully! 1. 2. Stanley had a poster made from a picture of his dog Tasha. The poster image is eight times the size of the picture. If the poster image is 120 cm. in height, what was the height of Stanley's original picture of Tasha (in centimeters)? 3. A model ATV is 8 inches long. After a dilation, the model is 2.4 incheslong.
PRACTICE SINE AND COSINE GRAPHS The angle of inclination of the sun changes throughout the year. This changing angle affects the heating and cooling of buildings. The overhang of the roof of a house is designed to shade the windows for cooling in the summer and allow the sun's rays to enter the house for heating in the winter. PRACTICE WITH MARGIN OF ERROR A drug company is testing a new cold medication for children. The average child's cold symptoms last for 7 days. The company tested 500 children with a cold and found that 250 of them shortened their cold symptoms when taking the new drug.MATHBITSNOTEBOOK
MathBitsNotebook - Common Core On-Line Study Resources for REGENTS EXAMINATION IN GEOMETRY (COMMON CORE) SAMPLE ITEMS With the adoption of the New York P-12 Common Core Learning Standards (CCLS) in ELA/Literacy and Mathematics, the Board of Regents signaled a shift in both instruction and assessment.MATHBITSNOTEBOOK
Common Core On-Line Study Mathematical Resources for High School Students. CCSS Algebra 1, CCSS Geoemtry, other levels to follow. GEOMETRY AND DENSITY PRACTICE An older method of estimating body fat percentage was to measure a person's average density (total mass divided by total volume), and apply a formula to convert to a body fat percentage. Formula: BF = (4.57/ p - 4.142) x 100. where BF = body fat and p = density in g/cm3. A man weighs 175 pounds. GEOMETRY AND MODELING PRACTICE Geometry and Modeling Practice - MathBitsNotebook (Geo - CCSS Math) Directions: Read carefully and choose the best answer. You may access the following section of the PARCC reference sheet when solving these problems. Be sure to show your work. 1. A thermal insulating sleeve is used to cover the lateral surface of a hot water heater to help PRACTICE WITH VOLUME (C) A smaller cone of base radius 4 inches and height of 12 inches is cut off the top. The remaining bottom section of the original cone which is left behind is called a frustum. Not drawn to scale. a) Find the volume of the frustum. Leave answer in terms of π. Choose: 64π cu.in. 448π cu. in.
PRACTICE WITH ANGLES OUTSIDE THE CIRCLE Area of sector = 3.93/ (2 • pi • r) • area of circle. 2. Find the area of the sector shown at the right. The radius of the circle is 9 cm. and the central angle of the sector is 120º. Express the answer to the nearest tenth of a square centimeter. Hint: Find the fractional part of the circle by using 120/360.DILATION PRACTICE
Directions: Read carefully! 1. 2. Stanley had a poster made from a picture of his dog Tasha. The poster image is eight times the size of the picture. If the poster image is 120 cm. in height, what was the height of Stanley's original picture of Tasha (in centimeters)? 3. A model ATV is 8 inches long. After a dilation, the model is 2.4 incheslong.
PRACTICE SINE AND COSINE GRAPHS The angle of inclination of the sun changes throughout the year. This changing angle affects the heating and cooling of buildings. The overhang of the roof of a house is designed to shade the windows for cooling in the summer and allow the sun's rays to enter the house for heating in the winter. PRACTICE WITH MARGIN OF ERROR A drug company is testing a new cold medication for children. The average child's cold symptoms last for 7 days. The company tested 500 children with a cold and found that 250 of them shortened their cold symptoms when taking the new drug.MATHBITSNOTEBOOK
MathBitsNotebook - Common Core On-Line Study Resources for REGENTS EXAMINATION IN GEOMETRY (COMMON CORE) SAMPLE ITEMS With the adoption of the New York P-12 Common Core Learning Standards (CCLS) in ELA/Literacy and Mathematics, the Board of Regents signaled a shift in both instruction and assessment. SEQUENCES AND WORD PROBLEMS- MATHBITSNOTEBOOK(A1 Sequences and Word Problems- MathBitsNotebook (A1 - CCSS Math) Directions: Read carefully. 1. The Greek theater shown at the right has 30 seats in the first row of the center section. Each row behind the first row gains two additional seats. How many seats are in the 5th row in the center section? VOLUME AND SURFACE AREA The number of cube faces seen in the face of the figure, comprise the area of the face of the figure. The new pattern is expressed as: Volume = (area of face) • (depth of face) = (4 • 2) • 2 = 16 square units. This will be a popular strategy to determine the volume of many solids. This pattern utilizes a "limiting argument" with thearea
PRACTICE WITH BIG CIRCLES Practice with BIG Circles - MathBitsNotebook (Geo - CCSS Math) Directions: Read carefully! Do not assume the diagrams are drawn to scale. It may not be possible to find the missing angles in numerical order. 1. Find the measures of angles 1 through 8. Explanation. GEOMETRIC RULES QUICK REFERENCE First a few words that refer to types of geometric "rules": • A theorem is a statement (rule) that has been proven true using facts, operations and other rules that are known to be true. These are usually the "big" rules of geometry. A short theorem referring to a "lesser" rule is called a lemma. • A corollary is a follow-up to an existing proven theorem. PROBABILITY INVOLVING AND AND OR The rule for OR must take into account values that may get counted more than once where the sets overlap. In the first version, this overlap is dealt with when finding n(A or B). In the second version, this overlap is dealt with in the subtraction of the intersection, P(A and B). If sets A and B are mutually exclusive (no elements in common), P(A and B) = 0, SIMILARITY PROOF PRACTICE Similarity Proof Practice - MathBitsNotebook (Geo - CCSS Math) Directions: Prepare a formal proof for each problem. While more than one method of proof may be possible, only one possible answer will be shown for each question. 1. BINOMIAL THEOREM PRACTICE Binomial Theorem Practice - MathBitsNotebook (A2 - CCSS Math) Directions: Work carefully! Mistakes can happen easily with all of these calculations. Binomial Theorem. (or Binomial Expansion Theorem) The rth term of the expansion of ( a + b) n is: 1. Using the binomial theorem, expand ( x + y) 6. POLYGON AREA PRACTICE Polygon Area Practice - MathBitsNotebook (Geo - CCSS Math) Directions: Grab a paper and pencil to make your computations. 1. Given equilateral triangle ABCSCIENTIFIC NOTATION
Scientific notation is a shorthand method of expressing very large or very small numbers. Calculators, scientists and engineers find this base 10 method of expressing values to be very helpful, as it allows for very precise calculations. PRACTICE WITH MARGIN OF ERROR A drug company is testing a new cold medication for children. The average child's cold symptoms last for 7 days. The company tested 500 children with a cold and found that 250 of them shortened their cold symptoms when taking the new drug.MATHBITSNOTEBOOK
Common Core On-Line Study Mathematical Resources for High School Students. CCSS Algebra 1, CCSS Geoemtry, other levels to follow. GEOMETRY AND DENSITY PRACTICE An older method of estimating body fat percentage was to measure a person's average density (total mass divided by total volume), and apply a formula to convert to a body fat percentage. Formula: BF = (4.57/ p - 4.142) x 100. where BF = body fat and p = density in g/cm3. A man weighs 175 pounds. GEOMETRY AND MODELING PRACTICE Geometry and Modeling Practice - MathBitsNotebook (Geo - CCSS Math) Directions: Read carefully and choose the best answer. You may access the following section of the PARCC reference sheet when solving these problems. Be sure to show your work. 1. A thermal insulating sleeve is used to cover the lateral surface of a hot water heater to help PRACTICE WITH VOLUME (C) A smaller cone of base radius 4 inches and height of 12 inches is cut off the top. The remaining bottom section of the original cone which is left behind is called a frustum. Not drawn to scale. a) Find the volume of the frustum. Leave answer in terms of π. Choose: 64π cu.in. 448π cu. in.
PRACTICE WITH ANGLES OUTSIDE THE CIRCLE Area of sector = 3.93/ (2 • pi • r) • area of circle. 2. Find the area of the sector shown at the right. The radius of the circle is 9 cm. and the central angle of the sector is 120º. Express the answer to the nearest tenth of a square centimeter. Hint: Find the fractional part of the circle by using 120/360.DILATION PRACTICE
Directions: Read carefully! 1. 2. Stanley had a poster made from a picture of his dog Tasha. The poster image is eight times the size of the picture. If the poster image is 120 cm. in height, what was the height of Stanley's original picture of Tasha (in centimeters)? 3. A model ATV is 8 inches long. After a dilation, the model is 2.4 incheslong.
PRACTICE SINE AND COSINE GRAPHS The angle of inclination of the sun changes throughout the year. This changing angle affects the heating and cooling of buildings. The overhang of the roof of a house is designed to shade the windows for cooling in the summer and allow the sun's rays to enter the house for heating in the winter. PRACTICE WITH MARGIN OF ERROR A drug company is testing a new cold medication for children. The average child's cold symptoms last for 7 days. The company tested 500 children with a cold and found that 250 of them shortened their cold symptoms when taking the new drug.MATHBITSNOTEBOOK
MathBitsNotebook - Common Core On-Line Study Resources for REGENTS EXAMINATION IN GEOMETRY (COMMON CORE) SAMPLE ITEMS With the adoption of the New York P-12 Common Core Learning Standards (CCLS) in ELA/Literacy and Mathematics, the Board of Regents signaled a shift in both instruction and assessment.MATHBITSNOTEBOOK
Common Core On-Line Study Mathematical Resources for High School Students. CCSS Algebra 1, CCSS Geoemtry, other levels to follow. GEOMETRY AND DENSITY PRACTICE An older method of estimating body fat percentage was to measure a person's average density (total mass divided by total volume), and apply a formula to convert to a body fat percentage. Formula: BF = (4.57/ p - 4.142) x 100. where BF = body fat and p = density in g/cm3. A man weighs 175 pounds. GEOMETRY AND MODELING PRACTICE Geometry and Modeling Practice - MathBitsNotebook (Geo - CCSS Math) Directions: Read carefully and choose the best answer. You may access the following section of the PARCC reference sheet when solving these problems. Be sure to show your work. 1. A thermal insulating sleeve is used to cover the lateral surface of a hot water heater to help PRACTICE WITH VOLUME (C) A smaller cone of base radius 4 inches and height of 12 inches is cut off the top. The remaining bottom section of the original cone which is left behind is called a frustum. Not drawn to scale. a) Find the volume of the frustum. Leave answer in terms of π. Choose: 64π cu.in. 448π cu. in.
PRACTICE WITH ANGLES OUTSIDE THE CIRCLE Area of sector = 3.93/ (2 • pi • r) • area of circle. 2. Find the area of the sector shown at the right. The radius of the circle is 9 cm. and the central angle of the sector is 120º. Express the answer to the nearest tenth of a square centimeter. Hint: Find the fractional part of the circle by using 120/360.DILATION PRACTICE
Directions: Read carefully! 1. 2. Stanley had a poster made from a picture of his dog Tasha. The poster image is eight times the size of the picture. If the poster image is 120 cm. in height, what was the height of Stanley's original picture of Tasha (in centimeters)? 3. A model ATV is 8 inches long. After a dilation, the model is 2.4 incheslong.
PRACTICE SINE AND COSINE GRAPHS The angle of inclination of the sun changes throughout the year. This changing angle affects the heating and cooling of buildings. The overhang of the roof of a house is designed to shade the windows for cooling in the summer and allow the sun's rays to enter the house for heating in the winter. PRACTICE WITH MARGIN OF ERROR A drug company is testing a new cold medication for children. The average child's cold symptoms last for 7 days. The company tested 500 children with a cold and found that 250 of them shortened their cold symptoms when taking the new drug.MATHBITSNOTEBOOK
MathBitsNotebook - Common Core On-Line Study Resources for REGENTS EXAMINATION IN GEOMETRY (COMMON CORE) SAMPLE ITEMS With the adoption of the New York P-12 Common Core Learning Standards (CCLS) in ELA/Literacy and Mathematics, the Board of Regents signaled a shift in both instruction and assessment. SEQUENCES AND WORD PROBLEMS- MATHBITSNOTEBOOK(A1 Sequences and Word Problems- MathBitsNotebook (A1 - CCSS Math) Directions: Read carefully. 1. The Greek theater shown at the right has 30 seats in the first row of the center section. Each row behind the first row gains two additional seats. How many seats are in the 5th row in the center section? VOLUME AND SURFACE AREA The number of cube faces seen in the face of the figure, comprise the area of the face of the figure. The new pattern is expressed as: Volume = (area of face) • (depth of face) = (4 • 2) • 2 = 16 square units. This will be a popular strategy to determine the volume of many solids. This pattern utilizes a "limiting argument" with thearea
PRACTICE WITH BIG CIRCLES Practice with BIG Circles - MathBitsNotebook (Geo - CCSS Math) Directions: Read carefully! Do not assume the diagrams are drawn to scale. It may not be possible to find the missing angles in numerical order. 1. Find the measures of angles 1 through 8. Explanation. GEOMETRIC RULES QUICK REFERENCE First a few words that refer to types of geometric "rules": • A theorem is a statement (rule) that has been proven true using facts, operations and other rules that are known to be true. These are usually the "big" rules of geometry. A short theorem referring to a "lesser" rule is called a lemma. • A corollary is a follow-up to an existing proven theorem. PROBABILITY INVOLVING AND AND OR The rule for OR must take into account values that may get counted more than once where the sets overlap. In the first version, this overlap is dealt with when finding n(A or B). In the second version, this overlap is dealt with in the subtraction of the intersection, P(A and B). If sets A and B are mutually exclusive (no elements in common), P(A and B) = 0, SIMILARITY PROOF PRACTICE Similarity Proof Practice - MathBitsNotebook (Geo - CCSS Math) Directions: Prepare a formal proof for each problem. While more than one method of proof may be possible, only one possible answer will be shown for each question. 1. BINOMIAL THEOREM PRACTICE Binomial Theorem Practice - MathBitsNotebook (A2 - CCSS Math) Directions: Work carefully! Mistakes can happen easily with all of these calculations. Binomial Theorem. (or Binomial Expansion Theorem) The rth term of the expansion of ( a + b) n is: 1. Using the binomial theorem, expand ( x + y) 6. POLYGON AREA PRACTICE Polygon Area Practice - MathBitsNotebook (Geo - CCSS Math) Directions: Grab a paper and pencil to make your computations. 1. Given equilateral triangle ABCSCIENTIFIC NOTATION
Scientific notation is a shorthand method of expressing very large or very small numbers. Calculators, scientists and engineers find this base 10 method of expressing values to be very helpful, as it allows for very precise calculations. PRACTICE WITH MARGIN OF ERROR A drug company is testing a new cold medication for children. The average child's cold symptoms last for 7 days. The company tested 500 children with a cold and found that 250 of them shortened their cold symptoms when taking the new drug.MATHBITSNOTEBOOK
Common Core On-Line Study Mathematical Resources for High School Students. CCSS Algebra 1, CCSS Geoemtry, other levels to follow.MATHBITSNOTEBOOK
MathBitsNotebook - Geometry is a series of lesson and practice pages for students studying high school Geometry. These materials cover a variety of topics including all standards stated in the Common Core State Standards, and the NY Next Generation Standards for Mathematics. GEOMETRY AND DENSITY PRACTICE An older method of estimating body fat percentage was to measure a person's average density (total mass divided by total volume), and apply a formula to convert to a body fat percentage. Formula: BF = (4.57/ p - 4.142) x 100. where BF = body fat and p = density in g/cm3. A man weighs 175 pounds. PRACTICE WITH ANGLES OUTSIDE THE CIRCLE Area of sector = 3.93/ (2 • pi • r) • area of circle. 2. Find the area of the sector shown at the right. The radius of the circle is 9 cm. and the central angle of the sector is 120º. Express the answer to the nearest tenth of a square centimeter. Hint: Find the fractional part of the circle by using 120/360. PROBABILITY INVOLVING AND AND OR The rule for OR must take into account values that may get counted more than once where the sets overlap. In the first version, this overlap is dealt with when finding n(A or B). In the second version, this overlap is dealt with in the subtraction of the intersection, P(A and B). If sets A and B are mutually exclusive (no elements in common), P(A and B) = 0, PROBABILITY PRACTICE 8. In a Math Honors class of 30 students, 16 are boys and 14 are girls. On the final exam, 7 boys and 8 girls received an "A" score. If a student is chosen at random from this class, what is the probability of choosing a girl or a student that received an "A" score? Choose: 21/30. 29/30. 15/30. PRACTICE WITH VOLUME (C) The cone shown at the right is a right circular cone with a base radius of 8 inches. The cone is sliced parallel to the base. A smaller cone of base radius 4 inches and height of 12 inches is cut off thetop.
PRACTICE WITH MARGIN OF ERROR A drug company is testing a new cold medication for children. The average child's cold symptoms last for 7 days. The company tested 500 children with a cold and found that 250 of them shortened their cold symptoms when taking the new drug.MATHBITSNOTEBOOK
MathBitsNotebook - Common Core On-Line Study Resources for REGENTS EXAMINATION IN GEOMETRY (COMMON CORE) SAMPLE ITEMS With the adoption of the New York P-12 Common Core Learning Standards (CCLS) in ELA/Literacy and Mathematics, the Board of Regents signaled a shift in both instruction and assessment.MATHBITSNOTEBOOK
Common Core On-Line Study Mathematical Resources for High School Students. CCSS Algebra 1, CCSS Geoemtry, other levels to follow.MATHBITSNOTEBOOK
MathBitsNotebook - Geometry is a series of lesson and practice pages for students studying high school Geometry. These materials cover a variety of topics including all standards stated in the Common Core State Standards, and the NY Next Generation Standards for Mathematics. GEOMETRY AND DENSITY PRACTICE An older method of estimating body fat percentage was to measure a person's average density (total mass divided by total volume), and apply a formula to convert to a body fat percentage. Formula: BF = (4.57/ p - 4.142) x 100. where BF = body fat and p = density in g/cm3. A man weighs 175 pounds. PRACTICE WITH ANGLES OUTSIDE THE CIRCLE Area of sector = 3.93/ (2 • pi • r) • area of circle. 2. Find the area of the sector shown at the right. The radius of the circle is 9 cm. and the central angle of the sector is 120º. Express the answer to the nearest tenth of a square centimeter. Hint: Find the fractional part of the circle by using 120/360. PROBABILITY INVOLVING AND AND OR The rule for OR must take into account values that may get counted more than once where the sets overlap. In the first version, this overlap is dealt with when finding n(A or B). In the second version, this overlap is dealt with in the subtraction of the intersection, P(A and B). If sets A and B are mutually exclusive (no elements in common), P(A and B) = 0, PROBABILITY PRACTICE 8. In a Math Honors class of 30 students, 16 are boys and 14 are girls. On the final exam, 7 boys and 8 girls received an "A" score. If a student is chosen at random from this class, what is the probability of choosing a girl or a student that received an "A" score? Choose: 21/30. 29/30. 15/30. PRACTICE WITH VOLUME (C) The cone shown at the right is a right circular cone with a base radius of 8 inches. The cone is sliced parallel to the base. A smaller cone of base radius 4 inches and height of 12 inches is cut off thetop.
PRACTICE WITH MARGIN OF ERROR A drug company is testing a new cold medication for children. The average child's cold symptoms last for 7 days. The company tested 500 children with a cold and found that 250 of them shortened their cold symptoms when taking the new drug.MATHBITSNOTEBOOK
MathBitsNotebook - Common Core On-Line Study Resources for REGENTS EXAMINATION IN GEOMETRY (COMMON CORE) SAMPLE ITEMS With the adoption of the New York P-12 Common Core Learning Standards (CCLS) in ELA/Literacy and Mathematics, the Board of Regents signaled a shift in both instruction and assessment. PROBABILITY INVOLVING AND AND OR The rule for OR must take into account values that may get counted more than once where the sets overlap. In the first version, this overlap is dealt with when finding n(A or B). In the second version, this overlap is dealt with in the subtraction of the intersection, P(A and B). If sets A and B are mutually exclusive (no elements in common), P(A and B) = 0, MORE FEATURES OF FUNCTION GRAPHS More Features of Function Graphs - MathBitsNotebook (A1 - CCSS Math) If looking for Intercepts, Positive/Negative, and Increasing/Decreasing, see Function Features. "Turning Points". A "turning point" on a graph is a point at which the graph changes from increasing to decreasing (it looks like a "hill"), or from decreasingto increasing (it
SEQUENCES AND WORD PROBLEMS- MATHBITSNOTEBOOK(A1 Sequences and Word Problems- MathBitsNotebook (A1 - CCSS Math) Directions: Read carefully. 1. The Greek theater shown at the right has 30 seats in the first row of the center section. Each row behind the first row gains two additional seats. How many seats are in the 5th row in the center section? FORMULAS FOR ANGLES IN CIRCLES A central angle is an angle formed by two radii with the vertex at the center of the circle. Central Angle = Intercepted Arc. In the diagram at the right, ∠AOB is a central angle with an intercepted minor arc from A to B. m∠AOB = 82º. In a circle, or congruent circles, congruent central angles have congruent arcs. FACTORING - MATHBITSNOTEBOOK (A1 - CCSS MATH) Algebra 1 CCSS Lessons and Practice is a free site for students (and teachers) studying a first year of high school algebra under the Common Core State Standards.CIRCLE OUTLINE
Angles and Circles (central, inscribed, tangent chord, 2 chords, 2 secants, 2 tangents, secant-tangent) •. Working with BIG Circles. •. Arc Length and Radian Measure. •. Area of Sectors and Area of Segments. For constructions involving circles see Constructions.PRACTICE:
COMPLETE SQUARE PRACTICE MathBitsNotebook Algebra 1 CCSS Lessons and Practice is free site for students (and teachers) studying a first year of high school algebra. EXPONENTIAL GROWTH AND DECAY PRACTICE 1. Given the equation: y = 50 (1.15) x. a) Does this equation represent exponential growth or decay? b) What is the initial value? c) What is the rate of growth or decay? d) What is the value of y (to the nearest tenth), when x = 3? 2. A citrus orchard has 180 orange trees. A fungus attacks the trees.PROJECTILE MOTION
Projectile Motion - MathBitsNotebook (A1 - CCSS Math) A projectile is an object that rises and falls under the influence of gravity, and projectile motion is the height of that object as a function of time. Projectile motion can be modeled by a quadratic function. Projectile motion involves objects that are dropped, thrown straight up, or REFLECTION - MATHBITSNOTEBOOK(JR) • The object and its reflection are the same distance from the line of reflection, line k.The line of reflection is the perpendicular bisector of the segment joining every point and its image point. • Since under a reflection, the figures remain congruent (same size and shape), a reflection is called a rigid transformation and is said topreserve length.
MATHBITSNOTEBOOK
Common Core On-Line Study Mathematical Resources for High School Students. CCSS Algebra 1, CCSS Geoemtry, other levels to follow.MATHBITSNOTEBOOK
MathBitsNotebook - Geometry is a series of lesson and practice pages for students studying high school Geometry. These materials cover a variety of topics including all standards stated in the Common Core State Standards, and the NY Next Generation Standards for Mathematics. GEOMETRY AND DENSITY PRACTICE An older method of estimating body fat percentage was to measure a person's average density (total mass divided by total volume), and apply a formula to convert to a body fat percentage. Formula: BF = (4.57/ p - 4.142) x 100. where BF = body fat and p = density in g/cm3. A man weighs 175 pounds. PRACTICE WITH ANGLES OUTSIDE THE CIRCLE Area of sector = 3.93/ (2 • pi • r) • area of circle. 2. Find the area of the sector shown at the right. The radius of the circle is 9 cm. and the central angle of the sector is 120º. Express the answer to the nearest tenth of a square centimeter. Hint: Find the fractional part of the circle by using 120/360. PROBABILITY INVOLVING AND AND OR The rule for OR must take into account values that may get counted more than once where the sets overlap. In the first version, this overlap is dealt with when finding n(A or B). In the second version, this overlap is dealt with in the subtraction of the intersection, P(A and B). If sets A and B are mutually exclusive (no elements in common), P(A and B) = 0, PROBABILITY PRACTICE 8. In a Math Honors class of 30 students, 16 are boys and 14 are girls. On the final exam, 7 boys and 8 girls received an "A" score. If a student is chosen at random from this class, what is the probability of choosing a girl or a student that received an "A" score? Choose: 21/30. 29/30. 15/30. PRACTICE WITH VOLUME (C) The cone shown at the right is a right circular cone with a base radius of 8 inches. The cone is sliced parallel to the base. A smaller cone of base radius 4 inches and height of 12 inches is cut off thetop.
PRACTICE WITH MARGIN OF ERROR A drug company is testing a new cold medication for children. The average child's cold symptoms last for 7 days. The company tested 500 children with a cold and found that 250 of them shortened their cold symptoms when taking the new drug.MATHBITSNOTEBOOK
MathBitsNotebook - Common Core On-Line Study Resources for REGENTS EXAMINATION IN GEOMETRY (COMMON CORE) SAMPLE ITEMS With the adoption of the New York P-12 Common Core Learning Standards (CCLS) in ELA/Literacy and Mathematics, the Board of Regents signaled a shift in both instruction and assessment.MATHBITSNOTEBOOK
Common Core On-Line Study Mathematical Resources for High School Students. CCSS Algebra 1, CCSS Geoemtry, other levels to follow.MATHBITSNOTEBOOK
MathBitsNotebook - Geometry is a series of lesson and practice pages for students studying high school Geometry. These materials cover a variety of topics including all standards stated in the Common Core State Standards, and the NY Next Generation Standards for Mathematics. GEOMETRY AND DENSITY PRACTICE An older method of estimating body fat percentage was to measure a person's average density (total mass divided by total volume), and apply a formula to convert to a body fat percentage. Formula: BF = (4.57/ p - 4.142) x 100. where BF = body fat and p = density in g/cm3. A man weighs 175 pounds. PRACTICE WITH ANGLES OUTSIDE THE CIRCLE Area of sector = 3.93/ (2 • pi • r) • area of circle. 2. Find the area of the sector shown at the right. The radius of the circle is 9 cm. and the central angle of the sector is 120º. Express the answer to the nearest tenth of a square centimeter. Hint: Find the fractional part of the circle by using 120/360. PROBABILITY INVOLVING AND AND OR The rule for OR must take into account values that may get counted more than once where the sets overlap. In the first version, this overlap is dealt with when finding n(A or B). In the second version, this overlap is dealt with in the subtraction of the intersection, P(A and B). If sets A and B are mutually exclusive (no elements in common), P(A and B) = 0, PROBABILITY PRACTICE 8. In a Math Honors class of 30 students, 16 are boys and 14 are girls. On the final exam, 7 boys and 8 girls received an "A" score. If a student is chosen at random from this class, what is the probability of choosing a girl or a student that received an "A" score? Choose: 21/30. 29/30. 15/30. PRACTICE WITH VOLUME (C) The cone shown at the right is a right circular cone with a base radius of 8 inches. The cone is sliced parallel to the base. A smaller cone of base radius 4 inches and height of 12 inches is cut off thetop.
PRACTICE WITH MARGIN OF ERROR A drug company is testing a new cold medication for children. The average child's cold symptoms last for 7 days. The company tested 500 children with a cold and found that 250 of them shortened their cold symptoms when taking the new drug.MATHBITSNOTEBOOK
MathBitsNotebook - Common Core On-Line Study Resources for REGENTS EXAMINATION IN GEOMETRY (COMMON CORE) SAMPLE ITEMS With the adoption of the New York P-12 Common Core Learning Standards (CCLS) in ELA/Literacy and Mathematics, the Board of Regents signaled a shift in both instruction and assessment. PROBABILITY INVOLVING AND AND OR The rule for OR must take into account values that may get counted more than once where the sets overlap. In the first version, this overlap is dealt with when finding n(A or B). In the second version, this overlap is dealt with in the subtraction of the intersection, P(A and B). If sets A and B are mutually exclusive (no elements in common), P(A and B) = 0, MORE FEATURES OF FUNCTION GRAPHS More Features of Function Graphs - MathBitsNotebook (A1 - CCSS Math) If looking for Intercepts, Positive/Negative, and Increasing/Decreasing, see Function Features. "Turning Points". A "turning point" on a graph is a point at which the graph changes from increasing to decreasing (it looks like a "hill"), or from decreasingto increasing (it
SEQUENCES AND WORD PROBLEMS- MATHBITSNOTEBOOK(A1 Sequences and Word Problems- MathBitsNotebook (A1 - CCSS Math) Directions: Read carefully. 1. The Greek theater shown at the right has 30 seats in the first row of the center section. Each row behind the first row gains two additional seats. How many seats are in the 5th row in the center section? FORMULAS FOR ANGLES IN CIRCLES A central angle is an angle formed by two radii with the vertex at the center of the circle. Central Angle = Intercepted Arc. In the diagram at the right, ∠AOB is a central angle with an intercepted minor arc from A to B. m∠AOB = 82º. In a circle, or congruent circles, congruent central angles have congruent arcs. FACTORING - MATHBITSNOTEBOOK (A1 - CCSS MATH) Algebra 1 CCSS Lessons and Practice is a free site for students (and teachers) studying a first year of high school algebra under the Common Core State Standards.CIRCLE OUTLINE
Angles and Circles (central, inscribed, tangent chord, 2 chords, 2 secants, 2 tangents, secant-tangent) •. Working with BIG Circles. •. Arc Length and Radian Measure. •. Area of Sectors and Area of Segments. For constructions involving circles see Constructions.PRACTICE:
COMPLETE SQUARE PRACTICE MathBitsNotebook Algebra 1 CCSS Lessons and Practice is free site for students (and teachers) studying a first year of high school algebra. EXPONENTIAL GROWTH AND DECAY PRACTICE 1. Given the equation: y = 50 (1.15) x. a) Does this equation represent exponential growth or decay? b) What is the initial value? c) What is the rate of growth or decay? d) What is the value of y (to the nearest tenth), when x = 3? 2. A citrus orchard has 180 orange trees. A fungus attacks the trees.PROJECTILE MOTION
Projectile Motion - MathBitsNotebook (A1 - CCSS Math) A projectile is an object that rises and falls under the influence of gravity, and projectile motion is the height of that object as a function of time. Projectile motion can be modeled by a quadratic function. Projectile motion involves objects that are dropped, thrown straight up, or REFLECTION - MATHBITSNOTEBOOK(JR) • The object and its reflection are the same distance from the line of reflection, line k.The line of reflection is the perpendicular bisector of the segment joining every point and its image point. • Since under a reflection, the figures remain congruent (same size and shape), a reflection is called a rigid transformation and is said topreserve length.
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