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**8TH GRADE COMPREHENSIVE REVIEW**

MATHEMATICS Created by: Jessie Minor

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MATHEMATICS Purpose: PSSA Review for 8th Grade Mathematics (Can be used as enrichment or remediation for middle school levels) Contents: Concept vocabulary & practice exercises/ solutions. Fill-in-the-blank, Multiple Choice, Short & Extended Response Sources: PA Assessment Anchors & Eligible Content for 8th Grade Mathematics PA Assessment Anchor Glossary for 7th & 8th Grade Mathematics PDE Standard Aligned Systems Online Resources McGraw Hill Pre-Algebra & Algebra I 2012 Series Holt McDougal 8th Grade Mathematics 2012 Series Reinforcement: PSSA Coach, Assessment Anchors Measuring Up to the Pennsylvania Academic Standards

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INSTRUCTIONS There are five categories tested; Numbers & Operations, Measurement, Geometry, Algebraic Concepts, Data Analysis & Probability. Each category has a two page vocabulary (fill-in-the-blank) review, followed by multiple choice, short response, and extended response exercises that are aligned with each of the Assessment Anchor subcategories. Navigate through the review as you would a regular PowerPoint slide show. Fill-in-the-blank answers will appear, in order, at the click of a mouse. Exercise answers will also appear at the click of a mouse. Use the reference symbol to access the 8th Grade Formula Sheet if needed. Use the symbol found on the Formula Sheet to return to your previous slide. PLEASE BEGIN!!

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**Numbers & Operations Vocabulary Review**

The product of a number and its __________ is 1. Any number that can be written as a fraction is called a _________. ________________ is a short-hand way of writing extremely large or extremely small numbers. The set of ____________ is the set of all rational and irrational numbers. The product of an integer multiplied by itself is called a _____________. Reciprocal Rational number Scientific notation Real numbers Perfect square Word Bank: Proportion Real numbers Rational number Reciprocal Square root Scientific notation Unit price Expanded form Order of Operations Perfect square

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**Numbers & Operations Vocabulary Review**

A number written as the sum of values of its digits is called _________. A number that is multiplied by itself to form a product is called a ___________ of that product. A(n) __________ is used to compare price per item. Rules describing what sequence to use in evaluating expressions is known as __________________. A ___________ is an equation showing that two ratios are equal. Expanded form Square root Unit price Order of Operations Proportion Word Bank: Proportion Real numbers Rational number Reciprocal Square root Scientific notation Unit price Expanded form Order of Operations Perfect square

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**Practice… Representing Numbers in equivalent forms.**

Numbers & Operations Practice… Representing Numbers in equivalent forms. Scientific Notation The Earth is approximately 93,000,000 miles from the sun. What is the distance written in scientific notation? 9.3 x 106 93 x 106 93 x 107 9.3 x 107 Exponential Form Which number represents 4.5 x 104 written in standard notation? 45,000 450,000

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**Practice… Representing Numbers in equivalent forms.**

Numbers & Operations Practice… Representing Numbers in equivalent forms. Expanded Notation Which expression is equivalent to the number 8,006,425? (8x107)+(6x106)+(4x103)+(2x102)+(5x101) (8x10)+(6x10)+(4x10)+(2x10)+(5x10) (8x106)+(6x105)+(4x104)+(2x103)+(5x102) (8x106)+(6x103)+(4x102)+(2x101)+(5x100)

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**Practice… Representing Numbers in equivalent forms.**

Numbers & Operations Practice… Representing Numbers in equivalent forms. Square Root LeAnn got an answer of about 3.87 when she entered 15 on her calculator and pressed the (√) key. Which of the following statements is the most likely explanation for her to believe that her calculator’s answer is or not reasonable? It is not reasonable, because the answer should be a whole number. It is reasonable because 3 squared is 9 while 4 squared is 16. It is not reasonable, because the answer should be only slightly more than 3. It is reasonable, because 15 is and odd number.

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**Practice… Completing calculations by applying the order of operations.**

Numbers & Operations Practice… Completing calculations by applying the order of operations. Order of Operations 3³ + 4(8-5) ÷ 6 = 6.5 11 29 27.5 Evaluate 7 + 5[(3 + 2)² - (2³ + 1)] 97 87 36 22

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**Practice… Completing calculations by applying the order of operations.**

Numbers & Operations Practice… Completing calculations by applying the order of operations. Order of Operations Karen is solving this problem. (3² + 4²)² = ? Which step is correct in the process of solving this problem? (3² + 4⁴) (9² + 16²) (7²)² (9 + 16)² Which statement is correct? (2 x 3) + 5 ÷ 8 = 2 (2 x 3 + 5) ÷ 8 = 2 2 x (3 + 5) ÷ 8 = 2

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Numbers & Operations Practice… Represent or solve problems using rates, ratios, proportions and/or percents. Rates A secretary can type 56 words per minute. How much time will she need to type a 4200-word report? 7 hours 30 minutes 1 hour 4 minutes 1 hour 28 minutes 1 hour 15 minutes Ratios In 1991, and American, Ann Trason, set a world record by running 100km in Which is the best estimate of her average speed? 12 km per hr 14 km per hr 16 km per hr 18 km per hr Hours Minutes Seconds 7 50 09

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Grade 8 Formula Sheet

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Numbers & Operations Practice… Represent or solve problems using rates, ratios, proportions and/or percents. Proportions (Short Response) Julio’s wages vary directly as the number of hours that he works. If his wages for 5 hours are $29.75, how much will he earn for 30 hours? Scoring Rubric: **[2 points] $178.50, and appropriate work is shown, such as solving a proportion, using a table, or trial and error with at least three trials and appropriate checks. *[1 point] An incorrect proportion is set up, but no solution or an incorrect solution is found. *[1 point] $178.50, but no work is shown or fewer than three trials with appropriate checks are shown. [0 points] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure.

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Numbers & Operations Practice… Represent or solve problems using rates, ratios, proportions and/or percents. Distance & Rates (Short Response) Bob and Rebecca both drove to a baseball game at a college stadium. Bob lives 70 miles from the stadium and Rebecca lives 60 miles from it, as shown in the accompanying diagram. Bob drove at a rate of 50 miles per hour, and Rebecca drove at a rate of 40 miles per hour. If they both left home at the same time, who got to the stadium first? 70 miles 60 miles Bob’s House Rebecca’s House Scoring Rubric: **[2 points] Bob, and appropriate work is shown, such as using the distance formula to calculate the two travel times or setting up a proportion. *[1 point] Appropriate work is shown, but one computational or conceptual error is made but an appropriate answer is found. *[1 point] Appropriate work is shown, but no answer or an incorrect answer is found. [0 points] Bob, but no work or inappropriate work is shown. [0 points] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure.

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**Practice… Using estimation strategies in problem-solving situations.**

Numbers & Operations Practice… Using estimation strategies in problem-solving situations. Estimation Ken bought a used car for $5,375. He had to pay an additional 15 percent of the purchase price to cover both sales tax and extra fees. Of the following, which is the closest to the total amount Ken paid? $806 $5,510 $5,760 $6,180 The state law requires that students attend school 180 days out of the 365 days in a year. Approximately what percent of a year must students attend school? 2% 50% 75% 200%

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Numbers & Operations Practice… Computing and/ or explaining operations with integers, fractions and/ or decimals. Fractions A grocery store sells brown sugar by the pound. The table below shows how many cups of sugar a customer will get for the number of pounds purchased. The pattern continues. What is the total number of cups of brown sugar in a 7-pound package? 15 2/3 16 1/3 16 2/3 17 1/3 Number of Pounds Number of Cups 3 7 4 9 1/3 5 11 2/3 6 14

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Numbers & Operations Practice… Computing and/ or explaining operations with integers, fractions and/ or decimals. Fractions Subtract (-) 14 5/8 - 6 3/8 8 3/8 7 2/8 8 1/4 9 Decimals Divide (÷) 3 0.24 0.08 8.0 0.72 12.5

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**Subtracting Negatives**

Numbers & Operations Practice… Computing and/ or explaining operations with integers, fractions and/ or decimals. Subtracting Negatives Solve: 27 – (-9) -3 -18 18 36 Adding Negatives Solve: -19 19 20 -27

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**Practice… Calculating mean.**

Numbers & Operations Practice… Calculating mean. Average (Short Response) TOP Electronics is a small business with five employees. The mean (average) weekly salary for the five employees is $360. If the weekly salaries of four of the employees are $340, $340, $345, and $425, what is the salary of the fifth employee? Scoring Rubric: **[2 points] $350, and appropriate work is shown, such as (1450 +x) ÷ 5 = 360, or trial and error with at least trials and appropriate checks. *[1 point] Appropriate work is shown, but one computational error is made *[1 point] The total of the five salaries is shown to be 5 · 360 = 1800, but no further correct work is shown. *[1 point] $350, but no work is shown or fewer than three trials with appropriate checks are shown. [0 points] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure.

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**Measurement Vocabulary Review**

____________ is the sum of the areas of all the faces of a 3-D figure. The sum of ___________________ is equal to 180°. A _______ is a 2-D shape that can be folded to create a 3-D figure. A 3-D solid that has two congruent and parallel faces is known as a _______. The sum of ____________________ is equal to 90°. Surface area Supplementary angles Net Prism Complementary angles Word Bank: Supplementary angles Polygon Net Complementary angles Surface area Circumference Formula Interior angle Volume Prism

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**Measurement Vocabulary Review**

A(n) _____________ is an angle inside of a shape. A (n) _________ is a closed plane figure formed by three or more line segments that intersect only at their endpoints (vertices). The number of cubic units needed to fill a given space is known as ________. ______________ is the measured distance around a circle. A ________ is a rule showing relationships among quantities. Interior angle Polygon Volume Circumference Formula Word Bank: Supplementary angles Polygon Net Complementary angles Surface area Circumference Formula Interior angle Volume Prism

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**Practice… Converting measurements.**

Customary measurements How many feet are in 15 miles? 352 35,200 79,200 89,760 Metric measurements Greg is 150 centimeters tall. How many meters is that? 0.500 1.5 15 15,000

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Grade 8 Formula Sheet

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Measurement Practice… Determining the measurement of a missing side(s) or angle(s) in a polygon. Missing Angles In a quadrilateral, each of two angles has a measure of 115°. If the measure of a third angle is 70°, what is the measure of the remaining angle? 60° 70° 130° 140° Find the measure in degrees, of the smallest angle in this triangle: 20 40 60 80 3x 2x 4x

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Grade 8 Formula Sheet

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Measurement Practice… Determining the measurement of a missing side(s) or angle(s) in a polygon. Missing Angles (Short Response) In the accompanying diagram of ∆BCD, m<C=70, m<CDE=130, and side BD is extended to A and to E. Find m<CBA. A B C D E 70° 130° Scoring Rubric: **[2 points] 120, and appropriate work is shown, such as m<CDB= 180 – 130 = 50 and m<CBA = = 120 or correctly labeled angles in a diagram. *[1 point] Appropriate work is show, but one computational error is made. *[1 point] Appropriate work is show, but one conceptual error is made. *[1 point] m<CBD = 60 is found, but no further correct work is shown. *[1 point] 120, but no work is shown [0 points] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure.

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Measurement Practice… Determining the measurement of a missing side(s) or angle(s) in a polygon. Missing Sides The length of each side of a figure below is 4 inches (in.). What is the perimeter of the figure? 12 in. 16 in. 20 in. 24 in. The interior angles of a sign total 1080°. What type of polygon is the sign? Hexagon Pentagon Heptagon Octagon 4 in.

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Grade 8 Formula Sheet

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Measurement Practice… Determining measures of perimeter, circumference, area, surface area and/ or volume. Scaling Area A farmer has a rectangular field that measures 100 feet by 150 feet. He plans to increase the area of the field by 20%. He will do this by increasing the length and width by the same amount, x. Which equation represents the area of the new field? ( x)(150 + x) = 18,000 2(100 + x) + 2(150 + x) = 15,000 (100 + x)(150 + x) = 18,000 (100 + x)(150 + x) = 15,000

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Measurement Practice… Determining measures of perimeter, circumference, area, surface area and/ or volume. Surface Area The box pictured below is open at the top. Find its outside surface area. 45 cm² 1150 cm² 1300 cm² 3750 cm² Volume The volume of the rectangular solid below is 1,440 cubic inches. What could be the length and width of this rectangular solid? 4 inches by 10 inches 8 inches by 20 inches 10 inches by 48 inches 30 inches by 40 inches 10 cm 15 cm 20 cm 3 in

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Grade 8 Formula Sheet

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Measurement Practice… Determining measures of perimeter, circumference, area, surface area and/ or volume. Perimeter Delroy’s sailboat has two sails that are similar triangles. The larger sail has sides of 10 feet, 24 feet, and 26 feet. If the shortest side of the smaller sail measures 6 feet, what is the perimeter of the smaller sail? 15 ft 36 ft 60 ft 100 ft Circumference The circumference of a circle is 16∏. What is the radius of the circle? 4 8 16 32

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Grade 8 Formula Sheet

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Measurement Practice… Determining measures of perimeter, circumference, area, surface area and/ or volume. Perimeter How does the perimeter of a rectangle change when each side is increased by 2 units The perimeter doubles The perimeter quadruples The perimeter increases by 4 units The perimeter increases by 8 units Area If the diameter of a car tire is 30 cm, what is the area of that circle? Round your answer. 30.14 cm² 314 cm² 7,070 cm² 707 cm²

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Grade 8 Formula Sheet

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**Geometry Vocabulary Review**

When a transversal intersects two lines, ___________________ are on the same side of the transversal and on the same side of the given lines. (Also, similar or congruent figures.) A(n) _________________ has exactly two congruent sides. The ____________________ is a formula for finding the length of a side of a right triangle when the lengths of two sides are given. A pair of ________________ angles are located outside a set of parallel lines and on opposite sides of the transversal. A pair of opposite congruent angles formed when two lines intersect are called _____________. Corresponding angles Isosceles triangle Pythagorean Theorem Alternate exterior Vertical angles Word Bank: Acute triangle Vertical angles Isosceles triangle Corresponding angles Alternate exterior Adjacent angles Pythagorean Theorem Alternate interior Coordinate plane Scalene triangle

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**Geometry Vocabulary Review**

A(n) _______________ has no congruent sides. A (n) ____________ has each angle measuring less than 90°. A pair of _______________ angles are located between a set of parallel lines and on opposite sides of the transversal. A ________________ is a 2-D system which contains both horizontal and vertical axes. _______________ share a common side and common vertex and do not overlap. Scalene triangle Acute triangle Alternate interior Coordinate plane Adjacent angles Word Bank: Acute triangle Vertical angles Isosceles triangle Corresponding angles Alternate exterior Adjacent angles Pythagorean Theorem Alternate interior Coordinate plane Scalene triangle

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Geometry Practice… Identifying, using, and/or describing properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, prisms, spheres, cones and/or cylinders.. Circular Geometry A duck swims from the edge of a circular pond to a fountain in the center of the pond. Its path is represented by the dotted line in the diagram below. What term describes the duck’s path? Chord Radius Diameter Central angle Duck’s Path

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Geometry Practice… Identifying, using, and/or describing properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, prisms, spheres, cones and/or cylinders.. Parallelograms The height of a parallelogram is 13.5 feet. The base is four times the height. What is the area of the parallelogram? ft² 54 ft² ft² 729 ft² Prisms What is the volume of a rectangular prism with a length of 16 inches, a height or 4 inches, and a width of 12 inches? 48 in.³ 768 in.³ 1810 in.³ 2413 in.³

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Grade 8 Formula Sheet

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Geometry Practice… Identifying, using, and/or describing properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, prisms, spheres, cones and/or cylinders.. Parallelograms (Short Response) Is it possible for two parallelograms to have the same area but not be congruent? Explain why or why not. Scoring Rubric: **[2 points] Yes, two parallelograms can have the same area but not be congruent. Let one parallelogram have a base of 6 units and a height of 4 units. Its area is 24 square units. Let another parallelogram have a base of 8 units and a height of 3 units. Its area is also 24 units, but the two parallelograms are not congruent. *[1 point] Yes, two parallelograms can have the same area but not be congruent. No explanation or example is given. *[1 point] Yes, two parallelograms can have the same area but not be congruent. A poor or incorrect explanation is given. [0 points] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure.

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Geometry Practice… Identifying, using, and/or describing properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, prisms, spheres, cones and/or cylinders.. Angles Which angles are complementary? <2 and <3 <3 and <4 <4 and <5 <1 and <2 The ratio of two supplementary angles is 2:7. What is the measure of the smaller angle? 10° 14° 20° 40° 1 2 3 4 5

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Geometry Practice… Identifying, using, and/or describing properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, prisms, spheres, cones and/or cylinders.. Net Which of the following figures is the net of a square based pyramid? 1 C. 3 2 D. 4

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Geometry Practice… Identifying, using, and/or describing properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, prisms, spheres, cones and/or cylinders.. Regular Polygons (Extended Response) The top of the picnic table shown has the shape of a regular polygon. Sketch and classify the polygon. Is it convex or concave? Draw a single segment that divides the polygon in your sketch into two trapezoids. Find the sum of the measures of the angles of the polygon. Solution: a–b. The polygon is a regular hexagon. It is convex. c = 720 The sum of the measures of the angles of the polygon is 720°.

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Grade 8 Formula Sheet

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Geometry Practice… Identifying, using, and/or describing properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, prisms, spheres, cones and/or cylinders. Line p is parallel to line k in the figure shown below Which statement about the lines in the figure is true? Line k is parallel to line m. Line m is parallel to line j. Line p is perpendicular to line k. Line j is perpendicular to line p. Angles & Lines In the diagram below, line l is parallel to line m and line p is parallel to line q? Which angle has the same measure as <1? <2 <3 <4 <5 j m k p 2 1 3 4 5 l m q p

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Geometry Practice… Computing measures of sides of right triangles using the Pythagorean Theorem. Pythagorean Theorem Mr. Kyle drives eight miles south and then six miles east. What was the diagonal distance from his starting point? 2 miles 10 miles 14 miles 48 miles What is the length of the missing side in this triangle? 14 15 16 18 12 x 20

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Grade 8 Formula Sheet

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**Practice… Plot and/or identify ordered pairs on a coordinate plane.**

Geometry Practice… Plot and/or identify ordered pairs on a coordinate plane. Which building is located at (-2, 3)? School Library Market Bank Coordinate System At what point does the line intersect the y-axis? (5, 0) (0, 5) (0,-3) (-3, 0) Library School Bank Market

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**Algebraic Concepts Vocabulary Review**

A ______________ is an equation whose graph in a coordinate plane is a straight line. _____________ is the distance of a number from zero on a number line; shown by | |. A(n) __________________ is a group of two or more equations that contain two or more variables. A phrase that contains operations, numbers, and/or variables is a(n) ____________. A relationship that has exactly one output for each input is called a ________. Linear equation Absolute value System of equations Expression Function Word Bank: Absolute value Equation Function Expression Inequality Function table Inverse operations Linear function System of equations Terms

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**Algebraic Concepts Vocabulary Review**

An _________ shows the relationship between quantities that are not equal. A sentence that shows that two expressions are equivalent is a(n) ________. ______ in an expression are set apart by plus or minus signs. A table of ordered pairs that represent solutions of a function is called a _____________. _________________ undo each other; addition and subtraction, multiplication and division. Inequality Equation Terms Function table Inverse operations Word Bank: Absolute value Equation Function Expression Inequality Function table Inverse operations Linear function System of equations Terms

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Algebraic Concepts Practice… Analyzing, extending or developing descriptions of patterns or functions. Patterns Fiona created a pattern using numbers as shown below. 0, 2, 6, 12 The pattern continues. What is the next number in the pattern? 14 18 20 24 List the next two values in this sequence: 4, 10, 22, __, __ 34, 46 34, 48 40, 62 46, 94

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Algebraic Concepts Practice… Analyzing, extending or developing descriptions of patterns or functions. The table below shows a relationship between the values of x and y. Which equation describes the relationship? y = x – 3 y = x +3 y = -x -3 y = -x +3 Functions What is the solution of x > -3?. 3 x < -1 x > -1 x < -9 x > -9 x y -7 -10 -2 -5 3 8 5

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Algebraic Concepts Practice… Select and/ or use a strategy to simplify an expression, solve an equation or inequality and/ or check the solution for accuracy. Solving Equations Dora owns a card store. After a full week, she made $ by selling cards (c). Using the equation c = 250, how many cards did Dora sell that week? 125 200 251 312 In which equation is m = 28 the solution? m – 3 = 5 5 (m – 3)5 = 5

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Algebraic Concepts Practice… Selecting and/ or using a strategy to simplify an expression, solve an equation or inequality and/ or check the solution for accuracy. Expressions If k can be replaced by any number, how many different values can the expression k + 6 have? One Six Seven Infinitely many Inequalities There is $150 in Dave’s bank account. He deposits $200 into the account each month. Dave needs at least $700 to buy a used car. The inequality below can be solved for x to find the number of deposits Dave must make to reach his goal. 200x ≥ 700 How many deposits must Dave make? x ≥ 2.75 x ≤ 2.75 x ≥ 4.25 x ≤ 4.25

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Algebraic Concepts Practice… Selecting and/ or using a strategy to simplify an expression, solve an equation or inequality and/ or check the solution for accuracy. Checking for Accuracy (Short Response) Brett was given the problem: “Evaluate 2x² + 5 when x = 3.” Brett wrote that the answer was 41. Was Brett correct? Explain your answer. Scoring Rubric: **[2 points] No, and an appropriate explanation is given or the expression is evaluated correctly. *[1 point] No, and the correct order of operations is used to evaluate 2(3)² + 5, but one computational error is made. *[1 point] One conceptual error is made in evaluating the expression, but the question is answered appropriately. *[1 point] Appropriate work is shown, but the question is not answered. [0 points] No, but no explanation or an inappropriate explanation is given. [0 points] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure.

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Algebraic Concepts Practice… Creating and/ or interpreting expressions, equations or inequalities that model problem situations. Inequalities When Bernie earns 5 times more than the amount (a) of money he has plus another $1,000, he will have at least $16,000 to start a small business. Which statement represents this situation? 5a + 1,000 ≥ 16,000 5 + 1,000a ≤ 16,000 5a +1,000 ≤ 16,000 5 + 1,000a ≥ 16,000 Expressions Which expression represents 4 times the sum of x squared and 6? 4x² + 6 4(x² + 6) 4(x + 6)² (4x + 6)²

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Algebraic Concepts Practice… Creating and/ or interpreting expressions, equations or inequalities that model problem situations. Creating Equations A wooden box with 8 DVDs inside weighs 4.2 kilograms. The box weighs 0.6 kg when empty. Using w to represent the weight of one DVD, which of the following describes this situation? 8w = 4.2 8w = 4.2 8w – 0.6 = 4.2 8(w + 0.6) = 4.2 Which equation shows that the sum of x and 2 is twice as much as 6? x = 2 · 2 · 6 x + 2 · 2 =6 2(x +2) = 6 x + 2 = 2 · 6

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Algebraic Concepts Practice… Represent relationships with tables or graphs on the coordinate plane. Functions Given the function y = ½x -2, which set of numbers completes the table? {4, 3, 2} {-4, -3, -2} {-4, 3, 2} {4, -3, -2} Tables Which linear function is graphed below? y = x + 3 y² = 3x y = 3 x = 3 x y -4 -2

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**Data Analysis & Probability Vocabulary Review**

___________ describes the relationship between two sets of data. A graphic method for showing a summary using median, quartiles and extremes of data is known as a(n) ____________________. A(n) ___________ is a possible order or arrangement of a set of items. A statement of _____________________ is based on the results of a series of trials. Two events that cannot occur at the same time are known as _______________________. Correlation Box-and-whisker plot Permutation Experimental probability Mutually exclusive events Word Bank: Box-and-whisker plot Mutually exclusive Compound event Experimental probability events Stem-and-leaf plot Independent events Scatter plot Theoretical probability Permutation Correlation

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**Data Analysis & Probability Vocabulary Review**

___________________ is a statement of the probability of an event without doing an experiment or analyzing. A _______________ is made up of two or more simple events. Two events in which the outcome of one event does not affect the outcome of the other event are known as _________________. A graph with points plotted to show a relationship between two variables is called a ___________. A(n) ________________ displays groups of data arranged by place value. Theoretical probability Compound event Independent events Scatter plot Stem-and-leaf plot Word Bank: Box-and-whisker plot Mutually exclusive Compound event Experimental probability events Stem-and-leaf plot Independent events Scatter plot Theoretical probability Permutation Correlation

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**Practice… Choosing, displaying or interpreting data.**

Data Analysis & Probability Practice… Choosing, displaying or interpreting data. Charts According to the graph, what percent of the students chose generic brands? 15% 14% 17% 16% Stem-and-Leaf Plots The table below shows test scores for a class. How many students scored in the 80’s? 2 students 6 students 7 students 9 students Stem Leaf 9 8 7 6 5 2 3 4

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**Practice… Choosing, displaying or interpreting data.**

Data Analysis & Probability Practice… Choosing, displaying or interpreting data. Interpreting Data The test scores for 10 students in Ms. Sampson’s homeroom were 61, 81, 83, 87, 88, 89, 90, 98, and 100. Which frequency table is accurate for this set of data? 1) C. 3) 2) D. 4) Interval Frequency 61-70 2 71-80 81-90 7 91-100 10 Interval Frequency 61-70 2 71-80 81-90 8 91-100 10 Interval Frequency 61-70 2 71-80 81-90 8 91-100 10 Interval Frequency 61-70 2 71-80 81-90 6 91-100

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**Practice… Calculating the probability of an event.**

Data Analysis & Probability Practice… Calculating the probability of an event. There are 15 girls and 11 boys in a mathematics class. If a student is selected at random to run an errand, what is the probability that a boy will be selected? 4/26 11/26 15/26 11/15 There are 9 packages, 5 red and 4 green. There are calculators inside 4 of the red packages and inside 2 of the green packages. What is the probability of choosing a package containing a calculator from the entire group of packages? 4/5 2/3 1/2 4/9 Probability

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**Practice… Calculating the probability of an event.**

Data Analysis & Probability Practice… Calculating the probability of an event. Probability While watching a game at a carnival where participants guess which of three cups is covering a ball, Jeremy tallies that following results. Find the experimental probability of the following as a fraction in its simplest form AND an approximate percentage. Find the experimental probability of the ball being under the right cup. Find the experimental probability of the ball not being under the middle cup. Ball Location left middle right Frequency 16 18 33 33 or about 50% 67 49 or about 73% 67

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**Data Analysis & Probability**

Practice… Determining the number of combinations and/ or permutations for an event. Combination Sarah and Tom belong to a soccer league that has 8 teams. Each team will play all of the other teams twice. How many games will be played in all? 16 28 56 64 Permutation Edward conducts a simulation using a coin, a number cube, and a spinner as shown below. What is the number of outcomes for this simulation? 3 8 12 48

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**Data Analysis & Probability**

Practice… Determining the number of combinations and/ or permutations for an event. Combinations (Short Response) In Jackson County, Wyoming, license plates are made with two letters (A through Z) followed by three digits (0 through 9). The plates are made according to the following restrictions: the first letter must be J or W, and the second letter can be any of the 26 letters of the alphabet no digit can be repeated How many different license plates can be made with these restrictions? Scoring Rubric: **[2 points] 37,440 and appropriate work is shown, such as 2 x 26 x 10 x 9 x 8 or 2P1 x 26P1 x 10P3. *[1 point] Appropriate work is show, but one computational error is made. *[1 point] Appropriate work is shown for at least one restriction, such as 2x26 or 10 x 9 x 8. *[1 point] 37,440 but no work is shown. [0 points] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure.

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**Data Analysis & Probability**

Practice… Drawing conclusions, making inferences and/ or evaluate hypotheses based on statistical and data displays. Drawing Conclusions From a batch of 3000 light bulbs, 100 were selected at random and tested. If 5 of the light bulbs in the sample were found to be defective, about how many defective light bulbs would be expected in the entire bunch? 15 60 150 300 Correlation The data represented in the scatter plot below can be described as having… Positive correlation Negative correlation No correlation Both positive and negative correlation

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**Data Analysis & Probability**

Practice… Drawing conclusions, making inferences and/ or evaluate hypotheses based on statistical and data displays. Drawing Conclusions An animal shelter needs to find homes for 40 dogs and 60 cats. If 15% of the dogs are female and 25% of the cats are female, what percent of the animals are female? 21% 22% 40% 42% Correlation Which data sets have a negative correlation? A person’s eye color and height A person’s height and weight The distance traveled and the time it takes to travel The outdoor temperature and the number of hours a heater is used

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**Data Analysis & Probability**

Practice… Drawing conclusions, making inferences and/ or evaluate hypotheses based on statistical and data displays. Drawing Conclusions John left his home and walked 3 blocks to his school, as shown in the accompanying graph. What is one possible interpretation of the section of the graph from point B to point C? John reached the top of a hill and began walking on level ground. John waited before crossing a busy street. John arrived at school and stayed throughout the day. John returned home to get his mathematics homework. A B C D 1 3 2 Time

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