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1. 1. • 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 8 th Grade Mathematics PA Assessment Anchor Glossary for 7 th & 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: www.studyisland.com http://www.ixl.com/math/grades www.mathmaster.org
2. 2. 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!!  3
3. 3. Numbers & Operations Vocabulary Review Reciprocal 1. The product of a number and its __________ is 1. Rational 2. Any number that can be written as a fraction is called a _________. number Scientific notation 3. ________________ is a short-hand way of writing extremely large or extremely small numbers. Real numbers 4. The set of ____________ is the set of all rational and irrational numbers. Perfect square 5. The product of an integer multiplied by itself is called a _____________. Word Bank: Rational number Scientific notation Order of Operations Proportion Reciprocal Unit price Perfect square Real numbers Square root Expanded form 4
4. 4. Numbers & Operations Vocabulary Review Expanded 6. A number written as the sum of values of its digits is called _________. form 7. A number that is multiplied by itself to form a product is called a Square root ___________ of that product. Unit price 8. A(n) __________ is used to compare price per item. 9. Rules describing what sequence to use in evaluating expressions is Order of Operations known as __________________. Proportion 10.A ___________ is an equation showing that two ratios are equal. Word Bank: Rational number Scientific notation Order of Operations Proportion Reciprocal Unit price Perfect square Real numbers Square root Expanded form 5
5. 5. Numbers & Operations Practice… Representing Numbers in equivalent forms. Scientific Notation Exponential Form  The Earth is approximately 93,000,000 miles from the sun. What is the distance written in scientific notation?  Which number represents 4.5 x 104 written in standard notation? A. B. C. D. 9.3 x 106 93 x 106 93 x 107 9.3 x 107 A. B. C. D. 0.00045 0.000045 45,000 450,000 6
6. 6. Numbers & Operations Practice… Representing Numbers in equivalent forms. Expanded Notation  Which expression is equivalent to the number 8,006,425? A. B. C. D. (8x107)+(6x106)+(4x103)+(2x102)+(5x101) (8x10)+(6x10)+(4x10)+(2x10)+(5x10) (8x106)+(6x105)+(4x104)+(2x103)+(5x102) (8x106)+(6x103)+(4x102)+(2x101)+(5x100) 7
7. 7. 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? A. 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. B. C. D. 8
8. 8. Numbers & Operations Practice… Completing calculations by applying the order of operations. Order of Operations  3³ + 4(8-5) A. B. C. D. 6.5 11 29 27.5 6=  Evaluate 7 + 5[(3 + 2)² - (2³ + 1)] A. B. C. D. 97 87 36 22 9
9. 9. 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?  Which statement is correct? A. B. C. D. (2 x 3) + 5 (2 x 3 + 5) 2 x (3 + 5) (2 x 3) + 5 8=2 8=2 8=2 8=2 A. (3² + 4⁴) B. (9² + 16²) C. (7²)² D. (9 + 16)² 10
10. 10. 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? Ratios  In 1991, and American, Ann Trason, set a world record by running 100km in 7 hours 30 minutes 1 hour 4 minutes 1 hour 28 minutes 1 hour 15 minutes Minutes Seconds 7 A. B. C. D. Hours 50 09 Which is the best estimate of her average speed? A. B. C. D. 12 km per hr 14 km per hr 16 km per hr 18 km per hr 11
11. 11. 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. 13
12. 12. 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 Bob’s House 60 miles Scoring Rubric: Rebecca’s House **[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 14 response that was obtained by an obviously incorrect procedure.
13. 13. Numbers & Operations Practice… Using estimation strategies in problem-solving situations. Estimation  A. B. C. D. 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  A. B. C. D. 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% 15
14. 14. 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. Number of Pounds Number of Cups 3 7 4 9 1/3 5 11 2/3 6 14 The pattern continues. What is the total number of cups of brown sugar in a 7-pound package? A. B. C. D. 15 2/3 16 1/3 16 2/3 17 1/3 16
15. 15. Numbers & Operations Practice… Computing and/ or explaining operations with integers, fractions and/ or decimals. Fractions Decimals  Subtract (-) 14 5/8 - 6 3/8  Divide ( ) 3 0.24 A. B. C. D. 8 3/8 7 2/8 8 1/4 9 A. B. C. D. 0.08 8.0 0.72 12.5 17
16. 16. Numbers & Operations Practice… Computing and/ or explaining operations with integers, fractions and/ or decimals. Subtracting Negatives Adding Negatives  Solve: 27 – (-9)  Solve: -4 + 23 A. B. C. D. -3 -18 18 36 A. B. C. D. -19 19 20 -27 18
17. 17. 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) or trial and error with at least trials and appropriate checks. 5 = 360, *[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. 19
18. 18. Measurement Vocabulary Review Surface area 1. ____________ is the sum of the areas of all the faces of a 3-D figure. 2. The sum of Supplementary angles is equal to 180 . ___________________ Net 3. A _______ is a 2-D shape that can be folded to create a 3-D figure. 4. A 3-D solid that has two congruent and parallel faces is known as a Prism _______. Complementary angles 5. The sum of ____________________ is equal to 90 . Word Bank: Net Circumference Prism Supplementary angles Complementary angles Formula Interior angle Polygon Surface area Volume 20
19. 19. Measurement Vocabulary Review Interior angle 6. A(n) _____________ is an angle inside of a shape. Polygon 7. A (n) _________ is a closed plane figure formed by three or more line segments that intersect only at their endpoints (vertices). 8. The number of cubic units needed to fill a given space is known as Volume ________. Circumference 9. ______________ is the measured distance around a circle. Formula 10.A ________ is a rule showing relationships among quantities. Word Bank: Net Circumference Prism Supplementary angles Complementary angles Formula Interior angle Polygon Surface area Volume 21
20. 20. Measurement Practice… Converting measurements. Customary measurements Metric measurements  How many feet are in 15 miles?  Greg is 150 centimeters tall. How many meters is that? A. B. C. D. 352 35,200 79,200 89,760 A. B. C. D. 0.500 1.5 15 15,000 22
21. 21. Measurement Practice… Determining the measurement of a missing side(s) or angle(s) in a polygon. Missing Angles  A. B. C. D. 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: 3x A. B. C. D. 20 40 60 80 2x 4x 24
22. 22. 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. C 70 Scoring Rubric: A B 130 D E **[2 points] 120, and appropriate work is shown, such as m<CDB= 180 – 130 = 50 and m<CBA = 70 + 50 = 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. 26
23. 23. 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.). 4 in. What is the perimeter of the figure? A. B. C. D.  The interior angles of a sign total 1080 . What type of polygon is the sign? A. B. C. D. Hexagon Pentagon Heptagon Octagon 12 in. 16 in. 20 in. 24 in. 27
24. 24. 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? A. (100 + 2x)(150 + x) = 18,000 B. 2(100 + x) + 2(150 + x) = 15,000 C. (100 + x)(150 + x) = 18,000 D. (100 + x)(150 + x) = 15,000 29
25. 25. 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. Volume  The volume of the rectangular solid below is 1,440 cubic inches. 20 cm 3 in 15 cm 10 cm A. B. C. D. 45 cm² 1150 cm² 1300 cm² 3750 cm² What could be the length and width of this rectangular solid? A. B. C. D. 4 inches by 10 inches 8 inches by 20 inches 10 inches by 48 inches 30 inches by 40 inches 30
26. 26. Measurement Practice… Determining measures of perimeter, circumference, area, surface area and/ or volume. Perimeter  A. B. C. D. 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? A. B. C. D. 4 8 16 32 32
27. 27. 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 A. The perimeter doubles B. The perimeter quadruples C. The perimeter increases by 4 units D. 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. A. B. C. D. 30.14 cm² 314 cm² 7,070 cm² 707 cm² 34
28. 28. Geometry Vocabulary Review 1. When a transversal intersects two lines, Corresponding angles are ___________________ on the same side of the transversal and on the same side of the given lines. (Also, similar or congruent figures.) Isosceles triangle 2. A(n) _________________ has exactly two congruent sides. Pythagorean Theorem 3. The ____________________ is a formula for finding the length of a side of a right triangle when the lengths of two sides are given. Alternate exterior 4. A pair of ________________ angles are located outside a set of parallel lines and on opposite sides of the transversal. 5. A pair of opposite congruent angles formed when two lines intersect Vertical angles are called _____________. Word Bank: Isosceles triangle Adjacent angles Coordinate plane Acute triangle Vertical angles Corresponding angles Alternate exterior Pythagorean Theorem Alternate interior Scalene triangle 36
29. 29. Geometry Vocabulary Review Scalene triangle 6. A(n) _______________ has no congruent sides. Acute triangle 7. A (n) ____________ has each angle measuring less than 90 . Alternate interior 8. A pair of _______________ angles are located between a set of parallel lines and on opposite sides of the transversal. Coordinate plane 9. A ________________ is a 2-D system which contains both horizontal and vertical axes. 10._______________ share a common side and common vertex and do Adjacent angles not overlap. Word Bank: Isosceles triangle Adjacent angles Coordinate plane Acute triangle Vertical angles Corresponding angles Alternate exterior Pythagorean Theorem Alternate interior Scalene triangle 37
30. 30. Practice… Geometry Identifying, using, and/or describing properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, pris ms, 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. Duck’s Path What term describes the duck’s path? A. B. C. D. Chord Radius Diameter Central angle 38
31. 31. Practice… Geometry 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? A. B. C. D. 45.5625 ft² 54 ft² 182.25 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? A. B. C. D. 48 in.³ 768 in.³ 1810 in.³ 2413 in.³ 39
32. 32. Practice… Geometry 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. 41
33. 33. Practice… Geometry Identifying, using, and/or describing properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, pris ms, spheres, cones and/or cylinders.. Angles  Which angles are complementary? 1 5 A. B. C. D. 2 4 <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? A. B. C. D. 10 14 20 40 3 42
34. 34. Practice… Geometry Identifying, using, and/or describing properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, pris ms, spheres, cones and/or cylinders.. Net  Which of the following figures is the net of a square based pyramid? A. 1 C. 3 B. 2 D. 4 43
35. 35. Practice… Geometry 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. a. Sketch and classify the polygon. Is it convex or concave? b. Draw a single segment that divides the polygon in your sketch into two trapezoids. c. 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. 360 + 360 = 720 The sum of the measures of the angles of the polygon is 720 . 44
36. 36. Practice… Geometry Identifying, using, and/or describing properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, pris ms, spheres, cones and/or cylinders. Angles & Lines  Line p is parallel to line k in the figure shown below p k  In the diagram below, line l is parallel to line m and line p is parallel to line q? m 2 3 4 1 5 j l Which statement about the lines in the figure is true? A. Line k is parallel to line m. B. Line m is parallel to line j. C. Line p is perpendicular to line k. D. Line j is perpendicular to line p. p q m Which angle has the same measure as <1? A. <2 B. <3 C. <4 D. <5 46
37. 37. 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?  What is the length of the missing side in this triangle? 20 12 A. B. C. D. 2 miles 10 miles 14 miles 48 miles x A. B. C. D. 14 15 16 18 47
38. 38. Geometry Practice… Plot and/or identify ordered pairs on a coordinate plane. Coordinate System  Which building is located at (-2, 3)? Library  At what point does the line intersect the y-axis? A. B. C. D. (5, 0) (0, 5) (0,-3) (-3, 0) Market School Bank A. B. C. D. School Library Market Bank 49
39. 39. Algebraic Concepts Vocabulary Review Linear equation 1. A ______________ is an equation whose graph in a coordinate plane is a straight line. Absolute value 2. _____________ is the distance of a number from zero on a number line; shown by | |. System of equations 3. A(n) __________________ is a group of two or more equations that contain two or more variables. 4. A phrase that contains operations, numbers, and/or variables is a(n) Expression ____________. 5. A relationship that has exactly one output for each input is called a Function ________. Word Bank: Function Function table System of equations Absolute value Expression Inverse operations Terms Equation Inequality Linear function 50
40. 40. Algebraic Concepts Vocabulary Review Inequality 6. An _________ shows the relationship between quantities that are not equal. 7. A sentence that shows that two expressions are equivalent is a(n) Equation ________. Terms 8. ______ in an expression are set apart by plus or minus signs. 9. A table of ordered pairs that represent solutions of a function is called a Function table _____________. Inverse operations 10._________________ undo each other; addition and subtraction, multiplication and division. Word Bank: Function Function table System of equations Absolute value Expression Inverse operations Terms Equation Inequality Linear function 51
41. 41. 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? A. B. C. D. 14 18 20 24  List the next two values in this sequence: 4, 10, 22, __, __ A. B. C. D. 34, 46 34, 48 40, 62 46, 94 52
42. 42. Algebraic Concepts Practice… Analyzing, extending or developing descriptions of patterns or functions. Functions  What is the solution of x > -3?. 3  The table below shows a relationship between the values of x and y. x A. B. C. D. x < -1 x > -1 x < -9 x > -9 y -7 -10 -2 -5 3 0 8 5 Which equation describes the relationship? A. y = x – 3 B. y = x +3 C. y = -x -3 D. y = -x +3 53
43. 43. Practice… Algebraic Concepts Select and/ or use a strategy to simplify an expression, solve an equation or inequality and/ or check the solution for accuracy. Solving Equations  A. B. C. D. Dora owns a card store. After a full week, she made \$250.00 by selling cards (c). Using the equation 1.25c = 250, how many cards did Dora sell that week? 125 200 251 312  In which equation is m = 28 the solution? A. m – 3 = 5 5 B. m – 3 = 5 5 C. m – 3 = 5 5 D. (m – 3)5 = 5 54
44. 44. Practice… Algebraic Concepts 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? A. B. C. D. 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 + 150 ≥ 700 How many deposits must Dave make?  A. B. C. D. x ≥ 2.75 x ≤ 2.75 x ≥ 4.25 x ≤ 4.25 55
45. 45. Practice… Algebraic Concepts 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. 56
46. 46. Algebraic Concepts Practice… Creating and/ or interpreting expressions, equations or inequalities that model problem situations. Inequalities  A. B. C. D. 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? A. B. C. D. 4x² + 6 4(x² + 6) 4(x + 6)² (4x + 6)² 57
47. 47. Algebraic Concepts Practice… Creating and/ or interpreting expressions, equations or inequalities that model problem situations. Creating Equations  A. B. C. D. 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 + 0.6 = 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? A. B. C. D. x=2·2·6 x + 2 · 2 =6 2(x +2) = 6 x+2=2·6 58
48. 48. 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? x Tables  Which linear function is graphed below? A. B. C. D. y=x+3 y² = 3x y=3 x=3 y -4 -2 0 A. B. C. D. {4, 3, 2} {-4, -3, -2} {-4, 3, 2} {4, -3, -2} 59
49. 49. Data Analysis & Probability Vocabulary Review Correlation 1. ___________ describes the relationship between two sets of data. 2. A graphic method for showing a summary using median, quartiles and Box-and-whisker plot extremes of data is known as a(n) ____________________. Permutation 3. A(n) ___________ is a possible order or arrangement of a set of items. Experimental probability 4. A statement of _____________________ is based on the results of a series of trials. 5. Two events that cannot occur at the same time are known as Mutually exclusive events _______________________. Word Bank: Compound event Stem-and-leaf plot Theoretical probability Box-and-whisker plot Experimental probability Independent events Permutation Mutually exclusive events Scatter plot 60 Correlation
50. 50. Data Analysis & Probability Vocabulary Review 6. Theoretical probability is a statement of the probability of an event ___________________ without doing an experiment or analyzing. 7. A Compound event is made up of two or more simple events. _______________ 8. Two events in which the outcome of one event does not affect the Independent events outcome of the other event are known as _________________. 9. A graph with points plotted to show a relationship between two Scatter plot variables is called a ___________. Stem-and-leaf plot 10.A(n) ________________ displays groups of data arranged by place value. Word Bank: Compound event Stem-and-leaf plot Theoretical probability Box-and-whisker plot Experimental probability Independent events Permutation Mutually exclusive events Scatter plot 61 Correlation
51. 51. Data Analysis & Probability Practice… Choosing, displaying or interpreting data. Charts  Stem-and-Leaf Plots According to the graph, what percent of the students chose generic brands? Favorite Sneakers at Sherman High School  Brand A, 8% Stem A. B. C. D. 15% 14% 17% 16% 9 5 2 3 4 A. B. C. D. 7 7 8 9 6 Brand D, 30% 0 0 2 4 6 7 9 7 Brand C, 15% 0 1 1 5 7 8 Generic brands Leaf 9 Brand B, 5% Brand E, 27% The table below shows test scores for a class. How many students scored in the 80’s? 4 2 students 6 students 7 students 9 students 62
52. 52. 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? Interval Frequency 61-70 2 2 71-80 0 81-90 7 81-90 8 91-100 B. 2) Interval Frequency 61-70 2 71-80 A. 1) 10 91-100 10 Interval Frequency Interval Frequency 61-70 2 61-70 2 71-80 2 71-80 0 81-90 8 81-90 6 91-100 10 91-100 2 C. 3) D. 4) 63
53. 53. Data Analysis & Probability Practice… Calculating the probability of an event. Probability  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? A. B. C. D. 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? A. B. C. D. 4/5 2/3 1/2 4/9 64
54. 54. 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. Ball Location left middle right Frequency 16 18 33 Find the experimental probability of the following as a fraction in its simplest form AND an approximate percentage. a. Find the experimental probability of the ball being under the right cup. 33 or about 50% 67 b. Find the experimental probability of the ball not being under the middle cup. 49 or about 73% 67 65
55. 55. Data Analysis & Probability Practice… Determining the number of combinations and/ or permutations for an event. Permutation 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?  A. B. C. D. 16 28 56 64 What is the number of outcomes for this simulation? A. B. C. D. Edward conducts a simulation using a coin, a number cube, and a spinner as shown below. 3 8 12 48 66
56. 56. Practice… Data Analysis & Probability 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. 67
57. 57. 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? A. B. C. D. 15 60 150 300 Correlation  The data represented in the scatter plot below can be described as having… A. B. C. D. Positive correlation Negative correlation No correlation Both positive and negative 68 correlation
58. 58. Data Analysis & Probability Practice… Drawing conclusions, making inferences and/ or evaluate hypotheses based on statistical and data displays. Drawing Conclusions  A. B. C. D. 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. A person’s eye color and height B. A person’s height and weight C. The distance traveled and the time it takes to travel D. The outdoor temperature and the number of hours a heater is used 69
59. 59. 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. D 3 B C 2 1 A Time What is one possible interpretation of the section of the graph from point B to point C? A. B. C. D. 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. 70 John returned home to get his mathematics homework.
60. 60. Good luck to all!!! Feel free to repeat the review as many times as you like or continue studying your own additional resources! 71