Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name:__________________________________2016 Math 8 Final Review Module 1 Real Numbers 1.1 Rational number, terminating decimal, repeating decimal, square root, principal sq. root, perfect square, cube root, perfect cube, irrational numbers 1.2 Real numbers (know the chart pg. 15) 1.3 Compare Rational Numbers < = > 1 1. Does equal a terminating decimal or a 15 repeating decimal? 2. Divide 7 by 12 to change 36.5 106 7. Write 3.65 105 in standard notation. 8. Write your answer in scientific notation. (6.4 103) + (5.2 104) 9. Change a length of 0.00000843 meter to scientific notation. 7 to a repeating 12 decimal. 10. What power of ten makes this statement true? 78,000,000,000 7.8 ____ Module 3 Proportional and Nonproportional 3. Between which two whole numbers would you Relationships and Functions 3.1 Proportional Relationship (goes thru the place 40 on a number line? origin), constant of proportionality (k), 𝑦 proportional equations y = kx or k = 𝑥 3.2 Rate and Change and slope; m = 4. Is the square root of 13 a rational number or an irrational number? 5. Order the numbers from least to greatest. 8.33 , 3, 17 , 2 64 Module 2 Exponents and Scientific Notation 2.1 Integer Exponents, Simplifying Expressions with Exponents (PEMDAS) 2.2, 2.3 Scientific Notation, Standard Notation 2.4 Operations with Scientific Notation (add, sub, mult., divide) 6. Why is this number not in scientific notation? 𝑦2−𝑦1 𝑥2−𝑥1 = slope; rise over run, 3.3 Unit Rate (per one); *a graph is proportional if it goes thru the origin * an equation is proportional Y = mx + b, when b = 0 Module 4 Nonproportional Relationships 4.1 Y= mx + b, nonproportional when b ≠ 0 Ex: y = 4x – 2 *nonproportional 4.2 Y = mx + b, when b M = slope b = y-intercept 4.3 Graphing y = mx + b on a coordinate plane Use the graph for 11 –12. 11. Complete the table to display the data shown on the graph. 15. The graph shows 2 objects moving at a constant speed. Find the speed of Object A in meters per second. Time (weeks) Savings ($) 12. Find the constant of proportionality and write an equation for the relationship. 16. Which moving object has a greater unit rate? Explain how you know. 13. Carla is renting a canoe. It costs $80 for 2 hours and $160 for 4 hours. What is the rate per hour? (unit Rate) 17. A company prints T-shirts. They charge $40 plus $12 per shirt. So, the cost for n shirts is 40 (12n). Complete the table that shows this situation. 14. Plot points at (0, 0) and (3, 4). Draw a line through the points. What is the slope of your line? Shirts 1 2 3 4 Cost ($) Use this grid for 12–13. Use the graph for 15 - 16. 18. Graph y 2x 3 using the slope and y-intercept. slope ________ y-intercept: ________ 19. Graph x y 3 by making a table of ordered pairs. x y 20. The graphs show the equations from Exercise 15. ‘ Is either of the relationships proportional? Explain. Module 5 Writing Linear Equations 5.1 Writing an equation from a graph, a description 5.2 Writing an equation from a table 5.3 Bivariate Data 21. A line has a slope of 1 and a y-intercept of 2. What is an equation that could represent this line? Module 6 Functions 6.1 Indentifying and Representing Functions, Input, Output, A function assigns exactly one output to each input; Identify function from graph 6.2 Describing Functions, linear, nonlinear 6.3 Comparing Functions (table and an equation, table and graph, graph and description) 6.4 Analyzing Graphs 24. Sketch a graph that shows Maria walking for a while at an increasing speed, stopping to talk to a friend, then continuing to walk at that speed. 22. A line is represented by the equation y 2 3 x 1. What is the slope of the line with that equation? 23. A line is graphed on the coordinate grid below. What is the equation of this line? 25. Determine whether the relationship shown in the table below is a function. Write function or not a function. Input 9 8 9 10 Output 27 32 36 40 (HINT: one input MUST be paired with only one output value for the relationship to be a function) 7.1 Equations with the Variable on Both Sides 7.2 Equations with Rational Numbers 7.3 Equations with Distributive Property Use the table for 29 and 30. 26. The graph shows the total cost if a customer buys 1, 2, 3, 4, 5, or 6 gizmos. Determine whether the relationship is a function. Write function or not a function. Computer Repair Service Cost Tech Rite $75 service charge plus $50 an hour Best Byte $25 service charge plus $70 an hour 29. Use x for the number of hours. Which expression shows the total charges for Tech Rite? A 75 50x B (75 50)x 27. A cell phone company charges $50 for the phone plus a monthly service charge of $30. The 30. equation y 30x 50 gives the cost y after x months. Which is true of the relationship between x and y? C 75x 50x For how many hours of service will the costs charged by the two companies be equal? Solve the equation below to find out. 75 50x 25 70x A It is linear and proportional. A 0.4 h B It is linear and nonproportional. B 2.5 h C It is not linear. C 5h Use the diagrams below for 28. 31. Complete and solve an equation for the relationship described below. Three times a number minus five equals two times the number. equation: _________________________________ 28. Which mapping diagram represents a relationship that is a function? solution: _________________________________ A Mapping A B Mapping B C both Mapping A and Mapping B 32. Ayesha earns a 10% bonus based on her annual salary plus the number of sales she makes. She made 250 sales and earned a $5,000 bonus last year. Solve the equation below to find her salary last year. 0.1(x 250) 5,000 Module 7 Solving Linear Equations solution: _________________________________ 35. Add the equations to find the solution to the system 4 x y 8 6 x y 2 . 33. Solve the equation below. 12 x 3 4 x 36. Solve the systems by elimination (multiplication) x y 3 3x 2y 7 Module 8 Solving Systems of Linear Equations By Graphing By Substitution Method By Elimination Method 34. Solve this system by graphing. The first equation is Module 9 and 10 Transformations 9.1 Properties of Translations, transformation, graphed for you below. preimage, image, translation (slide) 2x y 3 9.2 Properties of Reflections; reflection(mirror image, over y-axis over x-axis), line of reflection y x 3 9.3 Properties of Rotations, rotation (90 Deg. Which point is the solution? Clockwise, 90 Deg. Counter Clock, and 180 Deg) 9.4 Algebraic Representations of Transformations – need to know how to USE the Algebraic Rep. of Translations and write the RULE of a translation, NEED TO KNOW algebraic rep of reflections and rotations 10.1 Dilations, center of dilation, enlargement, reduction, scale factor 10.2 Algebraic Representations of Dilations A (2, 1) B (1, 2) C (2, 1) Use the diagram for 37-39. 41. The vertices of a triangle are located at the following points on a coordinate grid. (1, 1), (1, 5), (4, 1) The triangle is reflected across the y-axis. What are the coordinates of the image of the triangle? 37. Where would the shape be located after a translation of 5 units to the right? A Quadrant I B Quadrant II C Quadrant III 38. Where would the shape be located after a reflection across the x-axis? A Quadrant I 42. Which of the following describes a figure and its image under a dilation? B Quadrant II A They are equivalent. C Quadrant III B They are congruent. C They are similar. 39. Where would the shape be located after a rotation of 90 clockwise about the origin? A Quadrant I B Quadrant II C Quadrant III 40. The vertices of a trapezoid are located at the following points on a coordinate grid. 43. The black triangle was transformed to make the gray triangle. Which represents the transformation? (1, 2), (3, 1), (3, 5), (1, 4) The trapezoid is translated 2 units to the right. What are the coordinates of the image of the trapezoid? A (3, 2), (5, 1), (5, 5), (3, 4) B (3, 2), (5, 1), (5, 5), (3, 4) C (1, 4), (3, 3), (3, 7), (1, 6) A (x, y) (x 3, y 3) B (x, y) (3x, 3y) C (x, y) (x 2, y 2)