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Math 8 Semester 1 Review Guide #2 (2014-2015) Name: ______________________ Unit 1: Number Sense 1. 2. ____ Write as a decimal. A 3.249 C 3.25 B 3.15 D 3.24 Write the decimal as a mixed number or fraction in simplest form. 2. 0. A B 3. 3 17 4 1 5 C D Is the number -125.45 a rational number? Explain. A Yes, it is a repeating decimal. B Yes, it is a terminating decimal. C No, negative numbers are not rational. D No, the number goes on infinitely. 2 11 9 50 4. Match5. ____ Compare. Write <, >, or =. A < B > C = 1 3 8 4 Order the set of numbers from least to greatest. 4. –2.7, –3.6, A 2 , 7 B 6. − − 9 25 , 25 9 2 7 , –2.7, –3.6 –3.6, –2.7, − 9 25 , 2 C D 7 − − 9 , 2 , –2.7, –3.6 25 7 9 , –3.6, –2.7, 25 What is the side length of a square whose area is 50 square inches? A 12.5 in C √50 in B 25 in D 225 in 2 7 7. 8. If the volume of a cube is 1331 cubic centimeters, about how long is each of the edges of the cube? A 11 cm C 665.5 cm B -11 cm D 444 cm Graph the following value on the number line: √3 What is its decimal equivalent? -5 9. -4 -3 -2 -1 0 1 2 A 1.5 C 1.3 B 1.73 D 3 3 4 5 What makes a number an irrational number? A It can be written as a repeating decimal. B It cannot be written as a fraction, , where a and b are integers and b does not 𝑎 𝑏 equal zero. C Its square root is an integer. D It cannot be graphed on a number line. 10. 11. 12. 13. Which set contains only rational numbers? A -1, 125.2, √50 C − √81, √100 , 9.87 B √31, -0.67, 43 D √75 , -3.245, -0.454545… Between which two integers does √34 lie? A 3 and 4 C 5 and 6 B 4 and 5 D 6 and 7 Evaluate √625 A 312.5 C 25 B 125 D 208 What is the best estimate of the value of √120 ? A 10 C 60 B 11 D 80 14. 15. 16. Tommy wants to build a square fence border around his skate park. If the skate park covers an area of 361 square meters, what is the length of each side of the park? A 19 meters C 180.5 meters B 90 meters D 722 meters What is the value of 3 √4096? A 14 C 1366 B 16 D 2048 The value of 3 √205 lies between which of the following pairs of numbers? A 102 and 103 C 3 and 4 B 60 and 61 D 5 and 6 Unit 2: Exponents and Scientific Notation 17. Simplify this expression using a single exponent. 75 ∙ 76 18. A 4930 C 4911 B 730 D 711 Simplify this expression using a single exponent. 28 27 19. A 21 C 256 B 28÷7 D 215 Simplify this expression. (−1)0 A 0 C −1 B 1 D −0 20. Simplify this expression using a single exponent. 82 ∙ 85 83 21. A 87 C 84 B 810 D 14 Simplify this expression using a positive exponent. (14)−4 A B 22. 1 144 −56 C D 1 14 1 14−4 Write the number in standard notation. 5.42 × 105 23. A 5,420,000 C 54,200 B 542,000 D 54,200,000 Write the number in standard notation. A cell has an approximate diameter of 3.656 × 10−5 millimeters. A 0.0003656 C 0.000003656 B 0.0000003656 D 0.00003656 24. Write the number in scientific notation. 26,050 25. A 2.605 × 104 C 2.605 × 103 B 26.05 × 103 D 2.605 × 105 Write the number in scientific notation. 0.000046 26. 27. A 4.6 × 10−6 C 4.6 × 10−5 B 4.6 × 10−4 D 46 × 10−5 A city planner plans to lay a fiber optic cable around a city. The cable will be laid out in a rectangle with sides measuring (2.9 × 101 )𝑚 by (1.7 × 105 )𝑚. What is the area of the city located within the fiber optic rectangle? A 4.93 × 106 𝑚2 C 4.6 × 105 𝑚2 B 4.93 × 105 𝑚2 D 4.6 × 106 𝑚2 Simplify (5×109 ) (2×108 ) A 2.5 × 101 C 2.5 × 102 B 3.0 × 101 D 3.0 × 102 28. The average distance from the center of Earth to the center of the Moon is (3.844 × 108 ) meters. The average distance from the center of Earth to the center of the Sun is (1.496 × 1011 ) meters. From Earth, about how many times farther is it to the Sun than to the Moon? A 2.57 × 10−3 C 2.57 × 103 B 3.89 × 102 D 3.89 × 103 Unit 3: Linear versus Non-Linear 29. Solve the equation. – 3 + 6x = – 99 30. A x = 16 C x = 17 B x = –16 D x = -17 C x= D x=− Solve the equation. 𝑥 31. 4 A x=4 B x = –4 +5=6 11 4 11 4 Solve the equation. −2𝑥 + 4𝑥 = 4 32. A x= 8 C x= 2 B x= –8 D x=–2 Solve the equation. −3 − 18𝑥 = 33 A x = – 1.6 C B x= 2 D x = 1.6 X=–2 33. Solve the equation. 5(𝑥 + 8) = −5𝑥 − 40 34. A x= –8 C No solution B x= 8 D Infinite solutions Solve the equation. -3x + 15 = 3(5 – x) 35. A x=0 C Infinitely Many Solutions B x=6 D No Solution Solve the equation. 7x – 9 = 4 + 7x 36. A x = 20 C Infinitely Many Solutions B x = 13/14 D No Solution Solve the equation. 2 5 (5x – 10) = – 6 A x= –1 C Infinitely Many Solutions B x=4 D No Solution 37. 38. Which of the following equations will not produce a straight line? A y 2x 4 C x2 y2 0 B y 4x 3 D x y 10 Which of the given tables represents a linear function? Table A: x –6 0 6 9 y –12 0 12 18 Table C: x –1 0 2 4 y –1 0 8 64 Table B: x –6 0 6 9 y 36 0 36 81 Table D: x –6 0 6 9 y –36 0 –36 –81 A Table A C Table C B Table B D Table D 39. 40. Lena makes home deliveries of groceries for a supermarket. Her only stops after she leaves the supermarket are traffic lights and homes where she makes deliveries. The graph shows her distance from the store on her first trip for the day. What is the greatest possible number of stops she made at traffic lights? A 3 B 4 C 9 D 5 Samantha graphed the line y = 8x + 3. Meredith graphed the line based on this table: x y -2 -3 -1 -1 0 1 1 3 2 5 How would the graphs of the two lines compare? A. B. C. D. Meredith’s Meredith’s Meredith’s Meredith’s slope slope slope slope is is is is steeper and y intercept is lower. steeper and y intercept is lower. not as steep and y intercept is lower. not as steep and y intercept is higher. 41. Sketch a graph of a city bus on a daily route. Label each section A - E according to the information below. A Bus pulls away from the stop and increases speed 42. B Bus is at a constant speed between stops C Bus slows down to a stop D Bus is stopped E Bus increases speed after stopping The data points in the table are linear. Use the table to find slope. x y A B C D 2 1 3 2 − 3 2 − 2 3 2 3 4 -2 6 -5 8 -8 43. Write an equation for the line. A y=x+2 B y= -x + 2 C y=x–2 D Y = -x – 2 44. The data points in the table are linear. Use the table to find the slope. Then graph the data and the line. x y A B 0 -5 − 3 2 2 3 2 -2 4 1 6 4 C D 2 3 3 2 45. 46. You have a balance of $270 in your bank account, and starting in January, you will deposit $45 each month. Let January = 1, and February = 2, and so on. Write an equation for this situation. Use the equation to find the balance in June. A Y = 45x + 270; The balance in June is $540. B 270 = 45x; The balance in June is $540. C Y = 45x – 270 ; The balance in June is $300 D Y = 270 – 45x ; The balance in June $540. The data points in the table are linear. Write and equation in slope-intercept form. x y 0 -5 A y = 1.5x + 2 B y = 1.5x – 5 C y = 0.67x – 5 D y = – 0.67x – 5 2 -2 4 1 6 4 47. The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. Time (days) 3 4 5 6 A 25 B 1 1 25 C dollars per day; the cost is $25 for each day. dollars per day; the cost is $25 for each day. 75 1 D Cost($) 75 100 125 150 1 150 dollars per day; the cost is $75 for each day. dollars per day; the cost is $1 fpr 150 days. 48. Use the slope and y-intercept to graph the equation. Y= 3 4 𝑥−3 A C B D