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* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
It’s the Final Countdown 1. Express in simplest form: x2 4 x 3 a. 2 x 11x 24 x x b. (7 x 3 ) 2 2 8 2 ab c. ab2 c ________________________ ________________________ ________________________ 2. Find LCD, and express each fraction with the LCD a. 2a 3b a 2b 1 , , 3a 2b 4ab 2 6ab ________________________ 3. Simplify a. x 2 x 2 10 x 25 x 5 3x 2 b. a c. 2 6 a 1 x2 x 2 x2 4 x 2x ________________________ ________________________ ________________________ 4. Divide and write your answer as a polynomial or mixed expression. a. x 2 15 x 56 x7 ________________________ 5. Write each ratio in simplest form using common units. a. 2 ft: 8 in ________________________ 1 6. Solve and check. a. y 5 7 5 2 y 3 y 12 ________________________ b. v 1 v 3 v3 v ________________________ 7. Percentages – find each number. a. 20% of 75 is what number? ________________________ b. 66 is 55% of what number? ________________________ c. 48 is what percent of 150? ________________________ 8. Word problems – solve. a. Two printing presses can turn out one day’s newspapers in 6 hours. The faster press can do the job, operating alone, in 10 hours. How long would it take the slower press, operating alone, to do the job? ________________________ b. Two numbers are in the ratio 7:8, and their sum is 135. What are the numbers? ________________________ 9. Give answers in terms of positive exponents a. a 6 a 3 b. 6a b c 2 3 ________________________ 3 ________________________ c. a 0 ________________________ d. 5 2 ________________________ 102 e. 105 ________________________ 2 10. Scientific Notation a. 3.75 105 (Write without scientific notation.) ________________________ b. .00000047 (Write with scientific notation.) 32 105 c. 16 104 ________________________ ________________________ 11. Find the slope and y – intercept of the line determined by the given condition. a. Equation 3x 6 y 2 ________________________ b. Containing the points (2, 4) and (3, 5) ________________________ 12. Graph the following lines in parts a - f on the axes on the following page. a. x = 7 (Is this line horizontal or vertical? What is the slope?) ________________________ b. y = - 2 (Is this line horizontal or vertical? What is the slope?) ________________________ c. 3 x 4 y 12 (What is the slope? What is the y – intercept? Is (3, 5) on this line? Is this line parallel to y 3x 12 ?) ________________________ d. The line passing through (1, 3) and (-2, 9) (What is the equation? What is the y – intercept? What is the slope?) ________________________ e. Find the equation of a line in slope-intercept form that is parallel to the line y = 2x + 8 and which goes through the point (3, -5) ________________________ f. Graph 2 x y 2 3 10 9 8 7 6 5 4 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 For a, b, e -10 10 9 8 7 6 5 4 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 For c, d -10 10 9 8 7 6 5 4 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 For f 4 4 3 2 1 -2 -1 1 2 -1 -2 13. Find the equation of this line. ________________________ 14. Hooke’s Law states that the distance d that a spring is stretched by a hanging object varies directly as the weight W of the object. If a 6 – kg weight stretches a particular spring 72 cm, how far will the spring stretch when W = 4 kg? ________________________ 15. Find all of the solutions to the following sets of equations. a. y 3x 2 9x 3y 6 ____________________ c. 2y x 2 b. 1 x3 2 ____________________ y 2 x 5 y 1 3x y 5 ____________________ 5 15.3. Word problem – solve. a. Pat biked 1 miles in 3 minutes with the wind at his back, and then he returned in 4 minutes riding against the wind. What was the speed of the wind? ________________________ b. Cullen is 20 years younger than Mr. Schlegel. In three years, Mr. Schlegel will be twice as old as Cullen will be. How old is each now? ________________________ c. How much water must be added to 3 quarts of a 30% acid solution to form a 20% acid solution? ________________________ 16. Express as a fraction in the simplest form a. 3.27 ________________________ 17. Find the indicated roots. a. 484 ________________________ b. 169 441 ________________________ c. 425m6 n10 ________________________ 18. Solve: a. 12 x 2 27 0 b. 2x 3 7 ________________________ ________________________ c. 5 4 x 3 15 ________________________ d. 16 x 2 100 ________________________ 6 19. Simplify 5 3 8 2 ____________________ a. 3 2 ____________________ c. e. 6 5 ab 2 3 a ____________________ g. 3 2 6 3 12 ____________________ b. d. 5 20 45 ____________________ f. 2 3 5 2 3 3 ____________________ 2 h. 3 12 3 ____________________ ____________________ i. a 7 ____________________ j. 4 2 2 5 ____________________ 20. Rationalize the denominator 5 2 3 1 ____________________ a. 8 13 ____________________ b. 21. Solve with both the quadratic formula and completing the squares. You will need to know both methods for the test. a. y 2 4 y 3 0 b. 2 y 2 12 y 18 ____________________ ____________________ c. Is 2 3, 2 3 a solution set for x 2 4 x 1 ? (True or False) 22. Simplify completely a. 168 ________________________ 7 23. Consider the parabola f ( x) 2 x 2 4 x 5 a. Find the vertex ____________________ b. Find f (-2) ____________________ 10 9 8 7 6 5 4 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 c. Graph the parabola. -10 24. The point (-2, 8) is in which quadrant? (I, II, III, IV)? _________ 25. Solve and graph a. 12 t 4 20 b. 2 4 x 3 3 10 26. Simplify leaving as a single fraction with no negative exponents. 1 1 a. x y 3 2 ______________ 4x 2 b. 3 = __________________ y 27. Simplify, leaving in radical form. 2 128x5 y 2 3 = _____________________ Have Fun. Good Luck! 8