Alg One - FGCU Mathematics Contest 200 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the set in set-builder notation. ) {-6, -5, -4, -,...} ) A) {x x is any integer} B) {x x is an integer greater than -6} C) {x x is an integer between -7 and -2} D) {x x is an integer greater than -7} Graph each number on the number line. 2) - 5 4, -, -, 4 2) A) B) C) D) Use =, <, or > to write a true statement. ) 7 - A) > B) = C) < ) Translate the description to a variable expression. 4) The surface area of a box is twice the sum of the product of the length and width, the product of the length and height, and the product of the width and height. Write an expression for finding the surface area of a box. A) 2lwh B) 2(l + w + h) C) 2(lw + lh + wh) D) 2lw + lh + wh 5) Albert Einstein's theory of relativity includes an expression that is the square root of the difference of and the quotient of the square of the velocity, v, of an object in motion and the square of the speed of light, c. Write this expression as an algebraic expression. A) - v 2 v2 B) - C) - v 2 D) - c 2 v2 4) 5)
Simplify by combining like terms. 6) 0.5t - 5 2 t 2 + t - 7 + 5 t + t 2 6) A) - 2 t 2 +.7t - 7 B) 7 2 t 2-0.t - 7 C) - 2 t 2 + 0.7t - 7 D) - 5 2 t 2 + 2.7t - 7 Evaluate using the order of operations. 7) -2 + 2 - (-8) 2-9 + 2 A) 5 B) - C) D) -5 7) Factor out the GCF. 8) 4wy2 + 2w2y - 8wy 8) A) 2wy2(7 + 6w - 8wy) B) 2wy(7y + 6w - 8) C) wy(4y + 2w - 8) D) 2wy(7y + 6w - 4) 9) j(k - 4) - 0(k - 4) 9) A) (j - 0)(k - 4) B) (j - 0)(k + 4) C) -0j (k - 4) D) (j + 0)(k - 4) 0) The growth of revenue R(t) over a 2-year time period for Acme Computer Products is given by R(t) = 0.5t + 5t2 thousand dollars, where t = time in years. Find an equivalent expression for R(t) by factoring out a common factor. A) 7t(0. + 5t) B) 5t(0. + 7t) C) -5t(0. - 7t) D) 5(0.t + t2) ) The FDA approves a new drug and has confirmed by independent research that the strength of the reaction to the drug is given by the formula S(d) = d 2-4 d, where d is the dosage amount of 0) ) the drug and is a constant. Find an equivalent expression for S(d) by factoring out a common factor. A) d2-4 d B) d 2 4 - d C) d 2 + 4 d D) d 2 ( - d) Solve the system using substitution. 2) y = - 5 x 2) -5x + y = -2 A) - 5, - B) no solution C) 5, D) 5, - Write the equation of a line through the given points in the form Ax + By = C, where A, B, and C are integers and A > 0. ) (5, ), (-2, 5) ) A) 7x - 2y = - B) 2x + 7y = C) 7x + 2y = D) 2x - 7y = - 2
Write the equation of a line that passes through the given point and is perpendicular to the given line. Write the equation in the form Ax + By = C, where A, B, and C are integers and A > 0. 4) (-5, -9); y = x + 2 4) A) x + y = -24 B) x + y = -2 C) x - y = -6 D) x - y = 22 Provide an appropriate response. 5) What is the equation of a vertical line through (, )? 5) A) x = B) y = C) y = D) x = Solve and graph. Write the solution in interval notation. 6) 5 x + 2 > 9 6) A) ( 9 5, ) B) (-, - 9 5 ) (9 5, ) C) (-, - 7 ) (7 5 5, ) D) ( 7 5, ) 7) A bookstore determines the retail price by marking up the wholesale price 25%. The retail price of a physics book is $.60. What was the wholesale price? A) $8.70 B) $89.28 C) $9.50 D) $64.28 7) Use long division to divide the polynomials. 8) x + 64 x + 4 A) x2-8x + 6 B) x2-4x + 6 C) x2 + 4x + 6 D) x2-4x - 6 8)
Solve the problem. 9) If a submarine goes k + 9k2 + 7k - 49 miles in k + 7 hours, what is its rate of speed? 9) A) k2 + k - 7 miles/hr B) k2 + 4k - 7 miles/hr C) k + 4k2-7k miles/hr D) k2-4k + 7 miles/hr Simplify using scientific notation. Give your answer in scientific notation. 7600 20) 660,000,000 A).5 05 B).5 0 C).42 0-4 D).5 0-5 20) Solve the problem. 2) The sun is surrounded by an extremely hot plasma called the "corona". The average kinetic energy E of a subatomic particle in the corona can be approximated by the model E = kt, where E is in 2 2) joules, T is the Kelvin temperature of the corona, and k is Boltzmann's constant, k =.8 0-2 J/K. Find the average kinetic energy for a proton in a coronal region with T = 2. 06 K. A) 8.69 0-7 J B) 5.76 0-7 J C) 4.5 0-2 J D) 4.5 0-7 J Simplify using the power rule of exponents and the rule for raising a product to a power. 22) x 9y 2 22) A) 6 x 8y B) 9 x y C) 9 x 8y2 D) x 8y2 Provide an appropriate response. 2) Describe the graph of the function f(x) = x + 2 if the domain is {, 2,, 4}. 2) A) The graph is a line through the four points (, ), (2, 4), (, 5), and (4, 6). B) The graph is a line through the four points (, 2), (2, 2), (, 2), and (4, 2). C) The graph consists of the four points (, ), (2, 4), (, 5), and (4, 6). D) The graph consists of the four points (, 2), (2, 2), (, 2), and (4, 2). Use the four-step method in problem solving to solve the problem. 24) City A has an elevation of 546 feet above sea level while city B has an elevation of 58 feet below sea level. How much higher is City A than City B? A) -488 feet B) 704 feet C) 604 feet D) -88 feet 25) Andrea decided to rollerblade to her mother's house. Four blocks from her home, one of the wheels on her skate broke, and she had to walk the remaining six blocks to her mother's. She could not repair her skate and had to walk all the way back home. How many more blocks did Andrea walk than she skated? A) 20 blocks B) 0 blocks C) 6 blocks D) 2 blocks 24) 25) Solve the problem. 26) Claire has received scores of 85, 88, 87, and 95 on her algebra tests. What is the minimum score she must receive on the fifth test to have an overall test score average of at least 90? A) 96 B) 94 C) 9 D) 95 26) 4
Use a proportion to solve the problem about inverse variation. 27) The current in a circuit varies inversely as the resistance. If the current is 490 milliamperes (ma) when the resistance is 5 ohms, find the current when the resistance is 5 ohms. A) 70 ma B) 50 ma C) 42 ma D) 40 ma 27) Write the number as a decimal. 28) There are 2.968 06 miles of highways, roads, and streets in a certain country. 28) A) 2,968,000 B) 29,680,000 C) 296,800,000 D) 296,800 Factor by grouping. 29) p2 + 2p + 4p + 8 29) A) (p + 2)(p - 4) B) (p - 2)(p - 4) C) (p + 2)(p + 4) D) p(p + 8) 0) 0) 4x 2x + 2 x Find an expression for the area of the figure above and write an equivalent expression by factoring out a common factor. A) 60x2 + 0x = 0x2(6 + 0x) B) 60x2 + 0x = 60x(x + ) C) 60x2 + 0x = 0x(6x + ) D) 60x2 + 0x = 0x(6x + 0) 5