MATH MET *** SAMPLE*** The actual test will have questions (At least 0 will be multiple choice similar to below) Update Fall 0 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Linear when = - minutes ) The temperature in a room is changing at a stead rate. If is the number of minutes since noon, the temperature was -4 C when = - minutes and the temperature was 6 C when = - minutes. Find the rate of change in temperature in degrees per minute. A) 0 B) C) - D) ) Sketch the line with slope that passes through the point (4, ) A) B) - - - - C) D) - - - - ) The charge for renting a car is $6 per da plus an initial fee of $. Write a formula for the cost of renting a car for das. A) = + B) = + 6 C) = + 6 D) = 6 + 4) A water tank is empting steadil b liters of water per hour. There were liters of water 6 hours after midnight. Let represent the number of hours since midnight, and let represent the number of liters of water in the tank. Find the equation showing the amount of water at time. A) = - - 0 B) = - + 8 C) = - 4 D) = - + 4
) Find an equation of the line through (, -) and (, -) A) = -6 + 7 B) = -6 - C) = - 6-4 D) = 6-7 6) Find the equation of the line perpendicular to = +, passing through (8, -6) A) = - + 6 B) = - 4 C) = -0 + 9 D) = - + 4 7) The graphs shows the elevation in feet of a hot air balloon minutes after noon. Write an equation for the graph in slope-intercept form. 4 - -4 - - - 4 - - - -4 - A) = - - B) = - - C) = - - D) = - 8) The equation below gives the number of acres of rain-forest left in the world, where is in millions of square kilometers, and is the number of ears since 90. 00 + 8 = 60 What does the -intercept of the graph tell ou? A) In 8 ears, there will be 00 million square kilometers of rain-forest left. B) The rain-forest is shrinking b 8 million square kilometers per ear. C) In 90, there were.6 million square kilometers of rain forest. D) It will take.6 ears for the rain forest to deplete. 9) The equation below gives the number of acres of rain-forest left in the world, where is in millions of square kilometers, and is the number of ears since 90. 00 + 8 = 60 What does the -intercept of the graph tell ou? A) It will take 4 ears for the rain forest to deplete. B) There are 4 million square kilometers of rain-forest left. C) The rain-forest is shrinking b 8 million square kilometers per ear. D) In 8 ears, there will be 00 million square kilometers of rain-forest left.
0) Which table could be described b a linear equation? A) - 0 B) 0 4 0 4 4 6 8 C) 4 7 0 D) 4 4 9 6 ) A person is driving a car along a straight road. The graph shows the distance in miles that the driver is from home after hours. The graph passes through the point (, 00). What is the meaning of this point? 00 7 0 00 7 0 4 A) It will take the driver hours to complete the trip, which requires driving 00 additional miles. B) The driver has driven for hours and must drive an additional 00 miles to complete the trip. C)After hours the driver is 00 miles from home. D) After 00 hours, the driver is miles from home. ) The graph shows the number of gallons of water in a swimming pool after hours. There is a pump that can either add or remove water from the pool. Find the slope of the line, and interpret the slope as a rate of change. 700 600 00 400 00 00 00 4 A) The pump adds water at a rate of 00 gallons per hour for two hours. B) The pump adds 600 gallons of water. C)The pump adds water for 00 hours D) The pump adds water at a rate of 00 gallons per hour. ) In 9, the glacier on Mount Kilimanjaro in Africa covered acres. B 00, this glacier melted to onl acre. Assuming this glacier melted at a constant rate each ear, write a linear equation that gives the acres,, of this glacier ears after 9. A) = + B) = -. + 9 C) = - + D) =.04-4
Solve. 4) - + 7( - 6) = -4-6 A) - B) C) - D) - Solve the equation. ) -(k + ) - (-4k- 4) = A) B) 7 C) - 7 D) 6)Decide if the given value for the variable is a solution to the inequalit (Y/N). z - 7 < 6z - (4z + ); z = A) Yes B) No 7)Solve the inequalit: 0-6 > 4(4-8) A) < B) > C) > 0 D) < 0 8)Solve the inequalit: -a - 9 > - A) a -8 B) a > -8 C)a -8 D) a < -8 Shade the solution. 9) + A) B) 0 0-0 - 0-0 - 0 - - -0-0 C) D) 0 0-0 - 0-0 - 0 - - -0-0 4
0)What is the -value of the solution to the sstem? -7 + = + = A) = B) =- C) =0 D) No solutions )What is the -value of the solution to the sstem? - + z = -4 + z = 0 + + z = 0 A) = B) =0 C) =4 D) No solution )What is the -value of the solution to the sstem? + + z = - - + 4z = - 4 + + z = A) =- B) =-4 C) =4 D) No solution ) When 7% of a number is added to 6, the result is more than the number. Write the equation that models this problem. A) 0.7 +6 = + B) 0.7 + 6 = + C)0.7 + + 6 = + D) 0.7 = 6 + Write a sstem of linear equations that models the situation. 4) 6 boes of chocolate-covered almonds and soft drinks cost $8, 7 boes of chocolate-covered almonds and soft drinks cost $7. Let be the price of a bo of chocolate-covered almonds and be the price of a soft drink. A) + 6 = 8 7 + = 7 B) 6 + = 8 + 7 = 7 C)6 + = 8 7 + = 7 D) 6 + 7 = 8 + = 7 Write a sstem of linear equations that models the situation. ) There were 0 people at a pla. The admission price was $ for adults and $ for children. The admission receipts were $0. Let be the number of adults that attended the pla and be the number of children who attended the pla. A) = 0 - + = 0 B) 0 - = 0 = 0 C) + = 0 + = 0 D) + = 0 + = 0 6) A certain aircraft can fl 80 miles with the wind in hours and travel the same distance against the wind in 8 hours. Let be the speed of the plane in still air and be the speed of the wind. A) = 80 8 =80 B) + = 80 8 = C) + = 80 8-8 =80 D) + 8 = 80 = 8 7) Mardi received an inheritance of $0,000. She invested part at 7% and deposited the remainder in ta-free bonds at 8%. Her total annual income from the investments was $700. Find the amount invested at 7%. A) $,000 B) $0,000 C) $46,00 D) $9,000 8) How much pure acid (00% acid solution) should be mied with 6 gallons of a 0% acid solution in order to get an 80% acid solution? A) gal B) 4 gal C)9 gal D) gal
9) Linda and Dave leave simultaneousl from the same starting point biking in opposite directions. Linda bikes at 6 miles per hour and Dave bikes at 9 miles per hour. How long will it be until the are miles apart from each other? A) 4 hrs B) hrs C) hrs D) 8 hrs 0) A basketball fieldhouse seats 000. Courtside seats sell for $9, endzone for $6, and balcon for $. The game is a sell-out if it makes $89,000 in ticket sales There are 7000 more seats in balcon than in courtside. Write a sstem of equations that models this situation where is the number of courtside seats in the fieldhouse, is the number of endzone seats in the fieldhouse and z is the number of balcon seats in the fieldhouse. A) + + z = 000 9 + 6 + z = 89000 z = 7000 + B) + + z = 89000 9 + 6 + z = 000 z = 7000 + C) + + z = 000 9 + 6 + z = 89000 = 7000 + z D) + + z = 000 + + z = 89000 + z = 7000 Quadratics )Solve the equation: m - 4m = 0 A) - 4, 4 B) 0, 4 C)0 D) - 4, 0 ) Which of the following is a step in the solution of - - 8 = 0 b completing the square? A) - + 6 = -8 + 6 B) ( - 6) = 8 + 6 C)( - 6)= 8 D) ( - )= 8 + ) Solve for r: A = P + r A) r = ± A - P B) r = ± A P - C)r = ± A P - D) r = ± A - P - 4) Use the quadratic formula to solve the equation. + 8 + = 0 A) C) -4-0 -4 + 0, -4-0 -4 + 0, 4 4 B) D) -8-0 -8 + 0, -4 - -4 +, ) A window washer accidentall drops a bucket from the top of a 6-foot building. The height h of the bucket after t seconds is given b h = -6t + 6. When will the bucket hit the ground? A) 6 sec B) 64 sec C)4 sec D) -4 sec 6)Find the verte of the parabola. f() = - 0 + A) (, ) B) (0, ) C)(, 7) D) (0, 7) 6
7) Find an equation for the parabola with verte (-, -) and intercept (0, ). A) = - - + B) = + + C) = - + D) = (+) - 8) A hotel finds that its revenue is given b R = 8000 + 760-0 when it charges 80 + 0 dollars for a room. To the nearest dollar, what is the maimum revenue it can earn? A) $9,90 B) $,0 C) $,8 D) no maimum 9)Solve the inequalit: - 4 > 0 A) > 4 B) > 0 or > 4 C) < -4 or > 4 D) < 0 or > 4 40) Find the equation for the parabola in the graph: 4 - - - - - A) =(- ) B) =(-)+ C) =(+)+ D) =(+)- 4) Find an equation for the parabola: 0 8 6 4-8 -6-4 - 4 - -4 A) = - + 4 + 9 B) = - - 4 + C) = - + + D) = - + 9 Polnomials 4)Subtract: (-6 + 9 + 4) - (- + - ) A) - + 9 + - B) - + 9 + - C) - + 9 - + 9 D) -6 + 94 - + 9 7
4)Multipl: ( - )(7 + + 8) A) 7 - + - 4 B) 7-0 + - 4 C)7-0 + - 4 D) 7 + 0 + - 4 44) Factor: - 86 A) - B) - + 8 C) - + 44 D) - + + 44 Algebraic Fractions 4)Multipl: k + k + 8 k + k + 6 k + 4k k + 9k + 4 A) k k + 7 B) k + 7 C) k k + k + 6 D) k + 4k k + 7 46)Divide: 6 - - 64 6 - + 8 A) 6 + - 8 B) - 8 6 + C) (6 - )(6 - ) ( + 8)( + 8) D) 6 - + 8 47) Add. Simplif if possible. + + 4 + + A) 4 B) 9 C) D) 0 48) Subtract. Simplif if possible. 7 z - z A) z - 7 z B) 7 - z z C) 7z + z D) 7 + z z 49)Solve: + - 7 - = - A) = 4 B) = 7 C) = -6 D) = 6 8
0)Simplif: + - 9 A) - B) - C) - D) - ) is directl proportional to and = 6 when = 6. Find the constant of proportionalit k. Then, find when =. A) k = - 6; = - 78 B) k = 6; = 6 C)k = 8; = 04 D) k = 6; = 78 ) is inversel proportional to and =. when = 9. Find the constant of proportionalit k. Then, find when = 8. A) k = 0.; =. B) k = 6.8; =.8 C)k =.; = 0. D) k = 78.; =. ) The amount of force F in pounds needed to lift a heav object with a lever varies inversel with the length L of the lever. It took 00 pounds of force to lift a refrigerator with a -foot lever. Which equation models F as a function of L? A) F = 8.L B) F = 00L C)F = 8. L D) F = 00 L Rational Eponents and Radicals 4) Simplif the epression. Write with positive eponents. ( / ) / A) 4 / B) C)4 D) 4 7/4 ) Simplif and write answer with positive eponents: (a -) -4 A) -8 a6 B) a 8 8 a-4 C) a 6 D) -4 a8 6)Multipl: /4 - /4 A) / - /8 B) C) - 4 D) /4 - / Simplif the epression. Assume that all variables are positive. 7) 8 A) 6 B) 6 C) 6 D) 6 8) 4 78 A) 4 B) 4 7 C) 78 D) 4 9
9)Rationalize the denominator: 7a 6 A) 4 B) 49a 6 6 C)7a 6 D) 7a 6 6 60)Rationalize the denominator: 7 - A) + B) - 44 C) + 44 D) 7-6) Which graph represents f() = - A) B) 0 0-0 - 0-0 - 0 - - -0-0 C) D) 0 0-0 - 0-0 - 0 - - -0-0 6)Solve the equation. + 4 = + A) B) 4 C) D) no solution 0
6) The length that a spring is stretched beond its natural position is given b L = W k where work, W, is in foot-pounds and k is a constant for the given spring. If a certain spring has a constant of 66.8, and the spring is to be stretched a length of. feet beond its natural position, how much work will be necessar? A) 684 foot-pounds B) 06.9 foot-pounds C) 4 foot-pounds D) 9.7 foot-pounds 64) The length L of a river is related to the area A of its drainage basin b the formula L =.0 A0.. The Congo River is 46 miles long. What is the area of its drainage basin? A) 6 sq mi B) 689 sq mi C)about.6 0-7 sq mi D) about.6 07 sq mi 6)For the table given is a function of? - - 0 A) Function B) Not a function 66) Determine whether the graph given represents a function. 0-0 - 0 - -0 A) Function B) Not a function Functions 67) Using the graph of f provided below answer the following question. For what value(s) of is f() =? 4 - -4 - - - 4 - - - -4 A) - B) C) -, D) -.6,.6
68) Use the graph of f to evaluate f(-) = f() 4-6 - -4 - - - - - - -4 A) 0 B) -4 C) D) 69) Find f(-4) when f() = - - A) 8 B) 4 C)8 D) 48 70) The number of televisions in the average American home ears after 994 is given b N() =.0 +.4. Evaluate N(8) and interpret the result. A) N(8) =.8; there were an average of.8 televisions per home in 00. B) N(8) =.8; there were an average of.8 more televisions per home in 00 than in 994. C)N(8) =.; there were an average of. televisions per home in 00. D) N(8) =.; there were an average of. televisions per home in 00. 7) The population of Midville, in thousands of people, is given b P(t) =.t +, where t is the number of ears after 980. Choose the correct statement. A) In 99, the population was 6000. B) In 986, the population was,000. C) In 980, the population was 400. D) In 986, the population was 9,000. 7) Francine received 0 hours of free Internet time in a promotional offer. She spends. hours per da connected to the Internet. H = f(t) gives the number of free hours Francine has left after t das. What does the t-intercept of the graph tell us? A) How long Francine spends on the Internet ever da. B) Francine had 0 free hours initiall. C) She will use up the free hours in 80 das. D) The number of das that have gone b 7) The value, in dollars, of a cop machine is given b the function f() = -0 + 000, where is the number of ears that have passed since the machine was purchased. Interpret the slope of the graph of f as a rate of change. A) The cop machine was worth $000 initiall B) The cop machine depreciates entirel in 0 ears. C)The cop machine decreases in value b $0 each ear. D) The cop machine decreases in value b $0 each ear.
Eponential 74)Solve the equation: (9 - ) = 7 A) 9 B) C) D) - 7) Find an eponential function that models the data in the table. 0 4 0 80 0 80 A) f() = (4) B) f() = + C)f() = 4() D) f() = + 76) Mr. Monewell's art collection has been increasing in value b 6% per ear. This ear it was valued at $0,000. Write an eponential equation for the value V of the collection t ears from now. A) V = 0000 0.06 t B) V = 0000.06 t C)V = 0000 + 0.06t D) V = 0000 0.94 t 77)Solve the equation: + 6 = 4 A) log log + log 6 B) log 4 log 4 + 6 C) log 4-6 D) log 4 - log - log 6 log 78) Plutonium-8 decas at a rate of 0.8% per ear. How much of a 0-gram sample will be left after t ears? A) 0 0. t B) 0-0.8t C)0 0.99 t D) 0 0.8 t t 79) Solve the equation: 600 () = 7,000 A). B).6 C) 46. D) 6.7 80) Epand the epression. Assume that all variables are positive. log 8 4 z8 A) 4 log 8-4 log 8 + 4 log 8 z B) 4 log 8 - log 8 z8 C) 8 log 8 log 8 + 8 log 8 z D) 4 log 8 - log 8-4 log 8 z 8)Solve the equation: log ( + ) - log ( - 4) = log A) B) - C) D) No solution
8)Solve the equation: log 9 4 + log 9 = A) 4 9 B) 4 9 C) 4 D) 9 4 8) Find out how long it takes a $00 investment to double if it is invested at 8% compounded semiannuall. Round to the nearest tenth of a ear using the formula A = P + r n nt where P represents the principal (initial amount), r represents the annual interest rate as a decimal, n represents the number of times the interest is compounded per ear, t represents the number of ears, and A represents the amount after time t. A) 8.6 ears B) 8.8 ears C)9 ears D) 9. ears 84) f() =.4 +.4log ( + ) gives the salinit of ocean water at depth meters. Find the salinit (to the nearest hundredth) at a depth of 607 meters. A) -9.0 B) 9.8 C) 94.8 D) 7.0 8) How long will it take for a population of 4000 to double if its annual growth rate is 7.%? (Round to the nearest ear.) A) r B) 0 r C) 8 r D) 4 r Conics 86) Find the standard equation of the circle that has a enter at (-8, ) and a radius of A) ( - ) + ( + 8) = 4 B) ( + 8) + ( - ) = C)( + ) + ( - 8) = 4 D) ( - 8) + ( + ) = 87)Find the center and radius of the circle. + + = 8 A) (0, ); B) (0, ); C)(, 0); 4 D) (0,-); Use the graph to determine the equation of the ellipse. 88) 0-0 - 0 - -0 A) 7 + = B) 49 + = C)49 + = D) 7 + = 4
89) One of the graphs below is the graph of - =. Which one? A) B) - - - - - - C) D) - - - - - - - - - - WORKOUT. Write our answer in the space provided or on a separate sheet of paper. 90) The table below shows the amount of water in a tank w, in gallons, after t minutes. t (minutes) 4 8 6 w (gallons) 00 60 0 80 (a) Write a linear equation for the amount of water in the tank, w, in terms of the time t. (b) State the slope of the equation in part (a). What are the units of the slope? What does the slope mean in the contet of this problem? (c) State the w-intercept of the equation in part (a). What does the w-intercept tell us about this situation? (d) State the t-intercept of the equation in part (a). What does the t-intercept tell us about this situation? 9) A submarine is steadil descending. After minutes it is at an elevation of - meters, and after minutes it is at an elevation of -0 meters. Let be the submarine s elevation after minutes: (a) Find the slope (include units) of in terms of. Eplain what the slope tells us about the submarine. (b) Find the equation of in terms of. (c) Sketch a graph. (d) (,-0) is a point on the graph. What does this point tell us about the submarine? 9) A certain population of crickets triples ever da. If the population started with 0 crickets, how man crickets will there be after t das? (a) Write an eponential equation for the population, P, of crickets after t das. (b) What will the population be after das? (c) When will the population of crickets reach 00,000? Round to the nearest tenth.
9) Mr. Monewell's art collection has been increasing in value b 6% per ear. This ear it was valued at $0,000. (a) Write an eponential equation for the value V of the collection t ears from now. (b) What will the collection be worth 0 ears from now? (c) When will the collection double in value? (d) How long will it take the value to double again? 94) Suppose F() = - log (00 - ) 0.40 60 web-footed sparrows to die. represents the number of ears that it takes for percent of a population of (a) Find F(90). Eplain what F(90) means in the contet of this problem. Write our answer in a complete sentence. (b) Approimate the percentage (to the nearest whole per cent) of web-footed sparrows that died after 4 ears. 9) A student takes out two loans totaling $,000 to help pa for college epenses. One loan is at 8% simple interest, and the other is at 9% simple interest. The first-ear interest is $0. (a) Write a sstem of equations in two variables to find the amount of the 8% loan and 9% loan stating what our variables represent. (b) Solve the sstem found in part (a) (c) Find the amount of each loan and write our answer in complete sentence. 96) A cruise boat travels 7 miles downstream in 4 hours and returns upstream in 6 hours. (a) Write a sstem of equations in two variables to find the rate of the current and speed of the boat in still water. State what our variables represent. (b) Solve the sstem found in part (a) (c) What is the rate of the current? 6
Answer Ke Testname: MET SAMPLE FALL 0 MATH ) C ) D ) D 4) D ) A 6) D 7) C 8) C 9) A 0) C ) C ) D ) C 4) B ) B 6) A 7) B 8) D 9) D 0) C ) B ) C ) A 4) C ) D 6) C 7) B 8) C 9) B 0) A ) B ) B ) B 4) A ) C 6) C 7) B 8) C 9) D 40) C 4) B 4) C 4) B 44) D 4) A 46) A 47) B 48) B 49) C 0) C 7
Answer Ke Testname: MET SAMPLE FALL 0 MATH ) D ) A ) D 4) A ) C 6) D 7) B 8) D 9) D 60) C 6) D 6) B 6) C 64) D 6) A 66) B 67) C 68) D 69) B 70) A 7) B 7) C 7) D 74) C 7) A 76) B 77) C 78) C 79) D 80) D 8) C 8) D 8) B 84) D 8) B 86) B 87) D 88) B 89) C 90) (a) w = -0t + 40 (b) -0 gallons per minute. It tells ou that the amount of water in tank is decreasing b 0 gallons ever minite. (c) (0, 40). It tells us that originall the tank held 40 gallons of water. (d) (4,0). It tells ou that after 4 minutes the tank will be empt. 8
Answer Ke Testname: MET SAMPLE FALL 0 MATH 9) (a) - meter per minute. It tells us that the submarine is decending meters ever minute. (b) = - - (c) 6 4 - -4 - - - - 4 - - -4 - -6 (d) The point tells us that after minutes the submarince as descended to an elevation of -0 meters. 9) (a) P = 0() t (b) 4860 crickets (c) After about 8.4 das 9) (a) V = 0000(.06) t (b) About $,87 (c) About ears (c) About 4 ears 94) (a) F(90) =.. It takes two and a half ears for 90% of a population of 60 web-footed sparrows to die. (b) About 97% 9) (a) + = 000 0.08 + 0.09 = 0 (b) (6000,7000) (c) The student borrowed $6000 of the 8% loan and borrowed $7000 of the 9% loan 96) (a) 4 + 4 = 7 6-6 = 7 (b) (, ) (c) mph 9