ECM Final Exam Review. 6. Solve: 2x 3y =6 2x 6y =9

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1 Name: Date: 1. On January 1, 2000, a car had a value of $15,000. Each year after that, the car s value will decrease by 20 percent of the previous year s value. Which expression represents the car s value on January 1, 200? 4. One member of the solution set of x 1 4 is A. 1 B. 2 C. 5 D. 4 A. 15, 000(0.8) B. 15, 000(0.8) 4 C. 15, 000(0.2) D. 15, 000(0.2) 4 5. If Mrs. Vascik drives 20 miles in 5 hours, what is her average speed in miles per hour (mph)? 2. The graph of f (x) is shown here: If f (x) =ax 2 + bx + c, what is f (x) in factored form? 6. Solve: 2x y =6 2x 6y =9. Which sentence is an example of the distributive property? A. ab = ba B. a(bc) =(ab)c 7. Solve the following system for x and y. y = x 2 x 0 2x + y = 26 C. a(b + c) =ab + ac D. a 1=a page 1

2 8. A laboratory has a 75-gram sample of radioactive material. The half-life of the material is 10 days. (This means that it takes 10 days for half of the initial mass to decay.) The formula below can be used to find m, the remaining mass in grams, in terms of t, the number of 10-day intervals the mass has been decaying. 11. A supertanker travelling at 24 km/h needs 6 km to come to a complete stop. Suppose stopping distance varies directly as speed. Which of the following is a graph of the function of the stopping distance as related to speed? A. B. m = 75(0.5) t Based on the formula, what is the mass of the laboratory s sample remaining after 0 days? C. D. 9. Which inequality is the solution of 5x 1 < 29? A. x>7 B. x< What is the value of x in the equation 4 x +2= 5 4 x 6? C. x<6 D. x> Melinda invested $1000 in a retirement account. The formula below shows the amount of money, A, that will be in her account at the end of t years. A = 1000(1 + r) t 10. If y = 2x 2 +8x 5 were put in vertex form y = a(x h) 2 + k, then k =? In the formula, r is the interest rate, expressed as a decimal. Melinda s account has an interest rate of 6%. Which of the following is closest to the amount that will be in Melinda s account at the end of 2 years? A. $1120 B. $1124 C. $1256 D. $160 page 2

3 14. The smallest whole number that satisfies the inequality x 1 > 2 is A. 1 B. 2 C. D Which of the following graphs is a function? A. 15. Which equation illustrates the distributive property of multiplication over addition? B. C. 16. Which point is a solution for the system of inequalities shown on the accompanying graph? D. none of these 19. Find the solution set of this system: x 2 y =4 y =x 17. Find the point of intersection of the lines: y =4x + 1 and y = 2x +4 page

4 20. Debbie solved the linear equation (x + 4) 2=16 as follows: 24. Given the system below, solve by elimination. 4x +y =10 5x +4y =1 25. Find volume of the square pyramid if the area of the base is 72 cm 2 and the height is 1 cm. She made an error between lines 21. Dawn is years older than her sister Sara. If Dawn s age is represented by x, which expression represents Sara s age? A. x B. x + C. 1 x D. x 26. The expression 15 [2 + 6( )] simplifies to 22. Solve the following system of equations for x: 7x +5y =6 5x +2y =5 27. What is the value of x in the equation 5(2x 7) = 15x 10? 28. When using elimination to solve 2. Find the value of (x 2 5x + 4) if x = 7. x +4y = 6 4x 2y = what is a possible first step? page 4

5 29. Given f (x) = (x 7)(x + 2), which is the graph of f (x)? 0. Which ordered pair is in the solution set to the system of inequalities shown in the accompanying graph? A. B. C. D. 1. The graph of y = x 2 4x 5 is a parabola. (A portion of the graph is shown.) The x-intercepts of this parabola are 1 and. page 5

6 2. In 1997 the population of a small town was 700. If the annual rate of increase is about 0.8%, which value below expresses the population five years later? 5. The length of a rectangle is four meters less than twice its width. If the area of the rectangle is 96 square meters, what is the width? A. 5(700)(0.008) B. 5(700)(1.008) C. (700)(0.008) 5 D. (700)(1.008) 5. Which point is in the solution set of the system of inequalities shown in the accompanying graph? 6. What does the quadratic function f (x)=x 2 10x +9 look like when it is rewritten in the form f (x) =a(x p) 2 + q? 7. When Carmen and Eric tried to solve the following system of equations, Carmen said there were two real solutions and Eric said there was one real solution. Who is correct and why? y = x 2 +7x +10 y =5x What is the equation of the given parabola? 8. What is the solutions set of the equation 2x 2 + x = 0? page 6

7 9. Deion is making a smaller drawing of the plan shown. What would be the length of p? (Figures not drawn to scale.) 41. Cynthia opened her cylindrical container of oatmeal that has a height of 9 inches and a radius of 2 inches. The can was filled one inch below the top of the container. Which expression can be used to find the amount of oatmeal in the container? A. (4π 9) 1 B. 2π 8 C. π D. 4π Use elimination to solve the following system of equations for y. 40. The following system of equations intersects at one point. What is the x-coordinate of this point? 2x +y =8 x +2y = y = 1 2x 1 x 2y =1 4. To the nearest cubic centimeter, what is the volume of this cylinder? page 7

8 44. Solve the system: y = x 2 +1 y =2x Which pair of equations has no solution? A. 5x y =8 5x =12 y B. x + y =15 4x + y = 2 C. 6x 2y =5 y 6 = x 4 2 D. (2x +4y + ) = 6y + (x +4y ) y 8x = 4(2x + y + 2) 45. The following system of equations intersects at one point. What is the y-coordinate of this point? y = 1 2x 1 x 2y =1 48. What is the value of w in the equation w +8=w 7? Bacteria in a culture are growing exponentially with time, as shown in the table below. 49. What is the value of x in the equation 4(2x + 1) = 27 + (2x 5)? Which of the following equations expresses the number of bacteria, y, present at any time, t? A. y = t B. y = (100) (2) t C. y =2 t D. y = (200) (2) t 50. Solve the following system of equations for x: 9x +7y =17 6x 5y = 8 page 8