ࡱ> tv sz'` MbjbjLULU 4.?.?E.||||JJJ8KTdL4M XXXTY$h91||XTYd|X^TY~6JTY(M 0wJo&t0,m8\LS6,^DEJJ|||||| STANDARD 1: Students solve equations and inequalities involving absolute value 1. What is the complete solution to the equation:  EMBED Equation.DSMT4 ? 2. Which of the following are solutions to  EMBED Equation.DSMT4 ? 3. Which of the following is equivalent to  EMBED Equation.DSMT4 ? 4. Which of the following is equivalent to  EMBED Equation.DSMT4 ? STANDARD 2: Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices 1. For a wedding, Shereda bought several dozen roses and several dozen carnations. The roses cost $15 per dozen, and the carnations cost $8 per dozen. Shereda bought a total of 17 dozen flowers and paid a total of $192. How many roses did she buy? 2. A cashier at a restaurant made the chart below for popular lunch combinations. What is the individual price of soup? Soup + Salad = $4.25 Soup + Sandwich = $4.75 Salad + Sandwich = $5.50 3. To connect a VCR to a television set, you need a cable with special connectors at both ends. Suppose you buy a 6 foot cable for $15.50 and a 3 foot cable for $10.25. Assuming that the cost of a cable is the sum of the cost of the two connectors and the cost of the cable itself, what would you expect to pay for a 4 foot cable? 4. A caterer is planning a party for 64 people. The customer has $150 to spend. A $39 pan of pasta feeds 14 people and $12 sandwich tray feeds 6 people. How many pans of pasta and how many sandwich trays should the caterer make? 5. What is the solution to the system of equations shown below?  EMBED Equation.3  6. What is the solution of the following linear system?  EMBED Equation.3  7. What is the solution to the system of equations shown below?  EMBED Equation.3  8. What is the solution of the following linear system?  EMBED Equation.3  STANDARD 3: Students are adept at operations on polynomials, including long division. 9. Divide:  EMBED Equation.3  10. What is the quotient of  EMBED Equation.3  11.  EMBED Equation.3  12. What is the result of dividing  EMBED Equation.3 by  EMBED Equation.3 ? 13. Multiply:  EMBED Equation.3  14. Multiply:  EMBED Equation.3 ? 15. Multiply:  EMBED Equation.3 ? 16. Factor:  EMBED Equation.3  17.  EMBED Equation.3  18. What is the sum of  EMBED Equation.3  and  EMBED Equation.3 ? 19.  EMBED Equation.3  STANDARD 4: Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes. Factor:  EMBED Equation.3  Factor:  EMBED Equation.3  Factor:  EMBED Equation.3  Which of the following is the factorization of  EMBED Equation.3 ? A)  EMBED Equation.3  B)  EMBED Equation.3  C)  EMBED Equation.3  D)  EMBED Equation.3  The total area pf a rectangle is  EMBED Equation.3 . Which factors would represent the length times width? Factor:  EMBED Equation.3  Factor:  EMBED Equation.3  STANDARD 5: Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane. 1. If EMBED Equation.DSMT4 , what is the value of EMBED Equation.DSMT4 ? 2.  EMBED Equation.DSMT4  3. If  EMBED Equation.DSMT4 , which point shows the location of  EMBED Equation.DSMT4 on the plane?  A) Point A B) Point B C) Point C D) Point D STANDARD 6: Students add, subtract, multiply, and divide complex numbers 1. Simplify:  EMBED Equation.DSMT4  2. Simplify:  EMBED Equation.DSMT4  3. Multiply:  EMBED Equation.DSMT4  4. Multiply:  EMBED Equation.DSMT4  5. Divide:  EMBED Equation.DSMT4  6. Divide:  EMBED Equation.DSMT4  STANDARD 7: Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator. 1.  EMBED Equation.3  2.  EMBED Equation.3  3.  EMBED Equation.3  4. What is the difference  EMBED Equation.3 ? 5. Which is the simplified form of  EMBED Equation.3 ? 6. Which is the simplified form of  EMBED Equation.3 ? 7. Simplify  EMBED Equation.3 : Simplify  EMBED Equation.3 : What is  EMBED Equation.3 ? What is the quotient  EMBED Equation.3 ?  EMBED Equation.3   EMBED Equation.3  STANDARD 8: Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system. 1. What are the solutions of  EMBED Equation.DSMT4  2. Solve for x by using the quadratic formula:  EMBED Equation.DSMT4  3. Solve for x by completing the square:  EMBED Equation.DSMT4  4. There are two numbers with the following properties. 1. The second number is 3 more than the first number 2. The product of the two numbers is 9 more than their sum. What are the numbers? STANDARD 9: Students demonstrate and explain the effect that changing a coefficient has on the graph of a quadratic function; that is students can determine how the graph of a parabola changes as a, b, and c vary in the equation  EMBED Equation.DSMT4  1. Which of the following most accurately describes the translation of the graph  EMBED Equation.DSMT4  to the graph of  EMBED Equation.DSMT4 ? A) up 4 and to the right 5 B) down 2 and 2 to the right C) down 2 and 3 to the left D) up 4 and to the left 2 2. Which of the following sentences is true about the graphs of  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4 ? A) Their vertices are maximums B) The graphs have the same shape with different vertices C) The graphs have different shapes with different vertices D) One graph has a vertex that is a maximum, while the other graph has a vertex that is a minimum. STANDARD 10: Students graph quadratic functions and determine the maxima, minima, and zeros of the function. 1. What are the zeros of EMBED Equation.DSMT4 ? 2. Find the minimum point (vertex) on the graph of  EMBED Equation.DSMT4  3. Find the maximum point (vertex) on the graph of  EMBED Equation.DSMT4  4. Which is the graph of EMBED Equation.DSMT4 ?  A B C  STANDARD 11: (11.1) Students understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents. 1. What is the solution of the equation:  EMBED Equation.DSMT4  2. Write the exponential form:  EMBED Equation.DSMT4  3. If  EMBED Equation.DSMT4 , what is the value of x? 4. Which equation is equivalent to  EMBED Equation.DSMT4 ? A)  EMBED Equation.DSMT4  B)  EMBED Equation.DSMT4  C)  EMBED Equation.DSMT4  D)  EMBED Equation.DSMT4  (11.2) Students judge the validity of an argument according to whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step. 1. Which is the first incorrect step in simplifying  EMBED Equation.DSMT4 ? Step 1:  EMBED Equation.DSMT4  Step 2:  EMBED Equation.DSMT4  Step 3: = -15 A) Step 1 B) Step 2 C) Step 3 D) Each step is correct 2. Jeremy, Michael, Shanan, and Brenda each worked the same math problem at the whiteboard. Each students work is shown below. Their teacher said that while two of them had the correct answer, only one of them had arrived at the correct conclusion using correct steps. Jeremys Work Shanans Work  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  Michaels Work Brendas Work  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  Which is a completely correct solution? A) Jeremys work B) Shanans work C) Michaels work D) Brendas work STANDARD 12: Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay. 1. A certain radioactive element decays over time according to the equation  EMBED Equation.DSMT4 , where A = the number of grams present initially and t = time in years. If 1000 grams were present initially, how many grams will remain after 900 years? 2. Bacteria in a culture are growing exponentially with time as shown in the table below. DayBacteria010012002400 Which of the following equations expresses the number of bacteria, y, present at any time, t? A)  EMBED Equation.DSMT4  B)  EMBED Equation.DSMT4  C)  EMBED Equation.DSMT4  D)  EMBED Equation.DSMT4  3. If the equation  EMBED Equation.DSMT4 is graphed, which of the following values of x would produce a point closest to the x axis? A)  EMBED Equation.DSMT4  B)  EMBED Equation.DSMT4  C)  EMBED Equation.DSMT4  D)  EMBED Equation.DSMT4  STANDARD 13: Students use the definition of logarithms to translate between logarithms in any base. 1. Which of the following is equivalent to  EMBED Equation.DSMT4 ? A)  EMBED Equation.DSMT4  B)  EMBED Equation.DSMT4  C)  EMBED Equation.DSMT4  D)  EMBED Equation.DSMT4  2. Identify the expression that is equivalent to  EMBED Equation.DSMT4  A)  EMBED Equation.DSMT4  B)  EMBED Equation.DSMT4  C)  EMBED Equation.DSMT4  D) 5ln3 3. Use the change of base formula to identify the expression that is equivalent to  EMBED Equation.DSMT4  A)  EMBED Equation.DSMT4  B) 10 log 3 C)  EMBED Equation.DSMT4  D)  EMBED Equation.DSMT4  STANDARD 14: Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. 1. Evaluate  EMBED Equation.DSMT4  given that  EMBED Equation.DSMT4  2. Evaluate  EMBED Equation.DSMT4  given that  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  3. Evaluate  EMBED Equation.DSMT4  given that  EMBED Equation.DSMT4 and  EMBED Equation.DSMT4  4. What is the value of  EMBED Equation.DSMT4 ? 5. Evaluate:  EMBED Equation.DSMT4  STANDARD 15: Students determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true. 1. On a recent test, Jeremy wrote the equation  EMBED Equation.DSMT4 . Which of the following statements is correct about the equation he wrote? A) The equation is always true B) The equation is always true, except when x = 4 C) The equation is never true D) The equation is sometimes true when x = 4 2. If x is a real number, for what values of x is the equation  EMBED Equation.DSMT4  true? A) all values of x B) some values of x C) no values of x D) impossible to determine 3. Given the equation  EMBED Equation.DSMT4 where x > 0 and n < 0 which statement is valid for real values of y? A) y > 0 B) y = 0 C) y < 0 D)  EMBED Equation.DSMT4  STANDARD 16: Students demonstrate and explain how the geometry of the graph of a conic section (e.g. the asymptotes, foci, eccentricity) depends on the coefficients of the quadratic equation representing it. 1. What is the focus of the parabola with the equation EMBED Equation.DSMT4 ? 2. What is the directrix of the parabola with the equation EMBED Equation.DSMT4 ? 3. Find the standard equation of the ellipse with vertices at  EMBED Equation.DSMT4 and foci at  EMBED Equation.DSMT4  A)  EMBED Equation.DSMT4  B)  EMBED Equation.DSMT4  C)  EMBED Equation.DSMT4  D)  EMBED Equation.DSMT4  4. Find the vertices of the hyperbola:  EMBED Equation.DSMT4  STANDARD 17: Given a quadratic equation of the form EMBED Equation.DSMT4 , students can use the method for completing the square to put the equation into standard form and can recognize whether the graph of the equation is a circle, ellipse, parabola, or hyperbola. Students can then graph the equation. 1. What conic does the equation  EMBED Equation.DSMT4  represent? 2. Identify the graph of  EMBED Equation.DSMT4  A) Circle B) Ellipse C) Hyperbola D) Parabola  3. Match the graph with the correct equation. A)  EMBED Equation.DSMT4  B)  EMBED Equation.DSMT4  3. C)  EMBED Equation.DSMT4  D)  EMBED Equation.DSMT4  4. Match the graph with the correct equation.  A)  EMBED Equation.DSMT4  B)  EMBED Equation.DSMT4  4. C)  EMBED Equation.DSMT4  D)  EMBED Equation.DSMT4  STANDARD 18: Students use fundamental counting principles to compute combinations and permutations. 1. Natalie wants to create several different 8-character screen names. She wants to use arrangements of the first three letters of her first name (nat), followed by arrangements of the 5 digits in her zip code (92562). How many different screen names can she create in this way? 2. Andrew needs to create a 7-character password. He wants to use the arrangements of the first 3 letters of his first name (and) followed by arrangements of the letters in his middle name (john). How many different password can he create in this way? 3. Allison went to a buffet restaurant for lunch. She had to choose from four main courses, three side dishes, three drinks, and two desserts. How many different combinations could she have created? 4. Brooks was going to buy a car. The model he wanted came in three different exterior colors, with two different interiors (cloth and leather), and three different stereo options. How many ways could Brooks configure the car? STANDARD 19: Students use combinations and permutations to compute probabilities 1. Jack and Jill are among 12 students who have applied for a trip to Washington D.C. Two students from the group will be selected at random for the trip. What is the probability that Jack and Jill will be the two students? 2. Alexs math teacher told the class that if he rolled three dice and they all turned up one, he would let them skip their homework for a month. What is the probability of this actually happening? 3. Suppose you have the following five books in your backpack: Chemistry, Biology, Calculus, Physics, and Psychology. Without looking, you pick a book. You replace the book and repeat this process. What is the probability that the first time you pick Physics or Chemistry, and the second time you picked Physics? STANDARD 20: Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers 1.  EMBED Equation.DSMT4  2.  EMBED Equation.DSMT4  3.  EMBED Equation.DSMT4  STANDARD 22: Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series. 1. What is the sum of the infinite geometric series  EMBED Equation.DSMT4  2. Find the ninth term of the arithmetic sequence with  EMBED Equation.DSMT4 . Assume that the series begins with 1. 3. Find the common ratio of the geometric series:  EMBED Equation.DSMT4  STANDARD 24: Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions. 1. Which expression represents  EMBED Equation.DSMT4  if  EMBED Equation.DSMT4 and  EMBED Equation.DSMT4 ? 2. Given  EMBED Equation.DSMT4 and  EMBED Equation.DSMT4 , find  EMBED Equation.DSMT4 . 3. If  EMBED Equation.DSMT4 and  EMBED Equation.DSMT4 , find  EMBED Equation.DSMT4 . STANDARD 25: Students use properties from number systems to justify steps in combining and simplifying functions. 1. If  EMBED Equation.DSMT4 and  EMBED Equation.DSMT4 , find  EMBED Equation.DSMT4 ? 2. Given  EMBED Equation.DSMT4 and  EMBED Equation.DSMT4 , find  EMBED Equation.DSMT4 ? 3. Given  EMBED Equation.DSMT4 and  EMBED Equation.DSMT4 , find  EMBED Equation.DSMT4 ? STANDARD P.S. 2: Students know the definition of conditional probability and use it to solve for probabilities in the finite sample spaces. 1. A box contains 4 large red marbles, 8 large yellow marbles, 2 small red marbles, and 6 small yellow marbles. If a marble is drawn at random, what is the probability that it is red given that it is one of the small marbles? 2. A jar contains 2 red, 3 blue, and 4 green marbles. Niki draws one marble from the jar and then Tom draws a marble. What is the probability that Niki will draw a green marble and Tom will draw a blue marble? 3. What is the probability that a family will have four children, all of them girls?     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