ALGEBRA 2. Workbook Common Core Standards Edition. Published by TOPICAL REVIEW BOOK COMPANY. P. O. Box 328 Onsted, MI

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1 ALGEBRA Workbook Common Core Standards Edition Published by TOPICAL REVIEW BOOK COMPANY P. O. Box 38 Onsted, MI EXAM PAGE Reference Sheet...i January June August January June August

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3 ALGEBRA COMMON CORE January 07 Part I Answer all 4 questions in this part. Each correct answer will receive credits. No partial credit will be allowed. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question. Record your answers in the space provided. [48]. Relative to the graph of y = 3sin x, what is the shift of the graph of y = 3sin(x + π? 3 ( () 3 π right () 3 π left (3) 3 π up (4) 3 π down. A rabbit population doubles every 4 weeks. There are currently five rabbits in a restricted area. If t represents the time, in weeks, and P(t) is the population of rabbits with respect to time, about how many rabbits will there be in 98 days? () 56 () 5 (3) 3688 (4) 8,90 3. When factored completely, m 5 + m 3 6m is equivalent to () (m + 3)(m ) (3) m(m 4 + m 6) () (m 3 + 3m)(m ) (4) m(m + 3)(m ) 3 4. If sin (3 ) + cos (M) =, then M equals () 3 () 58 (3) 68 (4) What is the solution to the system of equations y = 3x and y = g(x) where g(x) is defined by the function? () {(0, )} () {(0, ),(, 6)} (3) {(, 6)} (4) {(, ),(6, 6)} 5 6. Which statement about statistical analysis is false? () Experiments can suggest patterns and relationships in data. () Experiments can determine cause and effect relationships. (3) Observational studies can determine cause and effect relationships. (4) Observational studies can suggest patterns and relationships in data. 6

4 ALGEBRA COMMON CORE January 07 m 7. The expression 3 m is equivalent to () - 6 m 5 5 () 6 m (3) -m 5 m (4) 5 m m 7 8. What is the inverse of the function y = log 3 x? () y = x 3 () y = log x 3 (3) y = 3 x (4) x = 3 y 8 9. Gabriel performed an experiment to see if planting 3 tomato plants in black plastic mulch leads to larger tomatoes than if 3 plants are planted without mulch. He observed that the average weight of the tomatoes from tomato plants grown in black plastic mulch was 5 ounces greater than those from the plants planted without mulch. To determine if the observed difference is statistically significant, he rerandomized the tomato groups 00 times to study these random differences in the mean weights. The output of his simulation is summarized in the dotplot below. Given these results, what is an appropriate inference that can be drawn? () There was no effect observed between the two groups. () There was an effect observed that could be due to the random assignment of plants to the groups. (3) There is strong evidence to support the hypothesis that tomatoes from plants planted in black plastic mulch are larger than those planted without mulch. (4) There is strong evidence to support the hypothesis that tomatoes from plants planted without mulch are larger than those planted in black plastic mulch If p(x) = ab x and r(x) = cd x, then p(x) r(x) equals () ac(b + d) x () ac(b + d) x (3) ac(bd) x (4) ac(bd) x 0. The solution to the equation 8x 4x + 87 = 0 is () 3 ± 6i 58 (3) ± 6i 58 3 () 3 ± 6 i 58 (4) 3 ± i 58 6

5 ALGEBRA COMMON CORE January 07. When g(x) = and h(x) = log(x + ) + 3 are graphed on the same x + set of axes, which coordinates best approximate their point of intersection? () ( 0.9,.8) () ( 0.9,.9) (3) (.4, 3.3) (4) (.4, 3.4) 3 3. The price of a postage stamp in the years since the end of World War I is shown in the scatterplot. The equation that best models the price, in cents, of a postage stamp based on these data is () y = 0.59x 4.8 () y =.04(.43) x (3) y = l.43(.04) x (4) y = 4sin(4x) The eighth and tenth terms of a sequence are 64 and 00. If the sequence is either arithmetic or geometric, the ninth term can not be () 8 () 80 (3) 80 (4) The loudness of sound is measured in units called decibels (db). These units are measured by first assigning an intensity I 0 to a very soft sound that is called the threshold sound. The sound to be measured is assigned an intensity, I, and the decibel rating, d, of this sound is found using d = 0 log I I 0. The threshold sound audible to the average person is.0 0 W/m (watts per square meter). Consider the following sound level classifications: How would a sound with intensity W/m be classified? () moderate (3) very loud () loud (4) deafening 5 6. Pedro and Bobby each own an ant farm. Pedro starts with 00 ants and says his farm is growing exponentially at a rate of 5% per month. Bobby starts with 350 ants and says his farm is steadily decreasing by 5 ants per month. Assuming both boys are accurate in describing the population of their ant farms, after how many months will they both have approximately the same number of ants? () 7 () 8 (3) 3 (4) x 7. What is the solution, if any, of the equation x+ 3 4 x = x x? () () 5 (3) all real numbers (4) no real solution 7

6 ALGEBRA COMMON CORE August 08 Part III Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [6] Solve the following system of equations algebraically for all values of x, y, and z. x + 3y 4z = x y + 5z = 3 4x + y + z = Evaluate j( ) given j(x) = x 4 x 3 35x + 6x Explain what your answer tells you about x + as a factor. Algebraically find the remaining zeros of j(x).

7 60 ALGEBRA COMMON CORE August Determine, to the nearest tenth of a year, how long it would take an investment to double at a 3 3 % interest rate, compounded continuously To determine if the type of music played while taking a quiz has a relationship to results, 6 students were randomly assigned to either a room softly playing classical music or a room softly playing rap music. The results on the quiz were as follows: Classical: 74, 83, 77, 77, 84, 8, 90, 89 Rap: 77, 80, 78, 74, 69, 7, 78, 69 John correctly rounded the difference of the means of his experimental groups as 7. How did John obtain this value and what does it represent in the given context? Justify your answer. To determine if there is any significance in this value, John rerandomized the 6 scores into two groups of 8, calculated the difference of the means, and simulated this process 50 times as shown. Does the simulation support the theory that there may be a significant difference in quiz scores? Explain.

8 ALGEBRA COMMON CORE August 08 Part IV Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided to determine your answer. Note that diagrams are not necessarily drawn to scale. A correct numerical answer with no work shown will receive only credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [6] 37. A major car company analyzes its revenue, R(x), and costs C(x), in millions of dollars over a fifteen-year period. The company represents its revenue and costs as a function of time, in years, x, using the given functions. R(x) = 550x 3,000x + 83,000x C(x) = 880x 3,000x + 50,000x 60,000 The company s profits can be represented as the difference between its revenue and costs. Write the profit function, P(x), as a polynomial in standard form. 6 Graph y = P(x) on the set of axes over the domain x 6. Over the given domain, state when the company was the least profitable and the most profitable, to the nearest year. Explain how you determined your answer.