Senior Math. The area enclosed by the graphs of y = x 2 and y = 2x + 3 is. A. B. A. 1 B. 0 C. D. C. D. Academic Coaches Conference

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1 Senior Math World War I cademic oaches onference Senior Math Program of the Indiana ssociation of School Principals I. Matrices and Determinants 24%. Equality, addition, subtraction, and scalar multiplication. Matrix multiplication and its properties. The identity matrix and the inverse of a matrix 1. alculating the inverse of a matrix will be limited to 2x2 matrices only D. Determinant of a matrix 1. alculating the determinant of a matrix will be limited to 2x2 and 3x3 matrices only II. Integral alculus 24%. Indefinite integral, definite integral, The Fundamental Theorem of alculus; Integrals of Trig and Inverse Trig functions are included. pplications SD-P-M-67 SD-P-M-68 The area enclosed by the graphs of y = x 2 and y = 2x + 3 is D.. D.

2 The volume of revolution formed by rotating the region bounded by y = x 3, y = x, x = 0, and x = 1 about the x-axis is represented by... SD-P-M-69. D. SD-P-M-73 which of the following is true?. a 43 > a 22. 2a 24 = a 42. a 45 + a 33 = a 15 D. a 442 = a 31 SD-P-M-75 If f(x) = sin x + cos x - 4, find F(X) given F(π) = 8-4π. III. Similar Triangles 20%. Show triangles that are similar 1., SSS Similarity Theorem, and SS Similarity Theorem. Find angles measures and lengths of sides when two triangles are similar 1. Includes ngle isector Theorem 2. Includes Right Triangle ltitude Theorem. sin x cos x 4x + 7. cos x sin x 4x + 8. sin x + cox x + 4x + 4 D. cos x + sin x 4x + π

3 ~ DEF implies corresponds to D, corresponds to E, and corresponds to F. ngle isector Theorem: In any, Figures will NOT be drawn to scale. Did not worry about measure of. will just be D Right Triangle ltitude Theorem: If is the altitude to the hypotenuse of right, then all these proportions are true:... D. leg 1 leg 2 alt seg D 1 seg hyp 2 Example 1: In the figure = 3, = 6, = 7, and D = 11. find DE * D D E

4 Example 2: In the figure = 5, = 6, = 7, and D = 11. find DE * D E Example 3: Kari lives in building, which is 305 ft. tall. She knows the distance between bldg. and bldg. is 250 ft. When the sun is just setting above bldg., she places a mirror, M, in the street so that a ray of sunlight reflects to the top of bldg. If the mirror is 75 ft. from the base of the bldg., how tall is bldg.?. 131 ft*. 133 ft ft. ldg. ldg D. 137 ft. M D IV. Statistics 20%. Mean, median, mode, and range of a set of data. The inomial Distribution. The Normal Distribution D. pproximating inomial Distribution with the Normal Distribution Will be given tables to calculate areas under the standard normal curve and to find binomial probabilities. No interpolation will be necessary in the tables. good concise reference for topics.,., and D., in this section of the study guide is Finite Mathematics, Daniel P. Maki, Maynard Thompson 5 th Ed.

5 Example 1: In both the sets = {1, 3, 5, 7, 8, X} and = {3, 6, 7, Y, 23, 30} the elements are in numerical order. If the MEN of = 7 and the MEDIN of = 13, find x + y.. 37* D. 40 Example 2: In an 8-question multiple choice test, each question has four choices. If you guess at all 8 questions, what is the probability that you get EXTLY 2 right? D..312* Example 3: Memory chips made by a certain company have a mean time to failure of 10,000 hours and a standard deviation of 1,000 hours. If time to failure is a normal random variable, what is the probability that a randomly selected chip will last at least 8,000 hours? D..977* Example 4: One-fifth of the holes punched by a machine are more than 1 mm out of place. If the positions of 400 randomly selected holes are checked, what is the probability that the number of holes more than 1 mm out of place is no more than 60? D..007*

6 V. Mathematicians 12%. David Hilbert ( ). Julia Robinson ( ). George antor ( ) D. George irkhoff ( ) E. Oswald Veblen ( ) antor s Set Theory and Hilbert s 23 Problems Only cardinalities I dealt with are those of countable sets and the continuum. Power sets and transfinite numbers beyond the continuum are not considered. Quickest reference for these topics are the internet, Wikipedia, MacTutor, Wolfram Math World, and many more Two excellent books that explain antor s development of cardinality are: To Infinity and eyond Eli Maor, Princeton Univ Press (1991) Journey Through Genius William Dunham, Wiley & Sons ((1990) Since the statements of the following can vary a little, here is what I used: a) ontinuum Hypothesis: There is no set where the cardinality lies between that of countable sets and the continuum b) Hilbert s 1 st Problem: Prove whether the continuum hypothesis is true or false c) Diophantine Equation is a polynomial in one or more variables in which the coefficients are integers and only integer solutions are sought d) Hilbert s 10 th Problem: Does there exist a universal algorithm for solving Diophantine equations? Example 1: Each number in the unit interval (0, 1) can be written as an infinite decimal X = 0.X 1 X 2 X 3 X 4 X 5 X 6. From this number form (0.X 1 X 3 X 5., 0.X 2 X 4 X 6 ). This process can also be reversed. From this idea, antor made the amazing conclusion that:. the unit interval is uncountable. the unit interval is equal to the continuum. the cardinality of the unit interval is less than the cardinality of the unit square D. the unit interval and the unit square have the same cardinality*

7 For questions or comments on similar triangles, statistics, and mathematicians, contact Danny Dixon at For questions or comments on matrices and calculus contact Garett ates at REMEMER: Only the TI-30X and the TI-30XIIS may be used during competitions! There are no exceptions!