Common Core Math III Summer Assignment 2016

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1 Common Core Math III Summer Assignment 2016 Type your responses and/or use a separate sheet of paper to complete your responses. Be sure to show all work for each problem to receive credit for this assignment. If you have any questions, latoya.clay@hillsidehornets.net or contact your grade level IB Coordinator. Part 1: Geometry Review 1. Which of the following is not true about the medians of a triangle? a. Regardless of the triangle s shape, the three medians always meet at a single point. b. The point where the medians intersect is called an incenter. c. The point where the medians intersect is called a centroid. 2. Which of the following is unnecessary to prove that the 2 base angles of an isosceles triangle are congruent? a. The angle sum theorem for triangles b. SAS postulate c. The definition of an angle bisector d. The definition of congruent triangles d. A triangle has three medians. 3. Which of the following is necessary to prove that a triangle s exterior angle equals the sum of the two remote interior angles? a. The definition of complementary angles b. The definition of an angle bisector c. The definition of supplementary angles d. The definition of congruent triangles 4. Similar triangles are triangles that are the same shape but not the same size. How can we determine whether triangles are similar or not? a. The ratio between each corresponding side is the same. b. One would lie directly on top of the other and match precisely. c. All three angles are equal. d. Both a. and c. are correct. 5. A segment connects the midpoints of two sides of a triangle. What is true about this segment? a. It is always horizontal and half the length of each side. b. It is always perpendicular to the two sides it joins and forms an isosceles triangle with the portions of the sides above it. c. It is always parallel to the third side and half as long as the third side. 6. Assuming that AB DC and that the two triangles in the figure are similar, which triangle is similar to ABE? A B E D C a. CDE b. DEC c. EDC d. All of the above d. It is always half the length of those two sides

2 and parallel to the third. 7. Mike has to build two similar tents for his buddy Jim. Both tents have a 70 angle at the top. He asks Jim for the blueprints, and Jim gives him the diagrams below. What are the side lengths of the larger tent? D A 6 ft B ft 6.96ft a. 6 ft, 6.96 ft, and 7.47 ft b. 8 ft, 9.96 ft, and ft c. 9 ft, ft, and ft d. 10 ft, ft, and ft C F y ft z E 8. In the diagram below, what is the measure of E if the two triangles are similar? a. 30 b. 60 c. 70 d. 90 A 30 D F E B C 9. A line parallel to a triangle s side splits AB into lengths 12 and 5. The other side, AC, is split into lengths of x and 10. What is the length of AC? 10. The hypotenuse of a right triangle has length 13 units, and one leg has length 12 units. How long is the other leg? 11. Given EFGH is a square with a diagonal drawn from E to G. Complete the proof that EFG GHE. a. Is EF GH and FG HE true? Why? 12. What is the measure of a central angle with an arc measure of 45? b. Is EG EG true? Why? c. Is EFG GHE true? Why? 13. What is the measure of an inscribed angle with arc measurement of 70? 14. What is the measure of the arc with an inscribed angle of 18?

3 Part 2: Functions Review 1. The Metropolis Zoo recently celebrated the birth of two new baby pandas! a) Which panda was heavier when they were born? b) Which panda is growing faster? c) Which panda will weigh more at 5 weeks? 2. Sally and Sam are testing out their new potato shooters from their tree houses which are at different heights. The table shows the time, t, in seconds and height, h(t), in meters of the potato pieces shot from Sam s shooter. The time, t, and height, H(t), of Sally s potato shooter can be represented by the following equation. Sally s Shooter: H(t) = t 2 + 4t + 5 Sam s Shooter: t h(t) a) Whose potato pieces went higher? Find Sally s vertex by completing the square. Use your calculator to find Sam s. b) Whose potato pieces stayed in the air longer, Sally s or Sam s? Show your work below and then justify your answer. 3. City A had a population of 72,000 people in 2010, and has been growing by 10,000 people each year. City B has been growing exponentially according to the following tables of values. City C has been increasing in population according to the following model where t represents the number of years since 2010 P(t) = 5t 3 + 7t 2 22t

4 Which city s population goes to positive infinity most quickly as t increases? For each of the following identify functions identify the key features listed. x 2 4. y 3(0.5) 5. y ( x 3) Rate of growth/decay: x-intercept(s): Axis of Symmetry: Vertex: What is the parent 6. y x y 2 x

5 What is the parent What is the parent function been transformed? 8. 9 y 1 x 2 9. y 2x 3 2x 2 4x 1 x-intercept(s): Horizontal Asymptote: Vertical Asymptote: Relative Minimum: Relative Maximum: X-values where Function is increasing: X-values where Function is decreasing: What is the parent

6 The graph to the left is a translation of the parent function f(x) = x 2 This is a graph of the function y = log(x), shifted down two units and left three Vertex: Vertical Asymptote: Equation: Equation: The graph to the left is a translation of the parent function f(x) = 4(2) x Period: Amplitude: Midline:

7 Equation: What is the parent Equation: You may be asked to "determine algebraically" whether a function is even or odd. To do this, you take the function and plug x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f( x) = f(x), so all of the signs are the same), then the function is even. If you end up with the exact opposite of what you started with (that is, if f( x) = f(x), so all of the "plus" signs become "minus" signs, and vice versa), then the function is odd. In all other cases, the function is "neither even nor odd". Use your calculator to determine whether each function is odd, even, or neither odd nor even. Explain how the table or graph supports your answer. 14. f(x) = 3x f(x) = 2x 3 4x 16. f(x) = 2x 3 3x 2 4x + 4 Part 3: Algebra Review: Polynomial and Rational Functions 1. Divide each of the polynomials. a. (6n 2 + 4n 2) (3n 1) b. (8v v 4 + 5v + 20) (v + 4)

8 2. The total number of visitors who went to a theme park from October 1 to 10 can be modeled by the function f(x) = 2x x 2 + 4x 37 and the number of shows played at the theme park from October 1 to 10 can be modeled by g(x) = 2x + 6, where x is the number of days since October 1. What expression describes the average number of visitors per show? 3. The volume of a rectangular prism is expressed as 36x x 2 + x 20. Its length is (6x + 5). What are the width and height of the prism? 4. Evaluate each function at the given value using the Remainder Theorem. a. f(a) = a 3 + 5a a + 12 at a = 2 b. f(a) = a 4 + 3a 3 17a 2 + 2a 7 at a = 3 5. Find the value of k if the division of 2x 2 kx + 2 by (x 2) gives a remainder of 4.

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