Team: Seat #: Name: Academy I Team Quiz 1 Show all work. When there is no work to show, explain your reasoning in complete sentences.

Transcription

1 Seat #: Name: Academy I Team Quiz 1 Show all work. When there is no work to show, explain your reasoning in complete sentences. 1. How many of the statements below are true? four apple Œ Ó + Ï = Î Ç = Ø 3.14 Ú Œ (V Î P) = V Ï P 2. Is the relation { (9, A), (4, B), (0, 4), (9, C), (2, A) } a function? no 3. Showing every step, solve x = 2 (5x 4) without rounding. 3 x = 104 / Convert 140 square centimeters per week to square meters per hour m 2 / hour 5. State the number of significant figures in , and then round it to seven SF and write it in scientific notation x 10 2

2 State true or false for each of the statements below. Î Œ = 4 5 Ú A Ï B = (A Ï B) Change one number in the relation (3, 0), (5, 6), (6, 6), (5, 2) to make it a function. Showing every step, solve 5 4 x = 2 (2x + 9) without rounding. 7 Convert $22 per square foot to cents per square inch. How many significant figures are in the number ?

3 Seat #: Name: Academy I Team Quiz 2 For #1-4, find each value based on the graphic shown and justify your steps using one or more geometric terms as appropriate; underline each term. For #5, explain your answer in complete sentences. 1. m CJK. A 70 H 2. mag ( B C D L 12 I J K > 110 > 12 M > G F E 3. the area of sector EJG Construct a line passing through K that is perpendicular with BH. 5. What is the advantage of vector graphics over bit-mapped graphics? They are scalable.

4 Using appropriate notations, sketch a transversal of parallel lines and use it to show that vertical angles are congruent and that alternate exterior angles are congruent. Find the length of the arc bounding the shaded area in the circle below Find the area of the shaded region in the circle below Construct a perpendicular bisector of the segment below. Identify each stationary point used. The image below is a copy of the one on the original team quiz. Explain why you can assume it is a vector graphic. A H B C D L 12 > > I 110 J 12 M K > G F E

5 Seat #: Name: Math Academy I Team Quiz 3-I Show all work. When there is no work to show, explain your reasoning in complete sentences. 1. State the inverse of f(x) = x 3 8. (x + 8) 1/3 2. If h(2) = 8, find h -1 (2) and h -1 (8) if possible. h -1 (8) = 2 h -1 (2) is unknown 3. Find f(g(x)) given f(x) = 2x 2 3x + 10 and g(x) = x 5. 2x 2 23x Find a(a(c -1 (c(b(c(a(c(4)))))))) given a(x) = x 5, b(x) = 6, and c(x) = 9x 3 8x + ½ Sketch and label f(x) = x, p(x) = - x, q(x) = -x, and r(x) = x on the same set of axes.

6 State the inverse of m(x) = 3x 10. Given v(5) = 10, fill in whatever blanks have known values and leave the others blank. v(10) = v -1 (5) = v -1 (10) = Find f(g(x)) given f(x) = 2x 2 3x + 10 and g(x) = x 5. Find g(g(f(10))) given f(x) = 2x 2 3x + 10 and g(x) = x 5. Sketch y = 2 x + 4, and explain how it is different from the graph of y = x.

7 Seat #: Name: Math Academy I Team Quiz 3-II Show all work. When there is no work to show, explain your reasoning in complete sentences. 1. Solve 4 (2 x) + 25 = 212 x = State the domain of a(x) = log (6 2x 8). 4 x < Find all real solutions to (2x 10) 6/5 = 3. none 4. Give two or more reasons why the graph below cannot be of the function f(x) = 1.5 x How long will it take a population to triple if it is increasing at a rate of 150% per year? 1.20 years

8 Solve 284 = 2(3 5x ). State the domain of b(x) = log (x 2 25). Find all real solutions to (2x 10) 7/5 = 3. Give two reasonable possibilities for the equation of the graph at right. 0 How long will it take a substance decaying at a rate of 0.6% per hour to decrease in mass from 20 grams to 8 grams?

9 Seat #: Name: Math Academy I Team Quiz 4-I Show all work. When there is no work to show, explain your reasoning in complete sentences. 1. Simplify / 2 2. Factor 1000x 4 8xy 6. 8x (5x y 2 ) (25x 2 + 5xy 2 + y 4 ) 3. Sketch (x 2)2 (y + 2) = Simplify 3 10xy x 5 y 6. 2x 2 y y 2 5. Sketch the parabola y = x 2 10x + 34 and find the vertex, the maximum or minimum value, the equation of the axis of symmetry, the equation of the parabola in vertex form, the zeros, and the x-intercepts. vertex: (5, 9) zeros: x = 5 ± 3i x-intercepts: none minimum value: y = 9 axis of symmetry: x = 5 vertex form: y = (x 5) 2 + 9

10 Simplify Factor 10x x 2. (x + 1)2 (y 3)2 Sketch = 1. Simplify 10xy 11 12x 5 y 6. Sketch the parabola y = x 2 + 8x + 18 and find the vertex, the equation of the axis of symmetry, the maximum or minimum value, the equation of the parabola in vertex form, and the x-intercepts (if any).

11 Seat #: Name: Math Academy I Team Quiz 4-II Show all work. 1. Simplify 6 + i i Solve 3x 2 (x 2 + 9x + 20) (2x 3) = 0. x = 0 x = -4 x = -5 x = 3 / 2 3. Find all solutions to 2(3x + 15) = 5. x = -5 ± 3i 2 4. Divide i 6i, and write the answer in a + bi form i Find the roots of 2x 2 + 3x + 10, and plot them on the complex plane. x ± 2.11i

12 Simplify i Solve 4x (x + 2) (5x 1) = 0. Solve 10 + (2x 8) 2 = 34 Divide i i, and write the answer in a + bi form. Solve 2(x 5) = -22, and plot the solutions on the complex plane.