Semester 2 Final Review

Transcription

1 Name: Date: Per: Unit 6: Radical Functions [1-6] Simplify each real expression completely x 2 y m n x 2 8x 3 y m 6 n 5 5. (6x 9 ) x 1 2 8x 3 [7-10] Perform the operation and simplify completely. 7. 8x 3 y 3 x 6 y 8. 3m 12m m 2 9. m 75mn 5 2n 2 8m 3 3 n 10. x 0x x 7

2 [11-1] Sketch the graph for each of the following. Identify its domain, range, x- and the y-intercepts. 11. f(x) = 2 x a) Domain & Range b) x and y intercept(s) c) The average rate of change for f on 3 x g(x) = 3 x + 3 a) Domain & Range b) x and y intercept(s) c) The open interval where g(x) > 0 and g(x) < h(x) = x 1 + a) Domain & Range b) x and y intercept(s) c) The average rate of change for h on 1 x 9

3 1. j(x) = 3 x a) Domain & Range b) x and y intercept(s) c) The open interval where j(x) > 0 and j(x) < 0 [15-18] Solve for x algebraically. {Don t forget to check for extraneous solutions.} x 8 = x = x 2 + = x x x = 7 [19-20] Simplify the expression. {Assume all variables represent positive numbers.} y 5 2

4 Unit 7: Parabolas & Circles 1. What is the definition of a circle? 2. What is the definition of a parabola? [3-] Find the center and the radius for the following and sketch the circle: 3. x 2 + y 2 + 8x 6y 3 = 0. x 2 + y y = Find the equation of a circle with center (, 1) and a radius of Find the equation of a circle with center ( 2,5) and a radius of. [7-9] Put the following into descriptive form, state the vertex and the direction the parabola opens. How many times does the graph intersect the x-axis?: 7. (x + 3) 2 = 2(y + ) 8. x = y 2 12y x 2 2x y + 0 = 0

5 [10-11] Put the following into descriptive form, state the vertex, focus, directrix, and sketch the graph. 10. y 1 = 1 y (x + 5)2 2 Vertex: Focus: x Directrix: 11. (y + 2) 2 = 8 (x ) y Vertex: x Focus: Directrix: [12-1] Using the distance formula and the definition of a parabola, write the equation of each parabola in descriptive form. Reminder: PF = PD and d = (x 2 x 1 ) 2 + (y 2 y 1 ) Focus is at (-5, 0) and the equation for the directrix is x = Focus is at (0, -6) and the equation for the directrix is y = Focus is at (-, 5) and the equation for the directrix is y = -3.

6 [15-17] Find and graph the vertex, focus, directrix, and focal chord endpoints. 15. y 2 = 2x y Vertex: Focus: x Directrix: Focal chord endpoints: and 16. x + 2 = 1 (y 3)2 8 y Vertex: Focus: x Directrix: Focal chord endpoints: and 17. y = 1 12 x2 2 y Vertex: Focus: x Directrix: Focal chord endpoints: and

7 Unit 8: Trigonometry 1. Select all of the following statements that are true. A) x = 15cos50 C) x= ytan 50 E) 15 x = tan50 B) 15 y = sin50 D) y = 15sin 50 F) y = xtan 50 [2-3] Solve for x. Leave you solution in exact form A C x 6 A x 2 B C 72 B [-9] Sketch each angle in standard position, identify the quadrant for the terminating ray, and find the reference angle, θ.. θ = θ = θ = 00 b) Quadrant b) Quadrant b) Quadrant c) Ref θ = c) Ref θ = c) Ref θ = 7. θ = 17π θ = 13π 5 9. θ = 1π 9 b) Quadrant b) Quadrant b) Quadrant c) Ref θ = c) Ref θ = c) Ref θ = [10-1] Find one positive angle and one negative angle that are coterminal with each angle: 10. θ = θ = 7π 12. θ = θ = 3π θ = 5π Pos = Pos = Pos = Pos = Pos = Neg = Neg = Neg = Neg = Neg =

8 [15-19] Convert each angle from degrees to radian measure or radians to degrees, whichever is appropriate. 15. θ = θ = 17π 17. θ = θ = π 19. θ = 3π 9 7 [20-25] Identify the sine, cosine, and tangent ratio for each. 20. θ = 5π 21. θ = 2π 22. θ = θ = θ = 3π θ = 5π sin θ = sin θ = sin θ = sin θ = sin θ = sin θ = cos θ = cos θ = cos θ = cos θ = cos θ = cos θ = tan θ = tan θ = tan θ = tan θ = tan θ = tan θ = 26. Find the missing coordinate for the point on the unit circle. Then find the simplified sine, cosine, and tangent ratios for the angle, θ, by using its reference angle, θ. [27-29] Find two solutions of θ in degrees without a calculator such that 0 θ < cos θ 6 3 = tan θ + 6 = sin θ + 6 = 0 [30-35] Find all solutions of θ in degrees without a calculator such that 0 θ < 2π sin θ 2 = tan 2 θ 6 = tan θ (cos θ + 1) = 0

9 33. cos θ (tan θ + 3) = 0 3. (2 sin θ + 3)(tan θ 1) = tan θ cos θ + 3 cos θ = 0 [36-38] If the terminating ray for θ in the th quadrant, determine if each of the following is true or false. 36. sin θ > cos θ < tan θ > 0 [39-2] Sketch the first period for each of the following functions. 39. f(x) = cos x f(x) = 2 sin x π π 2π 3π 2 π π 2π 3π 2 1. f(x) = 3 sin (x π 2 ) 1 2. f(x) = 1 2 cos (x + π 2 ) π π 2π 3π 2 π π 2π 3π 2

10 Unit 9: Logarithms - Scientific Calculator is not allowed! [1-9] Simplify log 3 2. ln 1 81 e 3. log log log ln log 8 8. log log 100 [10-11] Determine which two consecutive integers the following logarithms lie between: 10. log log 100 [12-15] Graph the logarithmic function and identify the asymptote, domain, and range. 12. f(x) = log 3 x 13. f(x) = log 3 (x 1) 2 Vertical Asymptote: Domain: Range: Vertical Asymptote: Domain: Range:

11 1. f(x) = log 2 x 15. g(x) = 3 + log 2 (x + 1) Vertical Asymptote: Domain: Range: Vertical Asymptote: Domain: Range: [16-17] Find the x- & y-intercepts of the logarithmic function. 16. f(x) = log (x + 16) f(x) = log 2 (x ) 3 [18] Find the rate of change for the function over the given interval. 18. y = log 3 (x + 9) 1, 8 x 18 [19-20] Expand. 19. ln e3 y 2 x 20. log 3 81x 2 y

12 [21-29] Solve for x x+5 = 16 x x = (5) x+2 = (10) x = e x 7 = e x+3 = log log 11 (x 2) = log log 5 12 log 5 (x + 2) = = log 5 (x 2 5x + 1) ln x 3 ln 2 = ln 18