Warm-Up: Final Review #1 A rectangular pen is made from 80 feet of fencing. What is the maximum area the pen can be?
Warm-Up: Final Review #2 1) Find distance (-2, 4) (6, -3) 2) Find roots y = x 4-6x 2 + 5 3) List all the possible rational roots for y = 3x 4 + 2x 3 6x 2 + 4x - 2
Warm-Up: Final Review #3 1) Find the distance between and the midpoint of (0, 6) and (-4, 3). 2) Find the equation of the perpendicular bisector of the segment joining points (2, 3) and (5, 9).
Warm-Up:Final Review #4 1) Solve log x 27 = 3 2) Expand xy log 6 z 2 4 3) Evaluate log 6 9 in calculator 4) Solve ln e 3x = 45 5) Simplify log 9 3 + log 9 27
Warm-Up: Final Review #5 1) f(x) = x 2 + x find f(x - 1) 2) f(x) = 2x, g(x) = 3x 2, find f(g(x))
Warm-Up: Final Review #6 1) What kind of symmetry does y 2 = 3x have? 2) Find the vertex of y = (x + 4) 2 + 2 7 3x 2 3) Graph f(x) = Give equations of asym. 4) Find the y int of y = x 2-10x + 24
Warm-Up: Final Review #7 1) Write an equation through (3, 4) with slope ½ 2) Find the slope of the line 2x 4y = 8 3) Write an equation through (5, -3) and perpendicular to the line 2x 3y = 12 4) Find distance (-2, 4) (6, 3) 5) Find the midpoint (3, 4) (-5, 16) 6) Find the slope (6, 12) (-8, 3)
Warm-Up: Final Review #8 1) Simplify i 23 2) Solve 3 3x+7 = 9 x-1 3) Simplify ((x -2 ) -1 ) 0 4) Solve 3 2x = 81 5) Simplify (a/25) 3/2
Warm-Up: Final Review #9 1) Find line perpendicular to 4x + 3y = -2 and through (5, 5) 2) Simplify 50 8 and 3 i 3 i 3) Solve x 2 4x = 9 4) Solve 7x 2 2 = 5x
Warm-Up: Final Review #10 1) Simplify 2 6i 2 2) Describe the roots of 3 2x 3x 8 0 3) Find the sum and product of the roots of 4 3 2 3x 8x 2x 9 0
Warm-Up: Final Review #11 1) Find the roots of y = (x + 2)(3x 1) 2) Solve f(x) = x 4-4x 2-12 3) List the possible rational roots of 5 4 2 f ( x) 3x 2x 9x 3x 14 4) Write the equation of the ellipse 2 2 9x 4y 126x 64y 661 0
Warm-Up: Final Review #12 1) Write an equation of hyperbola Write equations of asymptotes. V ( 1,0) F 2,0 2) Graph 2 2 x 2 y 1 4 9 1 Name vertices, foci, and equations of asymptotes.
Warm-Up: Final Review #13 1) Find the vertex of y = (x 7) 2 + 2 2) What is the vertical asymptote of f(x) = 7 2x 1 3) Find the equation of the circle with center at (6, 9) and radius 5. 4) Find the center of the hyperbola 2 2 9x y 54x 2y 71 0
Warm-Up: Final Review #14 1) Graph Name the center, vertices, co-vertices and foci. 2 x 3 y 2 36 4 2 1 2 x 1 y 2 1 2) Graph Name 25 9 the center, vertices, foci and equations of the asymptotes. 2
Warm-Up: Final Review #15 1) f(x) = x 2 +2x g(x) = x - 3, find f(g(x)) 2) If f(x) = x + 4 find the rule for f -1 (x) 3) How can you decide if a function has an inverse function? 4) Solve f(x) = x 4 4x 2 12 5) Find all the possible rational roots of 5 3 2 4x 3x 18x 3x 8 0 Is x + 2 a root?
Warm-Up: Final Review #16 1) Write 4 3 =64 as a log 2) Evaluate log x 64 = 3 3) Evaluate logn = 4 4) Expand ------------ log 5) Compress log525 log53 2 ab c 6) Solve lne 4x =60
Warm-Up: Final Review #17 1) Simplify i 33 2) Solve 3 2x-4 =27 x-3 3) Simplify ((x -3 ) 3 ) 0 4) Find the distance, midpoint and slope (4, 6) and (-8, 12)
Warm-Up: Final Review #18 1) Find the center of the hyperbola 2 2 x 4y 6x 16y 11 1) Find the vertex of y x a 2 b 2) Find the vertical asymptote of f( x) 5 3x 2
Warm-Up: Final Review #19 Convert 1) 127.6 to DMS 2) 8 21 30 to DD 3) 135 to Radians 4) 5 to Degrees 3
Warm-Up: Final Review #20 1) The sides of an isosceles triangle are 5, 10, 10. Find all the angle measures. 2) A = 45º, B = 60º, a = 14. Use the law of sines to find the missing measures.
Warm-Up: Final Review #21 1) Find a positive and negative angle that is 7 coterminal with angles -35 and 12 2) Convert 300 into radians in terms of pi and to the nearest hundredth of a radian. 3) Convert 1.3 radians to DMS.
Warm-Up: Final Review #22 1) Complete the following Pythagorean Identity: csc 2 A = 2) Simplify cotx(sinx) 3) Simplify sin(-x) 4) Name an angle coterminal to 5) Convert 36 20 to radians. 6) A circle of radius r has a central angle of 30 that subtends an arc of 12. Find the radius. 6
Warm-Up: Final Review #23 1) f(x) = 3sinx, find f(-30 ) 2) Find x in radians if tanx = 3.5678 3) Evaluate sincos -1 (-2/7) 4) Evaluate csc 5 3 5) What is the range of f(x) = sinx 6) Describe the movement/change of y 3 2sin 3 x 2
Warm-Up: Final Review #24 1) Convert 42 15 to radians. 2) Solve: secx sinx = 2sinx 3) Solve: 3tanx + 5 = 2 4) Evaluate 5) Find amplitude and period: y = 2sin3x 6) Simplify tan 1 1 sin cos x cot x sin x 1 ( 1 ) 2
Warm-Up: Final Review #25 Find the EXACT value of each. 1. cos 5 2. csc 90 3. sin -270 4. sec 45 5. cos (-300) 6. sin 7. tan -135 8. cot (-π) 9. sec 120 10. csc (0 ) 11. sin (Tan -1 ( )) 3 2 12. tan (Cos -1 ( )) 3 3
Warm-Up: Final Review #26 1) Find the exact value for all six trig functions for 225. 2) Find all six trig functions of an angle whose terminal ray goes through the point 5, 2 3) Sketch sine, cos, tan. What is the domain, range and zeros for each?
Warm-Up: Final Review #27 1) Find the area of a sector of a circle with central angle 30 and arc length 3.5 cm. 2) The diameter of the moon is 3500 km. The apparent size is 0.0087 radians. How far away is the moon from earth? 3) Find sin Θ and cos Θ of an angle whose terminal ray goes through the point 3, 1
Warm-Up: Final Review #28 1) Solve sin2x = 1 2) Find cosa if sina = -1/5 and tan < 0. 3) A man is 6 feet tall and casts a shadow 14 feet long. Find the angle of elevation of the sun. 4) Given an oblique triangle with C = 72, A = 15, and b = 342.8, find side a to two decimal places. 5) If sin A = 0.8, and sin B = 0.4 and b = 100, find a.
Warm-Up: Final Review #29 1) In triangle ABC, a = 80, b = 51, c = 113. Find measure of angle C. 2) Find sinx given cos(90-x) = ¾ 3) Find sin 15 4) Simplify 5) Simplify tan82 tan12 1 (tan82 )(tan12 sin 2A 2sin A )
Warm-Up: Final Review #30 1) Convert (-4, 4) to polar 7 6 2) Convert (-2, ) to rectangular 3) Convert 8-15i to polar 4) Convert 5 cis 120º to rectangular 5) Find z 1 z 2 if z 1 = 6cis150º and z 2 = 1/3cis30º
Warm-Up: Final Review #31 1) To convert polar to rectangular let y =? 2) To convert rectangular to polar let Θ =? 3) The coordinate system to graph a complex number is called the?
Warm-Up: Final Review #32 1) Express 4(cos30+isin30) in rectangular form 2) Rewrite -7i in polar form 3) Find z 1 z 2 if z1 = (7, 10 ) and z2 = (4, 70 )
Warm-Up: Final Review #33 1) Convert (-4, 4) to polar 7 2) Convert (-2, ) to rectangular 3) Convert 8-15i to polar 6 4) Convert 5 cis 120º to rectangular 5) Find z 1 z 2 if z 1 = 6cis150º and z 2 = 1/3cis30º