trianglestriangles 100 50 25 10 5graphsgraphs polar form functionsfunctions leftoversleftovers...
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TrianglesTrianglesTrianglesTriangles
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GraphsGraphsGraphsGraphs Polar FormPolar FormPolar FormPolar Form FunctionsFunctionsFunctionsFunctions LeftoversLeftoversLeftoversLeftovers
Review for the FinalReview for the Final
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The 104 ChallengeThe 104 ChallengeReview for the FinalReview for the Final
Final Round
Triangles
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In any right triangle, the sum of In any right triangle, the sum of the squares of the sides is equal the squares of the sides is equal
to the square of the to the square of the hypotenuse.hypotenuse.
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5 Point Question5 Point Question
What is the Pythagorean Theorem?What is the Pythagorean Theorem?
In the triangle ABC, C = 90In the triangle ABC, C = 90oo, A = 25, A = 25oo and a = 3. Find b.and a = 3. Find b.
10 Point Question10 Point Question
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b = 6.433b = 6.433
11.4911.49
25 Point Question25 Point Question
Find c in the triangle below:Find c in the triangle below:
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12 12 cmcm cc
3838oo
102102oo
13.099 13.099 cmcm
50 Point Question50 Point Question
Find the length of the missing side in Find the length of the missing side in the triangle below. the triangle below.
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6868oo
13 cm13 cm
10 cm10 cm
Find all three missing angles in the Find all three missing angles in the triangle below.triangle below.
100 Point Question100 Point Question
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A = 44.42A = 44.42oo B = 18.54 B = 18.54oo C = C = 117.04117.04oo
551414
1111
AA
BBCC
Graphs
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It has an even degree and negative It has an even degree and negative leading coefficient.leading coefficient.
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The graph of a polynomial falls to both The graph of a polynomial falls to both the left and right. What can we tell the left and right. What can we tell about the polynomial?about the polynomial?
5 Point Question5 Point Question
10 Point Question10 Point Question
Sketch the graph of y = 3cos(2x) – 5. Sketch the graph of y = 3cos(2x) – 5.
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period is Pi, amplitude is 3, period is Pi, amplitude is 3, midline midline
is -5. It starts at (0,-2).is -5. It starts at (0,-2).
25 Point Question25 Point Question
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Find the equation for a sine function that matches the graph below.
Y = 2sin(x-π/4) +4
(π/4, 4)(π/4, 4) (9π/4,4)(9π/4,4)
Find the equation for the polynomial Find the equation for the polynomial function graphed below.function graphed below.
50 Point Question50 Point Question
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Y = -2(x-3)(x+1)Y = -2(x-3)(x+1)22
(0,6)(0,6)
Find the equation for the rational Find the equation for the rational function graphed below.function graphed below.
100 Point Question100 Point Question
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Y = -2(xY = -2(x22-9)/(x-9)/(x22-x-2)-x-2)(0,-9)(0,-9)
Polar Form
Plot the polar point (3, 150Plot the polar point (3, 15000).).
5 Point Question5 Point Question
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3030oo
• 33
Convert the point (-8,-6) to Convert the point (-8,-6) to polar coordinates.polar coordinates.
10 Point Question10 Point Question
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(10, 216.9(10, 216.900))
-67.29i + 251.14j-67.29i + 251.14j
A plane flies N 15A plane flies N 1500 W at a speed of 260 W at a speed of 260 miles per hour. Write the plane’s velocity miles per hour. Write the plane’s velocity vector in component form.vector in component form.
25 Point Question25 Point Question
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50 Point Question50 Point Question
Write the complex number 5 – 3i in Write the complex number 5 – 3i in polar form.polar form.
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)54.0sin()54.0cos(34 i
Compute (1 – i)Compute (1 – i)1/31/3. Write your . Write your answer in polar form.answer in polar form.
221/6 1/6 ee--ππi/12i/12
100 Point Question100 Point Question
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Functions
A power functionA power function
5 Point Question5 Point Question
What type of function is this? What type of function is this? F(x) = 3x F(x) = 3x-2-2
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Find the equation for the power function Find the equation for the power function that passes through (1, 5) and (5, 1/25)that passes through (1, 5) and (5, 1/25)
10 Point Question10 Point Question
F(x) = 5xF(x) = 5x-3-3
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Graph the polynomial f(x) = 3(x - 3)Graph the polynomial f(x) = 3(x - 3)33 (x + (x + 20), labeling all zeros, y-intercepts and 20), labeling all zeros, y-intercepts and
asymptotes.asymptotes.
25 Point Question25 Point Question
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(3,0), (-20,0), (0,-1620)(3,0), (-20,0), (0,-1620)
50 Point Question50 Point Question
Asymptotes y = 0, x=2, and x=-5,Asymptotes y = 0, x=2, and x=-5,(which doesn’t show well)(which doesn’t show well)
Intercept Points: (-4,0),(0,1/5)Intercept Points: (-4,0),(0,1/5)
Sketch the graph ofSketch the graph of
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)5()2(
42 xx
xy
(-4,0)(-4,0)
100 Point Question100 Point Question
Find the exact value of Find the exact value of coscos-1-1(cos(28(cos(28ππ/25))./25)).
2222ππ/25/25
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Leftovers
U = 3i – 5 j, V = 4i – 2j. Find the U = 3i – 5 j, V = 4i – 2j. Find the dot product of the vectors U and V.dot product of the vectors U and V.
5 Point Question5 Point Question
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2222
What is the equation for a rose curve What is the equation for a rose curve with 8 petals of length 3.with 8 petals of length 3.
10 Point Question10 Point Question
R=3cos(4R=3cos(4ΘΘ))
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25 Point Question25 Point Question
Solve the equation: tan(2Solve the equation: tan(2ΘΘ) = √3.) = √3.
ΘΘ = = ππ/6 + /6 + ππk/2k/2
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50 Point Question50 Point Question
Solve the equation: Solve the equation: sin(x) + 2cossin(x) + 2cos22(x) = 2(x) = 2
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x = x = ππk, k, ππ/6 + 2/6 + 2ππk, k, 55ππ/6 + 2/6 + 2ππkk
Verify the identity: Verify the identity: 100 Point Question100 Point Question
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sure enough…sure enough…
)sec()cos()tan()sin( xxxx
Cable on right: Cable on right: 222 lbs. 222 lbs.
Cable on left: Cable on left: 141.8 lbs 141.8 lbs
A 235 lb weight is suspended by two cables A 235 lb weight is suspended by two cables as shown in the diagram. Find the force in as shown in the diagram. Find the force in each cable.each cable.
Final QuestionFinal Question
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235 lbs235 lbs
5454oo2323oo