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WorksheetsBQ 2024 CALCULUS 6-7
Total questions: 180
Worksheet time: 12hrs 27mins
What is the ratio for Tangent
Opp/Adj
Adj/Opp
Opp/Hyp
Hyp/Opp
Set up the problem so that you can solve for X.
sin X = 41/28
tan X = 41/28
cos X = 28/41
sin X = 28/41
Solve for the missing angle
50.5 degrees
12.7 degrees
36.9 degrees
72.2 degrees
Solve for x. Round to the nearest tenth.
15.3
16.6
24.1
24.3
Which trigonometric ratio should you use?
Tangent Ratio
Sine Ratio
Cosine Ratio
Any ratio
In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. The value of cos C is
7/25
1/5
8/25
2/5
Find the length of the missing side
48
108
83.6
72
Find the missing value.
Round to the nearest tenths.
52.1o
37.9o
52.1 cm
50.6 cm
Find the missing value.
Round to the nearest tenths.
33.9 mm
3.4 mm
10.5 mm
36.2 mm
Find the missing value.
Round to the nearest tenths.
34.2o
55.8o
39.6o
29.7o
Find the missing value.
Round to the nearest tenths.
36.6 in
43.7 in
47.8 in
37.4 in
Find the missing value.
Round to the nearest tenths.
50.6o
29.4o
34.8o
50.1o
Find the missing value.
Round to the nearest tenths.
23.6 miles
4.6 miles
.9 miles
20.7 miles
Find the missing value.
Round to the nearest tenths.
50.1o
39.9o
32.7o
51.6o
Find the missing value.
Round to the nearest tenths.
5.9 lightyears
5.0 lightyears
7.1 lightyears
7.5 lightyears
You are on a ship at sea. You see a lighthouse in the distance. You know the lighthouse is 175 feet tall. You measure the angle of elevation to the top of the lighthouse at 5o. How far are you from the bottom of the lighthouse?
2000.3 feet
2007.3 feet
1997.9 feet
2134.8 feet
You are attacking an enemy castle. Your strategy is to go over the castle wall. You are 1500 meters away from the bottom of the wall. You measure the angle of elevation to the top of the wall at 3o. How tall is the enemy castle wall?
78.6 meters
1498.0 meters
78.5 meters
75.3 meters
Which trigonometric ratio should you use?
Tangent Ratio
Sine Ratio
Cosine Ratio
Any ratio
Which trigonometric ratio should you use?
Tangent Ratio
Sine Ratio
Cosine Ratio
Any ratio
Which trigonometric ratio should you use?
Tangent Ratio
Sine Ratio
Cosine Ratio
Any ratio
Which trigonometric ratio should you use?
Tangent Ratio
Sine Ratio
Cosine Ratio
Any ratio
Which trigonometric ratio should you use?
Tangent Ratio
Sine Ratio
Cosine Ratio
Any ratio
Which of the following have a negative angle?
20°
What is the measure of the smallest positive angle coterminal with an angle that measures 73 degrees?
253 degrees
17 degrees
163 degrees
117 degrees
What is the reference angle of an angle the measures 53 degrees?
37 degrees
153 degrees
233 degrees
53 degrees
tan(x)csc(x)
The value of sin−1(−21)
3π
6π
−3π
−6π
The value of cos−1(−23) is
65π
−65π
6π
−6π
sin 90o
0
1
und
-1
Cos 180o
1
0
-1
und
sin 0
0
1
-1
und
cos 0
0
-1
1
und
sin 270o
0
1
-1
und
cos 90o
0
1
-1
und
cos 270o
0
1
-1
und
sin 180o
0
1
-1
und
tan 90o
0
1
-1
und
cot 270o
0
1
-1
und
sec 360o
0
1
-1
und
csc 180o
0
1
-1
und
tan 180o
0
1
-1
und
sin -90o
0
1
-1
und
sec π
1
-1
0
und
tan 270o
1
0
-1
und
csc 90o
1
0
-1
und
cot 450o
0
1
-1
und
cos 900o
1
0
-1
und
tan 0
0
1
-1
und
sin2θ + cos2θ = 1
1 + tan2θ = sec2θ
Which of the following is NOT a Pythagorean identity?
tan2x+1=sec2x
cos2x = cos2x−sin2x
sin2x + cos2x=1
1+cot2x = csc2x
Simplify: cotxsinxsec2x
cosx
tanx
cscx
secx
Simplify: cosx−cosxsin2x
sin3x
cos3x
tanxsec2x
1
Which of the following is false?
sin(−x)=−sin(x)
cos(−x)=−cos(x)
tan(−x)=−tan(x)
cot(−x)=−cot(x)
Simplify: 1+cosxsin2x−1
sinx1−cosx
0
−cosx
cscx−1
Simplify: cot2x−csc2x+sin2x+cos2x
0
2
tan2x
sec2x
Simplify: (cosx−sinx)2
1
cos2x
cos2x+sin2x
1−sin2x
Which of the following is false?
sin(a+b)=sinacosb−cosasinb
cos(a−b)=cosacosb+sinasinb
tan(a+b)=1−tanatanbtana+tanb
tan(a−b)=1+tanatanbtana−tanb
Simplify: sin(2x)cos(2x)
cosx
2cosx
sinx
2sinx
Simplify: 1−tanx1−1+tanx1
tan2x
tan2x
−tanx
tanx+tan22x
Find the midpoint of RT.
-1
1
0
2
Find the midpoint of the line.
(2,1)
(1,2)
(-2,1)
(1,-2)
Find the midpoint of PS.
-6
-6.5
-4
-4.5
Find the midpoint.
(2,6)
(2,12)
(4,12)
(1,6)
Calculate the distance between the points A(-4, 2) and B(15,6). Write your answer as simplified radical.
185
57
377
19.42
Determine the length of each segment with the given endpoints: C(1,4) and D(11, 28). Write your answer in simplified radical.
26
125
455
Determine the length of each segment with the given endpoints: Y(-2, 6) and Z(5, -8). Write your answer in simplified radical.
545
75
147
Determine the coordinates of the midpoint of the segment with endpoints R(3, 16) and S(7,-6).
(5,5)
(10, 10)
(-2, 11)
(5, 11)
What are the coordinates of the midpoint of a segment with endpoints at (-3,-4) and (5,8)?
(1,2)
(2,4)
(4,6)
(8,12)
Point C is the midpoint of segment AB. Point A has coordinates (2,4) and point C has coordinates (5, 0). What are the coordinates of point B?
(7, 4)
(3.5, 2)
(10, 0)
(8,-4)
The distance between A(3,1) and B(-2,-1) written correctly is:
(−2−3)2 + (−1−1)2
(1−3)2 + (−1−2)2
(−2−3)2 − (−1−1)2
(−2−3)2 − (−1−1)2
The distance between A(2,0) and B(-2,4) is written as
d = (4−2)2 − (0−2)2
d = (4−0)2 − (−2−2)2
d = (−2 +0)2 + (4+2)2
d = (−2−2)2 + (4−0)2
Which of the following is the correct midpoint formula given two endpoints (x1, y1) and (x2, y2)?
Find the midpoint of the line segment with the given endpoints (1,1) and (9,9)
(5,5)
(1,9)
(17,17)
(-4,-4)
Find the midpoint: (-8,6), (5,-7)
(−23,−21)
(23,21)
(7.5,7.5)
(−2,−1)
Find the midpoint:
(−1,3)
(3,4)
(4,3)
Find the midpoint:
(−21,0)
(0,−21)
(0,−2)
(−1,23)
Find the midpoint:
(−1,−3)
(−2,−23)
(−1,−25)
The vertical change is also known as _______.
rise
run
The slope (m) of a line is the ratio of the change in y to the corresponding change in x.
True
False
What is the slope of this graph?
positive
negative
zero
undefined
Which is the formula of slope?
What is the y-intercept in this form.
y
m
x
b
What does the graph shows?
positive slope
negative slope
zero slope
undefined slope
What is the slope of y=3x+2?
1
2
3
4
What is the value of p so that the line passing through (p, 1) and (3, 7) has a slope of -3/2.
3
-3
-7
7
Which of the following is in standard form?
y=-x-1
2x+3y=1
4x-5y+2=0
x-4=2y
Which of the following shows undefined slope? (You can choose more than one answer.)
(10, 1) and (5, 2)
y = − ⅚x - 9
y = 3x + 1
f(x) = 9 − x
Vertices ( 4, 3), (4, - 9)
Length of minor axis is 8
what are the a and b values?
Vertices ( 4, 3), (4, - 9)
Length of minor axis is 8
what type of an ellipse has the following characteristics?
What are the co-vertices of the ellipse?
(0, 0)
(7, 1) and (-1, 1)
(3, -5) and (3, 7)
(3, 1)
Find the standard equation of the given ellipse
Find the standard equation of the given ellipse
Find the standard equation of the given ellipse
What are the vertices of the ellipse?
(-5,3)
(-5,0) and (-5,6)
(3,-5)
(-10, 3) and (0,3)
Which of the following is the graph of 4(x+3)2+9(y+1)2=1
What are the co-vertices of the ellipse?
(-5,3)
(-5,0) and (-5,6)
(3,-5)
(-10, 3) and (0,3)
What type of conic section is 3x2–y2–11x–6y+4=0 ?
Ellipse
Hyperbola
Circle
Parabola
Check the box that shows a parabola.
If the plane cuts the cone in the similar fashion but at a certain angle, then the conic section is an (a) .
What type of conic section is 2x2+2y2−4x−16y−9=0 ?
Circle
Parabola
Ellipse
Hyperbola
What type of conic section is x2−x+3y+6=0 ?
Hyperbola
Ellipse
Circle
Parabola
What type of conic section is shown?
Ellipse
Parabola
Hyperbola
Circle
When the cutting plane intersects the two cones parallel to their vertical axes and perpendicular to their bases, then the conic section is a _______________.
Parabola
Circle
Hyperbola
Ellipse
These are figures that formed by intersecting two inverted cones and a plane.
Cross Sections
Conic Sections
Circles
Parabolas
Conics are special curves and are classified into four types. What are those?
Ellipse
Cone
Parabola
Hyperbola
Circle
Which equation shows an ellipse?
y2+x−3y−15=0
2x2−4y2+18x+120y−159=0
4x2+4y2−16y+81=0
16x2+11y2+54x−61y−121=0
