WorksheetsMath 2: Spring 2018 FINAL EXAM
Total questions: 60
Worksheet time: 30mins
A chord is a segment whose endpoints are on a circle.
True
False
Select ALL of the radii. (There may be more than 1 answer.)
AP
AU
HI
A(n) _____ angle is an angle of a circle whose vertex is at the center of the circle.
intercepted
inscribed
central
midpoint
Identify a tangent line.
XT
MN
VU
AP
Which of the following angles is not an inscribed angle?
∠UOK
∠ERU
∠UKZ
∠RUK
What is the measure of ∠BGT?
150°
110°
70°
75°
What is the measure of ∠KLS?
112°
180°
56°
68°
If m∠WYX is 80°, what is the m∠WCX?
80°
160°
120°
180°
If segment BF is 20 inches long, what is the length of HC?
20 inches
10 inches
5 inches
8 inches
What is m∠HJI? (Hint: remember the sum of the angles of a triangle.)
48°
66°
84°
70°
What is the length of arc RS?
20.9 in
80 in
10.5 in
15.0 in
Determine the area of the shaded sector.
565.5 mm2
24.1 mm2
1413.7 mm2
471.2 mm2
If the radius of the circle is 5 cm, determine the area of the shaded segment.
12.5 cm2
7.1 cm2
19.6 cm2
5.7 cm2
In order to calculate arc length, you must multiply the fraction of the circle the arc makes up by the ____ of the circle.
area
circumference
radius
diameter
The blue triangle is _____ the red circle because each vertex of the triangle is on the circle.
inscribed in
circumscribed about
adjacent to
tangent to
What is Cavalieri's principle?
"For two-dimensional figures, if the lengths of one-dimensional slices of two figures are the same, then the figures have the same area."
"For three-dimensional figures, the height divided by the base area is always congruent to the circumference."
"For one-dimensional figures, volume can be defined only using the base measurements, when compared to one-dimensional figures."
Calculate the volume of the cone.
7068.6 m3
2356.2 m3
471.2 m3
942.5 m3
Calculate the volume of the pyramid.
291.6 cm3
179.7 cm3
539.0 cm3
241.9 cm3
Calculate the volume of the sphere.
418.9 in3
4188.8 in3
41.9 in3
33510.3 in3
Determine the volume of the cylinder.
11404.0 yd3
45615.9 yd3
2073.5 yd3
660.0 yd3
Determine the length of the solid diagonal.
13.1 inches
12.3 inches
13.8 inches
14.1 inches
The x-intercepts of a graph of a quadratic function are also called the _____ of the quadratic function. Select ALL that apply (there may be more than one correct answer.)
endpoints
max and min
roots
zeros
Identify the interval of increase.
(-∞,-3)
[-6,0]
(-3,∞)
(-∞,∞)
Determine the x-intercepts of the functions f(x) = x2 + 8x +15.
(-5,0) (-3,0)
(5,0) (3,0)
(8,0) (15,0)
(0,0) (3,5)
Two symmetrical points on a parabola are (1,5) and (-7,5). What is the equation for the axis of symmetry? (Hint: sketch a diagram to help you visualize the problem.)
x = -3
x = 5
x = 8
x = 1
What is the vertex of the parabola with equation
f(x) = 2(x - 4)2 + 5 ?
(-4,5)
(4,5)
(2,4)
(2,5)
Describe the transformation of f(x) = -x2 - 7 from f(x) = x2.
Opens down, translated left 7
Opens down, translated down 7
Opens up, translated up 7
Opens up, translated down 7
Describe the transformation of
f(x) = 2(x + 3)2 + 4 from f(x) = x2.
compression factor 2, translated up 3 and right 4
stretch factor 2, translated left 3 and up 4
stretch factor 2, translated right 3 and up 4
compression factor of 2, translated left 3 and up 4
Factor x3 - 4x2 + 8x .
4x(x2 - x + 2)
x(x + 4 )(x + 2)
x(x2 - 4x + 8)
prime
Determine the zeros of the function
f(x) = x2 + 11x + 30 .
5 and 6
-5 and -6
-15 and -2
15 and 2
Factor f(x) = x2 - 121.
(x - 11)2
(x + 11)(x - 11)
(x - 11)(x - 11)
(x-11)(x2 + 11x + 121)
Factor f(x) = x3 + 1 .
(x + 1)(x2 - x + 1)
(x - 1)(x2 + x + 2)
(x + 1)(x - 1)
(x + 1)3
Factor f(x) = 2x2 - 3x - 14 .
(2x - 7)(x + 2)
(2x - 2)(x + 7)
(2x + 7)(x - 2)
2(x - 2)(x + 7)
Solve 9x2 - 1 = 0 .
± 3
± 1/3
± 1/9
± 9
Solve x2 = 27. Write your answer in simplified radical form.
± 3√3
± 9√3
± 3√9
± 3√27
Solve (x - 3)2 = 24.
3 ± 6√2
3 ± 2√6
3 ± 2√12
3 ± 12√2
The standard form of a quadratic equation is ____.
f(x) = a(x - r1)(x - r2)
f(x) = a(x - h)2 + k
f(x) = ax2 + bx + c
f(x) = mx + b
Use the quadratic formula to determine the roots of the equation
f(x) = 2x2 - 4x - 3.
(2 ± √10) / 2
(4 ± √40) / 2
(4 ± 2√5) / 4
(2 ± √10) / 4
The vertex form of a quadratic equations is ____.
y = a(x - h)2 + k
y = ax2 + bx + c
y = a(x - r1)(x - r2)
y = mx + b
Simplify i55 .
1
-1
-i
i
Simplify 3 - √-18 .
3 - 3i√2
3 + 3i√2
3 + 9√2
3 - 9√2
Simplify (4x + i)(2x - 2i) completely.
8x2 - 6xi - 2i2
8x2 - 6xi + 2
8x2 - 6xi - 2
8x2 + 6xi + 2i2
Simplify (x2 + 6x - 7i) - (x2 -3x + i) .
3x - 6i
9x - 8i
3x - 8i
9x + 6i
Rewrite f(x) = x2 - 8x + 10 in vertex form.
f(x) = (x - 4)2 + 26
f(x) = (x - 4)2 + 10
f(x) = (x - 4)2 - 6
f(x) = (x - 2)2 - 10
Simplify (3 - 2i)2 .
5 - 12i
9 - 4i
9 - 4i2
14
The "b2 - 4ac" portion of the quadratic formula is called the ____.
discriminant
radicand
determinant
radical
What is the conjugate of (-4 + 8i) ?
-4 - 8i
4 - 8i
4 + 8i
-4 + 8i
Calculate the quotient. (Hint: you will need to use the complex conjugate.)
2
6
3
8
Describe the roots of the graphed functions.
2 real roots
2 imaginary roots
1 real and 1 imaginary root
1 real root only
Determine the zeros of f(x) = x2 + 2x + 5.
-2 ± √-16
-2 ± 4i
-1 ± 2i
-2i
Identify the real part(s) of the complex number √3 + 6i.
√3 and 6i
√3 only
6i only
there are no real parts
Identify the function that is quadratic.
y = x
y =2
y = x2
y = x3
Which ordered pair is a solution to the equation y = -x2 + 7 ?
(1,8)
(-1,9)
(1,6)
(-1,6)
The shape of the graph of a quadratic function is a(n) ____.
curve
oblique line
parabola
piecewise function
Select the value that will complete the square.
x2 - 8x + _____
4
16
-16
-4
Which equation will result in a circle centered at (2,-4) with radius 3?
(x - 2)2 + (y + 4)2 = 9
(x + 2)2 + (y - 4)2 = 9
(x - 2)2 + (y + 4)2 = 3
(x + 2)2 + (y - 4)2 = 3
Select the equation of the graphed parabola.
f(x) = -16x2 + 120x
f(x) = 16x2 - 120x
f(x) = -16x - 120x
f(x) = 16x2 + 120x
Write "x is greater than 2, and less than or equal to 6" in interval notation.
[2,6)
(2,6)
(2,6]
[2,6]
What is the range of the graphed function?
(-∞,2]
(-∞,1]
[2,∞)
[1,∞)
What is the interval of decrease of the graphed function?
(2,∞)
(1,∞)
(-∞,1)
(-∞,2)
