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WorksheetsHBC_FInal_PartB
Total questions: 71
Worksheet time: 36mins
What is the name of the solid formed when you translate a rectangle through space in a direction that is not perpendicular to the plane containing the rectangle?
oblique rectangular prism
cylinder
cube
sphere
What is the name of the solid formed when you translate a triangle through space in a direction that is not perpendicular to the plane containing the triangle?
oblique triangular prism
rectangular prism
cylinder
pyramid
A function is a ________ function when both the function and its inverse are functions.
one-to-one
onto
constant
many-to-one
Which side is labeled as the opposite side in the diagram?
The side across from the reference angle is labeled as the opposite side.
The side adjacent to the reference angle is labeled as the opposite side.
The longest side of the triangle is labeled as the opposite side.
The side next to the right angle is labeled as the opposite side.
What is the shape that a quadratic function forms when graphed, as described in the glossary?
Line
Parabola
Circle
Ellipse
Fill in the blank: A perfect square trinomial is an expression in the form ________ or in the form ________.
a2+2ab+b2 ; a2−2ab+b2
a2−ab+b2 ; a2+ab+b2
a2+ab+b2 ; a2−ab+b2
a2+2ab+b2 ; a2+2ab−b2
According to the glossary, what does it mean for two lines to be perpendicular?
They are parallel
They intersect to form 90° angles
They never meet
They form acute angles
Which of the following is a paragraph proof?
A proof written in paragraph form with logical steps and reasons
A proof using only equations
A proof with only diagrams
A proof with no explanations
What is a perpendicular bisector?
A line that passes through a single point on a segment
A line, line segment, or ray that intersects the midpoint of a line segment at a 90° angle
A line that never touches a segment
A line that divides an angle into two equal parts
The graph represents a ________ function.
piecewise
linear
quadratic
exponential
What is a point in geometry?
A line with no thickness
A shape with area
A location with no dimension, often represented by a small dot
A segment with two endpoints
Which of the following is a polynomial?
3x3+5x−6x+1
x/2 + 3
2x
log(x)
A postulate is a statement that is accepted to be true without _______.
proof
evidence
reasoning
observation
What is the principal square root of a number?
The principal square root is the positive square root of a number.
The principal square root is the negative square root of a number.
The principal square root is the sum of all square roots of a number.
The principal square root is the product of a number and its square root.
A pure imaginary number is a number of the form ____, where b is not equal to 0.
bi
a+bi
a-b
ab
What is the probability of flipping heads when flipping a coin?
1/2
1/3
1/4
2/3
The Product Property of Radicals states that √a · √b = ____ when a and b are greater than 0.
√(a·b)
√a + √b
a + b
(√a) / (√b)
A proof is a series of statements and corresponding reasons forming a valid argument that starts with a hypothesis and arrives at a _____?
conclusion
contradiction
assumption
definition
According to the Pythagorean Theorem, if the legs of a right triangle are 0.6 in. and 0.8 in., what is the length of the hypotenuse?
1 in.
0.7 in.
1.2 in.
0.9 in.
What is the Quadratic Formula used to solve equations of the form ax2+bx+c=0 ?
x=(−b±b2−4ac)/2a
x = (b±b2+4ac)/2a
x=(−b±b2+4ac)/2a
x = (b±b2−4ac)/2a
What is a radian?
The measure of a central angle whose arc length is the same as the radius of the circle.
The distance around a circle.
The area of a circle.
The diameter of a circle.
What is the radius of a sphere?
The distance around the sphere.
A line segment with one endpoint on the sphere and one endpoint at the center.
The area of the sphere.
The diameter of the sphere.
Fill in the blank: The ratio of stars to circles in the given example is ____ or 3 to 2.
3/2
2/3
1/2
5/3
Fill in the blank: The ratio of circles to stars in the given example is ____ or 2 to 3.
2/3
3/2
1/2
3/5
What does it mean to rationalize the denominator?
To multiply the numerator and denominator by the same number.
To rewrite a fraction with no irrational numbers in the denominator.
To add fractions.
To subtract fractions.
Rationalize the denominator of the expression 5/√3. What is the result?
5/3
5√3/3
5/√3
√3/5
In a complex number of the form a + bi, what is the real part?
A) a
B) b
C) i
D) a + b
What is a reference angle in a right triangle?
The angle that defines the opposite and adjacent sides.
The largest angle in the triangle.
The sum of all angles in the triangle.
The angle opposite the hypotenuse.
What is a reflection in geometry?
A) A rigid motion that flips a figure across a line
B) A property that states a = a
C) The ratio of occurrences within a category
D) A disc translated through space
What does the Reflexive Property state?
a = b
a = a
a > a
a < a
Fill in the blank: The statement 2 = 2 is an example of the ________ Property.
Reflexive
Transitive
Associative
Distributive
What is relative frequency?
The ratio or percent of occurrences within a category to the total of the category
The sum of all frequencies
The difference between two categories
The number of students surveyed
In a survey of 100 students, 37 chose math as their favorite subject. What is the relative frequency of students who selected math as their favorite subject?
37/100 or 37%
63/100 or 63%
13/100 or 13%
50/100 or 50%
What are the remote interior angles of a triangle?
The two angles that are not adjacent to the specified exterior angle
The angles adjacent to the exterior angle
The sum of all angles in a triangle
The right angles in a triangle
What does it mean to restrict the domain of a function?
To define a new domain for the function that is a subset of the original domain
To increase the range of the function
To change the function's output
To remove all values from the domain
What is a right cylinder?
A disc translated through space in a direction perpendicular to the plane containing the disc
A triangle with a right angle
A cylinder with a slanted side
A sphere with a flat base
Fill in the blank: A rectangle translated through space in a direction perpendicular to the plane containing the rectangle forms a _________?
right rectangular prism
cylinder
sphere
cone
Fill in the blank: A triangle translated through space in a direction perpendicular to the plane containing the triangle forms a _________?
right triangular prism
cylinder
cube
rectangular prism
Fill in the blank: The root or roots of an equation indicate where the graph of the equation crosses the ________.
x-axis
y-axis
origin
vertex
What is a scale factor in a dilation?
the ratio of the distance of the new figure from the center of dilation to the distance of the original figure from the center of dilation
the sum of the distances from the center of dilation to both figures
the difference between the areas of the new and original figures
the angle formed between the original and new figures
Pentagon A'B'C'D'E' is a dilation of Pentagon ABCDE by a scale factor of ____.
1/2
1/3
1/5
2
What is the secant (sec) of an acute angle in a right triangle? Fill in the blank: The secant (sec) of an acute angle in a right triangle is
the ratio of the length of the hypotenuse to the length of the side adjacent to the angle
the ratio of the length of the side opposite the angle to the length of the hypotenuse
the ratio of the length of the side adjacent to the angle to the length of the hypotenuse
the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle
In the given triangle, if AB is the hypotenuse and AC is the side adjacent to angle A, what is sec A equal to?
AB/AC
AC/AB
AC/BC
BC/AB
What is a secant of a circle? Provide an example.
A secant of a circle is a line that intersects the circle at two points. Example: Line AB is a secant of Circle O.
A secant of a circle is a line that touches the circle at only one point. Example: Line AB is a tangent of Circle O.
A secant of a circle is a segment that lies entirely inside the circle. Example: Segment AB is a chord of Circle O.
A secant of a circle is a point inside the circle. Example: Point A is a secant of Circle O.
What are second differences? Use the given table to explain.
Second differences are the differences between consecutive values of the first differences. Example: In the table, the second differences are all -2.
Second differences are the differences between the original values in the table. Example: In the table, the second differences are all 2.
Second differences are the sum of the first differences. Example: In the table, the second differences are all 0.
Second differences are the differences between the first and last values in the table. Example: In the table, the second differences are all 4.
What is a sector of a circle? Provide an example.
A sector of a circle is a region of the circle bounded by two radii and the included arc.
A sector of a circle is the entire area inside the circle.
A sector of a circle is a line segment joining two points on the circle.
A sector of a circle is the circumference of the circle.
What is a segment of a circle? Provide an example.
A segment of a circle is a region bounded by a chord and the included arc.
A segment of a circle is the area enclosed by two radii and the included arc.
A segment of a circle is the entire area inside the circle.
A segment of a circle is a region bounded by a diameter and the circumference.
What are similar figures? Provide an example.
Similar figures are geometric figures where all pairs of corresponding angles are congruent and the lengths of all corresponding sides are proportional.
Similar figures are geometric figures where all sides are equal in length and all angles are right angles.
Similar figures are geometric figures that have the same area but different shapes.
Similar figures are geometric figures where only the perimeters are equal.
What are similar triangles?
Triangles with all pairs of corresponding angles congruent and all corresponding sides proportional
Triangles with all sides equal
Triangles with all angles equal
Triangles with no equal sides or angles
The sine (sin) of an acute angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the ________.
hypotenuse
adjacent side
base
perpendicular
A sphere is the set of all points in space that are a given distance from a fixed point called the ________ of the sphere.
center
radius
diameter
surface
A step function is a ________ function on a given interval whose pieces are discontinuous constant functions.
piecewise
linear
quadratic
exponential
What does the Substitution Property of Equality state?
If a and b are real numbers and a = b, then you can substitute a for b.
If a and b are real numbers and a ≠ b, then you can substitute a for b.
If a and b are real numbers and a = b, then you can substitute b for c.
If a and b are real numbers and a = b, then you can substitute b for a.
If AB = 12 ft and CD = 12 ft, then according to the Substitution Property of Equality, what is AB equal to?
CD
24 ft
6 ft
BC
What does the Subtraction Property of Equality state?
If a = b, then a − c = b − c.
If a = b, then a + c = b + c.
If a = b, then a × c = b × c.
If a = b, then a ÷ c = b ÷ c.
If x + 5 = 7, then x + 5 − 5 = 7 − 5. What is the value of x?
2
5
7
0
Two angles are supplementary angles when the sum of their angle measures is equal to _____
180°
90°
60°
120°
The tangent (tan) of an acute angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. What is the formula for tan A?
tan A = length of side opposite ∠A / length of side adjacent to ∠A
tan A = length of side adjacent to ∠A / length of side opposite ∠A
tan A = length of side opposite ∠A × length of side adjacent to ∠A
tan A = length of side adjacent to ∠A − length of side opposite ∠A
Tangent circles are circles that lie in the same plane and intersect at exactly how many points?
one point
two points
three points
no points
A tangent of a circle is a line that intersects the circle at exactly one point, called the _____
point of tangency
radius
diameter
center
Fill in the blank: A ____ is a statement that you can demonstrate to be true by accepted mathematical operations and arguments. Example: This famous ______ states that if a right triangle has legs of lengths a and b and hypotenuse of length c, then a2+b2=c2 .
theorem
hypothesis
formula
conjecture
Fill in the blank: The ______ ______ ______ of a three-dimensional figure is the sum of the areas of its bases and lateral faces. Example: The ______ ______ ______ of the right triangular prism is 132 square centimeters.
total surface area
volume
lateral edge length
base perimeter
Fill in the blank: A ______ is an operation that maps, or moves, a figure, called the pre-image, onto a new figure called the image. Three types of ______s are reflections, rotations, and translations.
transformation
equation
expression
variable
Fill in the blank: The ______ ______ states: If a = b and b = c, then a = c. Example: If x = y and y = 2, then x = 2 is an example of the ______ ______.
Transitive Property
Commutative Property
Associative Property
Distributive Property
What is a trinomial?
A polynomial with exactly two terms
A polynomial with exactly three terms
A polynomial with exactly four terms
A polynomial with more than three terms
Which of the following is an example of a trinomial?
5x2−6x+9
x2+4
3x - 7
2x3+x2+1+5x
What is a two-column proof?
A proof with two equations
A proof with two variables
A proof consisting of two columns: one for statements and one for reasons
A proof with two solutions
According to the two-way relative frequency table, what percentage of people who play on a team are right-handed?
36.5%
42.0%
28.7%
51.3%
In the two-way relative frequency table, how many people do not play and are left-handed?
8
2
5
10
What is the total percentage of people who are mixed-handed according to the two-way relative frequency table?
9.5%
3.2%
15.8%
22.4%
What is the vertex form of a quadratic function?
f(x)=ax2+bx+c
f(x)=a(x–h)2+k , where a ≠ 0
f(x)=a(x+h)2+k
f(x) = ax + b
