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Math 3 Notecards 59-94

Total questions: 92

Worksheet time: 51mins

Name
Class
Date
1.

What tool can you use to solve equations by typing them in different lines?

a)

Calculator

b)

Desmos

c)

Spreadsheet

d)

Text Editor

2.

What do you need to find after typing equations in Desmos?

a)

Y-value of intersection

b)

X-value of intersection

c)

Slope of the line

d)

Midpoint of the line

3.

What can you use Desmos for according to the text?

a)

To draw geometric shapes

b)

To see if two expressions are the same or simplified

c)

To solve equations

d)

To calculate integrals

4.

What should you do to check if two expressions are the same using Desmos?

a)

Type both expressions in the same line

b)

Type one expression in line 1 and another in line 2

c)

Type both expressions in line 2

d)

Type one expression in line 3 and another in line 4

5.

What does the symbol 's' represent in the formula for margin of error?

a)

Sample size

b)

Standard deviation

c)

Standard error

d)

Statistical mean

6.

In the formula for margin of error, what does 'n' stand for?

a)

Number of trials

b)

Normal distribution

c)

Sample size

d)

Null hypothesis

7.

What is the formula for the margin of error given in the image?

a)

2 * (s / n)

b)

2 * (s * n)

c)

2 * (s / √n)

d)

2 * (n / s)

8.

What is the purpose of a simulation in mathematics?

a)

To create artistic designs

b)

To use math models and probabilities

c)

To write computer programs

d)

To conduct physical experiments

9.

What is the main goal of an observation in sample design?

a)

To influence the responses

b)

To watch responses and avoid influencing

c)

To impose a treatment

d)

To pose questions and record responses

10.

In a survey, what is the primary action taken by the researcher?

a)

Imposes a treatment

b)

Watches responses

c)

Poses questions and records responses

d)

Avoids influencing

11.

What distinguishes an experiment from other sample designs?

a)

It involves posing questions

b)

It involves watching responses

c)

It involves imposing a treatment upon the subjects

d)

It involves avoiding influence

12.

What does the term "biased" mean?

a)

Preference for a specific outcome

b)

Choose to participate

c)

Easiest to reach

d)

Random selection

13.

What does "voluntary" refer to in the context of participation?

a)

Preference for a specific outcome

b)

Choose to participate

c)

Easiest to reach

d)

Mandatory involvement

14.

What does "convenience" mean in terms of reaching participants?

a)

Preference for a specific outcome

b)

Choose to participate

c)

Easiest to reach

d)

Most difficult to reach

15.

What is a characteristic of a random sample?

a)

Specific order

b)

Equal chance

c)

Sub-group

d)

Clusters of population

16.

Which sampling method involves selecting samples in a specific order?

a)

Random

b)

Systematic

c)

Stratified

d)

Multi-stage

17.

In which sampling method are sub-groups used?

a)

Random

b)

Systematic

c)

Stratified

d)

Multi-stage

18.

Which sampling method involves specific clusters of a population?

a)

Random

b)

Systematic

c)

Stratified

d)

Multi-stage

19.

What is the starting point of the x-value of the unit circle in the cosine function?

a)

(1,0)

b)

(0,1)

c)

(0,0)

d)

(1,1)

20.

In the cosine function y=acos⁡(bx)+dy = a \cos(bx) + d , what does 'a' represent?

a)

Period

b)

Midline

c)

Amplitude

d)

Frequency

21.

In the cosine function y=acos⁡(bx)+dy = a \cos(bx) + d , what does 'd' represent?

a)

Amplitude

b)

Midline

c)

Period

d)

Frequency

22.

What is the formula for the period of the cosine function y=acos⁡(bx)+dy = a \cos(bx) + d ?

a)

2πa\frac{2\pi}{a}

b)

2πb\frac{2\pi}{b}

c)

b2π\frac{b}{2\pi}

d)

a2π\frac{a}{2\pi}

23.

What does the variable 'a' represent in the sine function y = asin(bx) + d?

a)

Amplitude

b)

Midline

c)

Period

d)

Frequency

24.

In the sine function = asin(bx) + d, what does the variable 'd' represent?

a)

Amplitude

b)

Midline

c)

Period

d)

Frequency

25.

What is the period of the sine function (y = asin(bx) + d)?

a)

2πb\frac{2\pi}{b}

b)

b2π\frac{b}{2\pi}

c)

2π2\pi )

d)

ab\frac{a}{b}

26.

In work problems, how is the total work calculated when two jobs are combined?

a)

Total work = (job/time) + (job/time)

b)

Total work = job * time

c)

Total work = job + time

d)

Total work = (job + job) * time

27.

In motion problems, what is the formula for calculating distance?

a)

d = r + t

b)

d = r * t

c)

d = r / t

d)

d = t / r

28.

What is the formula for calculating time in motion problems?

a)

t = d * r

b)

t = d / r

c)

t = r / d

d)

t = r * d

29.

What is the formula for calculating rate in motion problems?

a)

r = d * t

b)

r = t / d

c)

r = d / t

d)

r = t * d

30.

What is the first step to take when one fraction equals another?

a)

Add the fractions

b)

Subtract the fractions

c)

Cross multiply

d)

Divide the fractions

31.

What should you do to eliminate the denominators when solving rational equations?

a)

Add the numerators

b)

Multiply the denominators

c)

Subtract the numerators

d)

Divide the denominators

32.

Which tool can be used to help solve rational equations?

a)

Calculator

b)

Ruler

c)

Desmos

d)

Protractor

33.

What is the first step in adding or subtracting rational expressions?

a)

Simplify

b)

Factor Denominators

c)

Combine Numerators

d)

Multiply to get common denominators

34.

After factoring the denominators, what is the next step in adding or subtracting rational expressions?

a)

Simplify

b)

Combine Numerators

c)

Multiply to get common denominators

d)

Factor Denominators

35.

What should you do after obtaining common denominators when adding or subtracting rational expressions?

a)

Simplify

b)

Factor Denominators

c)

Combine Numerators

d)

Multiply to get common denominators

36.

What is the final step in the process of adding or subtracting rational expressions?

a)

Factor Denominators

b)

Multiply to get common denominators

c)

Combine Numerators

d)

Simplify

37.

What is the first step when multiplying or dividing rational expressions?

a)

Cross off common factors

b)

Multiply if needed

c)

Factor everything

d)

Use Desmos to check

38.

What should you do if you are dividing rational expressions?

a)

Keep, change, flip

b)

Cross off common factors

c)

Multiply directly

d)

Use Desmos to check

39.

What can you do to verify your answers when working with rational expressions?

a)

Use a calculator

b)

Use Desmos to check

c)

Recalculate manually

d)

Ask a friend

40.

What should you do when the degrees of the numerator and denominator are equal in a rational function?

a)

Bigger on bottom, y = 0

b)

Bigger on top, none

c)

Divide the leading coefficient

d)

Multiply the leading coefficient

41.

What do common factors in the numerator and denominator create in a rational function graph?

a)

Vertical asymptotes

b)

Horizontal asymptotes

c)

Holes

d)

Intercepts

42.

How are vertical asymptotes created in a rational function?

a)

By setting the numerator to zero

b)

By setting the denominator to zero

c)

By factoring the numerator

d)

By solving for x-intercepts

43.

What determines the horizontal asymptotes in a rational function?

a)

The x-intercepts

b)

The y-intercepts

c)

The degree of the polynomials

d)

The common factors

44.

How is the x-intercept of a rational function found?

a)

By setting the denominator to zero

b)

By setting the numerator to zero

c)

By factoring the denominator

d)

By solving for y-intercepts

45.

How is the y-intercept of a rational function found?

a)

By setting x = 0 and solving

b)

By setting y = 0 and solving

c)

By factoring the numerator

d)

By determining the degree

46.

What is the first step in simplifying rational expressions?

a)

Add the numerators

b)

Factor

c)

Multiply by the reciprocal

d)

Subtract the denominators

47.

What should you do after factoring in order to simplify a rational expression?

a)

Add the fractions

b)

Cross off common factors

c)

Divide the numerators

d)

Multiply the denominators

48.

How are excluded values in a rational expression determined?

a)

By setting the numerator equal to zero

b)

By setting the denominator equal to zero

c)

By adding the numerator and denominator

d)

By subtracting the numerator from the denominator

49.

What is a key characteristic of a kite in geometry?

a)

It has two pairs of parallel sides.

b)

It has no parallel sides.

c)

All sides are equal.

d)

It has one pair of parallel sides.

50.

What is true about the base angles in an isosceles trapezoid?

a)

Base angles are not congruent

b)

Base angles are congruent

c)

Base angles are right angles

d)

Base angles are obtuse

51.

What is true about the diagonals in an isosceles trapezoid?

a)

Diagonals are not congruent

b)

Diagonals are congruent

c)

Diagonals are perpendicular

d)

Diagonals are parallel

52.

How many sets of congruent sides does an isosceles trapezoid have?

a)

Two sets

b)

One set

c)

No sets

d)

Three sets

53.

Which shape has all the properties of a parallelogram, rectangle, and rhombus?

a)

Square

b)

Circle

c)

Triangle

d)

Pentagon

54.

Which of the following is a property of a rhombus?

a)

All sides are congruent.

b)

Only opposite sides are congruent.

c)

Diagonals are parallel.

d)

Only one pair of sides is congruent.

55.

What is true about the diagonals of a rhombus?

a)

They are perpendicular and bisect angles.

b)

They are parallel and equal in length.

c)

They are perpendicular but do not bisect angles.

d)

They are equal in length but not perpendicular.

56.

A rhombus shares all properties with which other geometric shape?

a)

Parallelogram

b)

Rectangle

c)

Trapezoid

d)

Circle

57.

Which of the following is a property of a rectangle?

a)

All sides are equal

b)

All angles are congruent (90°)

c)

Diagonals are not congruent

d)

Opposite angles are not equal

58.

What is true about the diagonals of a rectangle?

a)

Diagonals are not congruent

b)

Diagonals are congruent

c)

Diagonals are perpendicular

d)

Diagonals are unequal

59.

Which shape shares all the properties of a rectangle?

a)

Square

b)

Circle

c)

Triangle

d)

Trapezoid

60.

What is true about the opposite sides of a parallelogram?

a)

They are perpendicular.

b)

They are parallel.

c)

They are unequal.

d)

They are curved.

61.

What is true about the opposite angles in a parallelogram?

a)

They are congruent.

b)

They are supplementary.

c)

They are right angles.

d)

They are acute.

62.

What is true about the diagonals of a parallelogram?

a)

They are equal.

b)

They bisect each other.

c)

They are perpendicular.

d)

They are parallel.

63.

What is the sum of consecutive angles in a parallelogram?

a)

90 degrees

b)

180 degrees

c)

270 degrees

d)

360 degrees

64.

Select all the shapes formed when a cone is cut?

a)

Circle

b)

Rectangle

c)

Parabola

d)

Triangle

65.

Select all the shapes formed when a cylinder is cut?

a)

Triangle

b)

Rectangle

c)

Oval

d)

Parabola

66.

Which 3D figure is formed by rotating a triangle?

a)

Sphere

b)

Cylinder

c)

Cone

d)

Cube

67.

What 3D figure is formed by rotating a rectangle?

a)

Sphere

b)

Cylinder

c)

Cone

d)

Pyramid

68.

Which 3D figure is formed by rotating a circle?

a)

Sphere

b)

Cylinder

c)

Cone

d)

Prism

69.

What is the line called that a shape is rotated around to form a 3D figure?

a)

Radius

b)

Diameter

c)

Height

d)

Base

70.

What is the formula for density?

a)

Density = Volume / Mass

b)

Density = Mass / Volume

c)

Density = Mass x Volume

d)

Density = Volume - Mass

71.

How is population density calculated?

a)

Population Density = Area / Population

b)

Population Density = Population x Area

c)

Population Density = Population / Area

d)

Population Density = Area - Population

72.

What is the formula for the volume of a prism?

a)

V = πr²h

b)

V = 1/3Bh

c)

V = Bh

d)

V = 4/3πr³

73.

Which formula represents the volume of a cylinder?

a)

V = Bh

b)

V = 1/3πr²h

c)

V = πr²h

d)

V = 4/3πr³

74.

How is the volume of a pyramid calculated?

a)

V = Bh

b)

V = 1/3Bh

c)

V = πr²h

d)

V = 4/3πr³

75.

What is the formula for the volume of a cone?

a)

V = 1/3πr²h

b)

V = Bh

c)

V = πr²h

d)

V = 4/3πr³

76.

Which of the following is the formula for the volume of a sphere?

a)

V = Bh

b)

V = 1/3Bh

c)

V = πr²h

d)

V = 4/3πr³

77.

What is the formula for the area of a square?

a)

A = s × s or A = lw

b)

A = ½ bh

c)

A = πr²

d)

A = ½ (b₁ + b₂) h

78.

What is the formula for the area of a rectangle?

a)

A = ½ bh

b)

A = lw or A = bh

c)

A = πr²

d)

A = ½ (b₁ + b₂) h

79.

What is the formula for the area of a triangle?

a)

A = s × s

b)

A = lw

c)

A = ½ bh

d)

A = πr²

80.

What is the formula for the area of a circle?

a)

A = s × s

b)

A = lw

c)

A = ½ bh

d)

A = πr²

81.

What is the formula for the area of a trapezoid?

a)

A = s × s

b)

A = lw

c)

A = ½ (b₁ + b₂) h

d)

A = πr²

82.

In a triangle, what is the orthocenter?

a)

The point where the medians intersect

b)

The point where the altitudes intersect

c)

The point where the angle bisectors intersect

d)

The point where the perpendicular bisectors intersect

83.

In a triangle, what is the circumcenter?

a)

The point where the medians intersect

b)

The point where the altitudes intersect

c)

The point where the angle bisectors intersect

d)

The point where the perpendicular bisectors intersect

84.

The circumcenter is equidistant from each​ (a)   of the triangle

Choose from the below words
vertex
side
85.

The incenter is equidistant from each​ ​ (a)   of the triangle

Choose from the below words
side
vertex
86.

In a triangle, what is the incenter?

a)

The point where the medians intersect

b)

The point where the altitudes intersect

c)

The point where the angle bisectors intersect

d)

The point where the perpendicular bisectors intersect

87.

In a triangle, what is the incenter?

a)

The point where the medians intersect

b)

The point where the altitudes intersect

c)

The point where the angle bisectors intersect

d)

The point where the perpendicular bisectors intersect

88.

How do you find circumference?

a)
C = 2r
b)
C = 3πr
c)
C = πr^2
d)
C = 2πr or C = πd
89.

How do you find area of a circle?

a)
A = 2πr
b)
A = πd
c)
A = r² + h²
d)
A = πr²
90.

How do you convert from degrees to radians?

a)
radians = degrees + 180
b)
radians = degrees × (180/π)
c)
radians = degrees ÷ 180
d)
radians = degrees × (π/180)
91.

How do you convert from radians to degrees?

a)
Degrees = Radians × (π/180)
b)
Degrees = Radians + 180
c)
Degrees = Radians ÷ (180/π)
d)
Degrees = Radians × (180/π)
92.

Match the formulas

Categorize the following

θ360⋅2πr\frac{\theta}{360}\cdot2\pi r  

θ⋅r\theta\cdot r  

θ360⋅πr2\frac{\theta}{360}\cdot\pi r^2  

12θr2\frac{1}{2}\theta r^2  

Arc length degree
Arc length radians
Sector area degree
Sector area radian

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