Course

by correctly solving problems involving internally or externally tangent circles or arcs

your answer has correct magnitude stated to the correct precision

your answer is labeled with the correct unit of measurement

you draw a line or lines passing through tangent points and circle centers

you correctly label unknowns, circle radii, and the distance between the circle centers on the diagram

you write an equation that correctly relates unknowns, circle radii and the distance between the circle centers

you write any other relevant equations that correctly relate other given distances to the circle distances

you manipulate the equations in a way that leads to the correct answer correctly

by correctly solving problems involving lines tangent to a circle

your answer has correct magnitude stated to the correct precision

your answer is labeled with the correct unit of measurement

you draw or identify lines that are tangent to a given circle and that contain an external point

you draw radii that contain the tangent points

you draw a line containing the circle center and the external point

you label congruent tangent segments

you label congruent radii

you label the right angle(s) formed by radii and tangent segments

you label other congruent angles

you label any unknowns or given dimensions on the diagram

you write relevant equations relating relevant unknowns, distances, and/or angles

you manipulate the equations in a way that leads to the correct answer correctly

by correctly solving complex machine application problems using right triangles and tangents to circles

your answer has correct magnitude stated to the correct precision

your answer is labeled with the correct unit of measurement

you draw relevant lines containing tangent points and circle centers

you draw relevant right triangles that relate given information

you label the right triangles with correct dimensions and unknowns

you label other quantities with the correct dimensions and unknowns

you write relevant equations relating relevant unknowns, distances and/or angles

you manipulate the equations in a way that leads to the correct answer correctly

by correctly drawing fundamental geometric constructions basic to the machine trades

you construct a perpendicular bisector of a line segment

you construct a bisector of a given angle

you construct a perpendicular line to a given line segment at a given point on the line segment

you construct a perpendicular line to a given line segment at a given point not on the line segment

you construct a parallel line to a given line segment at a given distance

you construct tangents to a given circle from an outside point

you divide a given line segment into a given number of equal parts

by correctly drawing typical machine shop layout problems using the methods of construction

you construct certain special angles, like 30 or 675 degrees

you construct a tangent circle of a given radius to a given angle

you construct regular polygons of a given diameter or side length

you copy polygons using geometric construction techniques

by correctly solving for unknown dimensions on oblique triangles

your answer has correct magnitude stated to the correct precision

your answer is labeled with the correct unit of measurement

you label sides and angles in a way that indicates you understand which sides are opposite which angles

you determine if enough information is given to solve the oblique triangle

you calculate the third angle when two angles are known

you choose between the Law of Sines and Law of Cosines, and write down the appropriate equation for your diagram

you identify the ambiguous case associated with the Law of Sines and correctly calculate both solutions when asked

you manipulate the equation in a way that leads to the correct answer

by correctly solving problems involving machine applications of oblique triangles

your answer has correct magnitude stated to the correct precision

your answer is labeled with the correct unit of measurement

you draw relevant auxiliary lines on a given diagram to generate solvable oblique triangles

you label sides and angles of the oblique triangles with given information in a way that indicates you understand which sides are opposite which angles

you choose to apply the Law of Sines or Law of Cosines to each oblique triangle

you write any other relevant equations relating relevant unknowns, distances and/or angles

you manipulate the equation or equations in a way that leads to the correct answer

by correctly solving problems involving the secant, cosecant, and cotangent functions

your answer has correct magnitude stated to the correct precision

your answer is labeled with the correct unit of measurement

you show how to calculate the secant, cosecant, or cotangent of a given angle using the cosine, sine, or tangent functions, respectively

you show how to calculate the arcsecant, arccosecant, or arccotangent of a given value using the arccosine, arcsine, or arctangent functions, respectively

you apply formulas for calculating the secant, cosecant, cotangent, or their inverse functions

by correctly calculating the true length and true angles of a body diagonal of a dimensioned rectangular solid

your answers have correct magnitudes stated to the correct precision

your answers are labeled with the correct unit of measurement

you label the length, width, and height of a rectangular solid

you draw and label the top, front, and end views of a rectangular solid

you draw and label the surface diagonal across the top (or bottom) face of a rectangular solid

you calculate the length of the surface diagonal across the top (or bottom) face of a rectangular solid

you calculate the angles made by the surface diagonal across the top (or bottom) face of a rectangular solid

you draw and label the body diagonal of a rectangular solid

you draw and label the right triangle containing the body diagonal of a rectangular solid

you calculate the length of the body diagonal of a rectangular solid

you calculate the angles of the right triangle containing the body diagonal of a rectangular solid

you apply formulas for calculating true lengths and true angles of a body diagonal

by correctly calculating the angles of rotation and tilt for drilling a compound angle hole in or machining a compound angle surface on a rectangular solid when given either lengths or apparent face angles

your answers have correct magnitudes stated to the correct precision

your answers are labeled with the correct unit of measurement

you draw and label a rectangular solid containing the compound angle hole as a body diagonal or containing the face to be machined off

you associate the angle of rotation for a compound angle hole with one of the angles made by the surface diagonal across the top (or bottom) face of the rectangular solid you drew

you write the correct equation to calculate the angle of rotation for a compound angle hole

you associate the angle of tilt for a compound angle hole with one of the angles of the right triangle containing the body diagonal of the rectangular solid you drew

you write the correct equation to calculate the angle of tilt for a compound angle hole

you associate the angle of rotation for a compound angle surface with the angle that is formed by the line perpendicular to the surface diagonal across the top face of the rectangular solid you drew

you write the correct equation to calculate the angle of rotation for a compound angle surface

you label the angle of tilt for a compound angle surface in the rectangular solid you drew

you write the correct equation to calculate the angle of tilt for a compound angle surface

you manipulate all equations in a way that leads to the correct answer

you apply given formulas for calculating angles of rotation and tilt when given either lengths or apparent face angles

by correctly stating the coordinates of a point located on a two-dimensional Cartesian coordinate system

your answer has correct magnitudes for the x and y values stated to the correct precision

your answer is labeled with the correct unit of measurement, when appropriate

your answer is stated in the correct format of (x, y)

you identify the given point as being in Quadrant I, II, III, or IV

by plotting points given their coordinates on a two-dimensional and three dimensional Cartesian coordinate system

you draw coordinate axes for either the two dimensional or three dimensional case

you label the axes as x, y, or z

the points you plot are correctly located relative to your axes

by correctly calculating absolute and incremental positioning from engineering drawings for a point-to-point two-axis control system

your answers have correct magnitudes stated to the correct precision

your answers are labeled with the correct unit of measurement

you determine the order in which holes are to be drilled which roughly minimizes the amount of tool travel, and label the drawing with this order

you make a table to contain the absolute and/or incremental position information

you identify or determine the origin for the system and draw coordinate axes centered at this origin

you write equations relating distances given that are parallel to coordinate axes

you draw any necessary triangles to locate holes that are on a circle or specified to be at an angle to the coordinate axes

you write equations relating distances for the triangles to calculate distances parallel to coordinate axes

you write all your equations in a clear and orderly manner

you manipulate the equations in a way that leads to the correct answer

by correctly converting between decimal and binary numbers

your answer has correct magnitude stated to the correct precision

you break a decimal number into groups of powers of two

you write the binary equivalent of a decimal number using those groups of powers of two

you write a decimal number as a sum of powers of two

you write the decimal equivalent of a binary number by evaluating the sum of powers of two

by correctly converting between decimal fractions, common fractions, and percent representations of parts of a whole

your answer has correct magnitude stated to the correct precision

your answer is labeled with the correct unit of measurement

you write the conversion from a common fraction to a decimal fraction

you write the conversion from a decimal fraction to a percent

you write the conversion from a percent to a decimal fraction

you write the conversion from a decimal fraction to a common fraction

by correctly calculating the percentage, base, or rate given two of the three quantities

your answer has correct magnitude stated to the correct precision

your answer is labeled with the correct unit of measurement

you write the equation to find the rate given the base and percentage and know when to use it

you write the equation to find the base given the percentage and rate and know when to use it

you write the equation to find the percentage given the rate and base and know when to use it

by correctly calculating the percentage, base, or rate in practical application problems

your answer has correct magnitude stated to the correct precision

your answer is labeled with the correct unit of measurement

you write the equation to find the rate given the base and percentage in practical application problems

you write the equation to find the base given the percentage and rate in practical application problems

you write the equation to find the percentage given the rate and base in practical application problems

you write any other equations relevant to solving practical applications relevant to percents