Problem Set |
Terms and
Concepts*
*please note that some terms may
repeat in multiple lessons; for geometry terms, please include
all relevant formulas with the definitions |
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1 Geometry Review |
primitive terms, undefined
terms, point, curve, line, plane, graph, line segment, segment, equal to,
grater than, less than, congruent, ray, half-line, origin, collinear,
opposite rays, intersection, coplanar, skew lines, geometric figure, region,
difference in direction, rotation of a ray, coterminal, vertex, initial side,
terminal side, straight angle, perpendicular lines, right angle, acute angle,
obtuse angle, tick marks, equiangular, isogonic triangle, right triangle,
acute triangle, obtuse triangle, oblique triangle, equilateral triangle, isosceles
triangle, scalene triangle, parallel lines, transversal, corresponding
angles, interior anglges, exterior angles, alternate interior angles,
alternate exterior angles, properties of parallel lines, conditions for lines
to be parallel, postulate, altitude, height, radius, circumference, arc,
sector, central angle
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2 More on Area Cones & Pyramids
Spheres Cylinders & Prisms |
area, cylindrical surface,
directrix, element, open surface, closed surface, parallel planes, bases, right
cylinder, right solid, circular cylinder, elliptical cylinder, right circular
cylinder, center, axis, oblique cylinder, right oval cylinder, right
triangular cylinder, prism, right rectangular cylinder, volume of cylinders
and prisms, lateral surface area of cylinders and prisms, cone, pyramid,
apex, slant height, faces, sphere, volume and surface areas of cone, pyramid,
sphere
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3 Pythagorean Theorem Triangle Inequalities (1) Similar Polygons Similar Triangles |
triangle inequality postulate,
Pythagorean inequalities, polygons, concave polygon, convex polygon, similar,
scale factor, vertices, sides, similar triangles
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4 Construction |
compass, protractor,
straightedge, copying line segments, copying angles, bisecting angles,
bisecting line segments, erecting perpendiculars, constructing triangles,
constructing parallels, equal segments
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5 Exponents and Radicals Complex
Numbers Areas of Similar Geometric Figures Diagonals of Rectangular Solids |
exponent, radical, a+bi,
complex number, standard form, similar geometric figures, scale factor,
diagonals of rectangular solids
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6 Fractional Equations Radical Equations Systems of Three
Linear Equations |
No new terms
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7 Inductive and Deductive Reasoning
Logic The Contrapositive Converse and Inverse |
inductive reasoning, induce,
deductive reasoning, syllogism, premises, categorical prepositions, universal
affirmatives, major premise, minor premise, argument, valid, invalid,
hypothesis, conclusion, contrapositive, converse, inverse, if-and-only-if
statements
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8 Statements of Similarity Proportional
Segments Angle Bisectors & Side Ratios |
No new terms
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9 Congruent Figures Proof Outlines |
numerical expressions,
numerals, idea, congruent, geometrically equivalent, congruent triangles,
postulate, SSS, SAS, ASA (or AAAS), HL, proof outline
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10 Equation of a Line Rational Denominators Completing the
Square |
horizontal line, slope,
vertical line, x intercept, y intercept, slope-intercept form, ratio,
rational number, root, rationalizing the denominator, conjugate, completing
the square
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11 Circles Properties of Circles The Quadratic Formula |
circle, center, radius, chord,
diameter, secant, tangent, perimeter,
arc, circumference, semicircle, central angle, major arc, minor arc,
congruent circles, measure of an arc, inscribed angle, product of chord
segments, quadratic formula
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12 Angles & Diagonals in
Polygons Proof of the Chord-Tangent
Theorem |
triangulate, exterior angles =
360°, # of
diagonals, proof of the chord-tangent theorem
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13 Intersecting Secants Intersecting Secants & Tangents Products of Chord Segments Products
of Secant and Tangent Segments |
tangent, secant, rules for
intersecting secants and tangents, chord, product of chord segments, secant
segment, external secant segment
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14 Sine, Cosine, and Tangent Angles of Elevation & Depression Rectangular & Polar Coordinates Coordinate Conversion |
sine, cosine, tangent, angles
of elevation, angles of depression, rectangular coordinates, carat, unit
vectors, ordered pair, vector notation, polar coordinates, (+ angles move
counterclockwise, (-) angles move clockwise, directed distance, 4 forms of polar
coordinates
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15 Assumptions Proofs |
theorems, axiom, postulate,
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16 Complex Fractions Abstract Equations Division of Polynomials |
complex fraction, well-chosen
one
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17 Proofs of the Pythagorean Theorem
Proofs of Similarity |
proofs of similarity, SSS, SAS,
AAA
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18 Advanced Word Problems |
No new terms
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19 Nonlinear Systems Factoring Exponentials Sum & Difference of Two Cubes |
nonlinear systems of equations,
exponential expressions, exponentials, factor, factoring
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20 Two Special Triangles |
30-60-90 triangle, 45-45-90
triangle
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21 Evaluating Functions Domain & Range Types of
Functions Tests for Functions |
function, independent variable,
dependent variable, domain, range, definition of a function, function
machine, relation, 1 to 1 function, rules for functions, vertical line test,
horizontal line test
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22 Absolute Value Reciprocal Functions |
absolute value, distance,
vertical asymptote, reciprocal function
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23 The Exponential Function Sketching
Exponentials |
powers, base, exponents,
exponential, exponential equations, sketching exponentials
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24 Sums of Trigonometric Functions
Combining Functions |
sum,
difference, product, quotient, composition
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25 Age Problems Rate Problems |
age problems, rate problems
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26 The Logarithmic Form of the Exponential Logarithmic Equations |
logarithm, log, N = bL,
logb N = L
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27 Related Angles Signs of Trigonometric Functions |
related angles, 4 quadrant
signs
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28 Factorial Notation Abstract Rate Problems |
No new terms
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29 The Unit Circle Very Large & Very Small
Fractions Quadrantal
Angles |
quadrantal angles, limit, undefined,
sine cosine and tangent of quadrantal angels
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30 Addition of Vectors Overlapping Triangles |
No new terms
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31 Symmetry Reflections Translations |
reflections, mirror images,
point of symmetry, axis of symmetry, symmetric about x axis, symmetric about
y axis, symmetric about the origin, translation, y = (x-h) + k, x-shift,
y-shift
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32 Inverse Functions Four Quadrant Signs Inverse Trigonometric Functions |
inverse function, 4 quadrant
signs, inverse cosine (0 £ x £ 180°),
inverse sine
(-90 £ x £ 90), inverse tan (-90 £ x £ 90), arccos, arcsin, arctan
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33 Quadrilaterals Properties of Parallelograms Types of
Parallelograms Conditions for Parallelograms
Trapezoids |
quadrilateral, trapezoid,
parallelogram, properties of parallelograms, rectangle, rhombus, square,
properties of rectangles, properties of rhombuses, properties of squares,
conditions for rectangle, conditions for square, bases, legs, median,
altitude, properties of a trapezoid, properties of an isosceles trapezoid
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34 Summation Notation Linear Regression Decomposing Functions |
sigma (S),
variable of summation, typical element, linear regression, experimental data,
trivial, identity function, non-trivial
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35 Change in Coordinates The Name of a Number The Distance Formula |
change in coordinates, directed
distance, DC,
Pythagorean theorem, distance formula
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36 Angles Greater Than 360° Sums of Trigonometric Functions Boat-in-the-River Problems |
coterminal angles, initial side,
terminal side, boat-in-the-river, downstream, upstream
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37 The Line as a Locus The Midpoint Formula |
locus, definition of a line,
midpoint formula
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38 Fundamental Counting Principle and
Permutations Designated Roots Overall Average Rate |
permutation, fundamental
counting principle, designated roots, overall average rate
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39 Radian Measure of Angles Forms of Linear Equations |
radian, Υ radians
= 180°, forms
of linear equations: general form, slope-intercept form, double intercept
form, point-slope form, two point form
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40 The Argument in Mathematics The Laws of Logarithms Properties of Inverse Functions |
argument, argument of the
function, laws of logarithms, definition of inverse functions
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41 Reciprocal Trigonometric Functions
Permutation Notation |
nPr =
n!/(n-r)!, permutation notation
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42 Conic Sections Circles Constants in
Exponential Functions |
circular cone, nappes, conic
sections, circle, parabola, hyperbola, locus, general form
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43 Periodic Functions Graphs of Sine and Cosine |
periodic functions, sinusoid,
amplitude, range, period
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44 Abstract Rate Problems |
No new terms
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45 Conditional Permutations Two-Variable Analysis Using a Graphing Calculator |
conditional permutation, linear
regression
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46 Complex Roots Factoring Over the
Complex Numbers |
Complex roots
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47 Vertical Sinusoid Translations Arctan |
No new terms
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48 Powers of Trigonometric Functions
Perpendicular Bisectors |
midpoint formula method, locus
definition method
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49 The Logarithmic Function Development
of the Rules for Logarithms |
No new terms
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50 Trigonometric Equations |
No new terms
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51 Common Logarithms and Natural Logarithms |
exponent, logarithm, number,
antilogarithm, common logarithm, natural logarithm
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52 The Inviolable Argument Arguments in Trigonometric Equations |
No new terms
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53 Review of Unit Multipliers Angular Velocity |
unit multipliers, angular
velocity (w), V=rw
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54 Parabolas |
parabola, axis of symmetry
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55 Circular
Permutations Distinguishable Permutations |
linear
permutation, circular permutation, distinguishable permutation
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56 Triangular Areas Areas of Segments Systems of Inequalities |
height, base, sector, segment
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57 Phase Shifts in Sinusoids Period of a Sinusoid |
phase angle, period, periodic
function
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58 Distance from a Point to a Line
"Narrow" and "Wide" Parabolas |
No new terms
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59 Advanced Logarithm Problems The Color
of the White House |
No new terms
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60 Factorable Trigonometric Equations
Loss of Solutions Caused by Division |
No new terms
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