- Day #, Chapter.Section Text Page & Content/Topic
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- 1 2.1, 2.2
- 2.1 The Rectangular Coordinate Systems and Graphs, pg. 74
- coord sys @ 74, plot @ 76, TI graph @ 78, intercepts @ 79, distance @ 80, midpoint @ 82, circle @ 83, exercises @ 84
- plot, graph
Cartesian -- definition and analytic history web page
graphing
"What's A Graph?"
- compute
distance.gsp -- start w/a segment, coordinatize it, build triangle, use Pythagorean Theorem to find distance
fx & ops - midpoint, slope, distance, ...
- circles, distance formula, tangents, normals
circle.tangent.normal.gsp
1 drag center & radius 2 create equation
2 enter h, k, r
3 input coord, m=, line=, perp=
4 slide, write tangent & normal
just circleFormula -- writes the formula for the depicted circle
just circleTangent -- writes the tangent to a given circle
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trace -- creates point defined by an x-intercept and a calculated value for y of point
then traces the path of the point controlled by the x-intercept
- 2.2 Linear Equations in One Variable, pg. 87
- lines @ 88, solve linear equ. @ 88, solve rational (fraction equation @ 89, Solving Rational Equations with a Binomial in the Denominator @ 91,
- slope @ 83, write equ of lines @ 94, parallel, perpendicular @ 96, exercises @ 100
- lines
LINES -- Notes, Discussion, Activities
Line Vocabulary
line.gsp -- slide points A and B and generate equation of the line in 4 forms.
line.gsp
-- line segment by dragging & by coordinates, midpoint, distance formula, point-slope equation, perpendicular, parallel lines
-- slide points A and B and generate equation of the line in 4 forms.
-- computes slopes and writes lines by sliding and by parameters
1 - drag segment endpoints to compute midpoint and distance
2 - show how the distance formula computes
3 - find a perpendicular w/input coordinates
4 - find parallel w/input coordinates
linear.xls for: graphs, slope
SLOPE SONG .htm
solve equ w/solver -- find x-intercepts
solve graphically
equations of lines .htm
fx & ops .htm - midpoint, slope, distance, ...
- circles, distance formula, tangents, normals
circle.tangent.normal.gsp
1 drag center & radius 2 create equation
2 enter h, k, r
3 input coord, m=, line=, perp=
4 slide, write tangent & normal
- Distance Formula, Midpoint Formula, Circles, Solving equations graphically
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- 2 2.5, 2.6
- 2.5 Quadratic Equations, pg. 119
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Graphing, Functions
Vocabulary
Basic Functions
Function Sketchpads
reciprocal gsp, 1/x, etc. -- reciprocal functions
* VERTICAL ASYMPTOTE MUST BE POSITIONED BY USER!
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absolute value gsp -- |x|, functions controlled by parameters and NOT controlled by parameters
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2graphs.gsp
-- 1,2 graphed functions, piece-wise, composite ready to edit, link to "coordinate" and more history, table of f(x) gps files
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graphs gsp -- 1 or 2 graphed functions ready to edit
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squaring gsp, parabola -- Multi page: 2 parabolas: 1 in general form, 1 in standard forms, ...
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square root gsp -- 2 square root functions defined by easy-edit parameters
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piece-wise gsp -- graphs a piecewise defined function when left function and right function
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absValu.gsp -- 2 absolute value functions controlled by parameters
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greatest integer function gsp, [[x]] -- also a[[bx+c]] + k
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reciprocal functions -- graph of parameter-defined reciprocal function,
* with slide-able tangent line,
* VERTICAL ASYMPTOTE MUST BE POSITIONED BY USER!
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composite functions gsp -- build 2 functions using other functions
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inverse gsp -- take an inverse of an invertable fdunction, horizontal & vertical line tests
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parentFX gsp -- function "manipulatives"
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parentFX2 gsp> -- revised function "manipulatives"
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2.6 Other Types of Equations -- Solving Equations Algebraically, pg. 131
3 2.7
2.7 Linear Inequalities and Absolute Value Inequalities -- Solving Quadratic and Rational inequalities, pg. 142
quadratic.xls- Enter h, k, and a to generate general form and x-intercepts.
- Multiply 2 binomials to find the product, vertex, discriminant.
- Solve a quadratic equation by entering the required constants and coefficients.
- Write general form in quadratic form.
composite, polynomial, rational functions
polynomial
linear
quadratic
quadratic formula
discriminant
4 3.1-3.3, 4.1
3.1 Functions and Function Notation, pg. 160
3.2 Domain and Range, pg. 180
3.3 Rates of Change and Behavior of Graphs, pg. 196
4.1 Review of slopes and functions, pg. 280
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ssong.gsp -- slope from history, to sound, to words & numbers, through examples, to computation
0 - toc, history
1 - only 1 function
2 - parabola w/tangent line
3 - cubic w/tangent line
4 - polynomial
5 - rational
6 - compute slope drag 2 points
7 - dy/dx by definition
8 - m= given A, B
9 - 3 points define a parabola
10 - notes on 3 points define a parabola
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2graphs.gsp
-- 1,2 graphed functions, piece-wise, composite ready to edit, link to "coordinate" and more history, table of f(x) gps files
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Cartesian -- definition and analytic history web page
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ssong.gsp -- slope from history, to sound, to words & numbers, through examples, to computation
0 - toc, history
1 - only 1 function
2 - parabola w/tangent line
3 - cubic w/tangent line
4 - polynomial
5 - rational
6 - compute slope drag 2 points
7 - dy/dx by definition
8 - m= given A, B
9 - 3 points define a parabola
10 - notes on 3 points define a parabola
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5 TEST#1 (10% of course grade and covers sections 2.1,2.2,2.5,2.6,2.7.3.1-3.3, 4.1)
5 3.5
3.5 Transformation of Functions - Graphing functions; Shifting, Reflecting, Stretching and Shrinking graphs, pg. 222
6 3.4, 3.7
3.4 Composition of Functions, pg. 209
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inverse.gsp
0 - vertical, horizontal line tests
1 - square root fx
2 - any function
3 - sqrt fx by parameters
4 - restricted domain on inverse
5 - arcsine
6 - arctangent
7 - f and inverse
8 - f, inverse, tangents --
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compositeFX.gsp --
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parabola.gsp --
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compositeFx.poly.ratl.gsp
0 - graph of 1 function
1 - graphs of 2 functions
2 - composite of 4 functions
3 - polynomial. links to polynomial, dilations gif, quatratic.htm, equation, discriminant
4 - rational, rational function features & how to find them
5 - end behavior, battle of (Ax^m)/(Bx^n)
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compositeFX.gsp -- build 2 functions using other functions
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inverse.gsp -- take an inverse of an invertable fdunction, horizontal & vertical line tests
3.7 Inverse Functions, pg. 254
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compositeFX.gsp -- build 2 functions using other functions
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parabola -- Multi page: 2 parabolas: 1 in general form, 1 in standard forms
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TracePoly -- drag point f(x) to state and show new ( x, f(x))
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inverse gsp -- take an inverse of an invertable fdunction, horizontal & vertical line tests
- COMPOSITION --
Composition of Functions
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Dilation notes
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Dilation creates functions
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dilation by a constant animation
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composite functions -- build 2 functions using other functions
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inverse gsp -- take an inverse of an invertable fdunction, horizontal & vertical line tests, restricted domain on inverse, arcsine, arctan
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compositeFX.gsp --
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parabola.gsp --
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compositeFx.poly.ratl.gsp
0 - graph of 1 function
1 - graphs of 2 functions
2 - composite of 4 functions
3 - polynomial. links to polynomial, dilations gif, quatratic.htm, equation, discriminant
4 - rational, rational function features & how to find them
5 - end behavior, battle of (Ax^m)/(Bx^n)
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7 3.4, 3.5, 3.7
3.4 Composition of Functions, pg. 209
3.5 Transformation of Functions, pg. 222
3.7 Inverse Functions, pg. 254
8 Test #2 (10% of course grade and covers sections 3.4, 3.5, 3.7)
8 5.1, 5.2
5.1 Quadratic Functions, pg. 344
5.2 Power Functions and Polynomial Functions, pg. 360
quadratic formula
discriminant
9 5.3, 5.4, 5.5
5.3 Graphs of Polynomial Functions, pg. 375
5.4 Dividing Polynomials, pg. 393
5.5 Zeros of Polynomial Functions, pg. 402
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zeros
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Polynomial functions notes
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poly.xls
- Graph a polynomial defined by degrees and coefficients.
y= anxn + an -1xn -1 + an - 2xn -2 + an - 3xn -3 + an - 4xn - 4 + an - 5xn - 5 + an-6xn - 6 + an -7xn -7
- Graph a polynomial displayed in factored form.
y = A(x - b)B(x - c)C(x - d)D
- Synthetically divide and then view the quotient polynomial and remainder.
Divide (anxn + an -1xn -1 + an - 2xn -2 + an - 3xn -3 + an - 4xn - 4 + an - 5xn - 5 + an-6xn - 6 + an -7xn -7) รท (x-c)
- Solves linear or quadratic equations. Multiplies 2 binomials or 3 binomials.
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parabola -- Multi page: 2 parabolas: 1 in general form, 1 in standard forms,
* both generated by equations defined by parameters.
* WITH SHOW/HIDE ACTION BUTTON
* graphs of 2 parabolas: 1 in general form, 1 in standard forms,
* 1 parabola, set a, then generat parabola w/2 points.
* 1 parabola controlled by 3 points, used for determinant analysis
* 1 vertical axis of symmetry, 1 horizontal "axis of symmetry
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TracePoly -- drag point f(x) to state and show new ( x, f(x))
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recipfx -- graph of parameter-defined reciprocal function,
* with slide-able tangent line,
* VERTICAL ASYMPTOTE MUST BE POSITIONED BY USER!
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- 10 5.6
- 5.6 Rational Functions: Asymptotes and Graphing, pg. 414
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ratl.xls
- Graph and table of (Axm)/(Bxn)
Watch the power of the top or bottom equal or dominate the other.
Examine hoirzontal asymptotes or infinite increase or decrease.
Think endbehavior and explore.
- Graph and table of rational function, polynomial A(x) divided by B(x).
Examine asymptotes.
Examine the role of factors A(x) and 1/B(x).
- Graph and table of rational functions written as A(x) / B(x) + C(x)
Really play with C(x), the asymptote
- Complete synthetic division and rewrite of quotient and remainder.
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- 11 twice 6.1-6.4 (Two-Days)
- 6.1 Exponential Functions, pg. 464
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- 6.2 Graphs of Exponential Functions, pg. 479
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- 6.3 Logarithmic Functions, pg. 491
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- 6.4 Graphs of Logarithmic Functions, pg. 499
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logs -- Multi page: 2 logs, log w/exponential
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exp2.xls
- Compute yearly, semiyearly, quarterly, monthly, daily, and every minute given initial principal, rate, and time.
- Solve for P, P0, r, t, but not n, for instantaneous and non-instantaneous interest.
- Graph two exponential curves w/user entry of parameters.
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- 12 6.5,6.6
- 6.5 Logarithmic Properties, pg. 516
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- 6.6 Exponential and Logarithmic Equations, pg. 526
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- 13 6.7
- 6.7 Growth and Decay Applications -- Exponential and Logarithmic Models, pg. 537
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- 14 There is no day 14.
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- 15 Test #3 (20% of course grade and covers sections 5.1-5.6, 6.1-6.7)
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- 16 7.1
- 7.1 Angles and their measures, pg. 576
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complsuppl -- just complementary & supplementary angles
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standardPosition.gsp
1 standard position angle central angle, negative & positive angle measures
2 angles coterminal?
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radianSector.gsp
1 intro angles degrees radians
2 radian questions
3 arc length angular speed sector area
4 sector and area
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veronica.gsp
1 - 1 standard position angle
2 - angles coterminal?
3 - 1 veronica angles -- trig fx of angles is 4 quadrants
4 - 2 veronica angles
5 - extra 2 veronica angles
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elevation.gsp - angle of elevation, depression, ladders w/h(x), y(x), and h(y), x(y), and h as variable, and h s a constant
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complsuppl -- just complementary & supplementary angles
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cosplay -- just right triangle cosine
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sinplay -- just right triangle sine
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tanplay -- just right triangle cosine
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NewCentral -- An angle in standard position.
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standardPosition.gsp
1 standard position angle central angle, negative & positive angle measures
2 angles coterminal?
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radianSector.gsp
1 intro angles degrees radians
2 radian questions
3 arc length angular speed sector area
4 sector and area
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veronica.gsp
1 - 1 standard position angle
2 - angles coterminal?
3 - 1 veronica angles -- trig fx of angles is 4 quadrants
4 - 2 veronica angles
5 - extra 2 veronica angles
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elevation.gsp - angle of elevation, depression, ladders w/h(x), y(x), and h(y), x(y), and h as variable, and h s a constant
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- 17 7.2
- 7.2 Right Triangle Trigonometry, pg. 593
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2TrigGraphs.gsp -- 1 blank function, 1 parameter-driven function on a "trig plane"
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sinplay -- just right triangle sine
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cosplay -- just right triangle cosine
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tanplay -- just right triangle tangent
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TraceSin -- drag point f(x) to state and show new ( x, f(x))
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TraceCos -- drag point f(x) to state and show new ( x, f(x))
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TraceTan -- just graph with a slideable point to display coordinates
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SinCosTan1stDay -- Just sine, cosine, tangent of right triangle angles.
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SinCosTan6fx -- All 6 functions in right triangle only.
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SinCosTanAllNumbers -- All 6 functions in right triangle and forall numbers,
* controlled by figure for right triangle,
* parameter-defined angle measure in degrees for all measures, and
* parameter-defined angle measure in decimal number times pi for radian measures
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sinNcos.gsp -- sine and cosine in right triangle only
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2 Sine Functions -- Asin(Bx-C) + D on 2 functions for comparison also h(x) = sine + cosine
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- 18 7.3
- 7.3 Trigonometric Functions of any angle -- Unit Circle, pg. 604
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- 19 8.1,8.2
- 8.1 Graphs of the Sine and Cosine Functions, pg. 642
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- 8.2 Graphs of the Other Trigonometric Functions, pg. 659
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jig1.xls -- UNIT CIRCLE JIG SAW PUZZLE
sine.xls
- Graphs y=Asin(Bx-C) +D, where A, B, C, D are input values.
- Scatter-Plots y=Atan(Bx-C)+D, where A, B, C, D are input values.
- Graphs two sine functions where A, B, C, D are input values.
- Graphs one sine function and one cosine function where where A, B, C, D are input values.
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- 20 8.3
- 8.3 Inverse Trigonometric Functions & Their Applications, pg. 677
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- 21 9.1
- 9.1 Using, Solving, and Verifying Trigonometric Identities, pg. 696
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- 22 9.5
- 9.5 Solving Trigonometric Equations, pg. 739
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solvtrg.xls
- Solve a right triangle.
- Solve a 45-45-90 triangle.
Input leg a. Seek a leg and hypotenuse.
Input side c. Seek two legs.
- Solve a 30-60-90 triangle.
Input leg a. Seek a leg and hypotenuse.
Input leg b. Seek a leg and hypotenuse.
Input side c. Seek the hypotenuse.
- Use Pythagorean Theorem and arithmetic and basic trig.
Input leg a and leg b. Seek the hypotenuse and the angles.
Input hypotenuse c and leg a. Seek a leg and the angles.
Input angle A and side a. Seek a leg, side, and hypotenuse.
- Solve any triangle.
Use the Sine Law, if a side and the opposite angle are given.
Input angles A , B, side a. Seek two sides and an angle.
Input angle A , side a, side b. Seek two angles and a side.
- Use the Law of Cosines.
Input sides a, b, c. Seek each angle.
Input angle A , sides b,c. Seek no solution, 1 solution, or 2 solutions.
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- 23 9.2,9.3,9.4
- 9.2 Sum and Difference Identities, pg. 706
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- 9.3 Double-Angle, Half-Angle, and Reduction Formulas, pg. 720
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- 9.4 Sum-to-Product and Product-to-Sum Formulas, pg. 732
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- 24 YELLOW -- NO SCHOOL!
- 24 GREEN -- 7.1-7.3, 8.1-8.3, 9.1-9.5 Review & Catch Up
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- 25 Twice 10.1, 10.2
- 10.1 Non-right Triangles: Law of Sines, pg. 762
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- 10.2 Non-right Triangles: Law of Cosines, pg. 776
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- 26 Test #4 (20% of course grade and covers sections 7.1-7.3, 8.1-8.3, 9.1-9.5, 10.1, 10.2)
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- 27 Review & Probable Course Grades
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- 28 Final Exam (20% of course grade and covers entire course)
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- 0 Calculator
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- calculator
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window
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ZOOM
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Calcu1: Change Mode, Store Number, Evaluate Expression .gif
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Calcu2: Zooming Feature .htm
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Calcu3: Calculator Solve (web page)
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Calcu4: Solve an Equation w/Solver .gif (image)
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Calcu5: Create a Program to Compute .gif
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Calcu6: Create CHEAT Program .gif
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Calcu7: Create SLOPE Program .gif
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Calcu8: Character & PRGM Menu .gif
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To better see the big picture of the kinds of solutions to a quadratic equation, see
"I Got Your Number". To learn of the evolution of numbers, read
"Imaginary Numbers Are Not Imaginary."
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COMPLEX NUMBER
-- solves all ax² + bx + c = 0, but, there are different kinds of answers (easily identified by the
discriminant). The kinds of answers are:
- a + bi, where a is not 0, b is not 0, where i² = -1
- a + bi, where a is 0, b is not 0, where i² = -1 -- These are pure
IMAGINARY
- a + bi, where a is not 0, b is 0, where i² = -1 -- These are pure
REAL NUMBER
-- solves x² - 4 = 0. There are two kinds of real numbers:
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IRRATIONAL
-- solves x² = 3, NON-FRACTIONS, a non-repeating, non-terminating decimal number
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RATIONAL
-- solves x² = 4, FRACTIONS, a repeating, terminating decimal number. There are two kinds of rational numbers:
- MIXED NUMBER - a rational number in which the
denominator DOES NOT evenly divides the
numerator
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INTEGER
-- solves x + 4 = 3, a number in which the denominatore DOES evenly divide the numerator, a whole number or the opposite of a whole number.
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WHOLE NUMBER
-- solves x + 4 = 4. The NATURAL NUMBERS and also ZERO.
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NATURAL NUMBER -- the COUNTING NUMBERS, solves x + 4 = 6
More Extra Stuff
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table -- build and edit a table of data
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pyth3.xls
- Examine Pythagorean Triangles -- triangles with "nice" sides, generated because:
If p > q,
then p and q may be used to generate the right triangle with
leg a = p2 - q2,
leg b = 2pq, and
hypotenuse c = p2 + q2.
Includes Heronian Triangles
Pythagorean Triples
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Heronian Triangles -- 2 right triangles butted up together and sharing a common side.
for all x, generate triples
for all even x, generate triples
Heronian triangles are a pair of right triangles with a "shared side."
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tiles.xls -- for the parent, teacher, professional educator contains ALL "manipulative graphics" and active hot cells.
© 2022, 2023, A. Azzolino |
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