The Academy for
MATHEMATICS, SCIENCE AND ENGINEERING
UNIT #1
FUNCTIONS [Chapter 1-2]
OBJECTIVES - the student will:
1.
2.
3.
4.
5.
6.
7.
8.
Analyze graphs of functions, their domains, find the asymptotes and symmetry.
Identify and graph transformations of functions.
Find arithmetic combinations and compositions of functions.
Find inverse functions graphically and algebraically.
Use synthetic division to divide polynomials by other polynomials.
Determine the numbers and type of zeros of polynomial functions, and find the zeros.
Perform operations with complex numbers and plot complex numbers in the complex plane.
Classify scatter plots and use a graphing utility to find models for data.
PROFICIENCIES: #
NJDOE Mathematical Standards: 4.1A, B, 4.2B, C, 4.3A, B, C, D, 4.4A, 4.5A, B, C, D, E, F
METHOD/ACTIVITIES
Day 1: Do Now: Functional Transformations Calisthenics
Review relations/functions, VLT, one-to-one correspondence, domain/range
KKK Journal: Families of functions
Descriptions of functions: Continuous/discontinuous (removable/asymptote/jump),
incr./decr./constant, min./max., end behavior, odd/even [alg/graph]
Practice: p.38, #1-4, 11-16, 50-58 even, 109
HW - P. 24, #1-4, 47-56, 59, 71,83, 85, 89-92 P. 39, #17-20, 47-61 odd, 84-87, 89-93
Day 2: Do Now: Functional Transformations Calisthenics – f(x) notation
Review: translations, reflections, stretches, periodic
Algebraic tests for symmetry: over x, over y, 180 rotational, over y=x
Practice P. 49, #20-26 even, 45-46
Combinations of functions [NCSSM 2.10-12, Foerster 5.4] and domain
Practice P.58, #4,-32 every 4th, 80
HW - P. 49, #39-44, 51, 63-71 odd, 72
P. 59, #35-43 odd, 51-57 odd, 65-71 odd,84-86
Day 3: Do Now: Functional Calisthenics – combinations
Inverse relations & functions: test graphically & algebraically
Derive algebraically
Relation vs. function: HLT, one-to-one correspondence
Correlation of scatter plots and least squares regression line
Practicep. P. 69, #21-24,
HW - P. 69, 25-49 every 4th, 67, 85-86
P. 82-84 optional
Day 4: Do Now: KKK Journal – polynomial graphs
Leading coefficient test, finding zeros, graphing polynomials
Review HW
Quiz 1
HW - P. 77, #3-6, 11, 17, 19-20
Read 2.1-2.6, write 3 questions
ASSESSMENT
Classwork:
Quiz/Test: Quiz ch1, Quiz ch2
Mar-16
The Academy for
MATHEMATICS, SCIENCE AND ENGINEERING
UNIT #1
FUNCTIONS [Chapter 1-2]
OBJECTIVES - the student will:
1.
2.
3.
4.
5.
6.
7.
8.
Analyze graphs of functions, their domains, find the asymptotes and symmetry.
Identify and graph transformations of functions.
Find arithmetic combinations and compositions of functions.
Find inverse functions graphically and algebraically.
Use synthetic division to divide polynomials by other polynomials.
Determine the numbers and type of zeros of polynomial functions, and find the zeros.
Perform operations with complex numbers and plot complex numbers in the complex plane.
Classify scatter plots and use a graphing utility to find models for data.
METHOD/ACTIVITIES
Day 5: Do Now: given roots, find the quadratic [discover sum=-b/a, product=c/a]
Review HW. Review questions from sections 1 to 6
Remainder Th./Factor Th./Rational Root Th.
Apply Descartes’s Rule of Signs and Upper & Lower Bound Rules
Practice P. 108, #1-8, 54, 66 P. 123, #8, 26, 44, 50
HW - P. 109, #27-71 every 4th, 93-98
P.123, #1,25-65 every 4th, 86-87
Day 6: Do Now: add, subtract, mult. and divide complex numbers
Review HW
Mandelbrot Set with recursive functions and complex numbers
Complex zeros of polynomials
Practice P. 140, #5-8, 40, 48
HW - P. 133, #25-69 every 4th
P. 140, #27-55 every 4th, 59-61
Day 7: Do Now: P.148, #7-12
Finding vertical and horizontal asymptotes
Review HW
Graphing rational functions: asymptotes, y-int., zeros, sign analysis, slant asymptotes
Practice DWFK p. 240-243
HW - P. 149, #22-23, 31-35, 43-46
P. 157, #9-25 every 4th, 37-42, 43-49 odd,
59, 63, 70, 73-78
Day 8: Quiz 2
Can do calculus: “Instantaneous Rate of Change”
Ch. 1 & 2 Review DWFK
Review trigonometry
HW - P. 170, #51, 53, 75-79 odd, 95-99 odd, 117-133, ev.4th, 142-146
Day 9: Do Now: trig value chart
Review HW
Unit 1 Test
HW - P. 335, #75-87 ev. 4th, 99-117 ev. 4th, 121, 141-146
ASSESSMENT
Classwork:
Quiz/Test: Quiz ch2, Test 1-2
Mar-16