MA61 PRECALCULUS (FOR BIOLOGY MAJORS)
Preliminary Course Content
(Subject to change as semester progresses)
Week 1:
Introduce the course – handout on BIO 2010 and other related handouts – introduce course web site and
process for the course – talk about modeling and graphing with Excel
NOTE: We will focus less on basic algebraic manipulation skills than a traditional MA61 course (you
may need to practice these skills separately and we will give you some guidance here), but you will have
a better understanding of how to apply the mathematics and you will also receive additional
reinforcement of the biological concepts in BY50 through the mathematics taught.
Overview of the scientific process:
 Collect data (measure)
 Organize data (formulas, tables, and graphs)
 Analyze/Understand/Predict (use mathematical functions to try and understand the process or
phenomenon your are observing) – making a model with functions
Mathematical Topics:
 Types of measurement: Length, area, volume (solid and liquid), temperature, time, mass/weight
(grams, Dalton’s, moles), rates of change and energy (joules, calories etc)
 Units of measurement: English and metric
 Working with standard geometric and temperature formulas
 Ratios & proportions: example Rf (Retardation factor) formula:
Rf = [distance run by pigment (distance from pencil dot to top end of pigment)]/[distance
run by solvent (should be distance between the two pencil lines)] The analytes that are
highly water-soluble or have the greatest hydrogen-bonding capacity move slower along
the paper, while less polar compounds will travel faster with the solvent.The degree of
retention of a component is called the retardation factor (Rf) retardation factor (in planar
chromatography), RF Ratio of the distance traveled by the center of the spot to the
distance simultaneously traveled by the mobile phase: RF = b/a. By definition the RF
values are always less than unity. They are usually given to two decimal places. In order
to simplify this presentation the hRF values may be used: they correspond to the RF
values multiplied by 100. Ideally, RF values are identical to the R-values used in column
chromatography.
 Scientific notation: example pH Scale
 Roots, exponents and logarithms
Use BIOMATH, Problem Solving for Biology Students by Keck & Patterson for some problems and
examples.
Biological Topics:
 Laboratory tools and techniques
 Themes in the study of life
o Life’s hierarchical order (DNA, cells, organisms and regulatory mechanisms)
o Evolution, unity and diversity
o Science as a process
 Malthus’s Essay on the Principle of Population – Geometric vs. arithmetic progressions (R&J
p11)
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Week 2
Mathematical Topics:
 Introduction to Functions (1.1-1.4 in textbook)
 Introduction to families of functions (2.1)
 Linear functions (2.2)
 Linear functions and data (2.3)
 Introduction to Excel
Biological Topics:
 Chemical context of life
o Chemical elements and compounds
o Atoms and molecules
 Water and the fitness of the environment
o Effects of water’s polarity
o Dissociation of water molecules
 Biomolecules I
o Carbohydrates: Benedict’s test for reducing sugars, IKI test for starch
o Lipids: Plasma membrane, Golgi complex
o Proteins
o Nucleic acids
Week 3
Mathematical Topics:
 Exponential growth functions (2.4)
 Exponential decay functions (2.5)
 Modeling with functions: Data collection and analysis
 More training with Excel
Biological Topics:
 Carbon and the molecular diversity of
life
o The importance of carbon
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o Functional elements (molecules
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of life)
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 The structure and function of
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macromolecules
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o Polymer principles
o Carbohydrates – Fuel and
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building material
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o Lipids – Diverse hydrophobic
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molecules
o Proteins – The molecular tools of

the cell
o Nucleic acids – Informational
polymers
How molecules “fit” together
Distinguish amino acids from proteins
Structure of polypeptides
Catalyst and enzyme
Exergonic vs. energonic reactions R&J
p158
Hydrolysis versus denaturation
Chromatography
The effect of temperature on the activity
of an enzyme
Enzyme sensitivity to environment
(temp & pH) – R&J p152
Week 4
Mathematical Topics:
TEST 1
 Logarithmic functions (2.6)
 Log – linear plot
 Power functions (2.7)
Biological Topics:
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Metabolism
o Metabolism, energy and life
o Enzymes
o The control of metabolism
RNA and DNA
Standard curves
Structure of DNA
Week 5
Mathematical Topics:
 Comparing rates of growth and decay (2.8)
 Inverse functions (2.9)
 Modeling with functions: Data collection and analysis
Biological Topics:
 The cell
o How we study cells
o View of cells
o Nucleus and ribosomes
o Endomembrane system
o Membraneous organelles
 Origin of species
o What is a species
o Modes of speciation
o Origin of evolutionary novelty
 Enzymes
 Product formation as a function of substrate concentration, pH, and temperature
 Enzyme saturation
 Gibbs free energy (pg 87): ratios, logarithms and exponents
Cell structure and function (size)
Surface area-to-volume ratio (R& J p 81)
 Cell theory
 Autotrophy, heterotroph, prokaryotic, eukaryotic cells
Week 6
Mathematical Topics:
 Linear regression analysis (3.2)
 Modeling with functions: Data collection and analysis
Biological Topics:
 Membrane structure and function
o Membrane structure
o Traffic across membranes
 Cell structure and function (size)
 Cell transport mechanisms
 Diffusion through a cell membrane: rates of change, linear and hyperbolic equations
 Kingdoms
 Golgi bodies
Week 7
Mathematical Topics:
 Fitting nonlinear functions to data (3.3)
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How to fit logarithmic and exponential functions to data (3.4)
 How to fit power functions to data (3.5)
 Modeling with functions: Data collection and analysis
Biological Topics:
 Eukaryotic cell structure
 Cell structure and function (size)
 Cell surfaces and junctions
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Week 8
Mathematical Topics:
TEST 2
 The tangent of an angle (6.1)
 Sine and cosine of an angle (6.2)
Biological Topics:
 Photosynthesis (trig functions)
o Photosynthesis in nature
o Pathways of photosynthesis
o Calvin cycle
o Structure of chlorophyll
o Electromagnetic spectrum
o Absorption spectrum
o ATP and NADPH
 Chromatography of photosynthetic pigments
 Purification of photosynthetic pigments
 Role of chloroplast and its membrane
 Autotrophic
 Mesophyl
Week 9
Mathematical Topics:
 Sine, cosine and tangent in general (6.3)
 Relationships among trigonometric functions (6.4)
 Introduction to sine and cosine functions (7.1)
Biological Topics:
 Cellular respiration
o Principles of energy harvest
o Process of cellular respiration
o Related metabolic processes
 Redox reactions
 Electron transport chains
 ATP
 NAD
 Glycolysis
 Krebs cycle
 Chemiosmosis
 Catabolism
 Feedback mechanisms control cellular respiration
 Effects of inhibitors on cellular response, lab results for graphing
 How pH affects rate of cellular respiration, lab results for graphing
 Dehydrogenation
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Week 10
Mathematical Topics:
 Modeling periodic behavior with sine and cosine functions (7.2)
 Solving equations with sine and cosine functions: The inverse functions (7.3)
 Modeling with functions: Data collection and analysis
Biological Topics:
 Cell reproduction
 Key roles of cell division
 Mitosis and cell cycle
 Mitotic cell cycle
 Cell division (lab)
 Regulation of the cell cycle
 Diploid, haploid, zygote and gamete
 Eukaryotic chromosomes
 Difference in arrangement of genetic
 Cytokinesis
material in prokaryotic and eukaryotic cells
 Bacterial dell division (binary fission)
 Standard curve
 Cancer cells escaped from cell-controls
 Population growth (doubling time), data for
 Growth of cancer
graphing
Week 11
Mathematical Topics:
TEST 3
 Linear models with several variables (3.7)
 Chi – square test
 Modeling with functions: Data collection and analysis
Biological Topics:
 Meiosis and sexual reproduction
o Introduction to heredity
o Role of meiosis in sexual life cycles
o Origins of genetic variation
 Genetics (lab): lab results for Chi-square test
 Genetic ratios
 Monohybrid cross
 Dominant and recessive
 Phenotypic ratio
 Genotype
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PTC – tasting
Gene frequencies and pool
Homologous chromosomes
Autosomes
Karyotype
Diploid and haploid cells
Mendelian patterns of inheritance
o Mendel’s discoveries
o Extending mendelian genetics
o Mendelian inheritance in humans
Week 12
Mathematical Topics:
 Introduction to polynomial functions (4.1)
 Behavior of polynomial functions (4.2)
 Modeling with polynomial functions (4.3)
Biological Topics:
 Chromosomal basis of inheritance
o Meselson-Stahl experiment
o Relating Mendelism to chromosomes
o Role of enzymes
o Sex chromosomes
o Telomerase
o Error and exceptions in
 From gene to protein
chromosomal inheritance
o Connection between genes and
 Molecular basis of inheritance
proteins
o DNA as genetic material
o Synthesis and processing of RNA
o DNA replication and repair
o Synthesis of proteins
o Hershey-Chase experiment
 DNA structure
 DNA replication
 Base pairs
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Codon
Complementary
Double helix
Genetic code
Mutation
Nitrogenous bases
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Nucleic acids
Nucleotide
Pairing rules
Replication
Transcription
Translation
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Phenotypes
Protein electrophoresis
-Globin gene
Week 13:
Mathematical Topics:
 Roots of polynomial equations (4.4)
 Building new functions from old: operations on functions (4.6)
 Building new functions from old: shifting, stretching and shrinking (4.7)
 Using shifting and stretching to analyze data (4.8)
Biological Topics:
 Evolution
 Gene
 Allele
 Mutation
 Natural selection
 Variation of allele, Hardy-Weinberg Equilibrium
 Population biology
Week 14
Mathematical Topics:
 Modeling with functions: Data collection and analysis
Biological Topics:
 Molecular basis of inheritance
 Gene expression – the genetic control of protein structure
Week 15
Mathematical Topics:
TEST 4
FINAL EXAM
 Modeling with functions: Data collection and analysis
Biological Topics:
 Natural selection and evolution
NEED TO ADD:
Systems of equations
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