STEM Readiness: Pre-Calculus Readiness - Exponentials/Logs: Logarithm Properties - Product, Quotient, Power Rules, Proof and Application

Must?Know (20–25 detailed bullets)

• Prokaryotic cells range from 0.1–5.0 ?m in diameter; eukaryotic cells range from 10–100 ?m.
• DNA in prokaryotes is located in the nucleoid, a region without a membrane; in eukaryotes, DNA is enclosed within a membrane-bound nucleus.
• Prokaryotes have 70S ribosomes (30S + 50S subunits); eukaryotes have 80S ribosomes (40S + 60S subunits).
• Mitochondria and chloroplasts contain 70S ribosomes, supporting their origin via endosymbiotic theory.
• Prokaryotic cell walls typically contain peptidoglycan; archaea lack peptidoglycan and have different wall chemistry.
• Plant cell walls are composed of cellulose; fungal cell walls contain chitin; animal cells lack a cell wall.
• Mycoplasma, a bacterium, lacks a cell wall and is resistant to antibiotics targeting peptidoglycan synthesis.
• Both prokaryotes and eukaryotes have a phospholipid bilayer plasma membrane with embedded proteins.
• Eukaryotes possess membrane-bound organelles (e.g., nucleus, mitochondria, lysosomes); prokaryotes do not.
• Bacteria (e.g., Escherichia coli) and archaea (e.g., Methanogens) are prokaryotes; animals, plants, fungi, and protists are eukaryotes.
• Red blood cells in mammals lack a nucleus at maturity, limiting their lifespan and preventing division.
• Mitochondria have double membranes, circular DNA, and replicate independently of the cell cycle.
• Chloroplasts are found in plants and algae, have double membranes, circular DNA, and perform photosynthesis.
• The endoplasmic reticulum (ER) is a network of membranes: rough ER has ribosomes; smooth ER synthesizes lipids and detoxifies.
• The Golgi apparatus modifies, sorts, and packages proteins for secretion or delivery to other organelles.
• Lysosomes contain hydrolytic enzymes for intracellular digestion; absent in most plant cells.
• Peroxisomes break down fatty acids and detoxify hydrogen peroxide; present in both plant and animal cells.
• Cytoskeleton components (microtubules, microfilaments, intermediate filaments) maintain cell shape and enable transport; more complex in eukaryotes.
• Flagella differ structurally: prokaryotic flagella are made of flagellin and rotate; eukaryotic flagella are made of microtubules (9+2 arrangement) and undulate.
• Pili (or fimbriae) are present in some prokaryotes for attachment and conjugation; absent in eukaryotes.
• Nuclear envelope in eukaryotes is a double membrane with nuclear pores regulating transport between nucleus and cytoplasm.
• Nucleolus within the nucleus is the site of ribosomal RNA synthesis and ribosome subunit assembly.
• Plasmids are small, circular DNA molecules found in prokaryotes and some yeasts (eukaryote exception); often carry antibiotic resistance genes.
• Plant cells have large central vacuoles for storage and turgor pressure; animal cells have smaller, multiple vacuoles.
• Chloroplasts and mitochondria replicate by binary fission, similar to prokaryotes, supporting endosymbiotic theory.

Difficulty Level

Intermediate – requires precise differentiation of structural and functional features across domains and organelles.

Common Traps (3–5 factual traps)

Trap: All cells with a nucleus are eukaryotic, so any cell without one must be prokaryotic – Fact: Mature mammalian red blood cells lack a nucleus but are eukaryotic; absence of nucleus does not imply prokaryotic status.

Trap: Ribosome size is the same across all organelles in eukaryotes – Fact: Mitochondria and chloroplasts have 70S ribosomes, unlike the 80S ribosomes in the eukaryotic cytoplasm.

Trap: Cell walls are present in all non-animal cells – Fact: Mycoplasma (bacteria) lack a cell wall, and some eukaryotic cells (e.g., protozoa) also lack walls despite not being animals.

Trap: Prokaryotes have no internal membranes – Fact: Some prokaryotes (e.g., cyanobacteria) have thylakoid membranes for photosynthesis, though not enclosed in organelles.

Practice MCQs (5–7 questions)

Question: Which of the following is a defining feature of eukaryotic cells but absent in prokaryotes?
A) Plasma membrane
B) Ribosomes
C) Circular DNA
D) Membrane-bound nucleus
Answer: D
Explanation: A membrane-bound nucleus is exclusive to eukaryotes.
Why the top distractor is wrong: Circular DNA is found in prokaryotes and also in mitochondria and chloroplasts of eukaryotes.

Question: A cell is observed to have a cell wall made of cellulose, chloroplasts, and a large central vacuole. It is most likely:
A) Fungal cell
B) Animal cell
C) Bacterial cell
D) Plant cell
Answer: D
Explanation: Cellulose cell wall, chloroplasts, and central vacuole are characteristic of plant cells.
Why the top distractor is wrong: Fungal cells have chitin in their walls and lack chloroplasts.

Question: Which structure is found in both prokaryotes and eukaryotes?
A) Mitochondria
B) 80S ribosomes
C) Phospholipid bilayer membrane
D) Golgi apparatus
Answer: C
Explanation: Both cell types have a plasma membrane composed of a phospholipid bilayer.
Why the top distractor is wrong: 80S ribosomes are only in eukaryotic cytoplasm; prokaryotes have 70S.

Question: Which of the following provides the strongest evidence for the endosymbiotic theory?
A) Mitochondria have double membranes and divide by binary fission
B) Lysosomes contain digestive enzymes
C) The nucleus contains linear chromosomes
D) The Golgi apparatus modifies proteins
Answer: A
Explanation: Mitochondria’s double membrane, circular DNA, and binary fission resemble bacteria.
Why the top distractor is wrong: Lysosome function is unrelated to bacterial ancestry.

Question: What is the sedimentation coefficient of cytoplasmic ribosomes in human liver cells?
A) 50S
B) 70S
C) 80S
D) 30S
Answer: C
Explanation: Eukaryotic cytoplasmic ribosomes are 80S.
Why the top distractor is wrong: 70S ribosomes are found in prokaryotes and in mitochondria, not in eukaryotic cytoplasm.

Last?Minute Revision (20–25 one?liners)

• Prokaryotic cell size: 0.1–5.0 ?m; eukaryotic: 10–100 ?m.
• Prokaryotes lack a membrane-bound nucleus; DNA in nucleoid.
• Eukaryotes have 80S ribosomes; prokaryotes have 70S.
• Mitochondria and chloroplasts have 70S ribosomes and circular DNA.
• Prokaryotic cell wall contains peptidoglycan; exceptions: Mycoplasma (no wall).
• Plant cell wall = cellulose; fungal = chitin; animal = no cell wall.
• Both domains have phospholipid bilayer plasma membranes.
• Eukaryotes have internal membranes (ER, Golgi, etc.); prokaryotes generally do not.
• Endosymbiotic theory supported by mitochondrial/chloroplast binary fission, double membranes, and 70S ribosomes.
• Bacteria and archaea are prokaryotes; archaea lack peptidoglycan.
• Red blood cells are eukaryotic but lack a nucleus when mature.
• Nuclear envelope has nuclear pores for RNA/protein transport.
• Nucleolus synthesizes rRNA and assembles ribosomal subunits.
• Rough ER has ribosomes; smooth ER makes lipids and detoxifies.
• Golgi apparatus modifies and packages proteins in vesicles.
• Lysosomes contain hydrolytic enzymes; absent in most plant cells.
• Peroxisomes break down fatty acids and neutralize H?O?.
• Cytoskeleton includes microtubules, actin filaments, intermediate filaments.
• Prokaryotic flagellum = flagellin, rotates; eukaryotic = microtubules (9+2), bends.
• Pili (fimbriae) in prokaryotes aid in attachment and conjugation.
• Plasmids = small circular DNA; common in bacteria, rare in eukaryotes (e.g., yeast).
• Plant cells have large central vacuole; animal cells have small vesicles.
• Chloroplasts perform photosynthesis; found in plants and algae.
• Mitochondria generate ATP via cellular respiration in eukaryotes.
• Some prokaryotes (e.g., cyanobacteria) have thylakoid membranes but no organelles.
• Verify from standard textbook: exact lipid composition of archaeal membranes.