STEM Readiness: Pre-Calculus Readiness - Mathematical Reasoning: Mathematical Induction - Base Case, Inductive Step, Applications

Must?Know (20–25 detailed bullets)

• Prokaryotic cells range from 0.1–5.0 ?m in diameter; eukaryotic cells range from 10–100 ?m.
• Prokaryotes include bacteria and archaea; eukaryotes include animals, plants, fungi, and protists.
• DNA in prokaryotes is located in the nucleoid, a region without a membrane; eukaryotes house DNA within a membrane-bound nucleus.
• Prokaryotes lack membrane-bound organelles; eukaryotes have endoplasmic reticulum, Golgi apparatus, mitochondria, and lysosomes.
• Ribosomes in prokaryotes are 70S (30S + 50S subunits); eukaryotic cytoplasmic ribosomes are 80S (40S + 60S).
• Mitochondria and chloroplasts in eukaryotes contain 70S ribosomes, similar to prokaryotes, supporting endosymbiotic theory.
• Prokaryotic cell walls typically contain peptidoglycan (e.g., Escherichia coli); archaea lack peptidoglycan but may have pseudopeptidoglycan.
• Plant cell walls are made of cellulose; fungal cell walls contain chitin; animal cells lack cell walls.
• Both prokaryotes and eukaryotes have a phospholipid bilayer plasma membrane with embedded proteins.
• Eukaryotes have internal membrane systems (nuclear envelope, ER, Golgi), forming compartments for specialized functions.
• Prokaryotes reproduce by binary fission; eukaryotes undergo mitosis and meiosis.
• Flagella in prokaryotes are made of flagellin and rotate; eukaryotic flagella are composed of microtubules (9+2 arrangement) and bend.
• Plasmids are small, circular DNA molecules commonly found in prokaryotes; rare in eukaryotes.
• Nuclear envelope in eukaryotes is double-membraned with nuclear pores regulating transport.
• Nucleolus within the nucleus is the site of ribosomal RNA synthesis and ribosome assembly.
• Mycoplasma species are bacteria without a cell wall, an exception among prokaryotes.
• Human red blood cells lack a nucleus and mitochondria in maturity, an exception among animal cells.
• Chloroplasts are eukaryotic organelles found in plants and algae, performing photosynthesis; absent in prokaryotes except in cyanobacteria (which are photosynthetic but lack chloroplasts).
• Cyanobacteria are prokaryotes that perform oxygenic photosynthesis using thylakoid membranes, not chloroplasts.
• Endosymbiotic theory is supported by mitochondria and chloroplasts having circular DNA, 70S ribosomes, and double membranes.
• Lysosomes are membrane-bound organelles in animal cells containing hydrolytic enzymes; absent in most plant cells (vacuoles perform similar function).
• Plant cells have a large central vacuole for turgor pressure and storage; animal cells have small or transient vacuoles.
• Intermediate filaments, microtubules, and actin filaments form the eukaryotic cytoskeleton; prokaryotes have analogous proteins (e.g., FtsZ, MreB) but no true cytoskeleton.
• Gram-positive bacteria have thick peptidoglycan and no outer membrane; Gram-negative have thin peptidoglycan and an outer membrane with lipopolysaccharide (LPS).
• Archaea lack peptidoglycan and have ether-linked lipids in their membranes, unlike ester-linked lipids in bacteria and eukaryotes.

Difficulty Level

Intermediate – requires distinguishing structural, genetic, and biochemical features across domains and recognizing exceptions.

Common Traps (3–5 factual traps)

Trap: All cells with cell walls have peptidoglycan – Fact: Only bacteria have peptidoglycan; plants (cellulose), fungi (chitin), and archaea (pseudopeptidoglycan or other) have different compositions.

Trap: Mitochondria are present in all eukaryotic cells – Fact: Mature human red blood cells lack mitochondria and generate ATP via glycolysis.

Trap: Prokaryotes have no internal membranes – Fact: Some prokaryotes (e.g., cyanobacteria) have thylakoid membranes; others have intracellular compartments like magnetosomes.

Trap: Ribosome size correlates with cell complexity – Fact: Mitochondria and chloroplasts have 70S ribosomes despite being in eukaryotic cells, due to prokaryotic ancestry.

Trap: The nucleus is the only site of DNA in eukaryotes – Fact: Mitochondria and chloroplasts contain their own DNA, separate from nuclear DNA.

Practice MCQs (5–7 questions)

Question: Which of the following is a feature shared by both prokaryotic and eukaryotic cells?
A) Membrane-bound nucleus
B) 80S ribosomes
C) Phospholipid bilayer plasma membrane
D) Mitochondria
Answer: C
Explanation: Both cell types have a phospholipid bilayer as the plasma membrane.
Why the top distractor is wrong: D (mitochondria) are present only in eukaryotes.

Question: A cell is observed to have a nucleus, mitochondria, and a cell wall made of cellulose. From which organism is this cell most likely derived?
A) Fungus
B) Bacterium
C) Animal
D) Plant
Answer: D
Explanation: Cellulose cell walls and chloroplasts (implied by context) are characteristic of plant cells.
Why the top distractor is wrong: A (fungus) has a chitin cell wall, not cellulose.

Question: Which structure is evidence supporting the endosymbiotic theory?
A) 80S ribosomes in the cytoplasm
B) Linear chromosomes in the nucleus
C) 70S ribosomes in mitochondria
D) Nuclear envelope with pores
Answer: C
Explanation: Mitochondria having 70S ribosomes, like prokaryotes, supports their bacterial origin.
Why the top distractor is wrong: A describes eukaryotic cytoplasmic ribosomes, not unique to endosymbiosis.

Question: Which of the following cells lacks a nucleus?
A) Yeast cell
B) Human neuron
C) Escherichia coli
D) Onion root cell
Answer: C
Explanation: E. coli is a prokaryote and lacks a membrane-bound nucleus.
Why the top distractor is wrong: A (yeast) is a eukaryotic fungus and has a nucleus.

Question: What distinguishes the flagellum of a eukaryotic cell from that of a prokaryotic cell?
A) Presence of flagellin protein
B) Rotational movement mechanism
C) 9+2 microtubule arrangement
D) Attachment to the cell wall
Answer: C
Explanation: Eukaryotic flagella have a 9+2 arrangement of microtubules; prokaryotic flagella are made of flagellin and lack microtubules.
Why the top distractor is wrong: A and B describe prokaryotic flagella, not eukaryotic.

Question: Which of the following is true of the nucleoid?
A) It is surrounded by a double membrane
B) It contains linear chromosomes
C) It is found in prokaryotic cells
D) It houses ribosomal RNA genes
Answer: C
Explanation: The nucleoid is an unenclosed region in prokaryotes containing circular DNA.
Why the top distractor is wrong: A describes the eukaryotic nucleus, not the nucleoid.

Question: Which organism lacks a cell wall entirely?
A) Staphylococcus aureus
B) Saccharomyces cerevisiae
C) Mycoplasma pneumoniae
D) Arabidopsis thaliana
Answer: C
Explanation: Mycoplasma is a bacterium without a cell wall, an exception among prokaryotes.
Why the top distractor is wrong: A is Gram-positive with thick peptidoglycan; B and D have cell walls (chitin, cellulose).

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

• Prokaryotic cell size: 0.1–5.0 ?m; eukaryotic: 10–100 ?m.
• Prokaryotes have nucleoid; eukaryotes have nucleus with nuclear envelope.
• Prokaryotic ribosome = 70S; eukaryotic cytoplasmic ribosome = 80S.
• Mitochondria and chloroplasts have 70S ribosomes and circular DNA – evidence of endosymbiosis.
• Bacteria: peptidoglycan cell wall; Archaea: no peptidoglycan, ether-linked lipids.
• Plant cell wall = cellulose; fungal = chitin; animal = no cell wall.
• Both domains have phospholipid bilayer plasma membrane.
• Eukaryotes have internal membranes (ER, Golgi, nucleus); prokaryotes generally do not.
• Mycoplasma – only bacteria without cell wall.
• Mature human red blood cells lack nucleus and mitochondria.
• Prokaryotes divide by binary fission; eukaryotes by mitosis/meiosis.
• Eukaryotic flagellum: 9+2 microtubule array; prokaryotic: flagellin, rotary motion.
• Plasmids: common in prokaryotes, rare in eukaryotes.
• Nuclear pores regulate RNA and protein transport across nuclear envelope.
• Nucleolus = site of rRNA synthesis and ribosome subunit assembly.
• Lysosomes: hydrolytic enzymes, found in animal cells, not typical in plants.
• Plant vacuole: large central, maintains turgor; animal vacuoles: small, temporary.
• Cytoskeleton: microtubules, actin, intermediate filaments – eukaryote-specific.
• Prokaryotic cytoskeletal analogs: FtsZ (tubulin-like), MreB (actin-like).
• Cyanobacteria perform photosynthesis but lack chloroplasts – use thylakoid membranes.
• Gram-positive: thick peptidoglycan, no outer membrane; Gram-negative: thin peptidoglycan, LPS outer membrane.
• Archaea membrane lipids: ether linkages, branched hydrocarbons.
• Endosymbiotic theory: mitochondria from alpha-proteobacteria, chloroplasts from cyanobacteria.
• Mitochondrial DNA is circular, like bacterial chromosomes.
• Verify from standard textbook: exact lipid composition in archaeal membranes varies by species.