STEM Readiness: Pre-Calculus Readiness - Functions/Algebra: Polynomial Zeros - Factor Theorem, Rational Root Theorem, Multiplicity

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 lack a membrane-bound nucleus; DNA is located in the nucleoid region.
• Eukaryotes have a true nucleus enclosed by a double membrane (nuclear envelope).
• Prokaryotic DNA is typically a single, circular chromosome; eukaryotic DNA is linear and organized into multiple chromosomes.
• Prokaryotes have 70S ribosomes (30S + 50S subunits); eukaryotes have 80S ribosomes (40S + 60S subunits).
• Mitochondria and chloroplasts in eukaryotes contain 70S ribosomes, supporting endosymbiotic origin.
• Bacteria have peptidoglycan in their cell walls; archaea lack peptidoglycan but may have pseudopeptidoglycan.
• Plant cells have cellulose in their cell walls; fungal cells have chitin.
• Animal cells lack a cell wall entirely.
• Both prokaryotes and eukaryotes have a phospholipid bilayer plasma membrane.
• Eukaryotes have internal membrane systems (endoplasmic reticulum, Golgi, lysosomes); prokaryotes do not.
• Eukaryotes possess mitochondria for aerobic respiration; prokaryotes perform respiration at the plasma membrane.
• Chloroplasts are found only in photosynthetic eukaryotes (plants, algae); absent in prokaryotes except cyanobacteria (which have thylakoid membranes but no organelles).
• Cyanobacteria are prokaryotes capable of oxygenic photosynthesis using thylakoid membranes, not chloroplasts.
• Endoplasmic reticulum (ER) is a eukaryotic organelle: rough ER has ribosomes; smooth ER synthesizes lipids and detoxifies.
• Golgi apparatus modifies, sorts, and packages proteins for secretion or delivery; absent in prokaryotes.
• Lysosomes contain hydrolytic enzymes for degradation; found only in animal eukaryotic cells.
• Vacuoles in plant cells are large and central; in animal cells, vacuoles are small or absent.
• Nuclear pores regulate transport between nucleus and cytoplasm in eukaryotes; nucleoid in prokaryotes has no such control.
• Mycoplasma species are bacteria without a cell wall; resistant to penicillin.
• Human red blood cells lack a nucleus and mitochondria, maximizing hemoglobin capacity.
• Archaea are prokaryotes but share some molecular features with eukaryotes (e.g., RNA polymerase).
• Flagella in prokaryotes are made of flagellin and rotate; in eukaryotes, they are made of microtubules (9+2) and undulate.
• Endosymbiotic theory is supported by mitochondria and chloroplasts having their own circular DNA, 70S ribosomes, and double membranes.
• Plasmids are small, circular DNA molecules found in many prokaryotes; also present in some eukaryotes (e.g., yeast 2-micron plasmid).

Difficulty Level

Intermediate – requires distinguishing structural and functional differences across domains and organelles, with several exceptions and overlapping features.

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 (no peptidoglycan) differ.
Trap: Prokaryotes have no DNA protection – Fact: Prokaryotic DNA is condensed via nucleoid-associated proteins, not histones (except some archaea).
Trap: Mitochondria are found in all eukaryotic cells – Fact: Some eukaryotic cells lack mitochondria (e.g., Giardia, a diplomonad with mitosomes).
Trap: Ribosome size correlates with cell complexity – Fact: Mitochondria and chloroplasts have 70S ribosomes despite being in eukaryotic cells.
Trap: Eukaryotes evolved from archaea – Fact: Current evidence suggests eukaryotes share a common ancestor with archaea but are a distinct domain.

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. This cell is most likely from a:
A) Fungus
B) Bacterium
C) Plant
D) Animal
Answer: C
Explanation: Cellulose cell walls and mitochondria with a nucleus are characteristic of plant cells.
Why the top distractor is wrong: A (fungi) have chitin in cell walls, not cellulose.

Question: Which structure is found in prokaryotes but not in eukaryotes?
A) Nucleoid
B) Nucleolus
C) Golgi apparatus
D) Endoplasmic reticulum
Answer: A
Explanation: The nucleoid is the region where prokaryotic DNA is located, lacking a membrane.
Why the top distractor is wrong: B (nucleolus) is present in the eukaryotic nucleus and involved in ribosome assembly.

Question: Which of the following provides evidence for the endosymbiotic theory?
A) Eukaryotic cells have linear DNA
B) Mitochondria have 70S ribosomes and circular DNA
C) Prokaryotes lack a nucleus
D) Lysosomes contain digestive enzymes
Answer: B
Explanation: Mitochondria resemble bacteria in ribosome type and genome structure, supporting bacterial origin.
Why the top distractor is wrong: A is a general eukaryotic feature but not evidence for endosymbiosis.

Question: Which organism lacks a cell wall and a nucleus?
A) Escherichia coli
B) Saccharomyces cerevisiae
C) Mycoplasma pneumoniae
D) Human red blood cell
Answer: D
Explanation: Human red blood cells lack both a nucleus and a cell wall.
Why the top distractor is wrong: C lacks a cell wall but is a prokaryote with a nucleoid (has DNA region).

Question: Where are 70S ribosomes found in eukaryotic cells?
A) Cytosol
B) Nucleus
C) Mitochondria
D) Golgi apparatus
Answer: C
Explanation: Mitochondria contain 70S ribosomes, similar to prokaryotes.
Why the top distractor is wrong: A (cytosol) contains 80S ribosomes in eukaryotes.

Question: Which of the following is NOT a function of the smooth endoplasmic reticulum?
A) Lipid synthesis
B) Protein synthesis
C) Detoxification of drugs
D) Calcium ion storage
Answer: B
Explanation: Protein synthesis occurs on the rough ER, not the smooth ER.
Why the top distractor is wrong: A is a primary function of the smooth ER.

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

• Prokaryotic cell size: 0.1–5.0 ?m; eukaryotic: 10–100 ?m.
• Prokaryotes have nucleoid; eukaryotes have membrane-bound nucleus.
• Prokaryotic ribosome = 70S; eukaryotic cytoplasmic ribosome = 80S.
• Mitochondria and chloroplasts have 70S ribosomes and circular DNA.
• Bacterial cell walls contain peptidoglycan; archaeal walls do not.
• Plant cell walls: cellulose; fungal: chitin; animal: no cell wall.
• Both cell types have phospholipid bilayer plasma membranes.
• Eukaryotes have internal membranes (ER, Golgi, lysosomes); prokaryotes do not.
• Rough ER has ribosomes; smooth ER makes lipids and stores Ca²?.
• Golgi apparatus modifies and packages proteins; absent in prokaryotes.
• Lysosomes are in animal cells; plant vacuoles can have degradative functions.
• Human red blood cells lack nucleus and mitochondria.
• Mycoplasma has no cell wall – smallest known cells.
• Cyanobacteria perform photosynthesis without chloroplasts.
• Nuclear pores regulate RNA and protein transport in eukaryotes.
• Flagellin = prokaryotic flagella protein; microtubules (9+2) = eukaryotic.
• Endosymbiotic theory evidence: organelle circular DNA, 70S ribosomes, double membranes.
• Plasmids are small circular DNA; common in bacteria, rare in eukaryotes.
• Archaea are prokaryotes but share transcription machinery with eukaryotes.
• Giardia lacks mitochondria but is a eukaryote (has mitosomes).
• Chloroplasts found in plants and algae; not in prokaryotes as organelles.
• Nuclear envelope is double membrane with pores; nucleoid has no membrane.
• Histones package DNA in eukaryotes and some archaea; bacteria use different proteins.
• Cristae are folds in mitochondrial inner membrane; increase surface area.
• Verify from standard textbook: exact composition of archaeal cell walls varies widely.