STEM Readiness: Pre-Calculus Readiness - Functions/Algebra: Complex Numbers - Arithmetic, Modulus, Polar Form, De Moivre’s Theorem

Must?Know

• Prokaryotic cells range from 0.1–5.0 ?m in diameter; eukaryotic cells range from 10–100 ?m.
• Prokaryotic DNA is located in the nucleoid, a region without a membrane; eukaryotic 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 endosymbiosis.
• Prokaryotic cell walls contain peptidoglycan; exceptions include Archaea, which lack peptidoglycan and have pseudopeptidoglycan or other polymers.
• Plant cells have cell walls made of cellulose; fungal cells have 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 have internal membrane systems including the endoplasmic reticulum, Golgi apparatus, and lysosomes; prokaryotes do not.
• The nuclear envelope in eukaryotes is a double membrane with nuclear pores that regulate transport.
• Chromosomes in prokaryotes are typically a single, circular DNA molecule; eukaryotes have multiple linear chromosomes.
• Histone proteins associate with eukaryotic DNA to form chromatin; most prokaryotes lack histones (except some Archaea).
• Binary fission is the primary mode of reproduction in prokaryotes; eukaryotes undergo mitosis and meiosis.
• Flagella in prokaryotes are made of flagellin and rotate; eukaryotic flagella are made of microtubules (9+2 arrangement) and undulate.
• Plasmids are small, circular DNA molecules commonly found in prokaryotes; rare in eukaryotes.
• Eukaryotic organelles include mitochondria (ATP synthesis), lysosomes (hydrolysis), and peroxisomes (detoxification of hydrogen peroxide).
• Smooth ER synthesizes lipids and detoxifies drugs; rough ER has ribosomes and synthesizes proteins for secretion.
• The Golgi apparatus modifies, sorts, and packages proteins into vesicles for transport.
• Mitochondria have a double membrane, contain their own DNA, and replicate independently of the cell.
• Chloroplasts are found in plant and algal cells, contain chlorophyll, and perform photosynthesis.
• Red blood cells in mammals lack a nucleus and organelles, maximizing space for hemoglobin.
• Archaea are prokaryotes but share some molecular features with eukaryotes (e.g., RNA polymerase, histones).
• Endosymbiotic theory is supported by mitochondria and chloroplasts having circular DNA, 70S ribosomes, and double membranes.

Difficulty Level

Intermediate – expected foundational knowledge in first-semester biology, with emphasis on structural and functional comparisons.

Common Traps

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

Trap: Prokaryotes have no internal structure.
Fact: Prokaryotes have ribosomes, nucleoid, and sometimes inclusions or protein microcompartments, but lack membrane-bound organelles.

Trap: Cell walls are present in all prokaryotes.
Fact: Mycoplasma and related bacteria lack cell walls entirely.

Trap: Eukaryotic ribosomes are only 80S.
Fact: Mitochondria and chloroplasts contain 70S ribosomes, reflecting their bacterial ancestry.

Trap: The plasma membrane is structurally different in prokaryotes and eukaryotes.
Fact: Both have a phospholipid bilayer with embedded proteins; differences lie in lipid composition and sterols (e.g., cholesterol in animal membranes).

Practice MCQs

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 only found in eukaryotic cells.

Question: Which structure is found in plant cells but not in animal cells?
A) Lysosome
B) Plasma membrane
C) Chloroplast
D) Ribosome
Answer: C
Explanation: Chloroplasts are organelles for photosynthesis and are present in plants and algae, not animals.
Why the top distractor is wrong: A (lysosomes) are present in both plant and animal cells, though less prominent in plants.

Question: What is the sedimentation coefficient of ribosomes in mitochondria?
A) 50S
B) 70S
C) 80S
D) 90S
Answer: B
Explanation: Mitochondrial ribosomes are 70S, similar to bacterial ribosomes.
Why the top distractor is wrong: A (50S) is a subunit of the 70S ribosome, not the whole ribosome.

Question: Which of the following provides evidence for the endosymbiotic theory?
A) Presence of a nucleoid in bacteria
B) Eukaryotic cells are larger than prokaryotic cells
C) Mitochondria have circular DNA and 70S ribosomes
D) Prokaryotes reproduce by binary fission
Answer: C
Explanation: Mitochondria resemble bacteria in having circular DNA and 70S ribosomes, supporting bacterial origin.
Why the top distractor is wrong: A describes a standard prokaryotic feature but does not link to endosymbiosis.

Question: Which organism lacks a cell wall and is therefore resistant to penicillin?
A) Escherichia coli
B) Bacillus subtilis
C) Mycoplasma pneumoniae
D) Saccharomyces cerevisiae
Answer: C
Explanation: Mycoplasma lacks a cell wall and thus is unaffected by antibiotics that inhibit peptidoglycan synthesis.
Why the top distractor is wrong: A (E. coli) has a peptidoglycan cell wall and is typically susceptible to penicillin.

Question: Where is DNA located in a eukaryotic animal cell?
A) Nucleoid and mitochondria
B) Nucleus and mitochondria
C) Nucleus only
D) Cytoplasm and nucleus
Answer: B
Explanation: Eukaryotic nuclear DNA is in the nucleus; mitochondrial DNA is in the mitochondria.
Why the top distractor is wrong: A (nucleoid) is a prokaryotic structure, not found in animal cells.

Question: Which of the following is a component of fungal cell walls?
A) Cellulose
B) Peptidoglycan
C) Chitin
D) Lignin
Answer: C
Explanation: Fungi have cell walls composed primarily of chitin, a nitrogen-containing polysaccharide.
Why the top distractor is wrong: A (cellulose) is found in plant cell walls, not fungal.

Last?Minute Revision

• Prokaryotic cell size: 0.1–5.0 ?m
• Eukaryotic cell size: 10–100 ?m
• Prokaryotic ribosome = 70S (30S + 50S)
• Eukaryotic cytoplasmic ribosome = 80S (40S + 60S)
• Mitochondria and chloroplasts have 70S ribosomes
• Mitochondria have circular DNA – evidence of endosymbiosis
• Nuclear envelope has double membrane and nuclear pores
• Prokaryotes lack membrane-bound organelles
• DNA in prokaryotes is in the nucleoid (no membrane)
• Eukaryotes package DNA with histones into chromatin
• Peptidoglycan is in bacterial cell walls, not Archaea or eukaryotes
• Archaea lack peptidoglycan but may have pseudopeptidoglycan
• Mycoplasma has no cell wall – resistant to penicillin
• Red blood cells lack a nucleus and mitochondria
• Plant cell wall: cellulose
• Fungal cell wall: chitin
• Animal cells: no cell wall
• Flagellin = protein in prokaryotic flagella
• Eukaryotic flagella have 9+2 microtubule arrangement
• Plasmids = small circular DNA, common in bacteria
• Smooth ER: lipid synthesis, detoxification
• Rough ER: protein synthesis (with ribosomes)
• Golgi: modifies, sorts, packages proteins
• Endosymbiotic theory supported by: double membrane, 70S ribosomes, circular DNA in mitochondria/chloroplasts
• Verify from standard textbook: histone presence in some Archaea