STEM Readiness: Pre-Calculus Readiness - Trigonometry: Inverse Trig Functions - Domain Restrictions, arcsin/arccos/arctan Ranges

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 in eukaryotic cells contain 70S ribosomes, similar to prokaryotes.
• Peptidoglycan is present in bacterial cell walls; absent in archaea and eukaryotes.
• Archaea lack peptidoglycan but may have pseudopeptidoglycan or other wall components.
• Plant cells have cell walls made of cellulose; fungal cells have walls made of chitin.
• Animal cells lack a cell wall entirely.
• Both prokaryotes and eukaryotes have a phospholipid bilayer plasma membrane.
• Only eukaryotes have membrane-bound organelles such as the endoplasmic reticulum, Golgi apparatus, lysosomes, mitochondria, and nucleus.
• Bacteria (e.g., Escherichia coli) and archaea (e.g., Methanogens) are prokaryotes; animals, plants, fungi, and protists are eukaryotes.
• Mycoplasma species are bacteria that lack a cell wall; they are the smallest known cells (?0.2 ?m).
• Red blood cells in mammals lack a nucleus and most organelles at maturity.
• Mitochondria have circular DNA and double membranes, supporting endosymbiotic origin.
• Chloroplasts also have circular DNA, 70S ribosomes, and double membranes.
• The nuclear envelope in eukaryotes is a double membrane with nuclear pores that regulate transport.
• Nucleolus is inside the nucleus and is the site of ribosomal RNA synthesis and ribosome assembly.
• Endosymbiotic theory is supported by mitochondria and chloroplasts dividing via binary fission, independently of the host cell.
• Lysosomes are membrane-bound organelles in animal cells containing hydrolytic enzymes for degradation.
• Vacuoles in plant cells are large and central, maintaining turgor pressure; animal cells have small or temporary vacuoles.
• Peroxisomes contain enzymes for fatty acid oxidation and detoxification of hydrogen peroxide.
• Cytoskeleton elements (microtubules, microfilaments, intermediate filaments) are present in eukaryotes; prokaryotes have analogous proteins (e.g., FtsZ, MreB).
• Flagella in prokaryotes are made of flagellin and rotate; eukaryotic flagella are made of microtubules (9+2 arrangement) and undulate.
• Plasmodesmata in plant cells and gap junctions in animal cells allow intercellular communication.

Difficulty Level

Intermediate – requires precise differentiation of structural and molecular features across domains and cell types.

Common Traps

• Trap: All cells with cell walls have peptidoglycan – Fact: Only bacteria have peptidoglycan; plants (cellulose), fungi (chitin), and archaea (no peptidoglycan) differ.
• Trap: Ribosome size is the same across all organisms – Fact: Prokaryotes have 70S ribosomes; eukaryotic cytoplasmic ribosomes are 80S; mitochondria and chloroplasts have 70S.
• Trap: The nucleus is the only organelle with a double membrane – Fact: Mitochondria and chloroplasts also have double membranes.
• Trap: Prokaryotes have no internal membrane structures – Fact: Some prokaryotes have protein-bound compartments (e.g., carboxysomes), but no membrane-bound organelles like eukaryotes.
• Trap: Eukaryotic cells are always larger and more complex than prokaryotic cells – Fact: While generally true, some giant bacteria (e.g., Thiomargarita namibiensis, up to 750 ?m) exceed typical eukaryotic size.

Practice MCQs

Question: Which of the following is a feature shared by both prokaryotic and eukaryotic cells?
A) Membrane-bound nucleus
B) Mitochondria
C) Phospholipid bilayer plasma membrane
D) 80S ribosomes
Answer: C
Explanation: Both cell types have a phospholipid bilayer as the plasma membrane.
Why the top distractor is wrong: D (80S ribosomes) is found only in eukaryotic cytoplasm; prokaryotes have 70S.

Question: Which structure is found in plant cells but not in animal cells?
A) Lysosome
B) Centriole
C) Central vacuole
D) Peroxisome
Answer: C
Explanation: The large central vacuole is a defining feature of mature plant cells.
Why the top distractor is wrong: A (lysosome) is present in animal cells; plant vacuoles can perform lysosomal functions but are structurally distinct.

Question: Which of the following provides the strongest evidence for the endosymbiotic theory?
A) Mitochondria are surrounded by a single membrane
B) Mitochondria have 80S ribosomes
C) Mitochondria have circular DNA and divide by binary fission
D) Mitochondria synthesize all their own proteins
Answer: C
Explanation: Circular DNA and binary fission in mitochondria mirror bacterial reproduction.
Why the top distractor is wrong: A is false—mitochondria have a double membrane, not single.

Question: A cell lacks a nucleus and has a cell wall containing peptidoglycan. Which domain does it belong to?
A) Eukarya
B) Archaea
C) Bacteria
D) Protista
Answer: C
Explanation: Bacteria are prokaryotes with peptidoglycan in their cell walls.
Why the top distractor is wrong: B (Archaea) lack peptidoglycan despite being prokaryotes.

Question: Which of the following organelles is responsible for modifying and packaging proteins for secretion?
A) Nucleolus
B) Smooth endoplasmic reticulum
C) Golgi apparatus
D) Lysosome
Answer: C
Explanation: The Golgi apparatus modifies, sorts, and packages proteins from the ER.
Why the top distractor is wrong: B synthesizes lipids and detoxifies, but does not package proteins for secretion.

Question: Which of the following cells lacks mitochondria?
A) Yeast cell
B) Liver cell
C) Mature human red blood cell
D) Leaf mesophyll cell
Answer: C
Explanation: Mature mammalian red blood cells lack a nucleus and mitochondria to maximize hemoglobin space.
Why the top distractor is wrong: A (yeast) is a fungus and has mitochondria despite being unicellular.

Question: What is the sedimentation coefficient of cytoplasmic ribosomes in eukaryotic cells?
A) 50S
B) 70S
C) 80S
D) 30S
Answer: C
Explanation: Eukaryotic cytoplasmic ribosomes are 80S (40S + 60S subunits).
Why the top distractor is wrong: B (70S) is the ribosome type in prokaryotes and organelles, not eukaryotic cytoplasm.

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 for endosymbiosis
• Nuclear envelope has double membrane and nuclear pores
• Nucleolus = site of rRNA synthesis and ribosome subunit assembly
• Bacteria: peptidoglycan in cell wall
• Archaea: no peptidoglycan (may have pseudopeptidoglycan)
• Plant cell wall: cellulose
• Fungal cell wall: chitin
• Animal cells: no cell wall
• Mycoplasma: smallest known cells, no cell wall
• Mature human red blood cells: no nucleus, no mitochondria
• Lysosomes: contain hydrolytic enzymes, found in animal cells
• Plant vacuole: maintains turgor pressure
• Peroxisomes: break down fatty acids and detoxify H?O?
• Endosymbiotic theory supported by: circular DNA, 70S ribosomes, binary fission in mitochondria/chloroplasts
• Eukaryotes have internal membranes (ER, Golgi, etc.); prokaryotes do not
• Prokaryotic DNA is in the nucleoid (no membrane)
• Eukaryotic DNA is in the nucleus (membrane-bound)
• Flagellin = protein in prokaryotic flagella
• Eukaryotic flagella: 9+2 microtubule arrangement
• Verify from standard textbook: presence of membrane-bound organelles in prokaryotes (e.g., anammoxosomes) – rare and not typical