STEM Readiness: Pre-Calculus Readiness - Trigonometry: Unit Circle - Exact Values, Radian/Degree Conversion, Quadrant Signs

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.
• 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 eukaryotes contain 70S ribosomes, supporting their origin via endosymbiosis.
• Prokaryotic cell walls typically contain peptidoglycan (e.g., Escherichia coli); 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.
• Both prokaryotes and eukaryotes have a phospholipid bilayer plasma membrane; only eukaryotes have internal membrane systems (e.g., ER, Golgi).
• Eukaryotic organelles include the nucleus, endoplasmic reticulum (ER), Golgi apparatus, lysosomes, mitochondria, and (in plants) chloroplasts.
• Prokaryotes lack membrane-bound organelles; metabolic functions occur in the cytoplasm or plasma membrane.
• Plasma membrane structure is a fluid mosaic of phospholipids, proteins, and cholesterol (in animals).
• Nuclear envelope in eukaryotes is a double membrane with nuclear pores that regulate transport.
• Nucleolus within the nucleus is the site of ribosomal RNA (rRNA) synthesis and ribosome assembly.
• Rough ER has ribosomes attached and synthesizes proteins for secretion or membranes; smooth ER lacks ribosomes and synthesizes lipids, detoxifies drugs.
• Golgi apparatus modifies, sorts, and packages proteins into vesicles for transport to lysosomes, plasma membrane, or secretion.
• Lysosomes contain hydrolytic enzymes for intracellular digestion; present in animal cells, rare in plants.
• Mitochondria have double membranes, cristae, and their own circular DNA; site of aerobic respiration and ATP production.
• Chloroplasts (in plants and algae) have thylakoids, grana, and their own circular DNA; site of photosynthesis.
• Endosymbiotic theory is supported by: 70S ribosomes, binary fission, circular DNA, and double membranes in mitochondria and chloroplasts.
• Mycoplasma species are bacteria that lack a cell wall; they are the smallest known cells (0.2 ?m).
• Human red blood cells lack a nucleus and mitochondria in maturity, maximizing hemoglobin capacity.
• Plant cells have large central vacuoles for turgor pressure and storage; animal cells have small or temporary vacuoles.
• Cytoskeleton (microtubules, microfilaments, intermediate filaments) is present in eukaryotes; prokaryotes have analogous proteins (e.g., FtsZ) but no true cytoskeleton.
• Flagella differ: prokaryotic flagella are made of flagellin and rotate; eukaryotic flagella are made of microtubules (9+2) and undulate.
• Plasmids are small, circular extrachromosomal DNA molecules common in prokaryotes; rare in eukaryotes.

Difficulty Level

Intermediate – requires distinguishing structural and functional differences across domains and recognizing exceptions.

Common Traps (3–5 factual traps)

Trap: All cells with cell walls have peptidoglycan – Fact: Only bacteria have peptidoglycan; archaea, plants (cellulose), and fungi (chitin) have different wall compositions.
Trap: Ribosome size is the same across all cells – Fact: Prokaryotes have 70S ribosomes; eukaryotes have 80S in cytoplasm, but 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: Eukaryotes are always larger because they are more complex – Fact: Size range overlaps slightly; some prokaryotes (e.g., Thiomargarita namibiensis, up to 750 ?m) exceed typical eukaryotic cells.
Trap: Lysosomes are present in all eukaryotic cells – Fact: Lysosomes are common in animal cells but not typically found in plant cells, which use vacuoles for degradation.

Practice MCQs (5–7 questions)

Question: Which of the following is a feature found in prokaryotic cells but not in eukaryotic cells?
A) Circular DNA
B) 70S ribosomes
C) Nucleoid region
D) Phospholipid bilayer
Answer: C
Explanation: The nucleoid is a non-membrane-bound region in prokaryotes where DNA is located.
Why the top distractor is wrong: 70S ribosomes (B) are also found in mitochondria and chloroplasts of eukaryotes, so not exclusive to prokaryotes.

Question: Which structure is present in plant cells but absent in animal cells?
A) Mitochondria
B) Golgi apparatus
C) Central vacuole
D) Plasma membrane
Answer: C
Explanation: Mature plant cells have a large central vacuole for storage and turgor; animal cells have only small vesicles.
Why the top distractor is wrong: Mitochondria (A) are present in both plant and animal cells.

Question: Which of the following provides the strongest evidence for the endosymbiotic origin of mitochondria?
A) Presence of a double membrane
B) Ability to synthesize proteins
C) Contain 70S ribosomes and circular DNA
D) Divide by mitosis
Answer: C
Explanation: Mitochondria have 70S ribosomes and circular DNA, like bacteria, supporting bacterial origin.
Why the top distractor is wrong: Double membranes (A) can form by other mechanisms; circular DNA and ribosomes are more specific evidence.

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: Archaea (B) lack peptidoglycan; Protista (D) are eukaryotes and have nuclei.

Question: Which organelle modifies and packages proteins for secretion?
A) Nucleus
B) Rough ER
C) Golgi apparatus
D) Lysosome
Answer: C
Explanation: The Golgi apparatus modifies and sorts proteins from the ER into vesicles for secretion.
Why the top distractor is wrong: Rough ER (B) synthesizes proteins but does not package them for secretion.

Question: Which of the following cells lacks mitochondria?
A) Fungal cell
B) Mature human red blood cell
C) Liver cell
D) Leaf cell
Answer: B
Explanation: Mature human red blood cells lack mitochondria and generate ATP via glycolysis.
Why the top distractor is wrong: Fungal cells (A) are eukaryotic and contain mitochondria.

Question: What is the primary structural component of fungal cell walls?
A) Cellulose
B) Peptidoglycan
C) Chitin
D) Silica
Answer: C
Explanation: Fungi have cell walls made of chitin, a nitrogen-containing polysaccharide.
Why the top distractor is wrong: Cellulose (A) is found in plant cell walls, not fungal.

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

• Prokaryotic cell size: 0.1–5.0 ?m; eukaryotic: 10–100 ?m.
• Prokaryotes: DNA in nucleoid; eukaryotes: DNA in nucleus.
• Prokaryotic ribosome = 70S; eukaryotic cytoplasmic ribosome = 80S.
• Mitochondria and chloroplasts have 70S ribosomes and circular DNA – evidence of endosymbiosis.
• Bacteria cell wall contains peptidoglycan; archaea do not.
• Plant cell wall = cellulose; fungal = chitin; animal = no cell wall.
• Both cell types have phospholipid bilayer plasma membranes.
• Eukaryotes have internal membranes (ER, Golgi, etc.); prokaryotes do not.
• Nuclear envelope is a double membrane with nuclear pores.
• Nucleolus = site of rRNA synthesis and ribosome subunit assembly.
• Rough ER = ribosomes attached, makes proteins; smooth ER = lipid synthesis, detox.
• Golgi apparatus = modifies, sorts, packages proteins into vesicles.
• Lysosomes = contain hydrolytic enzymes, found in animal cells.
• Mitochondria = double membrane, cristae, site of ATP production.
• Chloroplasts = contain thylakoids, site of photosynthesis.
• Mycoplasma = smallest known cells, no cell wall.
• Mature red blood cells = no nucleus, no mitochondria.
• Plant cells have large central vacuole; animal cells do not.
• Eukaryotic flagella = 9+2 microtubule arrangement; prokaryotic = flagellin, rotates.
• Cytoskeleton = microtubules, microfilaments – only in eukaryotes.
• Plasmids = small circular DNA – common in bacteria.
• Archaea lack peptidoglycan but are prokaryotes.
• Endosymbiotic theory supported by: binary fission, 70S ribosomes, circular DNA in mitochondria/chloroplasts.
• Human red blood cells rely on glycolysis for ATP (no mitochondria).
• Verify from standard textbook: Size of Thiomargarita namibiensis (can reach 750 ?m).