STEM Readiness: Pre-Calculus Readiness - Trigonometry: Solving Trig Equations - General Solutions, Unit Circle, Checking Validity

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 possess them, including mitochondria, endoplasmic reticulum, and Golgi apparatus.
• Prokaryotic ribosomes are 70S (composed of 50S and 30S subunits); eukaryotic cytoplasmic ribosomes are 80S (60S and 40S).
• Mitochondria and chloroplasts in eukaryotes contain 70S ribosomes, similar to prokaryotes, supporting the endosymbiotic theory.
• Most bacteria have a cell wall made of peptidoglycan; archaea lack peptidoglycan but may have pseudopeptidoglycan or other polymers.
• Plant cells have a cell wall composed of cellulose; fungal cells have chitin in their cell walls; animal cells lack a cell wall.
• Both prokaryotes and eukaryotes have a plasma membrane made of a phospholipid bilayer with embedded proteins.
• Eukaryotes have internal membrane systems including the nuclear envelope, endoplasmic reticulum, and Golgi apparatus; prokaryotes do not.
• The nucleus in eukaryotes is surrounded by a double membrane (nuclear envelope) with nuclear pores that regulate transport.
• Nuclear pores allow selective passage of molecules like mRNA and proteins; small molecules diffuse freely, large molecules require signal sequences.
• Chromosomes in prokaryotes are typically a single circular DNA molecule; eukaryotes have multiple linear chromosomes.
• Prokaryotes divide by binary fission; eukaryotes undergo mitosis and meiosis for cell division.
• Plasmids are small, circular DNA molecules found in many prokaryotes and occasionally in yeast (a eukaryote).
• Endosymbiotic theory proposes that mitochondria and chloroplasts originated from free-living prokaryotes engulfed by ancestral eukaryotic cells.
• Evidence for endosymbiosis includes: mitochondria and chloroplasts have their own circular DNA, 70S ribosomes, and double membranes.
• Mycoplasma species are bacteria without a cell wall, making them resistant to antibiotics like penicillin that target peptidoglycan.
• Human red blood cells lack a nucleus and mitochondria when mature, maximizing space for hemoglobin.
• Plant cells contain chloroplasts for photosynthesis; animal cells do not.
• Lysosomes are membrane-bound organelles in animal cells containing hydrolytic enzymes; plants use vacuoles for similar functions.
• Prokaryotes can have capsules, pili, and flagella for adhesion and motility; eukaryotic flagella are structurally different (9+2 microtubule arrangement).
• Eukaryotic cilia and flagella are covered by the plasma membrane and contain microtubules in a 9+2 arrangement; prokaryotic flagella lack membrane and are composed of flagellin.
• Archaea may live in extreme environments (e.g., high temperature, salinity) but lack peptidoglycan and have unique membrane lipids (ether linkages).
• The nucleolus within the nucleus is the site of ribosomal RNA synthesis and ribosome subunit assembly.

Difficulty Level

Intermediate – requires distinguishing structural and functional differences across domains and organelles, including exceptions and evolutionary evidence.

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: Ribosome size correlates with organism complexity – Fact: Mitochondria and chloroplasts in eukaryotes have 70S ribosomes, identical in size to prokaryotes.

Trap: The nucleus is the only organelle with a double membrane – Fact: Mitochondria and chloroplasts also have double membranes.

Trap: Prokaryotes have no internal structure – Fact: Prokaryotes have ribosomes, nucleoid, and may have inclusions or protein-based microcompartments.

Practice MCQs (5–7 questions)

Question: Which of the following is a defining feature of eukaryotic cells but absent in prokaryotic cells?
A) Plasma membrane
B) Ribosomes
C) Membrane-bound nucleus
D) Circular DNA
Answer: C
Explanation: A membrane-bound nucleus is exclusive to eukaryotes.
Why the top distractor is wrong: Circular DNA is common in prokaryotes but also found in mitochondria and chloroplasts.

Question: A cell is observed to have a cell wall, chloroplasts, and large central vacuoles. It is most likely:
A) Fungal cell
B) Animal cell
C) Bacterial cell
D) Plant cell
Answer: D
Explanation: Chloroplasts and large central vacuoles are characteristic of plant cells.
Why the top distractor is wrong: Fungal cells have cell walls but lack chloroplasts and large central vacuoles.

Question: Which structure is found in both prokaryotes and eukaryotes?
A) 80S ribosomes
B) Nuclear envelope
C) Plasma membrane
D) Mitochondria
Answer: C
Explanation: The phospholipid bilayer plasma membrane is universal in all cells.
Why the top distractor is wrong: 80S ribosomes are only in eukaryotic cytoplasm; prokaryotes have 70S.

Question: Mitochondria are thought to have originated from endosymbiotic bacteria. Which evidence best supports this?
A) They are surrounded by a single membrane
B) They contain 80S ribosomes
C) They have circular DNA and 70S ribosomes
D) They synthesize proteins for the entire cell
Answer: C
Explanation: Circular DNA and 70S ribosomes in mitochondria resemble prokaryotic features.
Why the top distractor is wrong: Mitochondria have a double membrane, not single, and do not use 80S ribosomes.

Question: Which of the following lacks a nucleus when mature?
A) Yeast cell
B) Human skin cell
C) Human red blood cell
D) Amoeba
Answer: C
Explanation: Mature human red blood cells eject their nucleus to carry more hemoglobin.
Why the top distractor is wrong: Yeast is a eukaryote and always has a nucleus.

Question: What is the primary component of the bacterial cell wall?
A) Chitin
B) Cellulose
C) Peptidoglycan
D) Phospholipids
Answer: C
Explanation: Peptidoglycan is a polymer unique to bacterial cell walls.
Why the top distractor is wrong: Chitin is found in fungi, cellulose in plants.

Question: Which of the following structures is present in eukaryotic flagella but absent in prokaryotic flagella?
A) Flagellin protein
B) 9+2 microtubule arrangement
C) Rotational movement
D) Attachment to cell membrane
Answer: B
Explanation: The 9+2 microtubule array is a hallmark of eukaryotic cilia and flagella.
Why the top distractor is wrong: Flagellin is the protein in prokaryotic flagella, not eukaryotic.

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

• Prokaryotic cell size: 0.1–5.0 ?m; eukaryotic: 10–100 ?m.
• Prokaryotes have no nucleus; DNA in nucleoid.
• Eukaryotes have membrane-bound nucleus with nuclear pores.
• 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.
• Plant cell wall: cellulose; fungal: chitin; animal: no cell wall.
• Both domains have phospholipid bilayer plasma membranes.
• Eukaryotes have internal membranes (ER, Golgi, nucleus); prokaryotes do not.
• Human red blood cells lack a nucleus and mitochondria.
• Mycoplasma: bacterium without cell wall.
• Endosymbiotic theory: mitochondria and chloroplasts originated from engulfed prokaryotes.
• Chloroplasts found only in plants and some protists.
• Lysosomes are primarily in animal cells; plants use vacuoles.
• Nuclear pores allow selective transport of mRNA and proteins.
• Nucleolus: site of rRNA synthesis and ribosome assembly.
• Prokaryotes have single circular chromosome; eukaryotes have multiple linear chromosomes.
• Prokaryotes divide by binary fission; eukaryotes by mitosis/meiosis.
• Plasmids: small circular DNA, common in bacteria, rare in eukaryotes (e.g., yeast).
• Eukaryotic flagella: 9+2 microtubule arrangement, covered by membrane.
• Prokaryotic flagella: made of flagellin, rotate; no membrane.
• Archaea: extremophiles, ether-linked membrane lipids, no peptidoglycan.
• Mitochondria have double membrane, circular DNA, 70S ribosomes.
• No organelle besides nucleus has pores – only nuclear pores regulate macromolecular traffic.
• Ribosome size (Svedberg units) not additive: 60S + 40S = 80S, not 100S.
• Verify from standard textbook: exact lipid composition in archaeal membranes.