STEM Readiness: Pre-Calculus Readiness - Functions/Algebra: Composition of Functions - f(g(x)), Domain of Composed Functions

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 have endoplasmic reticulum, Golgi apparatus, lysosomes, and mitochondria.
• Ribosomes in prokaryotes 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.
• Cell walls in bacteria contain peptidoglycan; archaea lack peptidoglycan but may have pseudopeptidoglycan or other polymers.
• Plant cell walls are made of cellulose; fungal cell walls contain chitin; animal cells lack cell walls.
• Both prokaryotes and eukaryotes have a phospholipid bilayer plasma membrane with embedded proteins.
• Eukaryotes have internal membrane systems including the nuclear envelope, ER, and Golgi, which prokaryotes lack.
• Prokaryotes reproduce by binary fission; eukaryotes divide by mitosis and cytokinesis.
• Plasmids are small, circular DNA molecules commonly found in prokaryotes; they can carry antibiotic resistance genes.
• Eukaryotic chromosomes are linear and complexed with histone proteins; prokaryotic chromosomes are circular and not associated with histones (though archaea have histone-like proteins).
• Flagella in prokaryotes are made of flagellin and rotate; eukaryotic flagella are composed of microtubules (9+2 arrangement) and bend.
• 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, maximizing space for hemoglobin.
• Endosymbiotic theory is supported by mitochondria and chloroplasts having their own circular DNA, 70S ribosomes, and double membranes.
• Chloroplasts are found in plants and some protists (e.g., algae), but not in fungi or animals.
• Lysosomes are membrane-bound organelles in animal cells containing hydrolytic enzymes; plants use vacuoles for similar degradation functions.
• The nuclear envelope in eukaryotes is a double membrane with nuclear pores that regulate transport between nucleus and cytoplasm.
• Prokaryotes can have capsules (e.g., Streptococcus pneumoniae) for protection and attachment; some eukaryotes have extracellular matrices (e.g., animal connective tissue).
• Cilia in eukaryotes have the same 9+2 microtubule arrangement as flagella and are shorter and more numerous.
• Archaea lack peptidoglycan and have ether-linked lipids in their membranes, unlike the ester-linked lipids in bacteria and eukaryotes.
• Peroxisomes are single-membrane organelles in eukaryotes that break down fatty acids and detoxify hydrogen peroxide; absent in prokaryotes.
• Nucleolus within the eukaryotic 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, with attention to 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 is the same across all organisms – Fact: Prokaryotes have 70S ribosomes; eukaryotes have 80S in cytoplasm (but 70S in mitochondria/chloroplasts).
Trap: The nucleus is the only organelle with a double membrane – Fact: Mitochondria and chloroplasts also have double membranes.
Trap: Prokaryotes have no DNA packaging – Fact: While lacking histones, some prokaryotes use nucleoid-associated proteins; archaea have histone-like proteins.
Trap: Eukaryotic cells are always larger and more complex than prokaryotes – Fact: Some eukaryotes (e.g., Ostreococcus) are <1 ?m, smaller than many prokaryotes.

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) Peptidoglycan in the cell wall
Answer: C
Explanation: The nucleoid is a distinct, non-membrane-bound region in prokaryotes where DNA resides.
Why the top distractor is wrong: While peptidoglycan is common in bacteria, it is not universal (e.g., Mycoplasma lack it), and the nucleoid is a definitive structural feature.

Question: Which organelle is present in plant cells but absent in animal cells?
A) Mitochondria
B) Golgi apparatus
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: Mitochondria 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 replicate independently
C) Containing 70S ribosomes and circular DNA
D) Involvement in ATP production
Answer: C
Explanation: 70S ribosomes and circular DNA are prokaryotic traits retained in mitochondria.
Why the top distractor is wrong: Double membranes can arise by other mechanisms; circular DNA and ribosome type are more specific evidence.

Question: A cell lacks a nucleus and has 70S ribosomes. It also has a cell wall containing peptidoglycan. This cell is most likely:
A) A plant cell
B) A fungal cell
C) A bacterium
D) An archaeon
Answer: C
Explanation: Bacteria have peptidoglycan, 70S ribosomes, and no nucleus.
Why the top distractor is wrong: Archaea lack peptidoglycan despite being prokaryotes.

Question: Which structure is found in both prokaryotes and eukaryotes?
A) Plasma membrane
B) Mitochondria
C) Nucleolus
D) Endoplasmic reticulum
Answer: A
Explanation: The phospholipid bilayer plasma membrane is universal in all cells.
Why the top distractor is wrong: Mitochondria are exclusive to eukaryotes.

Question: Human red blood cells lack a nucleus. What is a direct consequence of this?
A) They cannot synthesize proteins
B) They cannot divide
C) They have no DNA
D) They rely solely on anaerobic respiration
Answer: B
Explanation: Without a nucleus, red blood cells cannot undergo mitosis.
Why the top distractor is wrong: They can synthesize some proteins using existing mRNA and ribosomes early in maturation.

Question: Which of the following is true about ribosomes in eukaryotic cells?
A) All are 80S and located in the cytoplasm
B) Mitochondrial ribosomes are 70S
C) They are assembled in the Golgi apparatus
D) They are surrounded by a membrane
Answer: B
Explanation: Mitochondrial ribosomes are 70S, reflecting their prokaryotic origin.
Why the top distractor is wrong: Not all ribosomes are 80S; mitochondrial and chloroplast ribosomes are 70S.

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.
• Bacterial cell walls contain peptidoglycan; archaea do not.
• Plant cell wall = cellulose; fungal = chitin; animal cells = no cell wall.
• Both domains have phospholipid bilayer plasma membranes.
• Eukaryotes have internal membranes (ER, Golgi, lysosomes); prokaryotes do not.
• Mycoplasma lacks a cell wall – exception among bacteria.
• Human red blood cells lack nucleus and mitochondria.
• Prokaryotes divide by binary fission; eukaryotes by mitosis.
• Plasmids are small circular DNA molecules common in bacteria.
• Eukaryotic chromosomes are linear and bound to histones; prokaryotic DNA is circular.
• Prokaryotic flagella = flagellin, rotate; eukaryotic = microtubules (9+2), bend.
• Archaea have ether-linked lipids; bacteria and eukaryotes have ester-linked.
• Lysosomes are in animal cells; plants use vacuoles for degradation.
• Nuclear envelope = double membrane with pores.
• Peroxisomes break down fatty acids and detoxify H?O?; absent in prokaryotes.
• Nucleolus = site of rRNA synthesis and ribosome assembly.
• Chloroplasts found in plants and algae, not in fungi or animals.
• Cilia and flagella in eukaryotes share 9+2 microtubule arrangement.
• Endosymbiotic theory supported by double membranes, 70S ribosomes, and independent division of mitochondria/chloroplasts.
• Some eukaryotes (e.g., Ostreococcus) are smaller than typical prokaryotes – size alone doesn’t classify.
• Verify from standard textbook: histone-like proteins in archaea resemble eukaryotic histones.