STEM Readiness: Pre-Calculus Readiness - Functions/Algebra: Inequalities - Polynomial and Rational Sign Chart Method

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 surrounding membrane; eukaryotes house DNA within a membrane-bound nucleus.
• Prokaryotes lack membrane-bound organelles; eukaryotes have organelles such as 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 prokaryotes have a cell wall made of peptidoglycan; archaea lack peptidoglycan but may have pseudopeptidoglycan or other polymers.
• Plant cells have a cell wall made of cellulose; fungal cells have chitin; animal cells lack a cell wall.
• Both prokaryotes and eukaryotes have a plasma membrane composed of a phospholipid bilayer with embedded proteins.
• Eukaryotes have internal membrane systems including the nuclear envelope, endoplasmic reticulum, and Golgi apparatus; prokaryotes do not.
• Binary fission is the primary mode of reproduction in prokaryotes; eukaryotes divide by mitosis and meiosis.
• Prokaryotic DNA is typically a single circular chromosome; eukaryotic DNA is organized into multiple linear chromosomes.
• Plasmids are small, circular extrachromosomal DNA molecules commonly found in prokaryotes; rare in eukaryotes.
• Eukaryotic nucleus contains nuclear pores that regulate transport between nucleus and cytoplasm; prokaryotes lack nuclear pores.
• Nucleolus is present in the eukaryotic nucleus and is the site of ribosomal RNA synthesis; absent in prokaryotes.
• Mitochondria are the site of aerobic respiration and ATP production in eukaryotes; absent in prokaryotes.
• Chloroplasts are photosynthetic organelles in plants and algae; contain thylakoids and chlorophyll; absent in prokaryotes (except cyanobacteria, which have thylakoid membranes but no chloroplasts).
• Cyanobacteria are photosynthetic prokaryotes that perform oxygenic photosynthesis using thylakoid membranes, not chloroplasts.
• Mycoplasma species are bacteria without a cell wall, making them resistant to antibiotics like penicillin that target peptidoglycan.
• Mature mammalian red blood cells lack a nucleus and mitochondria, maximizing space for hemoglobin; an exception among eukaryotic cells.
• Endosymbiotic theory is supported by mitochondria and chloroplasts having their own circular DNA, 70S ribosomes, and double membranes.
• Lysosomes are membrane-bound organelles in animal cells containing hydrolytic enzymes for digestion; rare in plant cells.
• Vacuoles in plant cells are large and central, maintaining turgor pressure; animal cells have small, temporary vacuoles.
• Flagella in prokaryotes are made of flagellin and rotate; eukaryotic flagella are made of microtubules (9+2 arrangement) and undulate.
• Cilia are short, numerous motile structures in some eukaryotes (e.g., tracheal epithelium); prokaryotes lack cilia.

Difficulty Level

Intermediate – requires precise differentiation between structural and genetic features across domains and kingdoms.

Common Traps (3–5 factual traps)

Trap: All cells with cell walls have peptidoglycan – Fact: Only bacteria have peptidoglycan; plant cell walls are made of cellulose, fungi of chitin, and archaea lack peptidoglycan.

Trap: Eukaryotes are always larger and more complex than prokaryotes – Fact: While generally true, some prokaryotes (e.g., Thiomargarita namibiensis) can be larger than typical eukaryotic cells (up to 750 ?m).

Trap: Mitochondria and chloroplasts use 80S ribosomes like the rest of the eukaryotic cell – Fact: These organelles use 70S ribosomes, reflecting their prokaryotic ancestry.

Trap: Prokaryotes have no internal membranes – Fact: Some prokaryotes (e.g., cyanobacteria) have thylakoid membranes for photosynthesis, though not enclosed in organelles.

Practice MCQs (5–7 questions)

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) Linear chromosomes
Answer: C
Explanation: Both cell types have a plasma membrane made of a phospholipid bilayer.
Why the top distractor is wrong: D is incorrect because prokaryotes have circular, not linear, chromosomes.

Question: A cell is observed to contain 70S ribosomes, a nucleoid, and peptidoglycan in its cell wall. Which of the following is the most likely identity of the cell?
A) Fungal cell
B) Plant cell
C) Animal cell
D) Bacterial cell
Answer: D
Explanation: 70S ribosomes, nucleoid, and peptidoglycan are diagnostic of bacteria.
Why the top distractor is wrong: A is incorrect because fungi are eukaryotes with 80S ribosomes and chitin cell walls.

Question: Which structure is found in eukaryotic cells but absent in prokaryotic cells?
A) Plasma membrane
B) Ribosomes
C) Golgi apparatus
D) DNA
Answer: C
Explanation: The Golgi apparatus is a membrane-bound organelle unique to eukaryotes.
Why the top distractor is wrong: A is incorrect because both cell types have a plasma membrane.

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 using 80S ribosomes
C) Linear DNA molecules
D) Reproduction by mitosis
Answer: A
Explanation: Mitochondria have a double membrane and 70S ribosomes, supporting bacterial origin; double membrane suggests engulfment.
Why the top distractor is wrong: B is incorrect because mitochondria use 70S, not 80S, ribosomes.

Question: Which of the following cells lacks a nucleus?
A) Yeast cell
B) Human neuron
C) Mature human red blood cell
D) Amoeba
Answer: C
Explanation: Mature mammalian red blood cells eject their nucleus during development.
Why the top distractor is wrong: A is incorrect because yeast is a fungus and has a nucleus.

Question: Which organism has a cell wall but does not contain peptidoglycan?
A) Escherichia coli
B) Saccharomyces cerevisiae
C) Bacillus anthracis
D) Mycoplasma pneumoniae
Answer: B
Explanation: Saccharomyces cerevisiae is a fungus with a chitin-based cell wall, not peptidoglycan.
Why the top distractor is wrong: A is incorrect because E. coli is a bacterium with peptidoglycan.

Question: What is the primary function of the nucleolus?
A) DNA replication
B) Protein synthesis
C) Ribosomal RNA synthesis
D) ATP production
Answer: C
Explanation: The nucleolus is the site of rRNA transcription and ribosome subunit assembly.
Why the top distractor is wrong: B is incorrect because protein synthesis occurs on ribosomes in the cytoplasm.

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 cell types have phospholipid bilayer plasma membrane.
• Only eukaryotes have endoplasmic reticulum, Golgi apparatus, lysosomes, mitochondria.
• Prokaryotes reproduce by binary fission; eukaryotes by mitosis/meiosis.
• Prokaryotic DNA: single circular chromosome; eukaryotic: multiple linear chromosomes.
• Plasmids are common in prokaryotes, rare in eukaryotes.
• Nucleolus = site of rRNA synthesis and ribosome assembly – only in eukaryotes.
• Mature human red blood cells lack nucleus and mitochondria.
• Mycoplasma lacks a cell wall – smallest known cells.
• Cyanobacteria perform photosynthesis using thylakoid membranes, not chloroplasts.
• Eukaryotic flagella: 9+2 microtubule arrangement; prokaryotic: flagellin-based, rotating.
• Cilia are eukaryotic-only motile structures.
• Lysosomes are primarily in animal cells; plants use vacuoles for digestion.
• Mitochondria have double membrane and divide by binary fission.
• Endosymbiotic theory supported by organelle circular DNA, 70S ribosomes, independent division.
• Verify from standard textbook: exact size of Thiomargarita namibiensis (up to 750 ?m).
• Archaea lack peptidoglycan but may have pseudopeptidoglycan or S-layers.
• Eukaryotic nuclear envelope is continuous with rough ER.
• Rough ER has ribosomes; smooth ER does not.
• Golgi apparatus modifies, sorts, and packages proteins for secretion or delivery.