STEM Readiness: Pre-Calculus Readiness - Functions/Algebra: Function Notation - and Domain/Range

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 lack a membrane-bound nucleus; DNA resides in the nucleoid region.
• Eukaryotes have a true nucleus enclosed by a double membrane (nuclear envelope) with nuclear pores.
• Prokaryotic DNA is typically a single circular chromosome; eukaryotic DNA is linear and organized into multiple chromosomes.
• Ribosomes in prokaryotes are 70S (composed of 50S and 30S subunits); in eukaryotes, cytoplasmic ribosomes are 80S (60S and 40S).
• Mitochondria and chloroplasts in eukaryotes contain 70S ribosomes, supporting their origin via endosymbiosis.
• Cell walls in most bacteria contain peptidoglycan; archaea lack peptidoglycan but may have pseudopeptidoglycan or other polymers.
• Plant cells have cellulose-based cell walls; fungal cells have chitin-based cell walls.
• Animal cells lack a cell wall entirely.
• Both prokaryotes and eukaryotes have a phospholipid bilayer plasma membrane with embedded proteins.
• Eukaryotes possess internal membrane-bound organelles (e.g., ER, Golgi, lysosomes); prokaryotes do not.
• The endoplasmic reticulum (ER) is a eukaryotic organelle involved in protein (rough ER) and lipid (smooth ER) synthesis.
• The Golgi apparatus modifies, sorts, and packages proteins for secretion or delivery to other organelles.
• Mitochondria are the site of aerobic respiration in eukaryotes and contain their own circular DNA and 70S ribosomes.
• Chloroplasts (in plants and algae) perform photosynthesis and also have circular DNA and 70S ribosomes.
• Lysosomes (in animal cells) contain hydrolytic enzymes for intracellular digestion; absent in most plant cells.
• Peroxisomes break down fatty acids and detoxify alcohol; present in both plant and animal eukaryotic cells.
• Centrioles (involved in cell division) are found in animal cells but absent in most plant and fungal cells.
• Mycoplasma species are bacteria that lack a cell wall, making them resistant to penicillin.
• Mature mammalian red blood cells lack a nucleus and most organelles, maximizing hemoglobin capacity.
• Archaea are prokaryotes but share some molecular features with eukaryotes (e.g., RNA polymerase, histones).
• Endosymbiotic theory is supported by mitochondria and chloroplasts having double membranes, circular DNA, and 70S ribosomes.
• Binary fission is the primary mode of reproduction in prokaryotes; eukaryotes divide via mitosis and cytokinesis.
• Cytoskeleton (microtubules, microfilaments, intermediate filaments) is present in eukaryotes; prokaryotes have homologous proteins (e.g., FtsZ) but no true cytoskeleton.
• Nuclear pores regulate transport between nucleus and cytoplasm; prokaryotes lack such structures.

Difficulty Level

Intermediate – requires distinguishing structural and functional differences across domains and organelles, with attention to exceptions.

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 (other polymers) have different wall compositions.
Trap: Ribosome size is the same across all cells – Fact: Prokaryotes have 70S ribosomes; eukaryotic cytoplasmic ribosomes are 80S, 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 (outer and inner).
Trap: Prokaryotes have no internal membranes – Fact: Some prokaryotes (e.g., photosynthetic bacteria) have specialized membranes like thylakoids, but no membrane-bound organelles.
Trap: All eukaryotic cells have a cell wall – Fact: Only plants, fungi, and some protists have cell walls; animal cells do not.

Practice MCQs (5–7 questions)

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

Question: A cell is observed to have a cell wall, chloroplasts, and a large central vacuole. Which domain and kingdom is it most likely from?
A) Eukarya, Fungi
B) Eukarya, Plantae
C) Bacteria, Proteobacteria
D) Eukarya, Animalia
Answer: B
Explanation: Chloroplasts, cell walls (cellulose), and large central vacuoles are characteristic of plant cells.
Why the top distractor is wrong: Fungi have cell walls but lack chloroplasts and large central vacuoles.

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 ATP
C) Containing 70S ribosomes and circular DNA
D) Having their own membrane potential
Answer: C
Explanation: Mitochondria have 70S ribosomes and circular DNA, features shared with bacteria.
Why the top distractor is wrong: Double membranes are found in other organelles and do not alone prove endosymbiosis.

Question: Which cell type lacks a nucleus and has 70S ribosomes?
A) Fungal cell
B) Plant cell
C) Bacterial cell
D) Animal cell
Answer: C
Explanation: Bacterial cells are prokaryotes, lacking a nucleus and possessing 70S ribosomes.
Why the top distractor is wrong: Fungal cells are eukaryotes and have 80S ribosomes and a nucleus.

Question: Which of the following is true about ribosomes in mitochondria?
A) They are 80S, like cytoplasmic ribosomes
B) They are 70S, similar to bacterial ribosomes
C) They are synthesized entirely in the Golgi apparatus
D) They are absent in plant cells
Answer: B
Explanation: Mitochondrial ribosomes are 70S, supporting their bacterial origin.
Why the top distractor is wrong: 80S ribosomes are found in the eukaryotic cytoplasm, not in mitochondria.

Question: Which organism is an exception to the presence of a cell wall in prokaryotes?
A) Escherichia coli
B) Bacillus subtilis
C) Mycoplasma pneumoniae
D) Streptococcus aureus
Answer: C
Explanation: Mycoplasma species lack a cell wall, making them naturally resistant to beta-lactam antibiotics.
Why the top distractor is wrong: E. coli has a peptidoglycan cell wall typical of Gram-negative bacteria.

Question: Which organelle is responsible for modifying and packaging proteins for secretion in eukaryotic cells?
A) Nucleolus
B) Rough endoplasmic reticulum
C) Golgi apparatus
D) Lysosome
Answer: C
Explanation: The Golgi apparatus modifies, sorts, and packages proteins from the ER for secretion or delivery.
Why the top distractor is wrong: The rough ER synthesizes proteins but does not modify or package them for secretion.

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 a membrane-bound nucleus with nuclear pores.
• Prokaryotic ribosome = 70S; eukaryotic cytoplasmic ribosome = 80S.
• Mitochondria and chloroplasts have 70S ribosomes and circular DNA.
• Bacterial cell walls contain peptidoglycan; archaea do not.
• Plant cell walls = cellulose; fungal = chitin; animal cells = no cell wall.
• Mycoplasma lacks a cell wall – smallest known cells.
• Mature red blood cells lack a nucleus and mitochondria.
• Both prokaryotes and eukaryotes have phospholipid bilayer membranes.
• Eukaryotes have membrane-bound organelles (ER, Golgi, lysosomes, etc.); prokaryotes do not.
• Rough ER synthesizes proteins; smooth ER synthesizes lipids and detoxifies.
• Golgi apparatus modifies and packages proteins in vesicles.
• Lysosomes contain hydrolytic enzymes; found in animal cells.
• Peroxisomes break down fatty acids and detoxify hydrogen peroxide.
• Centrioles present in animal cells; absent in most plants.
• Mitochondria have double membranes, circular DNA, 70S ribosomes – evidence for endosymbiosis.
• Chloroplasts evolved from cyanobacteria via endosymbiosis.
• Archaea are prokaryotes but share transcription machinery with eukaryotes.
• Binary fission = prokaryotic division; mitosis = eukaryotic nuclear division.
• Cytoskeleton (microtubules, actin) is eukaryotic; prokaryotes have FtsZ, not tubulin.
• Nuclear envelope is continuous with the rough ER.
• Nuclear pores regulate RNA and protein transport.
• Verify from standard textbook: Exact ribosomal subunit composition (50S/30S vs 60S/40S).
• No organelles in prokaryotes – no mitochondria, no ER, no Golgi.