STEM Readiness: Pre-Calculus Readiness - Exponentials/Logs: Change of Base Formula - and Natural, Logarithm

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 organelles such as mitochondria, lysosomes, and peroxisomes.
• Ribosomes in prokaryotes are 70S (30S + 50S subunits); eukaryotic cytoplasmic ribosomes are 80S (40S + 60S subunits).
• Mitochondria and chloroplasts in eukaryotes contain 70S ribosomes, supporting their bacterial origin via endosymbiotic theory.
• Prokaryotic cell walls typically contain peptidoglycan (e.g., Escherichia coli); archaea lack peptidoglycan and have pseudopeptidoglycan or other polymers.
• Plant cell walls are made of cellulose; fungal cell walls contain chitin; animal cells lack cell walls.
• All cells have a plasma membrane composed of a phospholipid bilayer with embedded proteins.
• Eukaryotes have internal membrane systems including the endoplasmic reticulum (ER), Golgi apparatus, and nuclear envelope; prokaryotes do not.
• The nucleus in eukaryotes contains chromatin (DNA + histones) and a nucleolus where ribosomal RNA is synthesized.
• Prokaryotes have circular DNA as their main chromosome; eukaryotes have linear chromosomes.
• Prokaryotes can have plasmids (small, circular DNA); eukaryotes rarely have plasmids (e.g., in yeast).
• Binary fission is the method of prokaryotic cell division; mitosis and meiosis occur in eukaryotes.
• 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 penicillin.
• Human red blood cells lack a nucleus and mitochondria, maximizing space for hemoglobin.
• Plant cells have chloroplasts for photosynthesis and a central vacuole for turgor pressure; animal cells lack both.
• Lysosomes are membrane-bound organelles in animal cells containing hydrolytic enzymes; plant vacuoles can perform similar functions.
• Peroxisomes in eukaryotes break down fatty acids and detoxify alcohol; absent in prokaryotes.
• Endosymbiotic theory is supported by mitochondria and chloroplasts having their own DNA, 70S ribosomes, and double membranes.
• Archaea lack peptidoglycan and have ether-linked lipids in their membranes; bacteria have ester-linked lipids.
• Gram-positive bacteria have thick peptidoglycan and no outer membrane; Gram-negative bacteria have thin peptidoglycan and an outer membrane with lipopolysaccharide.
• Cilia in eukaryotes have the 9+2 microtubule arrangement and are powered by dynein motors; prokaryotes lack cilia.
• Nuclear pores regulate transport between the nucleus and cytoplasm in eukaryotes; prokaryotes lack nuclear pores.

Difficulty Level

Intermediate – expected foundational knowledge in first-semester biology but requires precise differentiation between cell types and organelle functions.

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) have different wall compositions.
Trap: Ribosome size correlates with cell complexity – Fact: Mitochondria and chloroplasts in eukaryotes have 70S ribosomes, not 80S, due to bacterial ancestry.
Trap: Prokaryotes have no DNA packaging – Fact: Prokaryotes use nucleoid-associated proteins (e.g., HU protein) to compact DNA, though not histones.
Trap: Eukaryotes are always multicellular – Fact: Many eukaryotes (e.g., yeast, amoeba) are unicellular; prokaryotes are always unicellular.
Trap: The nucleus is the only organelle with a double membrane – Fact: Mitochondria and chloroplasts also have double membranes.

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 is located.
Why the top distractor is wrong: While peptidoglycan is common in bacteria, some eukaryotes (e.g., algae) may have similar structural polymers, and it is not universal to all prokaryotes (e.g., Mycoplasma lacks it).

Question: Which structure is present in plant cells but absent in animal cells?
A) Mitochondria
B) Plasma membrane
C) Central vacuole
D) Ribosomes
Answer: C
Explanation: The central vacuole is a large, membrane-bound organelle in plant cells that maintains turgor pressure.
Why the top distractor is wrong: Mitochondria are present in both plant and animal cells for ATP production.

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) Containing 70S ribosomes and circular DNA
D) Having their own plasma membrane
Answer: C
Explanation: Mitochondria have 70S ribosomes and circular DNA, both characteristics of bacteria.
Why the top distractor is wrong: A double membrane alone is not sufficient evidence, as other organelles (e.g., nucleus) also have double membranes from invagination.

Question: A cell is observed to have a nucleus, mitochondria, and a cell wall made of cellulose. From which organism is this cell most likely derived?
A) Fungus
B) Bacterium
C) Animal
D) Plant
Answer: D
Explanation: Cellulose in the cell wall and the presence of mitochondria and nucleus are diagnostic of plant cells.
Why the top distractor is wrong: Fungi have chitin in their cell walls, not cellulose.

Question: Which of the following is true about ribosomes in eukaryotic cells?
A) All ribosomes are 80S, including those in mitochondria
B) Ribosomes are only found free in the cytoplasm
C) 80S ribosomes are found in the cytoplasm; 70S in mitochondria
D) Ribosomes are enclosed within the nucleus
Answer: C
Explanation: Cytoplasmic ribosomes in eukaryotes are 80S; mitochondrial ribosomes are 70S.
Why the top distractor is wrong: Mitochondrial ribosomes are 70S, not 80S, so not all ribosomes in eukaryotes are 80S.

Question: Which cell type lacks a membrane-bound nucleus but contains ribosomes?
A) Human red blood cell
B) Escherichia coli
C) Mature plant sieve tube element
D) Saccharomyces cerevisiae
Answer: B
Explanation: E. coli is a prokaryote with a nucleoid and 70S ribosomes.
Why the top distractor is wrong: Human red blood cells lack both nucleus and ribosomes; they cannot synthesize proteins.

Question: Which of the following structures is found in both prokaryotes and eukaryotes?
A) Golgi apparatus
B) Plasma membrane
C) Mitochondria
D) Nucleolus
Answer: B
Explanation: The plasma membrane, composed of a phospholipid bilayer, is universal to all cells.
Why the top distractor is wrong: Golgi apparatus is exclusive to eukaryotes.

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

• Prokaryotic cell size: 0.1–5.0 ?m; eukaryotic: 10–100 ?m.
• Prokaryotes have nucleoid; eukaryotes have nucleus with nuclear envelope.
• 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.
• All cells have a phospholipid bilayer plasma membrane.
• Eukaryotes have internal membranes (ER, Golgi, lysosomes); prokaryotes do not.
• Human red blood cells lack nucleus and mitochondria.
• Mycoplasma has no cell wall – smallest known cells.
• Prokaryotes divide by binary fission; eukaryotes by mitosis/meiosis.
• Prokaryotic flagella: flagellin, rotary motion; eukaryotic: microtubules (9+2), bending motion.
• Chromosomes: prokaryotes = circular; eukaryotes = linear.
• Plasmids common in bacteria; rare in eukaryotes (e.g., yeast 2-micron plasmid).
• Nuclear pores regulate nucleocytoplasmic transport in eukaryotes.
• Lysosomes are in animal cells; plant vacuoles can have degradative enzymes.
• Peroxisomes: break down fatty acids, detoxify H?O?; absent in prokaryotes.
• Endosymbiotic theory: mitochondria from alpha-proteobacteria; chloroplasts from cyanobacteria.
• Archaea membrane lipids: ether linkages; bacteria and eukaryotes: ester linkages.
• Gram-positive: thick peptidoglycan, no outer membrane; Gram-negative: thin peptidoglycan + outer membrane.
• Cilia and flagella in eukaryotes use dynein motors for movement.
• Nucleolus = site of rRNA synthesis and ribosome assembly.
• Plant cells have chloroplasts and large central vacuole; animal cells do not.
• Prokaryotes use nucleoid-associated proteins (not histones) for DNA compaction.
• Verify from standard textbook: exact protein composition of nuclear pore complex.