STEM Readiness: Pre-Calculus Readiness - Exponentials/Logs: Solving Exponential and Logarithmic Equations - Extraneous Solutions

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 contain endoplasmic reticulum, Golgi apparatus, lysosomes, mitochondria, and (in plants) chloroplasts.
• Ribosomes in prokaryotes are 70S (composed of 50S and 30S subunits); eukaryotes have 80S ribosomes (60S and 40S).
• Mitochondria and chloroplasts in eukaryotes contain 70S ribosomes, supporting their origin via endosymbiotic theory.
• Prokaryotic cell walls typically contain peptidoglycan (e.g., Escherichia coli); archaea lack peptidoglycan and have different wall chemistry.
• 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.
• Eukaryotic cells have internal membrane systems (e.g., nuclear envelope, ER, Golgi); prokaryotes do not.
• Prokaryotes reproduce by binary fission; eukaryotes divide by mitosis and cytokinesis.
• Prokaryotic DNA is typically a single circular chromosome; eukaryotes have multiple linear chromosomes.
• Plasmids are small, circular DNA molecules commonly found in prokaryotes; rare in eukaryotes.
• Eukaryotic nuclei are surrounded by a double membrane (nuclear envelope) with nuclear pores for RNA and protein transport.
• Nucleolus within the nucleus is the site of ribosomal RNA synthesis and ribosome subunit assembly.
• Mycoplasma species are bacteria without a cell wall, making them resistant to antibiotics like penicillin.
• Human red blood cells lack a nucleus and mitochondria in maturity, maximizing hemoglobin capacity.
• Chloroplasts are exclusive to plant cells and some protists; absent in animal and fungal cells.
• Lysosomes are membrane-bound organelles in animal cells containing hydrolytic enzymes; rare in plant cells (vacuole performs similar function).
• Endosymbiotic theory is supported by mitochondria and chloroplasts having circular DNA, 70S ribosomes, and double membranes.
• Cilia and flagella in eukaryotes are composed of microtubules in a 9+2 arrangement; prokaryotic flagella are made of flagellin and lack microtubules.
• Eukaryotic cells may have centrioles (involved in spindle formation); prokaryotes lack centrioles.
• Vacuoles in plant cells are large and central, maintaining turgor pressure; animal cells have small or temporary vacuoles.
• Peroxisomes in eukaryotes break down fatty acids and detoxify alcohol; absent in prokaryotes.
• Cell membranes in both domains contain proteins for transport, signaling, and adhesion, but eukaryotes have more complex membrane proteins.

Difficulty Level

Intermediate – expected prior knowledge from high school biology, but requires precise differentiation of organelles and exceptions common in university exams.

Common Traps (3–5 factual traps)

Trap: All cells with cell walls have peptidoglycan – Fact: Only bacterial cell walls contain peptidoglycan; plants (cellulose), fungi (chitin), and archaea (pseudopeptidoglycan or other) do not.

Trap: Ribosome size correlates with cell complexity – Fact: Mitochondria and chloroplasts have 70S ribosomes like prokaryotes, despite being in eukaryotic cells.

Trap: The nucleus is the only organelle that contains DNA in eukaryotes – Fact: Mitochondria and chloroplasts contain their own circular DNA, independent of nuclear DNA.

Trap: Prokaryotes have no internal structure – Fact: Prokaryotes have ribosomes, nucleoid, inclusions, and sometimes protein-based cytoskeletons, but no membrane-bound organelles.

Practice MCQs (5–7 questions)

Question: Which of the following is a defining feature of eukaryotic cells but absent in prokaryotes?
A) Plasma membrane
B) Ribosomes
C) Circular DNA
D) Membrane-bound nucleus
Answer: D
Explanation: Only eukaryotes have a membrane-bound nucleus enclosing their DNA.
Why the top distractor is wrong: Circular DNA is common in prokaryotes but also found in mitochondria and chloroplasts, so it is not exclusive to prokaryotes.

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

Question: Which structure is found in both prokaryotes and eukaryotes?
A) Mitochondria
B) 80S ribosomes
C) Plasma membrane
D) Golgi apparatus
Answer: C
Explanation: The plasma membrane is universal to all cells.
Why the top distractor is wrong: Mitochondria are only in eukaryotes; prokaryotes lack membrane-bound organelles.

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, supporting mitochondrial origin from bacteria.
Why the top distractor is wrong: A double membrane is suggestive but not exclusive evidence; circular DNA and ribosome type are more specific.

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 human red blood cells eject their nucleus to carry more hemoglobin.
Why the top distractor is wrong: Yeast is a fungus and has a nucleus; all other listed cells are nucleated eukaryotes.

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

• Prokaryotic ribosome = 70S; eukaryotic cytoplasmic ribosome = 80S.
• Mitochondria and chloroplasts have 70S ribosomes and circular DNA – evidence of endosymbiosis.
• Prokaryotes: 0.1–5.0 ?m; eukaryotes: 10–100 ?m.
• DNA in prokaryotes is in the nucleoid; no nuclear membrane.
• Eukaryotes have linear chromosomes; prokaryotes have circular chromosomes.
• Peptidoglycan is in bacterial cell walls only.
• Archaea lack peptidoglycan; wall composition varies.
• Plant cell wall = cellulose; fungal = chitin; animal = no cell wall.
• All cells have a phospholipid bilayer plasma membrane.
• Only eukaryotes have membrane-bound organelles (ER, Golgi, lysosomes, etc.).
• Mycoplasma – bacteria without a cell wall.
• Mature red blood cells lack a nucleus and mitochondria.
• Nuclear envelope is double-membraned with nuclear pores.
• Nucleolus makes ribosomal RNA.
• Plasmids are small, circular DNA; common in bacteria.
• Eukaryotic flagella: 9+2 microtubule arrangement; prokaryotic: flagellin protein, no microtubules.
• Lysosomes are primarily in animal cells; plant vacuoles handle degradation.
• Peroxisomes break down fatty acids and detoxify; only in eukaryotes.
• Centrioles in animal cells; absent in most plants and prokaryotes.
• Chloroplasts only in plants and some protists.
• Binary fission = prokaryotic division; mitosis = eukaryotic nuclear division.
• Mitochondria replicate independently via fission, like bacteria.
• Endosymbiotic theory: mitochondria from aerobic bacteria; chloroplasts from cyanobacteria.
• Cytoskeleton in eukaryotes (actin, microtubules); prokaryotes have simpler analogs.
• Verify from standard textbook: exact ribosomal subunit sizes (50S+30S=70S; 60S+40S=80S).