STEM Readiness: Pre-Calculus Readiness - Trigonometry: Law of Sines - Law of, Cosines Ambiguous, Case SSA

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 is in the nucleoid region (e.g., Escherichia coli).
• Eukaryotes have a true nucleus enclosed by a double membrane (nuclear envelope) containing linear DNA (e.g., human liver cell).
• Prokaryotic ribosomes are 70S (30S + 50S subunits); eukaryotic cytoplasmic ribosomes are 80S (40S + 60S).
• Mitochondria and chloroplasts contain 70S ribosomes, supporting their origin via endosymbiotic theory.
• Prokaryotic cell walls typically contain peptidoglycan (e.g., bacterial cell wall in Staphylococcus aureus).
• Archaea lack peptidoglycan; their cell walls are made of pseudopeptidoglycan or other polysaccharides.
• Plant cell walls are composed of cellulose; fungal cell walls contain chitin; animal cells lack cell walls.
• Mycoplasma species are bacteria that lack a cell wall, making them resistant to penicillin.
• Both prokaryotes and eukaryotes have a phospholipid bilayer plasma membrane with embedded proteins.
• Eukaryotes have internal membrane systems (endoplasmic reticulum, Golgi, lysosomes); prokaryotes do not.
• Nuclear pores in the nuclear envelope allow RNA and proteins to move between nucleus and cytoplasm.
• Chromosomes in prokaryotes are single, circular DNA molecules; eukaryotes have multiple linear chromosomes.
• Plasmids are small, circular DNA molecules found in prokaryotes (e.g., F plasmid in conjugation).
• Eukaryotic organelles include mitochondria (ATP production), lysosomes (digestion), and peroxisomes (detoxification).
• Endoplasmic reticulum (ER): Rough ER has ribosomes and synthesizes proteins; smooth ER synthesizes lipids and detoxifies.
• Golgi apparatus modifies, sorts, and packages proteins for secretion or delivery to other organelles.
• Mitochondria have double membranes, cristae, and their own circular DNA (maternally inherited in animals).
• Chloroplasts are found in plant and algal cells, have thylakoids, and perform photosynthesis.
• Red blood cells in mammals lack a nucleus and organelles, maximizing hemoglobin content.
• Cilia and flagella in eukaryotes are composed of microtubules in a 9+2 arrangement; prokaryotic flagella are made of flagellin and rotate.
• Lysosomes are membrane-bound vesicles containing hydrolytic enzymes active at acidic pH (~4.5–5.0).
• Vacuoles in plant cells are large and central, maintaining turgor pressure; animal cells have small or temporary vacuoles.
• Centrioles (involved in spindle formation) are present in animal cells but absent in most plant cells.
• Nucleolus within the nucleus is the site of ribosomal RNA synthesis and ribosome assembly.

Difficulty Level

Intermediate – requires precise differentiation of structures and exceptions commonly tested in introductory biology.

Common Traps (3–5 factual traps)

Trap: All cells with cell walls have peptidoglycan – Fact: Only bacteria have peptidoglycan; archaea, plants, and fungi have different wall compositions.
Trap: Ribosome size correlates with cell complexity – Fact: Mitochondria and chloroplasts have 70S ribosomes despite being in eukaryotic cells.
Trap: Prokaryotes have no internal structure – Fact: Prokaryotes have nucleoids, ribosomes, and some have protein-based microcompartments.
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 eukaryotic cells but NOT in prokaryotic cells?
A) Circular DNA
B) 70S ribosomes
C) Membrane-bound nucleus
D) Plasma membrane
Answer: C
Explanation: A membrane-bound nucleus is exclusive to eukaryotes.
Why the top distractor is wrong: 70S ribosomes are in prokaryotes and also in mitochondria/chloroplasts, so not exclusive.

Question: Which structure is present in plant cells but NOT in animal cells?
A) Mitochondria
B) Golgi apparatus
C) Central vacuole
D) Ribosomes
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: A cell is observed to have a cell wall, no nucleus, and 70S ribosomes. Which is the most likely identity?
A) Fungal cell
B) Plant cell
C) Bacterial cell
D) Animal cell
Answer: C
Explanation: Bacteria are prokaryotes with cell walls, no nucleus, and 70S ribosomes.
Why the top distractor is wrong: Fungal cells are eukaryotes with 80S ribosomes and a nucleus.

Question: Which organelle is believed to have originated via endosymbiosis and contains its own DNA?
A) Lysosome
B) Smooth ER
C) Mitochondrion
D) Golgi apparatus
Answer: C
Explanation: Mitochondria have circular DNA and 70S ribosomes, supporting endosymbiotic origin.
Why the top distractor is wrong: Lysosomes are derived from the Golgi and lack DNA.

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

Question: Which cell type lacks a nucleus and is capable of photosynthesis?
A) Cyanobacterium
B) Red blood cell
C) Yeast cell
D) Leaf mesophyll cell
Answer: A
Explanation: Cyanobacteria are prokaryotes with photosynthetic pigments and no nucleus.
Why the top distractor is wrong: Red blood cells lack a nucleus but cannot perform photosynthesis.

Question: What is the primary structural component of fungal cell walls?
A) Cellulose
B) Peptidoglycan
C) Chitin
D) Silica
Answer: C
Explanation: Fungi have cell walls made of chitin, a nitrogen-containing polysaccharide.
Why the top distractor is wrong: Cellulose is found in plant cell walls, not fungal.

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

• Prokaryotic cell size: 0.1–5.0 ?m; eukaryotic: 10–100 ?m.
• Prokaryotes have nucleoid, not nucleus.
• Eukaryotes have 80S ribosomes in cytoplasm; 70S in mitochondria/chloroplasts.
• Prokaryotic ribosome = 70S (30S + 50S); eukaryotic = 80S (40S + 60S).
• Bacterial cell wall contains peptidoglycan; archaea do not.
• Plant cell wall = cellulose; fungal = chitin; animal = no cell wall.
• Mycoplasma has no cell wall – smallest known cells.
• Red blood cells lack nucleus and organelles.
• Both cell types have phospholipid bilayer plasma membrane.
• Only eukaryotes have membrane-bound organelles (ER, Golgi, lysosomes).
• Nuclear envelope has nuclear pores for transport.
• Prokaryotic DNA = single circular chromosome; eukaryotic = multiple linear chromosomes.
• Plasmids are small, circular DNA in prokaryotes.
• Mitochondria have double membrane, circular DNA, and 70S ribosomes.
• Chloroplasts have thylakoids and perform photosynthesis.
• Endosymbiotic theory supported by mitochondrial/chloroplast DNA and ribosomes.
• Rough ER has ribosomes; smooth ER does not.
• Golgi apparatus modifies and packages proteins.
• Lysosomes contain hydrolytic enzymes; pH ~4.5–5.0.
• Plant vacuole maintains turgor pressure.
• Centrioles in animal cells; absent in most plants.
• Nucleolus = site of rRNA synthesis and ribosome assembly.
• Eukaryotic flagella = 9+2 microtubule arrangement; prokaryotic = flagellin, rotary.
• Cyanobacteria are photosynthetic prokaryotes.
• Archaea lack peptidoglycan; cell walls vary in composition.
• Verify from standard textbook: exact lipid composition of archaeal membranes.