STEM Readiness: Pre-Calculus Readiness - Trigonometry: Sum/Difference Double, Angle Half, Angle Identities

Must?Know

• Prokaryotic cells range from 0.1–5.0 ?m in diameter; eukaryotic cells range from 10–100 ?m.
• Prokaryotic DNA is located in the nucleoid, a region without a membrane; eukaryotic DNA is enclosed within a membrane-bound nucleus.
• Prokaryotes have 70S ribosomes (30S + 50S subunits); eukaryotes have 80S ribosomes (40S + 60S subunits).
• Mitochondria and chloroplasts contain 70S ribosomes, supporting their origin via endosymbiosis.
• Bacterial cell walls contain peptidoglycan; archaea lack peptidoglycan and have pseudopeptidoglycan or other polymers.
• Plant cell walls are composed of cellulose; fungal cell walls contain chitin; animal cells lack a cell wall.
• All cells have a phospholipid bilayer plasma membrane; eukaryotes have additional internal membranes enclosing organelles.
• Eukaryotes possess membrane-bound organelles including nucleus, endoplasmic reticulum, Golgi apparatus, lysosomes, mitochondria, and (in plants) chloroplasts.
• Prokaryotes lack membrane-bound organelles; metabolic functions occur in the cytoplasm or at the plasma membrane.
• Bacteria (e.g., Escherichia coli) and archaea (e.g., Methanogens) are prokaryotes; animals, plants, fungi, and protists are eukaryotes.
• Mycoplasma species are bacteria that lack a cell wall, making them resistant to antibiotics like penicillin.
• Human red blood cells lack a nucleus and mitochondria in maturity, maximizing space for hemoglobin.
• Nuclear envelope in eukaryotes is a double membrane with nuclear pores that regulate transport between nucleus and cytoplasm.
• Chromosomes in prokaryotes are typically a single circular DNA molecule; eukaryotes have multiple linear chromosomes.
• Plasmids are small, circular DNA molecules found in prokaryotes and some yeasts (eukaryotic fungi).
• Endosymbiotic theory proposes that mitochondria and chloroplasts originated from free-living bacteria engulfed by ancestral eukaryotic cells.
• Evidence for endosymbiosis: mitochondria and chloroplasts have circular DNA, 70S ribosomes, and double membranes.
• Mitochondria are sites of aerobic respiration and ATP production; chloroplasts perform photosynthesis in plants and algae.
• Smooth endoplasmic reticulum (SER) synthesizes lipids and detoxifies drugs; rough ER (RER) has ribosomes and synthesizes proteins for secretion.
• Golgi apparatus modifies, sorts, and packages proteins into vesicles for transport to lysosomes, plasma membrane, or secretion.
• Lysosomes contain hydrolytic enzymes for intracellular digestion; absent in most plant cells (vacuoles perform similar function).
• Peroxisomes break down fatty acids and detoxify hydrogen peroxide; present in both plant and animal eukaryotic cells.
• Cytoskeleton components (microtubules, microfilaments, intermediate filaments) are found in eukaryotes but not in prokaryotes.
• Flagella in prokaryotes are made of flagellin and rotate; eukaryotic flagella are composed of microtubules (9+2 arrangement) and bend.

Difficulty Level

Intermediate – requires precise differentiation of structural and functional features across domains and organelles.

Common 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 correlates with organism 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 sometimes protein-based microcompartments.
• Trap: The nucleus evolved after other organelles – Fact: The nucleus is a defining feature of eukaryotes and likely evolved early in eukaryotic lineage via infolding of the plasma membrane.

Practice MCQs

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) 80S ribosomes
Answer: C
Explanation: All cells, regardless of type, have a phospholipid bilayer plasma membrane.
Why the top distractor is wrong: D is incorrect because 80S ribosomes are only in eukaryotes; prokaryotes have 70S ribosomes.

Question: Which structure is found in plant cells but not in animal cells?
A) Lysosome
B) Mitochondrion
C) Central vacuole
D) Golgi apparatus
Answer: C
Explanation: Mature plant cells have a large central vacuole for storage and turgor pressure; animal cells have smaller vesicles.
Why the top distractor is wrong: A is incorrect because lysosomes are present in animal cells (though rare in plants, vacuoles perform similar roles).

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) Being involved in ATP production
Answer: C
Explanation: Circular DNA and 70S ribosomes in mitochondria are bacterial characteristics, supporting endosymbiosis.
Why the top distractor is wrong: A is less specific because double membranes can arise by other mechanisms; C is more direct evidence.

Question: A cell is observed to have a nucleus, mitochondria, and a cell wall made of cellulose. From which organism is it most likely derived?
A) Fungus
B) Bacterium
C) Animal
D) Plant
Answer: D
Explanation: Cellulose cell walls, nucleus, and mitochondria are characteristic of plant cells.
Why the top distractor is wrong: A is incorrect because 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 are 80S; mitochondrial ribosomes are 70S, reflecting bacterial ancestry.
Why the top distractor is wrong: A is false because mitochondrial ribosomes are 70S, not 80S.

Question: Which cell lacks a nucleus and mitochondria when mature?
A) Yeast cell
B) Neuron
C) Human red blood cell
D) Leaf mesophyll cell
Answer: C
Explanation: Mature human red blood cells eject their nucleus and mitochondria to carry more hemoglobin.
Why the top distractor is wrong: A is incorrect because yeast is a eukaryotic fungus and has both nucleus and mitochondria.

Question: What is the primary structural component of the bacterial cell wall?
A) Chitin
B) Cellulose
C) Peptidoglycan
D) Phospholipids
Answer: C
Explanation: Peptidoglycan is the defining component of bacterial cell walls.
Why the top distractor is wrong: A is found in fungi, not bacteria.

Last?Minute Revision

• Prokaryotic cell size: 0.1–5.0 ?m
• Eukaryotic cell size: 10–100 ?m
• Prokaryotic ribosome = 70S (30S + 50S)
• Eukaryotic cytoplasmic ribosome = 80S (40S + 60S)
• Mitochondria and chloroplasts have 70S ribosomes
• Mitochondria have circular DNA – evidence of endosymbiosis
• Nuclear envelope = double membrane with pores
• Bacteria: peptidoglycan cell wall
• Plants: cellulose cell wall
• Fungi: chitin cell wall
• Animals: no cell wall
• Mycoplasma: no cell wall – smallest known cells
• Human red blood cells: no nucleus, no mitochondria
• Prokaryotes: DNA in nucleoid (no membrane)
• Eukaryotes: DNA in nucleus (membrane-bound)
• Prokaryotes: single circular chromosome
• Eukaryotes: multiple linear chromosomes
• Endosymbiotic theory supported by: 70S ribosomes, circular DNA, double membranes in mitochondria/chloroplasts
• Smooth ER: lipid synthesis, detoxification
• Rough ER: protein synthesis (with ribosomes)
• Golgi: modifies, sorts, packages proteins
• Lysosome: contains hydrolytic enzymes; absent in most plants
• Cytoskeleton (microtubules, microfilaments) only in eukaryotes
• Prokaryotic flagellum: made of flagellin, rotates
• Eukaryotic flagellum: 9+2 microtubule arrangement, bends