Circulatory System
Name the two main circuits of the human circulatory system and briefly describe their roles.
(Pulmonary circuit: carries blood between the heart and lungs for gas exchange; systemic circuit: carries oxygenated blood from the heart to the rest of the body and returns deoxygenated blood to the heart.)
What is the main function of the alveoli in the respiratory system?
Gas exchange between air and blood.)
What is the main function of the lymphatic system?
(Returns excess tissue fluid to the bloodstream and defends against infection.)
Given a function f(x)=ax+b passes through the points (1,2) and (3,6), find the values of a and b.
(Substitute points: 2 = a(1) + b, 6 = a(3) + b; solve to get a = 2, b = 0.)
What is the general formula for alkenes?
(CₙH₂ₙ)
Explain the structural differences between arteries and veins and how these relate to their functions.
(Arteries have thicker, more muscular walls to withstand higher pressure; veins have thinner walls and valves to prevent backflow.)
Describe the process of ventilation, including the roles of the diaphragm and intercostal muscles.
Diaphragm contracts/flattens and intercostals lift ribs for inhalation; relaxation causes exhalation.)
Name the organ that filters blood and removes old red blood cells.
(Spleen.)
Given f(x)=x^2+px+q has a minimum at x=5 and passes through (7, 10), find p and q.
(Minimum at x = -p/2 = 5 → p = -10. 10 = 7^2 -10(7) + q → 10 = 49 - 70 + q → q = 31.)
Calculate the molar mass of ethanoic acid (CH₃COOH).
(12×2 + 1×4 + 16×2 = 60 g/mol.)
Describe the cardiac cycle, including the terms systole and diastole, and explain how they relate to heart sounds.
(Systole: contraction, pumping blood; diastole: relaxation, chambers fill. Heart sounds come from valve closures during these phases.)
Explain how oxygen and carbon dioxide are transported in the blood.
(Oxygen binds to hemoglobin; CO₂ is carried dissolved, as bicarbonate, and bound to hemoglobin.)
What is the role of lymph nodes in the immune response?
(Filter lymph and house lymphocytes that respond to pathogens.)
The function f(x)=1x−2f(x)=x−21 is defined for all real numbers except one value. What is the domain?
(Domain: all real numbers except x = 2.)
Define empirical formula and give the empirical formula for C₄H₁₀.
(Empirical formula is the simplest whole-number ratio of atoms; for C₄H₁₀, it is C₂H₅.)
Trace the pathway of blood through the heart, starting and ending at the right atrium, naming all valves and chambers traversed.
Right atrium → tricuspid valve → right ventricle → pulmonary valve → pulmonary artery → lungs → pulmonary veins → left atrium → mitral valve → left ventricle → aortic valve → aorta → body → vena cava → right atrium.)
Explain how the structure of the alveoli maximizes the efficiency of gas exchange in the lungs.
(Alveoli have thin walls (one cell thick) to minimize diffusion distance, a large surface area to volume ratio for maximum gas exchange, and are surrounded by a dense network of capillaries to maintain concentration gradients.)
Describe the pathway of lymph from tissues back to the circulatory system.
Lymph capillaries → lymph vessels → lymph nodes → lymph ducts → subclavian veins.)
300: Factorise the cubic polynomial x^3−5x^2+8x−4.
(Answer: (x−1)(x−2)2
A sample contains 0.5 mol of NaCl. How many grams is this?
(0.5 × 58.44 = 29.22 g.)
Explain how the structure of capillaries facilitates the exchange of substances between blood and tissues, and discuss how this structure differs from that of arteries and veins.
(Capillaries have extremely thin walls made of a single layer of endothelial cells, allowing efficient diffusion of oxygen, nutrients, carbon dioxide, and wastes between blood and surrounding tissues. Their small diameter slows blood flow, maximizing exchange time. Unlike arteries, which have thick muscular and elastic walls to withstand high pressure, and veins, which have thinner walls and valves to assist blood return, capillaries lack muscle and connective tissue layers, making them uniquely suited for exchange rather than transport.)
Describe the changes in lung volumes and capacities during exercise and explain how these changes meet the body’s increased oxygen demand.
(During exercise, tidal volume and respiratory rate increase, increasing minute ventilation. This enhances oxygen uptake and carbon dioxide removal to meet increased metabolic demands. Vital capacity remains the same, but the increased ventilation improves gas exchange efficiency.)
Explain how the lymphatic system helps maintain fluid balance and prevent edema.
(It collects excess interstitial fluid and returns it to the bloodstream; if blocked, fluid accumulates in tissues, causing edema.)
A farmer wants to construct a rectangular vegetable patch adjacent to a river, requiring fencing on three sides. The river forms one side of length yy, and the other two sides are each of length xx. The area of the patch must be 800 m2800m2, and the cost of fencing is $15 per meter for the sides perpendicular to the river and $10 per meter for the side parallel to the river. Determine the dimensions xx and yy that minimize the total cost of fencing.
Area Constraint:
x⋅y=800x⋅y=800 → y=800xy=x800.
Cost Function:
Total cost C=15(2x)+10(y)=30x+10yC=15(2x)+10(y)=30x+10y.
Substitute yy:
C=30x+10(800x)=30x+8000xC=30x+10(x800)=30x+x8000.
Optimization Using Calculus:
Find the derivative: C′(x)=30−8000x2C′(x)=30−x28000.
Set C′(x)=0C′(x)=0:
30=8000x230=x28000 → x2=800030≈266.67x2=308000≈266.67 → x≈16.33 mx≈16.33m.
Find yy:
y=80016.33≈49.0 my=16.33800≈49.0m.
Answer:
Dimensions are approximately x≈16.33 mx≈16.33m (width perpendicular to the river) and y≈49.0 my≈49.0m (length parallel to the river).
A hydrocarbon sample contains 82.8% carbon and 17.2% hydrogen by mass. Find its empirical formula.
(Assume 100 g: 82.8 g C (6.9 mol), 17.2 g H (17.2 mol); ratio C:H ≈ 1:2.5, so empirical formula is C₂H₅.)