| exam,exam_stage,subject,domain,subdomain,context,questions,answer | |
| naep,standalone,science,life_science,,Explain the evolution of an organism,"[""The overuse of antibiotics has led to an increase in the prevalence of antibiotic-resistant strains of bacteria. Explain how this occurred.""]","Student response explains that a mutation occurred in the DNA of some bacteria, so they were resistant to the antibiotic. The antibiotic-resistant bacteria then passed the resistance on (DNA mutation) when they reproduced." | |
| naep,standalone,science,life_science,,Explain fossil evidence based on evolutionary change,"[""Fossils of *Basilosaurus*, a primitive whale that lived in water and existed about 50 million years ago, have well-defined ankle bones and toes.\n\nWhat does this suggest about how the ancestors of this primitive whale moved and where they lived?""]","Student response explains that the ancestors of this whale probably walked (on limbs, feet) and lived on land (ground)." | |
| naep,standalone,science,earth_environmental,,Describe environmental impacts of human activities,"[""During winter a town has the choice of applying salt or sand to icy roads to help cars travel more safely. Both applications can impact the natural environment.\n\nDescribe one negative environmental impact of using salt on icy roads. Be specific.\n\nDescribe one negative environmental impact of using sand on icy roads. Be specific."", ""Describe one negative environmental impact of using salt on icy roads. Be specific."", ""Describe one negative environmental impact of using sand on icy roads. Be specific.""]","Student response is correct for Part 1 and Part 2 | |
| Part 1: Describes a plausible and specific negative environmental impact of using salt. | |
| Major response types include: | |
| - It directly harms (kills, dries out) roadside vegetation (plants, trees). | |
| - It changes the soil composition making it harder for plants to survive. | |
| - It makes streams and rivers salty and some organisms will not survive. | |
| - It reduces the oxygen supply in streams and therefore affects the survival of aquatic organisms. | |
| - It contaminates public drinking (well) water; reduces sources of freshwater; and changes the chemical composition of freshwater streams harming organisms. | |
| Part 2: Describes a plausible and specific negative environmental impact of using sand. | |
| Major response types include: | |
| - It produces solid waste so that clean-up is required to reduce possible harm (death) to animal and plant life. | |
| - It erodes slopes and stream banks as it is carried by storm water runoff. | |
| - It clogs storm drains (streams) causing flooding. | |
| - It buries aquatic floor life in streams and rivers. | |
| - It destroys roadside plants/animals by suffocating (crushing) them; and filling in animal homes. | |
| - It changes the composition of the soil, making it unsuitable for some types of organisms (more specifically, the soil will hold less water). | |
| - It increases air pollution when particulates (dust) escape into the air making it harder for organisms to breathe. | |
| Note: | |
| - Non-acceptable responses related to the non-natural environment include: damage to cars (metal, tires); damage to road (concrete); damage to gutters; less traction (slick roads); and pollution. | |
| - Non-natural environmental effects can be mentioned if a resulting natural effect is included (for example, clogging storm drains and flooding.)" | |
| naep,standalone,economics,The International Economy,,Provide an analysis of issues related to the imposition of a tariff,"[""Explain why United States steel manufacturers would support a tariff on imported steel."", ""Explain why United States steel workers would support a tariff on imported steel.""]","The response provides acceptable answers for all four parts of the question (A, B, C, and D) | |
| In part A: Gives an acceptable answer on the tariff's effect on domestic producers | |
| In part B: Gives an acceptable answer on the tariff's effect on steel workers | |
| In part C: Notes that consumers will pay a higher price for steel. (Also accept comments that refer to domestic businesses that use steel.) | |
| In part D: Gives an acceptable answer for the reason for the adoption of a tariff that addresses or acknowledges the fact that it hurts the consumer." | |
| naep,standalone,economics,The National Economy,,Identify two economic costs of unemployment,"[""A high rate of unemployment that lasts for several years has economic costs for a nation. What are two of these economic costs?""]",The response provides two economic costs of unemployment. | |
| naep,standalone,economics,The International Economy,,Describe how a change in the dollar-euro exchange rate will impact purchases of goods outside of the U.S.,"[""Annette is going on a trip to France. The currency used in France is the euro. When Annette planned for the trip, the exchange rate was 1 United States dollar = 1.40 euros. On the day Annette exchanges her money, she discovers that the exchange rate is now 1 United States dollar = 0.80 euros.\n\nDescribe what effect this change will have on Annette's ability to make purchases in France and explain why.""]","The response provides both the correct effect (A) and the correct explanation (B). | |
| A. Response must state that the effect is that Annette will make fewer purchases (not buy as much, have fewer euros to spend) or she will need more dollars to purchase the same amount of goods. | |
| B. The correct explanation: The dollar is weaker (depreciated, worth less in exchange for the euro, lost value in exchange for the euro) or the euro is stronger (appreciated, worth more in exchange for the dollar, gained value in exchange for the dollar)." | |
| naep,standalone,economics,The Market Economy,,Explain the rationale for a purchasing decision when considering interest rates and inflation,"[""Nancy has just inherited \\$2,000. Within the next year, she needs to purchase furniture that costs \\$2,000. If Nancy puts the \\$2,000 in her savings account, she will earn 2 percent interest for the year. Nancy expects that the current inflation rate of 3 percent will continue for at least one year. From an economic perspective, explain why Nancy should buy the furniture now instead of putting the \\$2,000 into her savings account.""]","The response explains that the real interest rate is negative or otherwise demonstrates an understanding that the purchasing power of Nancy's savings is decreasing (e.g., by saying that given the rate of inflation is greater than the interest she is earning, so at the end of the year Nancy would not be able to take her savings and purchase the same furniture). The response demonstrates an understanding that the negative real interest rate reduces the economic incentive for Nancy to deposit her money in the bank and not purchase the furniture." | |
| naep,standalone,economics,The National Economy,,Explain how and why a reduction in taxes would affect employment and interest rates in the short term,"[""Explain how and why a reduction in taxes would affect employment in the short term."", ""Explain how and why a reduction in taxes would affect interest rates in the short term.""]","The response indicates an understanding that reducing taxes both (A) promotes more employment and (B) places upward pressure on interest rates. The response indicates that (C) decreasing taxes increases income and spending, leading to an increase in employment; and (D) decreasing taxes increases income and spending, increasing the demand for money, which places upward pressure on interest rates." | |
| naep,standalone,economics,The Market Economy,,Describe two economic factors that could influence a household's decision making process,"[""Robert and Sally are a two-income married couple. They are starting a family and deciding whether one parent should stay at home with the children and not work for money. Briefly describe two economic factors that are most likely to influence their decision.\n\n1)\n\n---\n\n---\n\n---\n\n2)\n\n---\n\n---\n\n---\n\n---\n\n---""]",The response includes two economic factors. | |
| naep,standalone,economics,The Market Economy,,Determine how changes in production costs will affect the level of production and product price,"[""To meet new regulations, a company has decided to upgrade the pollution control equipment used in its production process. The equipment will increase the cost of production.\n\nHow will the installation of this equipment affect (1) the company's level of production and (2) the price of the company's product?""]","Response recognizes that the legislation will have the following effects: | |
| (A) The firm's level of production will decrease. (Output will decrease.) | |
| (B) The price of the product will increase." | |
| naep,standalone,economics,The Market Economy,,Identify and explain how a change in the price of a product affects quantity demanded,"[""Suppose that the price of grapes increases by a large amount. What will happen in the short term to the quantity of grapes demanded? Explain why.""]","The response states that quantity (demanded) decreases and offers one of the following explanations. [Note - if the explanation implies that quantity (demanded) decreases, the response need not say so explicitly]: | |
| - Because of the law of demand (or the response can describe the law of demand by saying there is an inverse relation between price and quantity or that when price increases, quantity decreases and vice versa) | |
| - Because of costs vs. benefits | |
| - Because consumers might buy substitutes" | |
| naep,standalone,economics,The International Economy,,Explain why United States steel manufacturers would support a tariff on imported steel.,"[""Explain why United States steel manufacturers would support a tariff on imported steel."", ""Explain why United States steel workers would support a tariff on imported steel."", ""Explain why United States consumers would be hurt by a tariff on imported steel."", ""Explain why a steel tariff might be adopted even if it hurts United States consumers.""]","Provides acceptable answers for all four parts of the question (A, B, C, and D) | |
| In part A: Gives an acceptable answer on the tariff's effect on domestic producers | |
| In part B: Gives an acceptable answer on the tariff's effect on steel workers | |
| In part C: Notes that consumers will pay a higher price for steel. (Also accept comments that refer to domestic businesses that use steel.) | |
| In part D: Gives an acceptable answer for the reason for the adoption of a tariff that addresses or acknowledges the fact that it hurts the consumer." | |
| sat,standalone,maths,Algebra,Elementary Algebra,The function $f$ is defined by $f(x) = x^2 + x + 71$.,"[""What is the value of $f(2)$?""]",77 | |
| sat,standalone,maths,Algebra,Elementary Algebra,An event planner is planning a party. It costs the event planner a onetime fee of \$35 to rent the venue and \$10.25 per attendee. The event planner has a budget of \$300.,"[""What is the greatest number of attendees possible without exceeding the budget?""]",25 | |
| sat,standalone,maths,Algebra,Elementary Algebra,"The solution to the given system of equations is $(x, y)$. What is the value of $y$?","[""What is the value of $y$?""]",1 | |
| sat,standalone,maths,Algebra,Elementary Algebra,"The function $f$ is defined by $f(x) = (x - 6)(x - 2)(x + 6)$. In the $xy$-plane, the graph of $y = g(x)$ is the result of translating the graph of $y = f(x)$ up 4 units.","[""What is the value of $g(0)$?""]",76 | |
| sat,standalone,maths,Algebra,Elementary Algebra,"The solution to the given system of equations is $(x, y)$. What is the value of $x - y$?","[""What is the value of $x - y$?""]",35 | |
| sat,standalone,maths,Geometry,Euclidean Geometry,"A right triangle has legs with lengths of 24 centimeters and 21 centimeters. If the length of this triangle's hypotenuse, in centimeters, can be written in the form $3\sqrt{d}$, where $d$ is an integer, what is the value of $d$?","[""What is the value of $d$?""]",113 | |
| sat,standalone,maths,Algebra,Elementary Algebra,What is the sum of the solutions to the given equation?,"[""What is the sum of the solutions to the given equation?""]",$\frac{29}{3}$ | |
| sat,standalone,maths,Statistics,Descriptive Statistics,"73, 74, 75, 77, 79, 82, 84, 85, 91","[""What is the median of the data shown?""]",79 | |
| sat,standalone,maths,Algebra,Elementary Algebra,The function $f$ is defined by $f(x) = 4x$. For what value of $x$ does $f(x) = 8$?,"[""For what value of $x$ does $f(x) = 8$?""]",2 | |
| sat,standalone,maths,Algebra,Elementary Algebra,"Vivian bought party hats and cupcakes for \$71. Each package of party hats cost \$3, and each cupcake cost \$1. If Vivian bought 10 packages of party hats, how many cupcakes did she buy?","[""How many cupcakes did she buy?""]",41 | |
| sat,standalone,maths,Algebra,Elementary Algebra,"The exponential function $g$ is defined by $g(x) = 19 \cdot a^x$, where $a$ is a positive constant. If $g(3) = 2,375$, what is the value of $g(4)$?","[""What is the value of $g(4)$?""]","11,875" | |
| sat,standalone,maths,Geometry,Analytic Geometry,"A circle in the $xy$-plane has a diameter with endpoints $(2, 4)$ and $(2, 14)$. An equation of this circle is $(x - 2)^2 + (y - 9)^2 = r^2$, where $r$ is a positive constant.","[""What is the value of $r$?""]",5 | |
| sat,standalone,maths,Algebra,Elementary Algebra,Line $\ell$ is defined by $3y + 12x = 5$. Line $n$ is perpendicular to line $\ell$ in the $xy$-plane.,"[""What is the slope of line $n$?""]",$\frac{1}{4}$ | |
| sat,standalone,maths,Geometry,Euclidean Geometry,"The perimeter of an equilateral triangle is 624 centimeters. The height of this triangle is $k\sqrt{3}$ centimeters, where $k$ is a constant.","[""What is the value of $k$?""]",104 | |
| dc,standalone,maths,algebra,linear_equations,"If Leah babysits for 7 hours this month, what is the minimum number of hours she would have to work at the ice cream shop to earn at least $120?","[""If Leah babysits for 7 hours this month, what is the minimum number of hours she would have to work at the ice cream shop to earn at least $120?""]",11 | |
| dc,standalone,maths,algebra,linear_equations,"Leah prefers babysitting over working at the ice cream shop. Out of 20 total hours, what is the maximum number of hours she can babysit to be able to earn at least $120 per month?","[""Out of 20 total hours, what is the maximum number of hours she can babysit to be able to earn at least $120 per month?""]",13 | |
| dc,standalone,maths,algebra,linear_equations,Create an equation to represent the total amount of money Matt and Phil earned at the fundraiser based on the number of cookies Matt made. Explain how you determined your equation.,"[""Create an equation to represent the total amount of money Matt and Phil earned at the fundraiser based on the number of cookies Matt made. Explain how you determined your equation.""]",see rubric | |
| dc,standalone,maths,algebra,linear_equations,Phil and Matt made a total of $72.00 selling the cookies. How many cookies did Phil make and how many cookies did Matt make? Show your work.,"[""How many cookies did Phil make and how many cookies did Matt make? Show your work.""]",see rubric | |
| dc,standalone,maths,algebra,linear_equations,"Next year Phil and Matt may sell the cookies for $5.50 each. They plan to make the same total number of cookies, but they predict that they will only sell 70% of them given the price increase. Based on their prediction, should Phil and Matt raise the price of the cookies? Justify your answer.","[""Based on their prediction, should Phil and Matt raise the price of the cookies? Justify your answer.""]",see rubric | |
| dc,standalone,maths,algebra,absolute_value,Determine the number of points that would be on the graph of the equation for each given case: Case 1: $c < 0$ Case 2: $c = 0$ Case 3: $c > 0$ Justify your answers.,"[""Determine the number of points that would be on the graph of the equation for each given case: Case 1: $c < 0$ Case 2: $c = 0$ Case 3: $c > 0$ Justify your answers.""]",see rubric | |
| olympiad,final,astrophysics,stellar_astrophysics,stellar_structure,,"[""1. A blue star with effective temperature $T_{\\mathrm{eff}} = 10,000\\mathrm{K}$ and apparent magnitude $m = 5$ is located 150 pc from Earth. Find the radius of the star. [2]""]","Given $T = 10000K$, $m = 5$, $d = 150$ pc. | |
| Using the distance modulus formula: $m - M = 5\log(d / 10)$, we find $M = 5 - 5\log(15) = -0.88$. | |
| Comparing with the Sun's absolute magnitude of 4.83, the luminosity ratio is $\frac{L}{L_{solar}} = 100^{(4.83 - (-0.88))/5} = 192L_{solar}$. | |
| Using the Stefan-Boltzmann Law $L = 4\pi R^2\sigma T^4$, the radius ratio is $\frac{R}{R_{solar}} = \left(\frac{L}{L_{solar}}\right)^{1/2} \left(\frac{T_{solar}}{T}\right)^2 = 4.6R_{solar}$." | |
| olympiad,final,astrophysics,celestial_mechanics,keplers_laws,,"[""2. The radial velocity curve of a nearby Solar-mass star shows that it has a planet orbiting it with a period of 3 days. This planet causes its host star to have a radial velocity semi-amplitude of $50\\mathrm{m / s}$ . Assuming that this planet's orbit is perfectly inclined to Earth, and has 0 eccentricity, what is the mass of this planet, in Jupiter masses? [2]""]","Given $T = 3$ days, $K = 50$ m/s, $M = 1M_{solar}$. | |
| Using Kepler's third law, the planet's orbital radius is $r = 0.041$ AU. | |
| The star's orbital radius is $r_s = 1.38 * 10^{-5}$ AU. | |
| Using the relation $m_p = \frac{r_s}{r_p} M$, we find $m_p = 3.36 * 10^{-4}M_{solar}$, which is approximately 0.11 Jupiter masses." | |
| olympiad,final,astrophysics,celestial_mechanics,n_body_dynamics,,"[""3. The Sun has a rotation rate of 24.5 days. Jupiter has a mass of $9.54\\times 10^{-4}$ solar masses, and a semimajor axis of 5.2 AU. Which object has more total angular momentum? [2]""]","Solar rotation rate is 24.5 days, $M_J = 9.54 * 10^{-4}M_{solar}$, $a = 5.2$ AU. | |
| Angular momentum of the Sun is $L_{solar} = 5 * 10^{10}$. | |
| Angular momentum of Jupiter is $L_J = 8.38 * 10^{11}$. | |
| Jupiter has more angular momentum." | |
| olympiad,final,astrophysics,stellar_astrophysics,stellar_evolution,,"[""4. What is the distance to a star cluster whose stars at the main sequence turn-off point have an apparent magnitude of $m = 10$ and an effective temperature of $T_{\\mathrm{eff}}\\approx 6000\\mathrm{K}$ ? How old is this cluster? [3]""]","Given $m = 10$, $T = 6000K$. | |
| Assuming the absolute magnitude of the stars at the turnoff point is 4.83, the distance is $d = 10 * 10^{(m - M)/5} = 108$ pc. | |
| The stars at the turnoff point are sunlike, so the cluster is approximately 10 Gyr old." | |
| olympiad,final,astrophysics,stellar_astrophysics,stellar_structure,,"[""6. A star has apparent magnitude $m = 8$ , parallax $p = 0.003$ and effective temperature $T_{\\mathrm{eff}}\\approx 6000\\mathrm{K}$ . What is the luminosity of the star? What is the likely spectral type of this star? Justify your answer. [3]""]","Given $m = 8$, $p = 0.003$, $T = 6000K$. | |
| Distance is $d = 1/p = 333$ pc. | |
| Using the distance modulus formula, the absolute magnitude is $M = 0.385$. | |
| Luminosity ratio is $\frac{L}{L_{solar}} = 59.9$. | |
| The star's temperature is approximately sunlike, suggesting class G, but it is significantly more luminous, suggesting a giant. GOIII would be a reasonable possible spectral type." | |
| olympiad,final,astrophysics,cosmology,cosmic_microwave_background,,"[""7. Assuming that the cosmic microwave background radiation has the spectrum of a blackbody throughout the evolution of the universe, determine how its temperature changes with redshift. In particular, find the temperature of the CMB at the epoch $z\\approx 10$ , knowing that the current temperature of the CMB is $2.73\\mathrm{K}$ . [3]""]","Using Wien's Law and the definition of redshift, the temperature at redshift $z = 10$ is $T = 30.03K$." | |
| olympiad,final,astrophysics,planetary_science,planetary_dynamics,,"[""8. Derive an expression for the blackbody temperature of a planet with radius $r$ and albedo $a$ , orbiting its sun at a certain distance $D$ . The star has a temperature $T_{\\star}$ and radius $R$ . You must show your derivation for credit, not just the final expression. [3]""]","At blackbody equilibrium, power in is equal to power out: | |
| $P_{out} = 4\pi R_p^2\sigma T_p^4$ | |
| $P_{in} = A(1 - a)\frac{L}{4\pi D^2} = \pi R_p^2(1 - a)\frac{4\pi R_p^2\sigma T_p^4}{4\pi D^2}$ | |
| Equating $P_{in} = P_{out}$, we get: | |
| $T_p^4 = (1 - a)T_\star^4\frac{R_\star^2}{4D^2}$ | |
| $T_p = (1 - a)^{1/4}T_\star\sqrt{\frac{R_\star}{2D}}$" | |
| olympiad,final,astrophysics,observational_astronomy,telescopes_instrumentation,,"[""9. A $2048\\times 3072$ pixel CCD camera with 7.2 micron pixels is attached to an f/10 telescope with a 0.256 m primary mirror. What is the angular resolution of the CCD, in arcseconds/pixel? [3]""]","Focal length is 2.56 m. | |
| Angular resolution is $\frac{7.2}{2.56} * 206265 = 0.58$ arcseconds/pixel." | |
| olympiad,final,astrophysics,celestial_mechanics,orbital_mechanics,,"[""10. An interplanetary spacecraft bound for Saturn (a = 9.6 AU) is launched into a 300 km, non-inclined parking orbit around the Earth. If the spacecraft takes a Hohmann transfer to Saturn, what is the delta-V required for trans-Saturn injection, and what is the required delta-V for insertion into a 100000 km circular orbit around Saturn? On what side of each planet should the burns occur? (Assume Saturn is in the same orbital plane as the Earth, and neglect the gravitational deflection of the ship's path after injection and before orbital insertion.) [4]""]","Using the vis-viva equation, the velocity at Earth's orbital distance is 40,080 m/s. | |
| The spacecraft's current maximum velocity relative to the Sun is 37540 m/s. | |
| The required $\Delta v$ is 2550 m/s, and the burn must occur on the night side of the Earth. | |
| The required $\Delta v$ for insertion into a 100000 km circular orbit around Saturn is 24900 m/s, and the burn must occur on the night side of Saturn." | |
| olympiad,final,astrophysics,celestial_mechanics,keplers_laws,,"[""11. Planet A orbits around Star A of mass $M = 0.54 M_{\\odot}$ with a period of $P = 6$ Earth years. Astronomers on this planet want to measure the distance of a distant Star B which happens to lie along the semimajor axis of Planet A's orbit, on the side of perihelion. They choose to do so using parallax, by noting the position of Star B with respect to the background stars at two different points in the orbit. These two points, X and Y, are located such that XY is perpendicular to the semimajor axis, and intersects it at the focus, i.e. where Star A is located. Astronomers measure the angle that Star B appears to change from X to Y as $\\theta = 0.05^{\\prime \\prime}$ . If Planet A is 0.537 AU from Star A at perihelion, what is the distance to Star B in parsecs? [4]""]","Using Kepler's third law, the semimajor axis is 2.69 AU. | |
| The latus rectum of the ellipse is 2.45 AU. | |
| Using the parallax equation, the distance to Star B is 49.0 pc." | |
| olympiad,final,astrophysics,coordinates_and_time,celestial_coordinates,,"[""12. On the vernal equinox, the Sun has a right ascension of 0 hours and a declination of $0^{\\circ}$ . Starting from the equinox, calculate the number of days, to the nearest tenth, that it takes for the Sun to have a right ascension of 4 hours. Assume a perfectly circular orbit and that the Earth is inclined $23.5^{\\circ}$ to the ecliptic plane. [4]""]","Using spherical trigonometry, the Sun traverses 62.1 degrees. | |
| The number of days is $\frac{62.1}{360} * 365 = 63.0$ days." | |
| olympiad,final,astrophysics,coordinates_and_time,celestial_coordinates,,"[""13. Rigel has equatorial coordinates $\\mathrm{RA} = 05\\mathrm{h}14\\mathrm{m}32.3\\mathrm{s}$ , $\\mathrm{Dec} = -08^{\\circ}12'06''$ , and Betelgeuse has coordinates $\\mathrm{RA} = 05\\mathrm{h}55\\mathrm{m}10.3\\mathrm{s}$ , $\\mathrm{Dec} = +07^{\\circ}24'25''$ . What is the angular separation between the two stars, and the position angle of Rigel relative to Betelgeuse? If a photographer wants to take a photo containing both stars, what is the maximum focal length they can use? [6]""]","Using spherical trigonometry, the angular separation is 18.59 degrees. | |
| The position angle is 33.12 degrees. | |
| The maximum focal length is 108 mm on 35mm film or 216 mm on 70mm film." | |
| olympiad,final,astrophysics,astrophysics_general,general_reasoning,,"[""1. Which of the following constellations are visible during the summer?\n\nA. Delphinus\nB. Taurus\nC. Monoceros\nD. Eridanus""]",A | |
| olympiad,final,astrophysics,astrophysics_general,general_reasoning,,"[""2. Which stars make up the Winter Triangle asterism?\n\nA. Regulus, Spica, Arcturus\nB. Sirius, Procyon, Betelgeuse\nC. Vega, Altair, Deneb\nD. Alpheratz, Algenib, Markab""]",B | |
| olympiad,final,astrophysics,celestial_mechanics,gravitation,,"[""3. The moon is at its upper culmination at 8pm, mean solar time. Estimate the phase of the moon.\n\nA. Waning Gibbous\nB. Waning Crescent\nC. Waxing Gibbous\nD. Waxing Crescent""]",C | |
| olympiad,final,astrophysics,stellar_astrophysics,stellar_evolution,,"[""4. Arrange the following stages of the life cycle of a star of one solar mass in chronological order - Red-giant branch, Planetary nebula, White dwarf, Main sequence star, Helium Flash.\n\nA. Main sequence star, Red-giant branch, Helium Flash, Planetary nebula, White dwarf\nB. Main sequence star, Helium Flash, Red-giant branch, Planetary nebula, White dwarf\nC. Main sequence star, Red-giant branch, Helium Flash, White dwarf, Planetary nebula\nD. Main sequence star, Helium Flash, Red-giant branch, White dwarf, Planetary nebula""]",A | |
| olympiad,final,astrophysics,planetary_science,solar_system,,"[""5. How are the rings of Saturn thought to be formed?\n\nA. They coalesced during the formation of the Solar System\nB. They were ejected from the surface of Saturn by a massive meteor impact.\nC. They are the disintegrated remains of some of Saturn's moons and captured meteorites\nD. They were gravitationally captured from the interstellar medium""]",C | |
| olympiad,final,astrophysics,observational_astronomy,telescopes_instrumentation,,"[""6. The James Webb Space Telescope is to be sent to the second Lagrange point of the Earth-Sun system. What is the significance of doing so?\n\nA. The telescope would require little expenditure of energy to maintain its orbit\nB. The Earth would shield the telescope from the intense solar radiation\nC. The Moon would shield the telescope from the intense solar radiation\nD. It allows for ground control to communicate easily with the telescope""]",A | |
| olympiad,final,astrophysics,planetary_science,exoplanets,,"[""7. Which of the following is not a possible method of detecting exoplanets?\n\nA. To observe the wobbling of the parent star due to the gravitational influence of the planet\nB. To observe the doppler shift of light emitted by the parent star due to the gravitational influence of the planet\nC. To observe the periodic dips in the brightness of the parent star due to planetary transits\nD. All of the above are possible methods for detecting exoplanets""]",D | |
| olympiad,final,astrophysics,observational_astronomy,telescopes_instrumentation,,"[""8. An 8 inch Dobsonian telescope with a focal ratio of f/6 is used with a 12mm Plossel eyepiece. Calculate the magnifying power of the telescope. (1 inch = 25.4mm)\n\nA. 30x\nB. 50x\nC. 100x\nD. 200x""]",C | |
| olympiad,final,astrophysics,observational_astronomy,photometry,,"[""9. Approximately how much higher is the limiting magnitude of a telescope than that of the human eye? Assume that the telescope has an aperture of 200mm and the diameter of the human iris is 5mm. (A magnitude difference of 5 corresponds to a 100-fold difference in luminosity).\n\nA. 6.0\nB. 7.0\nC. 8.0\nD. 9.0""]",C | |
| olympiad,final,astrophysics,observational_astronomy,telescopes_instrumentation,,"[""10. What is the advantage of an Equatorial telescope mount as compared to an Alt-az mount?\n\nA. Reduced vibrations and provides a more stable viewing platform\nB. Convenience of tracking the diurnal motion of the stars\nC. It can be made more compact than an Alt-az mount\nD. It is less complex than the Alt-az mount""]",B | |
| olympiad,final,astrophysics,observational_astronomy,photometry,,"[""11. Alberio (β Cygni) is a double star system in the constellation Cygnus. The magnitudes of the component stars Alberio A & Alberio B are given by 3.18 and 5.82 respectively. Find the apparent magnitude of Alberio.\n\nA. 2.96\nB. 3.09\nC. 3.49\nD. 4.75""]",B | |
| olympiad,final,astrophysics,coordinates_and_time,celestial_coordinates,,"[""12. Which of the following stars is circumpolar in Romania (44°25'N 26°06'E)? (Circum-polar stars are stars that never set).\n\nA. ζ Herculis (16h41m / 431°36')\nB. β Bóotis (15h01m / 402°23')\nC. θ Aurigae (5h59m / 437°12')\nD. γ Draconis (17h56m / 451°26')""]",D | |
| olympiad,final,astrophysics,celestial_mechanics,keplers_laws,,"[""13. Haley's comet last appeared in the night sky in 1986. The Perihelion and Aphelion of its orbit are given by 0.586AU & 35.1AU respectively. Predict when it will next return.\n\nA. 2036\nB. 2052\nC. 2061\nD. 2096""]",C | |
| olympiad,final,astrophysics,celestial_mechanics,gravitation,,"[""14. What would be the maximum speed of a meteor on a parabolic orbit around the sun, whose point of closest approach is 1 AU?\n\nA. 42.1 km/s\nB. 58.4 km/s\nC. 77.1 km/s\nD. 92.8 km/s""]",A | |
| olympiad,final,astrophysics,stellar_astrophysics,stellar_evolution,,"[""15. Estimate the lifespan of the Sun. (Mass of H : 1.00794u; Mass of He : 4.002602u)\n\nA. 8.5 Billion Years\nB. 9.6 Billion Years\nC. 10.2 Billion Years\nD. 10.7 Billion Years""]",D | |
| olympiad,final,astrophysics,coordinates_and_time,celestial_coordinates,,"[""16. Calculate the length of the shortest day that can be experienced in Romania (44°25'N 26°06'E). (Earth's axial tilt is 23.4)\n\nA. 8h 12m\nB. 8h 39m\nC. 9h 04m\nD. 9h 25m""]",B | |
| olympiad,final,astrophysics,celestial_mechanics,keplers_laws,One way to send a spacecraft to mars would be to employ an elliptical orbit with Earth at its perihelion and Mars at its aphelion. You may assume that Mars revolves around the Sun in a circular orbit of radius 1.52 AU.,"[""(a) How long does it take for the spacecraft to reach Mars? [4]""]","Semimajor axis of orbit (a) = 0.5(1 AU + 1.52 AU) = 1.26 AU | |
| T² (in years) = a³ (in AU) | |
| T = (1.26)^(3/2) = 1.41 years | |
| Time required = 0.5 × T = 0.707 years" | |
| olympiad,final,astrophysics,celestial_mechanics,keplers_laws,One way to send a spacecraft to mars would be to employ an elliptical orbit with Earth at its perihelion and Mars at its aphelion. You may assume that Mars revolves around the Sun in a circular orbit of radius 1.52 AU.,"[""(b) Assuming that the spacecraft is launched in the prograde direction, what elongation angle of mars should it be launched at to ensure that the spaceship reaches its destination? (A prograde direction is in the same direction as that of the orbits of the planets. The elongation angle of mars is the angle between the Sun and mars as seen from the earth.) [8]""]","T_Mars = (1.52)^(3/2) years = 1.87 years | |
| θ = (0.707 / 1.87) × 360° = 136° | |
| ME² = r_m² + r_e² - 2r_m r_e cos(180 - θ) | |
| ME = 1.06 AU | |
| r_m² = r_e² + ME² - 2r_e ME cos(φ) | |
| φ = 95°" | |
| olympiad,final,astrophysics,coordinates_and_time,celestial_coordinates,"Circumpolar stars are stars that never set below the horizon. Consider such a star with declination δ, as seen by a northern observer at latitude Φ.","[""(b) Find the condition δ and Φ must fulfill for the star to be circumpolar. [3]""]","(90° - Φ) + (90° - δ) < 90° | |
| Φ + δ > 90°" | |
| olympiad,final,astrophysics,cosmology,big_bang,"The critical density of the Universe is the density at which the gravitational attraction of matter within the universe is balanced with its expansion in such a way that neither will ultimately prevail. If the density of the universe were lower than this critical density, expansion will continue indefinitely. On the other hand, if the density of the universe were any higher, it would re-collapse upon itself.","[""(a) The critical density of the universe is given by:\n\nρ_c = 3H₀² / (8πG)\n\nIt is possible to arrive at this result through classical means. By modeling the universe as of having infinite extent and uniform density, expanding linearly with velocity ν = H₀κ derive the above expression. [6]""]","Consider a particle of mass m at a distance r from the center. | |
| Kinetic Energy = ½ mν² = ½ mH₀²r² | |
| Gravitational Potential Energy = -G M m / r = -G m / r (r²/3 π r² ρ_c) | |
| For the particle to be critically bound: Kinetic Energy + Gravitational Potential Energy = 0 | |
| ρ_c = 3H₀² / (8πG)" | |
| olympiad,final,astrophysics,cosmology,dark_matter,"The critical density of the Universe is the density at which the gravitational attraction of matter within the universe is balanced with its expansion in such a way that neither will ultimately prevail. If the density of the universe were lower than this critical density, expansion will continue indefinitely. On the other hand, if the density of the universe were any higher, it would re-collapse upon itself.","[""(b) The density of ordinary (baryonic) matter in the universe is determined to be about 3.8 × 10⁻²⁵ kg m⁻³. Hence, provide a justification for the existence of dark matter. (Latest estimates of the Hubble constant suggest a value of 2.20 × 10¹⁸ s⁻¹) [4]""]","ρ_c = 3H₀² / (8πG) = 8.66 × 10⁻²⁷ kg m⁻³ | |
| The density of the universe must be close to ρ_c | |
| Since 3.8 × 10⁻²⁵ kg m⁻³ << ρ_c, the remaining mass must be made up for by dark matter." | |