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Short passages, data and applied reasoning across maths, science, economics and social science. You answer questions about what is stated.
Every question below is original, written to the official task format, and answered in full. Work through them on paper first, then again without it — you cannot count on having anything to write on during the exam, so solving in your head is part of the skill.
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A drone starts at the origin and makes two displacement moves. First it flies along vector `u = (3, 4)`, then along vector `v = (-1, 2)`. All coordinates are in metres, measured east (x) and north (y).
What is the drone's final position relative to its start?
Correct answer: B — (2, 6)
Add the vectors componentwise: (3 + (-1), 4 + 2) = (2, 6).
What is the magnitude of the first displacement u = (3, 4)?
Correct answer: A — 5 m
sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5 m.
How far is the drone from its start after both moves? Round to one decimal place.
Correct answer: C — 6.3 m
The resultant is (2, 6); its magnitude is sqrt(2^2 + 6^2) = sqrt(40) = 6.3 m.
Passage
A constant force `F = (6, 8)` newtons acts on a crate while the crate is displaced by `s = (2, 0)` metres. The work done by a constant force equals the dot product `W = F . s` (in joules).
How much work does the force do on the crate?
Correct answer: D — 12 J
W = F . s = 6*2 + 8*0 = 12 J. The vertical force component does no work because the displacement is horizontal.
Passage
The gauge pressure at depth h below the surface of a fluid is `p = rho * g * h`, where rho is the fluid density, `g = 10 m/s^2` is the gravitational acceleration, and h is the depth. For fresh water `rho = 1000 kg/m^3`. Gauge pressure is the pressure above atmospheric.
What is the gauge pressure at a depth of 5 m in fresh water?
Correct answer: D — 50 kPa
p = rho*g*h = 1000 * 10 * 5 = 50 000 Pa = 50 kPa.
At what depth is the gauge pressure equal to 30 kPa?
Correct answer: D — 3 m
h = p / (rho*g) = 30 000 / (1000 * 10) = 3 m.
Seawater (rho = 1025 kg/m^3) is denser than fresh water. Compared with fresh water, the pressure at a given depth in seawater is:
Correct answer: D — slightly greater
Pressure is proportional to density (p = rho*g*h), so a higher density gives a slightly greater pressure at the same depth.
Passage
A researcher surveys 500 university students about their sleep habits and finds that students who drink more coffee report fewer hours of sleep. The study is observational: the researcher measured coffee intake and sleep but did not assign students to drink specific amounts.
The 500 students were all drawn from a single university. This mainly limits the study’s:
Correct answer: B — ability to generalise to other populations
Sampling from one university limits external validity (generalisability); the results may not extend to other populations.
Which conclusion is best supported by this observational study?
Correct answer: D — Coffee intake and sleep are negatively associated, but causation cannot be established.
An observational study can show association but cannot, on its own, establish the direction of causation.
A heavy course load might cause both higher coffee intake and less sleep. Such a variable is called a:
Correct answer: C — confounding variable
A confounding variable influences both the supposed cause and the effect, creating a misleading association.
Passage
An online store lists a jacket at EUR 80. During a sale the price is reduced by 25%. A loyalty member then receives a further 10% off the sale price at checkout.
What is the sale price of the jacket before the loyalty discount?
Correct answer: A — EUR 60
A 25% reduction leaves 75%: 80 * 0.75 = EUR 60.
What does a loyalty member finally pay at checkout?
Correct answer: B — EUR 54
The sale price is EUR 60; a further 10% off leaves 90%: 60 * 0.90 = EUR 54.
The two successive discounts (25% then 10%) are equivalent to a single discount of:
Correct answer: C — 32.5%
The final fraction paid is 0.75 * 0.90 = 0.675, so the combined discount is 1 - 0.675 = 0.325 = 32.5%.