Talas Review Co. — UPCAT Reviewer Kit

Sample Questions

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Language Proficiency 1 / 6

The committee's decision, along with the advisers' recommendations, ___ announced after the meeting, ___ many students who had expected a different result.

A were; surprising
B was; surprising
C were; surprised
D was; it surprised

Language Proficiency

B was; surprising

The true subject is "decision," which is singular. The phrase "along with the advisers' recommendations" is only an interrupting phrase, so it does not make the subject plural. Therefore, the verb should be "was," not "were." The participial phrase "surprising many students" also correctly explains the effect of the announcement without creating a wordy second clause.

Ignore interrupting phrases when checking subject-verb agreement. Find the core subject first.

Language Proficiency 2 / 6

Although the speaker's tone was courteous, the substance of his remarks was ___; each compliment was followed by a carefully worded accusation.

A conciliatory
B acerbic
C perfunctory
D ingenuous

Language Proficiency

B acerbic

The clue is in the contrast: the speaker sounded courteous, but each compliment was followed by an accusation. "Acerbic" means sharp, harsh, or biting in tone. Even if the delivery seemed polite, the content was actually critical. "Conciliatory" means peace-making, "perfunctory" means done with little care, and "ingenuous" means innocent or sincere.

For vocabulary questions, do not rely on one word alone. Use the entire sentence as context.

Science 3 / 6

A sealed flask contains aquatic plants, snails, water, and a carbon dioxide indicator. In bright light, the indicator shows that carbon dioxide decreases. After several hours in darkness, the same indicator shows that carbon dioxide increases. Which explanation best accounts for both observations?

A Photosynthesis occurs only in darkness, while cellular respiration occurs only in light.
B In light, photosynthesis uses carbon dioxide faster than respiration releases it; in darkness, respiration continues while photosynthesis stops.
C Plants release oxygen only in darkness, causing carbon dioxide to dissolve more easily in water.
D Snails stop respiring in light but begin photosynthesis in darkness.

Science

B In light, photosynthesis uses carbon dioxide faster than respiration releases it; in darkness, respiration continues while photosynthesis stops.

Both plants and snails carry out cellular respiration, which releases carbon dioxide. In bright light, aquatic plants also perform photosynthesis, which uses carbon dioxide. If carbon dioxide decreases in light, photosynthesis must be using it faster than respiration produces it. In darkness, photosynthesis cannot proceed because light is unavailable, but respiration continues, so carbon dioxide builds up again.

Photosynthesis uses CO₂ and releases O₂. Cellular respiration uses O₂ and releases CO₂. Plants do both, but photosynthesis requires light.

Science 4 / 6

A 0.50-kg cart moving at 6.0 m/s collides with and sticks to a 1.0-kg cart initially at rest on a frictionless track. What fraction of the original kinetic energy is lost during the collision?

A 1/3
B 1/2
C 2/3
D 3/4

Science

C 2/3

Because the carts stick together, this is a perfectly inelastic collision. Momentum is conserved, but kinetic energy is not. Initial momentum is (0.50 kg)(6.0 m/s) + (1.0 kg)(0) = 3.0 kg·m/s. The combined mass after collision is 1.5 kg, so the final velocity is 3.0/1.5 = 2.0 m/s. Initial kinetic energy is ½(0.50)(6.0²) = 9.0 J. Final kinetic energy is ½(1.5)(2.0²) = 3.0 J. Energy lost is 9.0 − 3.0 = 6.0 J. The fraction lost is 6.0/9.0 = 2/3.

In perfectly inelastic collisions, conserve momentum first. Do not assume kinetic energy is conserved.

Mathematics 5 / 6

Find the domain of the function f(x) = √((x + 1) / (x − 2)).

A (-∞, -1] ∪ (2, ∞)
B [-1, 2)
C (-∞, -1) ∪ [2, ∞)
D (-1, 2)

Mathematics

A (-∞, -1] ∪ (2, ∞)

The expression inside a square root must be greater than or equal to zero: (x + 1)/(x − 2) ≥ 0. The critical values are x = −1, which makes the numerator zero, and x = 2, which makes the denominator zero. Test the intervals: for x < −1, the fraction is positive; at x = −1, the value is 0, so it is allowed; between −1 and 2, the fraction is negative, so it is not allowed; for x > 2, the fraction is positive. x = 2 is excluded because division by zero is undefined.

For square roots of rational expressions, require the fraction to be ≥ 0 and exclude values that make the denominator zero.

Mathematics 6 / 6

A box contains 4 red balls, 3 blue balls, and 2 green balls. Three balls are drawn without replacement. What is the probability that exactly two of the three balls have the same color?

A 5/14
B 55/84
C 2/3
D 29/84

Mathematics

B 55/84

There are 9 balls total, so the number of ways to draw any 3 balls is C(9,3) = 84. We want exactly one pair of the same color and one ball of a different color. If the pair is red: choose 2 of 4 red balls and 1 non-red ball: C(4,2)·5 = 30. If the pair is blue: C(3,2)·6 = 18. If the pair is green: C(2,2)·7 = 7. Total favorable outcomes = 30 + 18 + 7 = 55. Therefore, the probability is 55/84.

For "exactly two of the same color," count one pair plus one different ball. Exclude cases where all three are the same color.