College-Level Examination Program (CLEP) Science and Mathematics Flashcards

24 sample cards from the Science and Mathematics deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. What is the difference between an arithmetic and a geometric sequence?

   Arithmetic adds a constant difference between terms (aₙ = a₁ + (n−1)d); geometric multiplies by a constant ratio (aₙ = a₁r^(n−1)).

2. What does it mean for the limit of f(x) as x approaches a to equal L?

   f(x) can be made arbitrarily close to L by taking x sufficiently close to a (from both sides).

3. What are the three conditions for a function to be continuous at x = a?

   f(a) is defined, the limit of f(x) as x→a exists, and that limit equals f(a).

4. What is the limit definition of the derivative f′(x)?

   f′(x) = lim(h→0) [f(x+h) − f(x)] / h.

5. State the power rule for differentiation.

   d/dx [xⁿ] = n·x^(n−1).

6. State the product rule for derivatives of f(x)·g(x).

   (fg)′ = f′g + fg′.

7. What does the first derivative tell you about a function's behavior?

   Its sign gives where the function is increasing (f′>0) or decreasing (f′<0); zeros indicate critical points (possible maxima/minima).

8. State the Fundamental Theorem of Calculus (Part 2) for evaluating definite integrals.

   ∫ₐᵇ f(x) dx = F(b) − F(a), where F is an antiderivative of f.

9. What is the power rule for integration of xⁿ (n ≠ −1)?

   ∫ xⁿ dx = x^(n+1)/(n+1) + C.

10. What are the four main biological macromolecules and their building blocks?

    Carbohydrates (monosaccharides), lipids (fatty acids/glycerol), proteins (amino acids), nucleic acids (nucleotides).

11. What is the role of mitochondria in the cell?

    They are the site of aerobic cellular respiration, producing ATP (the cell's energy currency).

12. What is the key structural difference between prokaryotic and eukaryotic cells?

    Eukaryotic cells have a membrane-bound nucleus and organelles; prokaryotic cells lack both.

13. State Mendel's Law of Segregation.

    Each organism carries two alleles for a trait that separate during gamete formation, so each gamete receives only one allele.

14. In DNA, which bases pair together?

    Adenine pairs with thymine (A–T), and guanine pairs with cytosine (G–C).

15. What is the central dogma of molecular biology?

    Genetic information flows DNA → RNA (transcription) → protein (translation).

16. What is the difference between mitosis and meiosis in terms of products?

    Mitosis produces two genetically identical diploid cells; meiosis produces four genetically varied haploid gametes.

17. State the four main mechanisms of evolution.

    Natural selection, genetic drift, gene flow (migration), and mutation.

18. What is the difference between a food chain's producers, consumers, and decomposers?

    Producers make their own food (autotrophs); consumers eat other organisms (heterotrophs); decomposers break down dead matter, recycling nutrients.

19. What information do the atomic number and mass number of an atom give?

    Atomic number = number of protons (defines the element); mass number = protons + neutrons.

20. What distinguishes the three states of matter—solid, liquid, and gas—at the particle level?

    Solids have fixed shape and volume (tightly packed); liquids have fixed volume but variable shape; gases have neither (particles far apart, fast-moving).

21. What does it mean to balance a chemical equation, and why is it required?

    Equal numbers of each type of atom appear on both sides; required by the law of conservation of mass.

22. State the first and second laws of thermodynamics.

    First: energy is conserved (cannot be created or destroyed). Second: the entropy of an isolated system always increases over time.

23. State Newton's three laws of motion.

    1) An object stays at rest or in uniform motion unless acted on by a net force (inertia). 2) F = ma. 3) Every action has an equal and opposite reaction.

24. What is the difference between the rock cycle's igneous, sedimentary, and metamorphic rocks?

    Igneous forms from cooled magma/lava; sedimentary from compacted/cemented sediments; metamorphic from existing rock altered by heat and pressure.

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