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

Science and Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Science and Mathematics in College-Level Examination Program (CLEP), not a summary of it.

1. 1

   College Mathematics

   5 topics

   • Logic and Sets
     • Logical statements and truth tables
     • Set operations and Venn diagrams
   • Number Systems and Algebra
     • Real number properties
     • Equations and inequalities
     • Functions and graphs
   • Probability and Statistics
     • Counting and probability
     • Measures of central tendency and dispersion
     • Data interpretation
   • Financial and Consumer Mathematics
     • Interest and growth
     • Proportions and percentages
   • Geometry and Measurement
     • Perimeter, area, and volume
     • Geometric reasoning
2. 2

   College Algebra and Precalculus

   5 topics

   • Algebraic Operations
     • Polynomials and factoring
     • Rational and radical expressions
   • Equations and Inequalities
     • Linear and quadratic equations
     • Systems of equations
     • Absolute value and inequalities
   • Functions and Their Properties
     • Function notation and operations
     • Exponential and logarithmic functions
     • Transformations and inverses
   • Trigonometry
     • Trigonometric functions and identities
     • Graphs and equations
   • Analytic Geometry and Sequences
     • Conic sections
     • Sequences and series
3. 3

   Calculus

   3 topics

   • Limits and Continuity
     • Evaluating limits
     • Continuity and asymptotes
   • Differential Calculus
     • Definition and rules of derivatives
     • Applications of derivatives
     • Related rates and optimization
   • Integral Calculus
     • Antiderivatives and definite integrals
     • Fundamental Theorem of Calculus
     • Applications of integration
4. 4

   Biology

   4 topics

   • Molecular and Cellular Biology
     • Chemistry of life
     • Cell structure and function
     • Energy and metabolism
   • Genetics and Molecular Inheritance
     • Mendelian genetics
     • DNA structure and gene expression
   • Organismal Biology
     • Plant structure and function
     • Animal systems and homeostasis
   • Evolution and Ecology
     • Mechanisms of evolution
     • Population and community ecology
     • Ecosystems and biodiversity
5. 5

   Chemistry

   4 topics

   • Structure of Matter
     • Atomic theory and structure
     • Periodic table and trends
     • Chemical bonding
   • States of Matter and Solutions
     • Gases and gas laws
     • Liquids, solids, and intermolecular forces
     • Solutions and concentration
   • Reactions and Stoichiometry
     • Chemical equations and stoichiometry
     • Types of reactions
     • Equilibrium
   • Thermodynamics and Kinetics
     • Energy and enthalpy
     • Reaction rates
     • Acids, bases, and electrochemistry
6. 6

   Natural Sciences

   4 topics

   • Biological Science
     • Cells, genetics, and evolution
     • Organisms and ecology
   • Physical Science: Chemistry
     • Atomic and molecular structure
     • Chemical reactions
   • Physical Science: Physics
     • Motion, force, and energy
     • Waves, electricity, and magnetism
   • Earth and Space Science
     • Geology and the atmosphere
     • Astronomy and the solar system

Science and Mathematics flashcards for College-Level Examination Program (CLEP)

20 of 51 cards from the Science and Mathematics deck — real questions with worked answers.

1. In set theory, what does the union of two sets A and B (A ∪ B) contain?

   All elements that belong to A, to B, or to both.

2. In logic, when is a conditional statement "if P then Q" false?

   Only when P is true and Q is false; in all other cases it is true.

3. What is the contrapositive of "if P then Q," and how does its truth value relate to the original?

   "If not Q then not P"; it is logically equivalent to the original (always shares the same truth value).

4. What distinguishes rational numbers from irrational numbers?

   Rational numbers can be written as a ratio a/b of two integers (b ≠ 0); irrational numbers cannot and have non-repeating, non-terminating decimals (e.g., π, √2).

5. State the commutative, associative, and distributive properties of real numbers.

   Commutative: a+b=b+a, ab=ba. Associative: (a+b)+c=a+(b+c). Distributive: a(b+c)=ab+ac.

6. What is the probability of two independent events A and B both occurring?

   P(A and B) = P(A) × P(B).

7. What is the difference between the mean, median, and mode of a data set?

   Mean is the arithmetic average; median is the middle value when ordered; mode is the most frequently occurring value.

8. What is the formula for the standard deviation's square, the variance, of a data set?

   Variance = the average of the squared deviations from the mean: σ² = Σ(xᵢ − μ)² / N.

9. What is the simple interest formula and what does each variable represent?

   I = Prt, where I is interest, P is principal, r is the annual rate (decimal), and t is time in years.

10. What is the compound interest formula for an amount compounded n times per year?

    A = P(1 + r/n)^(nt), where A is the final amount, P principal, r annual rate, n compoundings per year, t years.

11. How do you calculate the percent change between an old value and a new value?

    Percent change = ((new − old) / old) × 100%.

12. What is the formula for the area and circumference of a circle of radius r?

    Area = πr²; Circumference = 2πr.

13. State the Pythagorean theorem for a right triangle.

    a² + b² = c², where c is the hypotenuse and a, b are the legs.

14. What is the formula for the volume of a sphere of radius r?

    V = (4/3)πr³.

15. What is the sum of the interior angles of a triangle, and of a polygon with n sides?

    A triangle's angles sum to 180°; an n-sided polygon's interior angles sum to (n − 2) × 180°.

16. What are the exponent rules for multiplying and dividing powers with the same base?

    x^a · x^b = x^(a+b); x^a / x^b = x^(a−b).

17. How do you factor a difference of two squares, a² − b²?

    (a − b)(a + b).

18. State the quadratic formula for solving ax² + bx + c = 0.

    x = (−b ± √(b² − 4ac)) / (2a).

19. What does the discriminant b² − 4ac tell you about a quadratic's roots?

    Positive → two distinct real roots; zero → one repeated real root; negative → two complex conjugate roots.

20. When you multiply or divide both sides of an inequality by a negative number, what happens?

    The inequality sign reverses direction.

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