Examius
🇺🇸 College-Level Examination Program (CLEP) · subject
College-Level Examination Program (CLEP) Science and Mathematics Syllabus
The Science and Mathematics syllabus for College-Level Examination Program (CLEP) in full: 6 chapters, 25 topics and 62 sub-topics, every one listed below, plus 51 Science and Mathematics flashcards with answers.
Science and Mathematics syllabus: all 6 chapters
Expand any chapter to see its topics and sub-topics.
-
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
- Logic and Sets
-
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
- Algebraic Operations
-
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
- Limits and Continuity
-
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
- Molecular and Cellular Biology
-
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
- Structure of Matter
-
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
- Biological Science
College-Level Examination Program (CLEP) Science and Mathematics flashcards — 51 questions with answers
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.
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.
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).
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).
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.
What is the probability of two independent events A and B both occurring?
P(A and B) = P(A) × P(B).
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.
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.
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.
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.
How do you calculate the percent change between an old value and a new value?
Percent change = ((new − old) / old) × 100%.
What is the formula for the area and circumference of a circle of radius r?
Area = πr²; Circumference = 2πr.
State the Pythagorean theorem for a right triangle.
a² + b² = c², where c is the hypotenuse and a, b are the legs.
What is the formula for the volume of a sphere of radius r?
V = (4/3)πr³.
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°.
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).
How do you factor a difference of two squares, a² − b²?
(a − b)(a + b).
State the quadratic formula for solving ax² + bx + c = 0.
x = (−b ± √(b² − 4ac)) / (2a).
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.
When you multiply or divide both sides of an inequality by a negative number, what happens?
The inequality sign reverses direction.
Show the other 31 Science and Mathematics flashcards
What is the definition of a function in terms of inputs and outputs?
A relation that assigns exactly one output (y) to each input (x).
What is the difference between an even function and an odd function?
Even: f(−x) = f(x) (symmetric about the y-axis). Odd: f(−x) = −f(x) (symmetric about the origin).
What is the slope-intercept form of a line, and what do the constants mean?
y = mx + b, where m is the slope and b is the y-intercept.
Define sine, cosine, and tangent in terms of a right triangle's sides.
sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent (SOH-CAH-TOA).
State the fundamental Pythagorean trigonometric identity.
sin²θ + cos²θ = 1.
What are the exact values of sin and cos at θ = 30°, 45°, and 60°?
sin: 1/2, √2/2, √3/2; cos: √3/2, √2/2, 1/2 respectively.
What is the distance formula between points (x₁,y₁) and (x₂,y₂)?
d = √((x₂ − x₁)² + (y₂ − y₁)²).
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)).
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).
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).
What is the limit definition of the derivative f′(x)?
f′(x) = lim(h→0) [f(x+h) − f(x)] / h.
State the power rule for differentiation.
d/dx [xⁿ] = n·x^(n−1).
State the product rule for derivatives of f(x)·g(x).
(fg)′ = f′g + fg′.
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).
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.
What is the power rule for integration of xⁿ (n ≠ −1)?
∫ xⁿ dx = x^(n+1)/(n+1) + C.
What are the four main biological macromolecules and their building blocks?
Carbohydrates (monosaccharides), lipids (fatty acids/glycerol), proteins (amino acids), nucleic acids (nucleotides).
What is the role of mitochondria in the cell?
They are the site of aerobic cellular respiration, producing ATP (the cell's energy currency).
What is the key structural difference between prokaryotic and eukaryotic cells?
Eukaryotic cells have a membrane-bound nucleus and organelles; prokaryotic cells lack both.
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.
In DNA, which bases pair together?
Adenine pairs with thymine (A–T), and guanine pairs with cytosine (G–C).
What is the central dogma of molecular biology?
Genetic information flows DNA → RNA (transcription) → protein (translation).
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.
State the four main mechanisms of evolution.
Natural selection, genetic drift, gene flow (migration), and mutation.
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.
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.
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).
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.
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.
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.
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.
College-Level Examination Program (CLEP) Science and Mathematics FAQ
What is in the College-Level Examination Program (CLEP) Science and Mathematics syllabus?
College-Level Examination Program (CLEP) Science and Mathematics is split into 6 chapters: College Mathematics, College Algebra and Precalculus, Calculus, Biology, Chemistry and Natural Sciences. Together they contain 25 topics and 62 sub-topics.
How many chapters are in College-Level Examination Program (CLEP) Science and Mathematics?
6 chapters, containing 25 topics and 62 sub-topics. The largest chapter is College Mathematics, with 5 topics.
Are there flashcards for College-Level Examination Program (CLEP) Science and Mathematics?
Yes — a 51-card Science and Mathematics deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.