Question 1: If y = x³ + 2x and dx/dt = 3, what is dy/dt when x = 2?
Topic: Differential Calculus
- eighteen
- twelve
- fourteen
- forty-two (Correct Answer)
Loading...

Calculus is the mathematics of change; how things grow, shrink, and transform. It's the language of physics, engineering, economics, and any field dealing with dynamic systems.
Master the mathematics of change
Written by the Flying Prep Team
Reviewed by Alex Stone, who earned 99 credits via CLEP & DSST
Strong precalculus background essential. If you're comfortable with functions, graphs, and trigonometry, you're ready. Engineering, physics, and economics students often take this exam.
Content breakdown:
Graphing calculator NOT permitted. Questions test both computational skill and conceptual understanding.
Score of 50 earns 4 credits
Scores of 60+ show strong calculus skills
Valid 20 years
Calculus begins with a deceptively simple question: what happens as we get infinitely close to something? Limits capture this idea precisely. You'll evaluate limits algebraically and graphically, understand continuity, and see why these concepts matter. Limits are the foundation - without them, derivatives and integrals wouldn't exist. It's where calculus starts its magic.
Derivatives measure instantaneous rate of change - the slope at a single point! This massive section covers derivative rules, applications to curve sketching, and optimization problems. You'll find maxima and minima, analyze motion, and understand related rates. Differential calculus is everywhere: physics, economics, engineering, biology. It's the mathematics of change.
If derivatives take things apart, integrals put them back together! You'll learn antiderivative techniques, definite integrals, and the beautiful Fundamental Theorem connecting differentiation and integration. Applications include areas, volumes, and accumulation problems. Integration is surprisingly creative - sometimes art as much as science - and deeply powerful.
Preparing your assessment...
Week 1: Limits Concept of limits, computing limits, continuity.
Week 2: Derivative Concept Definition of derivative, tangent lines, rates of change.
Week 3: Derivative Rules Power rule, product rule, quotient rule, chain rule. Practice until automatic.
Week 4: More Derivatives Trigonometric, exponential, logarithmic derivatives. Implicit differentiation.
Week 5: Derivative Applications Related rates, optimization problems.
Week 6: Integrals Antiderivatives, basic integration, Fundamental Theorem.
Week 7: Integral Applications Area between curves, volumes (if covered), other applications.
Week 8: Review & Practice
2 months
~10 hours/week
Two valid IDs. No calculator allowed.
Retakes after 3 months.
The Calculus exam ranks among the more challenging CLEP tests, with pass rates typically around 60-65%. The difficulty stems from both computational demands and conceptual applications. Differential calculus problems often involve multi-step optimization or related rates scenarios requiring careful setup and execution. Integral calculus questions test your ability to select appropriate integration techniques quickly. Time pressure intensifies the challenge - you need both accuracy and speed. However, the exam tests standard first-semester calculus topics without advanced techniques like series or multivariable concepts. Success depends more on consistent practice with core techniques than memorizing obscure formulas. Students with recent calculus coursework generally perform better than those relying on distant math backgrounds.
ACE recommends a scaled score of 50 (out of 80) for college credit, but individual institutions set their own requirements. Community colleges typically accept 50, while four-year universities often require 55-65. Competitive programs may demand scores of 60 or higher. A score of 50 generally means answering 28-32 questions correctly (62-71% accuracy). Check with your target institution before testing - some schools have specific score requirements for prerequisite satisfaction or degree programs. Military education benefits typically follow ACE recommendations, accepting scores of 50 or above. Professional certification programs vary in their score requirements, so verify standards with the credentialing organization. Most test-takers aiming for selective programs target scores of 60 or above to ensure broad acceptance.
Study duration depends heavily on your mathematical background. Recent calculus students need 40-60 hours of focused review, emphasizing practice problems over concept review. Those with algebra and trigonometry skills but no recent calculus require 80-120 hours, spending significant time building derivative and integral techniques. Students starting with limited advanced math backgrounds need 150-200 hours minimum, including prerequisite review of functions, limits, and algebraic manipulation. Quality matters more than quantity - daily problem-solving sessions of 90-120 minutes prove more effective than marathon weekend sessions. Plan 8-12 weeks of consistent preparation for best results. Accelerated timelines work for mathematically strong candidates, but rushing typically results in gaps that surface during complex application problems on the exam.
Focus on problem-solving over passive reading. Work through 5-10 calculus problems daily across different topic areas, emphasizing timed practice as your test date approaches. Use a structured approach: master basic derivative rules first, then tackle applications like optimization and related rates. For integrals, practice pattern recognition - identifying which integration technique applies to specific problem types. Create a formula sheet early in your preparation, then practice working without it to build recall speed. Take multiple full-length practice exams under timed conditions to build stamina and identify weak areas. Review mistakes thoroughly, understanding both the correct solution method and why your initial approach failed. Group study works well for calculus - explaining solutions to others reinforces your own understanding while exposing gaps in reasoning.
No, the exam covers single-variable calculus only - equivalent to Calculus I or first-semester college calculus. You won't encounter multivariable calculus, differential equations, or infinite series. The content focuses on derivatives, integrals, and their applications within single-variable contexts. Advanced integration techniques like trigonometric substitution or partial fractions rarely appear. The exam emphasizes understanding core concepts and applying them to practical problems rather than testing exotic mathematical techniques. However, don't mistake 'introductory' for 'easy' - the exam requires solid mastery of fundamental techniques and the ability to apply them efficiently under time pressure. Success depends on fluency with basic calculus operations rather than knowledge of advanced mathematical theory.
Yes, a basic scientific calculator is provided through the computer interface, but don't rely on it heavily. The calculator handles arithmetic operations, square roots, and trigonometric functions, but lacks graphing capabilities or symbolic manipulation. Most successful test-takers use calculators primarily for verification and final computations rather than step-by-step problem solving. Strong mental math skills remain essential for efficiency - spending too much time on calculator operations will hurt your timing. Practice working with the same type of calculator interface available on the exam. Many derivative and integral problems require algebraic manipulation that calculators cannot perform, so focus your preparation on developing hand-computation skills. The calculator serves as a helpful tool, not a replacement for mathematical understanding and technique mastery.
Start mastering calculus for free. Our guide covers limits through integration with worked examples.
Get full access to flashcards, practice tests, and detailed explanations.