Using $\lim_{x\to a}f(x)=3$ and $\lim_{x\to a}g(x)=-2,$ evaluate $\lim_{x\to a}\left[2f(x)-g(x)\right].$
Correct answer: $8$
Why: By the limit laws, $2(3)-(-2)=8$.
AP Calculus AB Practice Questions
Answer original AP-style diagnostic questions, review explanations, and identify the next unit to study.
AP Calculus AB diagnostic practice set
These are original practice questions, not copied College Board items. Use official released questions for final calibration.
Question 1 of 3
Review the reasoning after you finish
The interactive set keeps answers hidden while you work. This review section remains crawlable and gives every student a complete correction path after the attempt.
If $f'(x)$ changes from positive to negative at $x=c$, what occurs at $x=c$?
Correct answer: A local maximum
Why: The function changes from increasing to decreasing, so $f$ has a local maximum at $x=c$.
What does $\int_a^b v(t)\,dt$ represent when $v$ is a velocity function?
Correct answer: Displacement
Why: The signed integral of velocity over $[a,b]$ gives displacement. Total distance requires integrating $|v(t)|$.
Practise each section under its own calculator rule
Practising with a calculator you will not be handed is the most common way a practice score stops predicting an exam score. Set each practice block up to match the section it rehearses.
| Section or part | What you may use | What that means for your work |
|---|---|---|
| Multiple choice, Part A | No calculator | Derivative and integral rules by hand, limits, and algebraic simplification. |
| Multiple choice, Part B | Graphing calculator required | Numerical answers and graph reading; some choices are close together on purpose. |
| Free response, Part A | Graphing calculator required | Only four uses are expected: graph in any window, find zeros, evaluate a derivative at a point, evaluate a definite integral. |
| Free response, Part B | No calculator | Antiderivatives, chain rule, implicit differentiation, and exact values. |
How practice should cover the complete course
Limits and Continuity
Limit estimates, properties, asymptotes, continuity, IVT
10–15%: practice one recognition question, one direct application, and one mixed prompt that requires you to choose this unit without being told.
Differentiation: Definition and Properties
Derivative definitions, rules, tangent lines
10–15%: practice one recognition question, one direct application, and one mixed prompt that requires you to choose this unit without being told.
Composite, Implicit, and Inverse Differentiation
Chain rule, implicit and inverse derivatives
5–10%: practice one recognition question, one direct application, and one mixed prompt that requires you to choose this unit without being told.
Contextual Applications of Differentiation
Motion, rates, related rates, local linearity
10–15%: practice one recognition question, one direct application, and one mixed prompt that requires you to choose this unit without being told.
Analytical Applications of Differentiation
MVT, extrema, monotonicity, concavity, optimization
15–20%: practice one recognition question, one direct application, and one mixed prompt that requires you to choose this unit without being told.
Integration and Accumulation of Change
FTC, antiderivatives, substitution, Riemann sums
15–20%: practice one recognition question, one direct application, and one mixed prompt that requires you to choose this unit without being told.
Differential Equations
Slope fields, separation, exponential models
5–10%: practice one recognition question, one direct application, and one mixed prompt that requires you to choose this unit without being told.
Applications of Integration
Average value, area, volume, accumulation
10–15%: practice one recognition question, one direct application, and one mixed prompt that requires you to choose this unit without being told.
Use the result to focus your AP Calculus AB review
Read the score as a map, not a verdict
Each answer shows a relationship between course knowledge and an exam decision. A miss may mean that a definition is unclear, a representation was misread, or the right method was not selected. Compare each miss with these AP Calculus AB priorities before choosing the next unit or practice set.
- FTC in both directions
- Derivative meaning from tables and graphs
- Sign charts and justification
- Calculator-active FRQ commands
- Units on rates and accumulated quantities
Next steps after the AP Calculus AB diagnostic
Use a four-step correction cycle
- Write the rule or idea behind every miss.
- Solve a second problem of the same type without looking back.
- Mix that skill with two older units tomorrow.
- Complete official released questions under authentic timing.
Questions about AP Calculus AB exam practice
How many questions are on the AP Calculus AB exam?
The published format is 42 questions on multiple choice and 6 questions on free response. Multiple choice — About 2.4 minutes each. If a Part A question takes more than three minutes of algebra, you missed a shortcut. Free response — About 15 minutes per question. Answer every part you can even after you get stuck on part (a) - later parts are scored separately.
Which AP Calculus AB units should I practise first?
Start with the heaviest published weightings: Analytical Applications of Differentiation (15–20%), Integration and Accumulation of Change (15–20%), Limits and Continuity (10–15%). Then repair whichever earlier unit those depend on.
Can I use a graphing calculator while I practise for AP Calculus AB?
Only where the exam allows one, and practising otherwise builds the wrong habit. Multiple choice, Part A: Derivative and integral rules by hand, limits, and algebraic simplification. Multiple choice, Part B: Numerical answers and graph reading; some choices are close together on purpose. Free response, Part A: Only four uses are expected: graph in any window, find zeros, evaluate a derivative at a point, evaluate a definite integral. Free response, Part B: Antiderivatives, chain rule, implicit differentiation, and exact values.
What is the most common way students lose points on AP Calculus AB?
On calculator-active parts, keep three decimal places or more and store values in the calculator. Rounding partway through changes the final digit and loses the answer point.
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