AP problems

408 problems for AP practice, each with a worked solution. Try each one on paper first, then check your answer.

All SubjectsPhysicsChemistryMathematicsBiologyPython ProgrammingStatistics & Data Science

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1.

A gas goes round a cycle of three steps.

High School (11–12) · Heat Engines, the Second Law and EntropyJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, IB, GaokaoStemPy Lab

Medium

2.

For N₂O₄(g) ⇌ 2NO₂(g), Δ H° = +57.2 kJ/mol and Δ S° = +175.8 J/(K mol). New

High School (11–12) · Entropy, Gibbs Energy and SpontaneityJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IBStemPy Lab

Hard

3.

cos x = -5/13, and x lies between π/2 and π. New

High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesBoard Exam, AP, A-Level, IB, GaokaoStemPy Lab

Medium

4.

A bacterium and a white blood cell of a human are both single cells.

High School (11–12) · Kingdom MoneraNEET, Board Exam, AP, A-Level, IBStemPy Lab

Medium

5.

Dev simulates Tt with tt using random.choice(mum) + random.choice(mum), where mum = "Tt" and dad =… New

High School (11–12), High School (9–10), Undergraduate, General · Biology by Computer, Simulation and RandomnessAPStemPy Lab

Medium

6.

A town wants to know how people feel about a new bus route.

Middle Stage (6–8), High School (9–10), High School (11–12), Undergraduate, General · Data and SamplingAP, SATStemPy Lab

Medium

7.

A gas goes round a rectangle on a pressure-volume graph.

High School (11–12) · Heat Engines, the Second Law and EntropyBoard Exam, AP, IBStemPy Lab

Easy

8.

A reaction has K = 2.5 × 10⁻³ at 500 K. Find Δ G° at this temperature. New

High School (11–12) · Entropy, Gibbs Energy and SpontaneityNEET, Board Exam, AP, A-Level, IBStemPy Lab

Medium

9.

sin A = 4/5 with π/2 < A < π, and cos B = -5/13 with π < B < 3π/2. New

High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesBoard Exam, AP, A-Level, IB, GaokaoStemPy Lab

Medium

10.

A meadow has four kinds of butterflies, with 18, 12, 6 and 4 individuals.

High School (9–10), General · Plant and Animal KingdomsAP, A-LevelStemPy Lab

Medium

11.

A walker takes 10 steps, each one to the left or one to the right with the same chance.

High School (11–12), High School (9–10), Undergraduate, General · Simulation and RandomnessAPStemPy Lab

Medium

12.

1.2 mol of a monatomic ideal gas at 450 K expands adiabatically until it has cooled to 310 K.

High School (11–12) · Thermodynamic Processes and Specific Heats of GasesNEET, Board Exam, AP, A-Level, IBStemPy Lab

Medium

13.

At 298 K a reaction has Δ G° = -17.1 kJ/mol. New

High School (11–12) · Entropy, Gibbs Energy and SpontaneityNEET, Board Exam, AP, A-Level, IBStemPy Lab

Medium

14.

Find the exact value of sin 105°. Then give it to three decimal places. New

High School (11–12) · Compound and Multiple Angles, Trigonometric IdentitiesBoard Exam, AP, A-Level, IBStemPy Lab

Easy

15.

The graph shows what happened to potato cylinders in salt solutions of different strength.

High School (9–10), General · Transport Across the Cell MembraneBoard Exam, AP, A-Level, IBStemPy Lab

Medium

16.

Estimate π by throwing random points at a unit square, with 1000 points and with 100 000 points.

High School (11–12), High School (9–10), Undergraduate, General · Simulation and RandomnessAPStemPy Lab

Medium

17.

A gas goes clockwise round a triangle ABCA on a pressure-volume graph.

High School (11–12) · Laws of ThermodynamicsJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IB, GaokaoStemPy Lab

Hard

18.

Four reactions have these signs. (a) Δ H < 0, Δ S > 0. New

High School (11–12) · Entropy, Gibbs Energy and SpontaneityBoard Exam, AP, A-Level, IBStemPy Lab

Easy

19.

For y = -2 cos(3x + π), find the amplitude, the period (to 3 decimal places) and the range. New

High School (11–12) · Trigonometric Functions and GraphsBoard Exam, AP, A-Level, IBStemPy Lab

Medium

20.

A plant cell and a red blood cell are both placed in pure water.

High School (9–10), General · Transport Across the Cell MembraneBoard Exam, AP, A-Level, IBStemPy Lab

Medium

21.

Three dice are rolled. What is the probability that the sum is 15 or more?

High School (11–12), High School (9–10), Undergraduate, General · Simulation and RandomnessBoard Exam, APStemPy Lab

Medium

22.

On a pressure-volume graph a gas goes from A (1.5 L, 4.6 × 10⁵ Pa) to B (3.5 L, 1.8 × 10⁵ Pa) along…

High School (11–12) · Laws of ThermodynamicsJEE Main, NEET, BITSAT, WBJEE, Board Exam, AP, A-Level, IBStemPy Lab

Medium

23.

Magnesium carbonate decomposes: MgCO₃(s) → MgO(s) + CO₂(g), with Δ H° = +117.6 kJ/mol and Δ S° =… New

High School (11–12) · Entropy, Gibbs Energy and SpontaneityNEET, Board Exam, AP, A-Level, IBStemPy Lab

Medium

24.

The depth of water in a harbour is h = 6 + 2.5 sin (π t)/6 metres, t hours after midnight. New

High School (11–12) · Trigonometric Functions and GraphsBoard Exam, AP, A-Level, IBStemPy Lab

Medium

25.

A cylinder of potato has a mass of 6.0 g.

High School (9–10), General · Transport Across the Cell MembraneBoard Exam, AP, A-Level, IBStemPy Lab

Medium