AP Biology Practice (Interactive)

AP — Biology Practice

10 auto-graded practice problems. Select an answer, submit, and review the explanation.

Worked Examples

Example 1: Hardy-Weinberg Equilibrium

Problem: In a population of 1000 individuals, 160 show the recessive phenotype. Calculate the frequency of the dominant allele.

Solution: Step 1: Let $q^2$ = frequency of homozygous recessive = $160/1000 = 0.16$

Step 2: $q = \sqrt{0.16} = 0.4$ (frequency of recessive allele)

Step 3: $p = 1 - q = 1 - 0.4 = 0.6$ (frequency of dominant allele)

Step 4: Verify: $p^2 + 2pq + q^2 = 0.36 + 0.48 + 0.16 = 1.0$ ✓

Key insight: The Hardy-Weinberg equation $p^2 + 2pq + q^2 = 1$ relates allele frequencies to genotype frequencies. It assumes no selection, mutation, migration, or genetic drift.

Example 2: ATP Calculation

Problem: How many ATP molecules are produced from one glucose molecule through complete aerobic respiration?

Solution: Step 1: Glycolysis → 2 ATP (net) + 2 NADH Step 2: Pyruvate oxidation → 2 NADH (per glucose, 2 pyruvates) Step 3: Krebs cycle → 2 ATP + 6 NADH + 2 FADH₂ Step 4: Total NADH = 2 + 2 + 6 = 10 NADH → ~25 ATP (2.5 ATP per NADH) Step 5: Total FADH₂ = 2 → ~3 ATP (1.5 ATP per FADH₂) Step 6: Grand total: 2 + 25 + 3 = ~30 ATP (modern estimate)

Key insight: Older textbooks say 36-38 ATP, but modern estimates are ~30 ATP due to the cost of transporting NADH into mitochondria.

Example 3: Chi-Square Test

Problem: A genetic cross produces 312 round seeds and 88 wrinkled seeds. Is this consistent with a 3:1 ratio?

Solution: Step 1: Null hypothesis: data fit 3:1 ratio Step 2: Expected: round = $\frac{3}{4} \times 400 = 300$, wrinkled = $\frac{1}{4} \times 400 = 100$

Step 3: Calculate $\chi^2$: $\chi^2 = \frac{(312-300)^2}{300} + \frac{(88-100)^2}{100} = \frac{144}{300} + \frac{144}{100} = 0.48 + 1.44 = 1.92$

Step 4: Degrees of freedom = $2 - 1 = 1$

Step 5: Critical value at $p = 0.05$ is $3.84$

Step 6: $1.92 < 3.84$, so we fail to reject the null hypothesis. The data are consistent with 3:1.

Key insight: A small $\chi^2$ means observed values are close to expected. A large $\chi^2$ means they differ significantly.

Chemistry of Life

Intuition: Biology starts with chemistry — the molecules of life (water, proteins, nucleic acids, lipids, carbohydrates) follow chemical rules, but their organisation creates something greater than the sum of parts.

Common Mistakes: Confusing DNA and RNA bases; mixing up enzyme inhibition types; forgetting that enzymes lower activation energy but don’t change ΔG.

Cell Structure and Function

Cellular Energetics

Heredity

Cross-References

• Chemistry of Life: Water, macromolecules, and enzyme fundamentals.
• Cell Structure: Cell organelles, membrane transport, and surface-area-to-volume ratio.
• Heredity: Mendelian genetics, Punnett squares, and chi-square tests.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.