Study Guide

Pre-calculus · AP

AP-aligned materials for 2.4 (Exponential and Logarithmic Functions). This topic is assessed on the AP Exam.

What this standard means

• Exponential Function Manipulation Exponential functions model growth patterns where successive output values over equal length input-value intervals are proportional. When the input values are whole numbers, exponential functions model situations of repeated multiplication of a constant to an initial value. 2.5.A.2 A constant may need to be added to the dependent variable values of a data set to reveal a proportional growth pattern. 2.5.A.3 An exponential function model can be constructed from an appropriate ratio and initial value or from two input-output pairs. The initial value and the base can be found by solving a system of equations resulting from the two input-output pairs. 2.5.A.4 Exponential function models can be constructed by applying tr o ansformations t f x( ) = ab x based on characteristics of a contextual scenario or data set. 2.5.A.5 Exponential function models can be constructed for a data set with technology using exponential regressions. 2.5.A.6 The natural base e, which is approximately 2.718, is often used as the base in exponential functions that model contextual scenarios.
• Demonstrate mastery on AP Exam-style questions for this topic.

_See printable PDF for diagram._

How to use the 20 practice sets

| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |

Pacing: 10–15 minutes per session.

How to practice

1. Label unit circle coordinates for key angles 2. Connect radians and degrees 3. Graph sine and cosine with amplitude and period

_See printable PDF for diagram._

Common mistakes

• Wrong quadrant signs
• Period or amplitude errors in graphs

Review and practice tests

1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for 2.4.

• [ ] Evaluates trig functions at standard angles
• [ ] Uses unit circle reasoning
• [ ] Graphs basic trig functions with transformations

Materials for this standard

• Practice Problems — 20 printable sets
• Review — 10 difficulty levels
• Practice Test — 10 difficulty levels
• Answer key — for parents and tutors