Study Guide
Pre-calculus · AP
AP-aligned materials for 2.1 (Exponential and Logarithmic Functions). This topic is assessed on the AP Exam.
What this standard means
- Change in Arithmetic and Geometric Sequences A sequence is a function from the whole numbers to the real numbers. Consequently, the graph of a sequence consists of discrete points instead of a curve. 2.1.A.2 Successive terms in an arithmetic sequence have a common difference, or constant rate of change. 2.1.A.3 The general term of an arithmetic sequence with a common difference d is denoted by an and is given by an = a d 0 + n, where a0 is the initial value, or by an = a + d(n k − ) k , where ak is the kth term of the sequence. 2.1.B 2.1.B.1 Express geometric sequences found in mathematical and contextual scenarios as functions of the whole numbers.
- 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 2.1.
- [ ] 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