---
title: "FRQs 1-2 – Graphing Calculator Required"
description: "Complete guide to Precalculus – FRQs 1-2 – Graphing Calculator Required. Detailed breakdown of what to expect and how to earn points."
canonical: "https://fiveable.me/ap-pre-calc/ap-precalculus-exam/pre-calc-frqs-graphing-calculator-required/study-guide/pre-calc-frqs-graphing-calculator-required"
type: "study-guide"
subject: "AP Pre-Calculus"
unit: "AP Precalculus Exam"
lastUpdated: "2026-07-02"
---

# FRQs 1-2 – Graphing Calculator Required

## Summary

Complete guide to Precalculus – FRQs 1-2 – Graphing Calculator Required. Detailed breakdown of what to expect and how to earn points.

## Guide

## Overview

- Section II, Part A contains **2 free-response questions in 35 minutes**
- Part A makes up **18.75% of the total exam score**
- A **graphing calculator is required**
- Calculators should be in **[radian](/ap-pre-calc/unit-3 "fv-autolink") mode**
- FRQ 1 and FRQ 2 are each worth **6 points**
- The AP Precalculus free-response section has 4 six-point questions, each weighted equally and scored on an analytic scale
- Two of the four free-response questions on the full exam incorporate a real-world [function](/ap-pre-calc/unit-1/change-tandem/study-guide/eQFiTo22fpkDFsnj "fv-autolink") modeling context
- Exam content comes from Units 1, 2, and 3

The graphing-calculator FRQs are:

- **FRQ 1: Function Concepts** - [Unit 1](/ap-pre-calc/unit-1 "fv-autolink") and [Unit 2](/ap-pre-calc/unit-2 "fv-autolink") focus, no real-world context
- **FRQ 2: Modeling a Non-Periodic Context** - Unit 1 and Unit 2 focus, real-world function modeling context

The official task-model overview places FRQ 1 and FRQ 2 together in Section II, Part A. FRQ 1 is the graphing-calculator function-concepts question without a real-world context, and its defining setup is multiple representations: graphical, numerical, and analytical. FRQ 2 is the graphing-calculator non-periodic real-world modeling question and is one of the two free-response questions on the exam that incorporate a real-world function modeling context.

Official Part A calculator instructions:

- Students are expected to use a graphing calculator for tasks such as producing graphs and tables, evaluating functions, solving equations, and performing computations.
- For Part A, the calculator must be in radian mode.
- It may be helpful to use the graphing calculator to store computed values for constants, functions you are working with, solutions to equations, and intermediate values so computations maintain precision.
- Avoid rounding intermediate computations; unless otherwise specified, decimal approximations should be accurate to three places after the decimal point.

Technology capabilities relevant to calculator-required Precalculus exam tasks include graphing functions and analyzing graphs, generating tables, finding [real zeros](/ap-pre-calc/key-terms/real-zero "fv-autolink"), finding points of intersection, finding minima and maxima, finding numerical solutions to one-variable equations, and using [regression](/ap-pre-calc/key-terms/regression "fv-autolink") or modeling support when a task provides data.

Show all work. Work is scored for correctness and completeness, including supporting work and answers; answers without supporting work may not receive credit in cases where supporting work is requested. Unless otherwise specified, the [domain of a function](/ap-pre-calc/key-terms/domain-of-a-function "fv-autolink") $f$ is the set of all real numbers $x$ for which $f(x)$ is a real number.

## FRQ 1: Function Concepts

FRQ 1 presents functions expressed graphically, numerically, and analytically. The official task [model](/ap-pre-calc/unit-2/competing-function-model-validation/study-guide/VeTW7I04PfukXfeT "fv-autolink") includes **three parts** and can ask students to work across these representations with several function concepts, including:

- [function composition](/ap-pre-calc/key-terms/function-composition "fv-autolink")
- [inverse functions](/ap-pre-calc/unit-2/inverse-functions/study-guide/JkTPSAR9TH5LfSXP "fv-autolink")
- function input-output values
- zeros of a function
- [end behavior](/ap-pre-calc/unit-1/equivalent-representations-polynomial-rational-expressions/study-guide/NRzwc7vjmULoqIyP "fv-autolink") of a function
- identifying an appropriate function type to construct a function model

Official point count by skill for FRQ 1:

| Skill | Points |
|---|---|
| 1.A: Determine values or solve for unknowns in functions and equations, using algebraic manipulation | 1 |
| 1.C: Determine new functions that can be constructed from known functions by addition, subtraction, multiplication, division, or composition | 1 |
| 2.A: Construct and interpret graphical representations of functions and relations | 2 |
| 3.A: Describe the characteristics of a function | 1 |
| 3.C: Verify that a function has a specific characteristic | 1 |

For inverse functions, focus on the relationship between input and output. If $f^{-1}(a)=b$, then $f(b)=a$. Depending on the representation, that may mean reading a graph, using a table, solving with technology, or interpreting an equation.

## FRQ 2: Modeling a Non-Periodic Context

FRQ 2 presents a real-world, non-periodic modeling context. The CED describes the task model this way:

- FRQ 2 has three parts: Part A, Part B, and Part C.
- Part A asks students to construct a function model by building a system of equations and finding parameters using a method of choice.
- Possible function types include polynomial, piecewise-defined, exponential, and logarithmic.
- Part B asks students to calculate, apply, and reason with average [rates of change](/ap-pre-calc/unit-1/rates-change/study-guide/P6aTsM1tBCZtaEPy "fv-autolink") and their units.
- Part C asks students to justify a conclusion about assumptions, limitations, or appropriate scope of the model.

Official point count by skill for FRQ 2:

| Skill | Points |
|---|---|
| 1.B: Determine values or solve for unknowns in functions and equations, using technology strategically | 1 |
| 1.C: Determine new functions that can be constructed from known functions by addition, subtraction, multiplication, division, or composition | 2 |
| 3.B: Construct mathematical expressions, equations, and inequalities to represent relationships | 1 |
| 3.C: Verify that a function has a specific characteristic | 2 |

When interpreting a model, [base](/ap-pre-calc/unit-2/inverses-exponential-functions/study-guide/7mdx6zi19alJ4hK3 "fv-autolink") conclusions on the specific function, parameters, [domain](/ap-pre-calc/key-terms/domain "fv-autolink"), and context. Do not assume all exponential models increase or all logarithmic models decrease; the behavior depends on the actual model.

## Task Verbs

Common AP Precalculus free-response task verbs include:

- **Construct/write a function/expression/equation/model**: Develop an analytical representation, with and without technology, consistent with a scenario, data set, or criteria.
- **Describe**: Develop a verbal representation consistent with a scenario, data set, function representation, or criteria.
- **Determine/find/identify**: Apply appropriate methods or processes.
- **Estimate/compare**: Use a function representation to find approximate values and/or compare results.
- **Explain/give a reason/provide a rationale/justify**: Use information from the scenario or function representation to support conclusions.
- **Express/indicate**: Provide information or a result in a requested form, including units when needed.
- **Interpret**: Describe the connection between a mathematical expression or solution and its contextual meaning.
- **Plot and label, sketch and label**: Develop a [graphical representation](/ap-pre-calc/unit-2/composition-functions/study-guide/glFlt2HgsCSjvjSL "fv-autolink") consistent with a scenario, data set, or other criteria.
- **Rewrite**: Apply appropriate methods to determine equivalent analytical representations of an expression.
- **Solve**: Apply appropriate methods to determine [solutions to an equation](/ap-pre-calc/unit-4/implicitly-defined-functions/study-guide/Mte9qLDnbtGWht7g "fv-autolink") or inequality.

## Calculator Use

Use the graphing calculator as an official Part A tool, especially for graphs, tables, function evaluation, equation solving, and computations. Still show supporting work when requested. Calculator output should support the mathematical claim; it should not replace the explanation.

Store computed values for constants, functions you are working with, solutions to equations, and intermediate values when useful so later calculations preserve precision. Computations that use stored information help maintain accuracy in final answers. Round final decimal approximations to three places unless the prompt says otherwise.

## Final Notes

FRQs 1 and 2 reward accurate use of representations, strategic technology, and contextual reasoning. Stay close to the prompt, use units in real-world contexts, and justify conclusions from the given model or representation.

## FAQs

### How long do you get for AP Precalc FRQs 1 and 2?

You get 35 minutes total for FRQs 1 and 2, which are Part A of Section II. A graphing calculator is required for both, so plan on roughly 15 minutes per question. Together they're worth 18.75% of your exam score.

### How many points is each AP Precalc FRQ worth?

Each of the four AP Precalc FRQs is worth 6 points, scored on an analytic scale. Points are awarded part by part for separate skills like computation, reasoning, and interpretation, so partial credit is common and showing your work directly earns points.

### Do you need a calculator for all parts of AP Precalc FRQs 1-2?

No. A graphing calculator is required for FRQs 1 and 2, but only some parts actually need it. Use it to store exact values, solve messy equations, and verify behavior, but the reasoning and interpretation points come from your written explanation, not the calculator.

### What is the difference between AP Precalc FRQ 1 and FRQ 2?

FRQ 1 (Function Concepts) gives you functions in graph, table, and equation form and tests composition, inverse functions, zeros, end behavior, and function-type identification. FRQ 2 (Modeling a Non-Periodic Context) is a real-world scenario where you build a polynomial, piecewise, exponential, or logarithmic model and analyze rate of change and limitations.

### How do you earn the reasoning and interpretation points on AP Precalc FRQs?

State a mathematical reason and tie it to context with units. Writing just 'the limit is infinity' or 'rate = -1.387' won't earn the point. Instead say why ('as x decreases the denominator approaches -2 so the fraction grows without bound') and what it means in the situation ('the score dropped about 1.387 points per month').

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