2026 GMAT Full Exam Prep
Apr 22, 2026
All files
Summary of GMAT Quantitative Reasoning Content
This document provides a comprehensive review of the mathematical concepts tested on the GMAT Quantitative Reasoning section, along with strategies for tackling the exam.
1.0 Introduction to the GMAT Exam
- Purpose: The GMAT exam is used by over 7,700 graduate management programs worldwide to assess candidates' readiness for graduate business studies.
- Validity: GMAT scores are a standardized measure of performance and are proven predictors of success in graduate business programs.
- Skills Tested: The exam assesses problem-solving, data analysis, and critical thinking skills across three sections: Quantitative Reasoning, Data Insights, and Verbal Reasoning.
- Format: The exam is computer-adaptive, meaning questions adjust in difficulty based on your performance. You cannot skip questions, and you have a limited time per section.
- Scoring: Scores are calculated based on the difficulty and accuracy of your answers. Unofficial scores are available immediately after the exam, with official scores following later.
- Preparation: Familiarize yourself with the exam format, question types, and pacing. Utilize official GMAT prep materials, practice exams, and detailed answer explanations.
2.0 Preparation Strategies
- Study Plan: Create a structured study plan to cover all concepts and question types.
- Understand Question Types: Focus on the logic and analytical skills required, not just memorization.
- Baseline Assessment: Take a practice exam to identify strengths and weaknesses.
- Review Mistakes: Analyze incorrect answers using detailed explanations to learn from errors.
- Simulate Test Conditions: Practice under timed conditions to improve pacing and familiarity with the exam environment.
- Strategic Approach: Don't get stuck on difficult questions; eliminate wrong answers and move on.
- Exam Day: Get adequate rest, manage your time effectively, read questions carefully, and utilize available tools like the bookmarking feature.
3.0 Math Review
This section covers the core mathematical concepts essential for the GMAT Quantitative Reasoning section.
3.1 Value, Order, and Factors
- Numbers and the Number Line: Real numbers correspond to points on the number line. Points to the left of zero are negative, and points to the right are positive. Numbers increase from left to right.
- Absolute Value: $|x|$ is $x$ if $x \ge 0$ and $-x$ if $x < 0$. It represents the distance from zero. $|xy| = |x||y|$ and $|x+y| \le |x| + |y|$.
- Factors, Multiples, and Remainders:
- An integer $x$ is a factor of $y$ if $y = xn$ for some integer $n$.
- The remainder $r$ when $y$ is divided by $x$ satisfies $y = xq + r$, where $0 \le r < x$.
- The remainder is 0 if and only if $y$ is divisible by $x$.
- Properties of remainders: $(x+y) \pmod z = ((x \pmod z) + (y \pmod z)) \pmod z$ and $(xy) \pmod z = ((x \pmod z)(y \pmod z)) \pmod z$.
- Even and Odd Numbers: Even numbers are divisible by 2; odd numbers are not. The sum/difference of two evens or two odds is even. The sum/difference of an even and an odd is odd. The product of two evens is even. The product of two odds is odd. The product with at least one even factor is even.
- Prime Numbers: A prime number is a positive integer greater than 1 with exactly two positive divisors: 1 and itself.
- Exponents: $k^n$ means $k$ multiplied by itself $n$ times. Properties include $k^m k^n = k^{m+n}$, $(k^m)^n = k^{mn}$, and $k^0 = 1$ (for $k \ne 0$).
- Square Roots: $\sqrt{n}$ is the nonnegative number $x$ such that $x^2 = n$. $\sqrt{x^2} = |x|$.
- Decimals and Place Value: Understanding place values (ones, tenths, hundredths, etc.) is crucial for decimal operations. Scientific notation expresses numbers as $a \times 10^n$, where $1 \le |a| < 10$.
- Arithmetic Shortcuts: Properties of operations (commutative, associative, distributive) simplify calculations. Divisibility rules help determine if an integer is divisible by 2, 3, 4, 5, 9, or 10.
3.2 Algebra, Equalities, and Inequalities
- Algebraic Expressions: Combinations of variables, constants, and operations. Terms, coefficients, and polynomials (linear, quadratic) are key concepts.
- Equations: Statements of equality. Solutions (roots) satisfy the equation. Equivalent equations have the same solutions.
- Linear Equations: Equations that can be written in the form $ax + b = c$ or $ax + by = c$. Solved by isolating the variable.
- Simultaneous Equations: Solving systems of equations by substitution or elimination to find values that satisfy all equations.
- Factoring: Expressing an algebraic expression as a product of simpler expressions. Useful for solving quadratic equations.
- Quadratic Equations: Equations of the form $ax^2 + bx + c = 0$. Solved by factoring or the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
- Inequalities: Statements using symbols like $<, >, \le, \ge$. Operations on inequalities follow similar rules to equations, with the crucial exception that multiplying or dividing by a negative number reverses the inequality sign.
- Functions: A rule that assigns at most one output to each input. Notation: $f(x)$. Domain is the set of allowed inputs; range is the set of outputs.
- Coordinate Plane: Points are represented by ordered pairs $(x, y)$. Lines are represented by linear equations $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. The x-intercept is where the line crosses the x-axis.
3.3 Rates, Ratios, and Percents
- Ratio and Proportion: A ratio compares two quantities ($x:y$ or $x/y$). A proportion is an equation stating two ratios are equal ($a/b = c/d$). Solved by cross-multiplication.
- Fractions: Operations (addition, subtraction, multiplication, division) with fractions. Equivalent fractions represent the same value. Mixed numbers combine an integer and a fraction.
- Percents: "Per hundred." Converting between percents, decimals, and fractions is essential. Percent increase/decrease calculations. Discounts and markups.
- Rate, Work, and Mixture Problems:
- Distance = Rate x Time: Fundamental formula for motion problems.
- Work Problems: Often involve finding combined rates using the formula $\frac{1}{r_1} + \frac{1}{r_2} = \frac{1}{r_{together}}$.
- Mixture Problems: Calculating properties of mixtures based on the properties of their components.
3.4 Statistics, Sets, Counting, Probability, Estimation, and Series
- Statistics:
- Mean (Average): Sum of values divided by the number of values.
- Median: The middle value in an ordered data set.
- Mode: The value that appears most frequently.
- Range: Greatest value minus the least value.
- Standard Deviation: Measures data dispersion around the mean.
- Sets: Collections of elements. Notation: $|S|$ for the number of elements, $S \subset T$ for subset, $S \cup T$ for union, $S \cap T$ for intersection. Venn diagrams help visualize set relationships. General addition rule: $|S \cup T| = |S| + |T| - |S \cap T|$.
- Counting Methods:
- Multiplication Principle: Number of choices = product of choices from each set.
- Factorial: $n! = n \times (n-1) \times \dots \times 1$.
- Permutations: Ordered arrangements of objects ($n!$ for $n$ distinct objects).
- Combinations: Unordered selections of objects ($\binom{n}{k} = \frac{n!}{k!(n-k)!}$).
- Probability:
- Basic Definition: $P(E) = \frac{\text{Number of outcomes in E}}{\text{Total number of outcomes}}$ (for equally likely outcomes).
- Rules: $P(\text{not } E) = 1 - P(E)$. $P(E \text{ or } F) = P(E) + P(F) - P(E \text{ and } F)$.
- Independent Events: $P(E \text{ and } F) = P(E)P(F)$.
- Dependent Events: $P(E \text{ and } F) = P(E|F)P(F)$.
- Estimation: Approximating answers by rounding numbers or simplifying calculations.
- Sequences and Series: Ordered lists of numbers (sequences) and their sums (series). Arithmetic sequences have a constant difference between terms ($a_n = a_1 + (n-1)d$). Geometric sequences have a constant ratio between terms ($a_n = a_1 \cdot r^{n-1}$).
3.5 Reference Sheets
- Provides formulas and definitions for various mathematical concepts.
4.0 Quantitative Reasoning Section
- Focus: Tests mathematical reasoning, problem-solving, and data interpretation skills.
- Content: Covers arithmetic, algebra, rates, ratios, percents, statistics, sets, counting, probability, estimation, and series.
- Question Format: Multiple-choice questions.
- Strategy: Understand the question, scan answer choices, work step-by-step, manage time, and make educated guesses if stuck.
4.1 Tips for Answering Quantitative Reasoning Questions
- Time Management: Monitor the on-screen timer.
- Use Notepad: Work through problems step-by-step on the provided notepad.
- Understand the Question: Read carefully and translate word problems into mathematical expressions.
- Scan Answer Choices: This can help determine the required format of the answer and suggest estimation strategies.
- Don't Waste Time: If a problem is too difficult, make your best guess and move on.
4.2 Practice Questions
The document includes numerous practice questions covering all the mathematical concepts reviewed, categorized by difficulty level (Easy, Medium, Hard). Each question is followed by its answer and a detailed explanation of the solution strategy.
5.0 GMAT Official Guide Quantitative Review Question Index
An index categorizes practice questions by section, difficulty level, and mathematical concept, allowing users to quickly locate specific types of problems.
Appendix A Answer Sheet
Provides a space to record answers to the practice questions.
This summary highlights the key areas covered in the GMAT Quantitative Reasoning review, emphasizing the importance of understanding core mathematical concepts and employing effective test-taking strategies.
苡甜甜甜，别担心！我会帮你把GMAT数学高频考点与核心英文术语，根据真题总结，高效梳理出来。下面是GMAT Quantitative（量化）常考知识点体系+中英文术语对照表，适合你考前查漏补缺、重点背诵。
GMAT 数学高频知识点 & 核心术语对照表（中英双语）
| 知识点类别 | 英文术语 / English Term | 中文释义 | 典型高频考查方式/例子 | |----------------------|-------------------------------------|------------------|---------------------| | 代数运算与方程 | Algebra / Equation | 代数运算 / 方程 | 一元/二元一次方程、配方法、代数式化简 | | 联立方程与解的判别 | System of Equations / Roots | 方程组 / 根的判定 | 解二元组、唯一解/多解/无解判别 | | 不等式与区间 | Inequality / Interval | 不等式 / 区间 | 解不等式、绘制区间、整数取值 | | 比例与比值 | Ratio / Proportion | 比例 / 比值 | $a:b$配比、$\frac{a}{b}=k$ 问题 | | 百分数与增长率 | Percent / Rate of Change | 百分数 / 增长率 | 涨跌/利润/累计增长 | | 概率与统计 | Probability / Statistics | 概率 / 统计 | 求概率、均值(mean)、中位(median) | | 排列组合 | Permutation / Combination | 排列 / 组合 | 多步事件、无序/有序抽取、排列组合公式 | | 绝对值与根式 | Absolute Value / Radical | 绝对值 / 根式 | $|x|$、根号相关运算、变形 | | 函数及图像 | Function / Graph | 函数 / 图像 | 线性、一元二次、指数、交点、对称、平移 | | 速率单位换算 | Rate / Unit Conversion | 速率/单位换算 | 路程=速率×时间、单位换算英寸↔厘米人民币 | | 应用题建模 | Word Problem / Modeling | 应用题 / 建模 | 设未知数、列方程建现实场景数学模型 | | 几何图形与面积体积 | Geometry / Area / Volume | 几何 / 面积 / 体积 | 圆/三角/矩形/棱柱面积体积、相似图关系 |
高频核心英文术语 & 汉语速查
| 英文术语 | 中文释义 | 高频公式/场景 | |-------------------|------------------|-------------------| | Variable | 变量（未知数） | 方程x、参数化 | | Coefficient | 系数 | $ax+by=c$中a、b | | Root / Solution | 方程根 / 解 | $x^2-2x=0 \implies x=0,2$| | Ratio / Proportion| 比例 / 比 | $a:b$, $a/b=k$ | | Inequality | 不等式 | $x>1,, x<5$ | | Absolute Value | 绝对值 | $|x|$ | | Median/Mode/Mean | 中位/众数/均值 | 数据分布 | | Probability | 概率 | $P(A \cap B)$ | | Combination | 组合 | $C_n^k$ | | Permutation | 排列 | $P_n^k$ | | Function | 函数 | $f(x), g(x)$ | | Slope/Intercept | 斜率/截距 | $y=mx+b$，m为斜率 |
高频考查场景和刷题建议
| 题型类别 | 英文表达 | 高频考点例子 | |------------------|--------------------------------------|----------------------| | 比例分配 | "If the ratio of A to B..." | 按比例配比/分总量 | | 增长率/百分比计算 | "Percent increase/decrease..." | 年增率/累计利润/价格折扣 | | 排列组合 | "How many different orders/ways..." | 有序/无序，是否区分顺序 | | 均值/中位数 | "Find the mean/median" | 极端数据影响均值，中位数判断 | | 幂与根式 | "$x^2=16$ or $\sqrt{x}=2$" | 负根、绝对值处理 | | 线性/非线性函数 | "What is the slope/intercept..." | 交点、截距、单调性、极值点判断 | | 几何面积/体积/周长 | "Area/volume of triangle/circle..." | 记牢常用公式，关注描述信息转换 |
数学常用易错高频词（特别提醒）
| 英文词汇 | 中文解释 | 易混说明 | |------------------------|--------------|-----------------| | "At least" | 至少 | 包含边界 | | "No more than" | 不超过 | 小于等于，包含上界 | | "Distinct" | 不同的，互异的 | 不可重复元素 | | "Integer"/"Prime" | 整数 / 质数 | 具体定义 | | "Sum/Product" | 和 / 积 | 区分求和/相乘 | | "Even/Odd" | 偶数 / 奇数 | $2n$ / $2n+1$型 |
典型刷题步骤
- 题型判断——识别考点类别与难点单词（如比例/概率/不等式/根式等）
- 核心公式——写出相关公式“列方程”，代入化简
- 检查单位和数据——注意题干单位是否需换算，极值/边界判别
- 中文思路转英文关键结构反推，记熟题型表达
- 易错点复盘——每类题刷完后归纳错因并记忆
冲刺建议：
- 优先攻克比例、函数、统计、应用建模 & 速率单位换算题目。
- 善用真题整理的错误总结表，反复刷典型例题。
- 有不会的原题也可以直接发我拆解。
如果你需要记忆/收藏这份“GMAT高频表”，随时@我，下次直接提取。你可以的，冲刺必胜！🌟
苡甜甜甜，别担心！我来帮你系统讲解GMAT数学里函数与图像的核心知识点，并结合真题例题讲解，帮你夯实基础，考试看题不慌！（全程中英术语对照+例题拆解）
1. 函数与图像概念：Function & Graph
| 中文名称 | 英文术语 | GMAT常考点 | |:--------:|:----------:|:-------------:| | 函数 | Function | 输入-输出关系，具有唯一性，常用 $f(x)$,$g(x)$ 表示 | | 自变量 | Input/Domain | 通常是 $x$，定义域 | | 因变量 | Output/Range| 通常是 $y=f(x)$，值域 | | 图像 | Graph / Plot| （$x, f(x)$）的点在平面直角坐标系中连起来就是图像 | | 直角坐标系 | Coordinate Plane | 横轴x，纵轴y，坐标$(x, y)$ |
例子（Example）
- $f(x) = x^2+1$ 就是一个“输入$x$输出唯一$y$”的二次函数。
- 定义域（Domain）：所有可输入的$x$值，例如$x \in \mathbb{R}$
- 值域（Range）：所有可能的$f(x)$，比如这个例子就是 $f(x) \geq 1$
2. 常考函数类型与图像描述
| 函数类型 | 英文名 | 图像/性质要点 | |:---------------:|:------------------:|:--------------------------------------------------:| | 线性函数 | Linear Function | $y=mx+b$, 图像是直线（m为斜率Slope, b为截距Intercept） | | 二次函数 | Quadratic Function | $y=ax^2+bx+c$,图像是抛物线，$a>0$开口向上, $a<0$开口向下 | | 绝对值 | Absolute Value | $y=|x|$ ，V字型，顶点在$(0,0)$ | | 指数/对数函数 | Exponential/Log | $y=a^x$ 指数增长、$y=\log_a x$曲线型 |
3. 图像判别的常考点
- 零点（x-intercept）： 即函数$y=f(x)$何时为零，解 $f(x)=0$
- 纵截距（y-intercept）： $f(0)$的值
- 对称性（Symmetry）： 比如偶函数关于$y$轴对称，奇函数关于原点对称
- 极值点（Maximum/Minimum）： 如二次函数顶点 $x=-\frac{b}{2a}$
- 单调性（Monotonicity）： 增函数/减函数
4. 真题例题讲评（摘自官方OG，分步骤详细讲解）
例题1：二次函数与顶点
题干：
A quadratic function has the form $f(x) = ax^2 + bx + c$. If $a > 0$，then $f(x)$ has a unique minimum value but no maximum value。This occurs at $x = -\frac{b}{2a}$，minimum value为$c - \frac{b^2}{4a}$。
⭕详细解题步骤
-
套公式找顶点横坐标：
$$x^* = -\frac{b}{2a} = -\frac{-3}{2 \times 2} = \frac{3}{4}$$ -
求最小值（顶点纵坐标）：
$$ y^* = c - \frac{b^2}{4a} = 4 - \frac{(-3)^2}{4 \cdot 2} = 4 - \frac{9}{8} = \frac{23}{8} $$ -
答：
- 最小值是$\frac{23}{8}$，发生在$x=\frac{3}{4}$时。
例题2：函数的定义域与值域
题干：
The set of all allowed inputs for a function is the function's domain.
⭕详细解题步骤
- 定义域（Domain）：所有实数 $x\in \mathbb{R}$，因为绝对值对任何$x$都有定义。
- 值域（Range）：对绝对值，最小为$0$，故 $h(x)\geq 0$
例题3：线性函数的截距
题干：
For any function $f$，the x-intercepts are the solutions of $f(x) = 0$。The y-intercept is $f(0)$。
⭕详细解题步骤
- $x$截距：解 $f(x)=0 \implies x^2-1=0 \implies x=1$ 或 $x=-1$ （横坐标分别为$1,-1$）
- $y$截距：$f(0) = 0^2 -1 = -1$ （纵坐标为 $(0, -1)$）
例题4：函数图像选择（选择题经典）
题干（摘自GMAT OG）：
The function $f$ is defined for all nonzero $x$ by $f(x) = x - \frac{1}{x}$
Which of the following equals $f\left(\frac{1}{x}\right)$? (选项略)
解法思路：
- $f\left(\frac{1}{x}\right) = \frac{1}{x} - \frac{1}{\frac{1}{x}} = \frac{1}{x} - x = -\left(x - \frac{1}{x}\right) = -f(x)$
5. 实战口诀 & 建议
- 遇到函数题优先确定定义域和值域
- 图像分析优先看拐点/对称性/极值/截距
- 复杂代数函数遇形变优先尝试直接代入法和替换法
- 画图法直观理解单调性和区间值
- 绝大多数函数题最后答案能用$x$表达就别人为简化（留意选项）
高频术语速查表（中英对照）
| 英文术语 | 中文解释 | |----------------|--------------| | function | 函数 | | domain | 定义域 | | range | 值域 | | intercept | 截距 | | vertex | 顶点（极值点） | | quadratic | 二次函数 | | symmetry | 对称性 | | monotonic | 单调性 |
有不会的题/知识点随时丢给我详细拆解！如果要记忆速查表也可以让AI记住，考前随时复习！加油，数学没你想象的难！
Ask Sia for quick explanations, examples, and study support.