# PCAT Quantitative Ability Study Guide

## Math Basics

### Lesson 1: Operations Basics

- Integers, Decimals, and Fractions
- Addition and Subtraction
- Multiplication and Division
- Exponents and Roots
- Associative Property
- Distributive Property
- Order of Operations

### Lesson 2: Factors and Multiples

- Prime Numbers, Factoring, and Prime Factorization
- Multiples
- Greatest Common Factor
- Least Common Multiple

## Fractions

### Lesson 1: Fraction Basics

- Improper Fractions and Mixed Numbers
- Fractions of a Whole
- Converting Improper Fractions to Mixed Numbers
- Changing Mixed Numbers to Improper Fractions
- Ordering Fractions

### Lesson 2: Fraction Operations

- Adding and Subtracting Fractions
- Multiplying and Dividing Fractions
- Converting Percentages to Decimals and Fractions
- Converting Mixed Numbers to Decimals and Improper Fractions
- Converting Improper Fractions to Mixed Numbers and Decimals

## Decimals

### Lesson 1: Decimal Basics

### Lesson 2: Decimal Operations

- Adding and Subtracting Decimals
- Multiplying Decimals
- Dividing Decimals
- Converting Decimals to Fractions and Percentages
- Converting Decimals to Improper Fractions and Mixed Numbers
- Scientific Notation
- Changing a Number from Standard Form to Scientific Notation

## Solving Equations

### Lesson 1: Equation Basics

- Arithmetic Sequences and their Formulas
- Absolute Value
- Solving Equation using Addition and Subtraction
- Solving Equation Using Multiplication and Division
- Solving Equation with Absolute Value
- Solving an Equation Using Four Basic Operations

### Lesson 2: Inequalities

- Equations and Inequalities
- Linear Inequalities
- Solving Inequalities Using All four Basic Operations
- Graphing Solutions to Linear Inequalities
- Solving Absolute Value Inequalities

### Lesson 3: Linear System of Equations

- System of Equations Basics
- Linear Equations Basics
- Comparison of Methods for Solving System of Equations

### Lesson 4: Graphing of Linear Equations and Functions

- Using a Graph
- Graphing Linear Equations
- Graphing the Inverse of a Function
- Graphing Absolute Value Equations
- Graphs of Functions
- Solutions of a Quadratic Equation on a Graph Changing Constants in Graphs of Functions: Linear Functions
- Changing Constants in Graphs of Functions: Quadratic Equations

### Lesson 5: Word Problems

- Word Problems and Subtraction
- Word Problems and Addition
- Word Problems and Multiplication
- Word Problems and Division
- Right Triangle Word Problem
- Linear Equation Word Problem

## Geometry

### Lesson 1: Angle Basics

### Lesson 2: Triangles

- Area and Perimeter of a Triangle
- Proof that a Triangle is 180 Degrees
- Similar Triangles
- Measurements for Similar Triangles
- Measurements for Similar Triangles Continued
- Measurements for Similar Triangles Continued II

### Lesson 3: Circles

- Area and Circumference of a Circle
- Unit Circles and Standard Position
- Finding Measurements for Parts of a Circle

### Lesson 4: Volume and Surface Area of 3D Shapes

- 3D Geometric Shapes
- Volume and Surface Area of a Cube
- Volume and Surface Area of a Pyramid
- Volume and Surface Area of a Rectangular Solid
- Volume and Surface Area of a Right Circular Cone
- Volume and Surface Area of a Right Circular Cylinder
- Volume and Surface Area of a Sphere

## Probability, Statistics, Percentages, Ratios, and Proportions

### Lesson 1: Probability

## PCAT Quantitative Ability Exam

Mathematics and the sciences always go hand in hand when it comes to determining values, finding logical outcomes, and deciphering formulas. Quantitative reasoning measures a person’s mathematical literacy and ability to solve problems. Because a pharmacist’s job involves working out complex equations and calculating precise measurements to create medicines, pharmacy students need to posses strong math and reasoning skills. The Pharmacy College Admission Test’s Quantitative Ability exam puts forth 48 questions on which examinees demonstrate their mathematical aptitude and abilities. As in the PCAT Chemistry section, 8 of the questions gather experimental data for future administrations of the test and are not scored. The PCAT board expects students to complete this part of the test within 45 minutes, making preparation critical. Testers will find using the PCAT Quantitative Ability Review to study gives them powerful leverage when test day arrives.

## What’s On The PCAT Quantitative Ability Exam?

The Quantitative Ability test begins with rudimentary math skills and works its way into advanced formulas and operations. Here, pharmacy candidates will find that employing the PCAT Quantitative Ability Flash Cards help them to memorize valuable definitions and functions necessary to successfully navigate the exam. The PCAT divides the questions into four separate categories covering a wide range of mathematical computations.

**Basic Math**–

Pharmacy colleges need to know that their students have mastered the fundamentals of math. No chance of completing pharmacy school with any success exists without these important building blocks.

*Fractions, Percentages, and Decimals*:

Measuring and combining substances demands the knowledge of how to divide or multiply quantities and represent them numerically. Practice multiplying and dividing these forms of numbers, and well as converting one into the others.

*Log Base 10*:

Know the definition and its use in transforming data.

*Ratios*:

Because understanding the relationships between quantities and being able to represent them as they relate to one another is a major component of pharmacology, prospective students need to be familiar with the computation of ratios. The PCAT Quantitative Ability Practice Test provides the opportunity to practice this skill and become comfortable using it to solve problems.

**Algebra**–

Comprising 20% of the exam, algebra uses symbols to represent unknown values. Using the PCAT Quantitative Ability Test Review is a great way to exercise and evaluate these skills.

*Equations, Expressions, and Inequalities*:

Understand the definition of these terms and how to manipulate them within the context of mathematical computations. Take given values and solve algebraic expressions. Create algebraic representations of real mathematical situations. Examinees should practice solving problems using linear equations and inequalities, as well as linear equations and inequalities that involve the use of absolute zero. Test takers will also want to review solving equations and inequalities that involve rational expressions, quadratic equations and inequalities, equations and inequalities dealing with one or two radicals, and equations and inequalities working with two or three radicals.

*Functions*:

Questions concerning algebraic functions require students to be able to perform algebraic operations as functions. Also, use the PCAT Quantitative Ability Review to review how to determine the composition and inverses of functions and calculate and use minimum and maximum points.

**Probability and Statistics**–

Typically one of the more difficult types of questions, probability and statistics comprise 20% of the Quantitative Ability test. Pharmacy college hopefuls benefit from reviewing this area of mathematics. PCAT Quantitative Ability Flash Cards are invaluable to students wanting to ace this portion of the test.

*Measures of Central Tendency*:

Know the definitions and be able to compute the mean, median, and mode of a given set of data.

*Variation*:

Study the formulas for the variation of a sample and the variation of a population. Graphical Models: Know the definitions and purposes of Bayesian and Markov networks, independence properties, inference, parameter estimation, and structure scores.

*Probability*:

Review the three types of probabilities: theoretical probability, relative frequency, and personal or subjective probability, and know their rules and how to apply them.

*Statistical Concepts*:

Understand dependent and independent variables, correlational and experimental research, and how to determine statistical significance and the reliability of relationships between variables.

**PreCalculus**–

Making up 22% of the Quantitative Ability exam, PreCal studies the foundations of the algebraic and trigonometric functions necessary to perform the more advanced level math of Calculus.

*Functions*:

Be able to graph and identify domains, ranges, intercepts, and zeros of exponential functions. Review natural and base logarithms and how they apply to multiple operations. Work on solving problems related to exponential and logarithmic functions. Successfully perform algebraic operations or functions, identify and use composite functions, and graph domains, ranges, intercepts, zeros, and inverses of the circular functions.

*Complex Numbers*:

Recognize the a+bi expression and the equation it is used to satisfy.

*Vectors*:

This mathematical structure represents a magnitude and a direction simultaneously. Students are expected to add vectors both graphically and algebraically, understand and perform scalar multiplications, and represent and recognize vector equations and planes.

**Calculus**–

These questions round out the exam with the last 22%. This branch of mathematics centers on certain variables’ function limits and differentiation and integration.

*Limits*:

Find the limits of functions, one-sided limits, and infinite limits.

*Continuity*:

Interpret graphs of continuous and discontinuous functions.

*Derivatives*:

Calculus focuses on derivatives. Examinees need to be able to find derivatives of algebraic functions, means of the sum and product, power rule, and apply the mean value theorem. Apply the chain rule to discover the derivatives of composite functions. Use differentiation to solve problems. Find extreme points of inflection and intervals in derivative tests. Possess knowledge of the derivatives of composite functions having to do with circular and transcendental functions, usage of implicit differentiation, and related rates.

**Integrals**–

Here mathematicians must find antiderivatives and interpret C, understand and use sigma notation for simplifying sums, and approximate areas bounded by curves.

**Integration**–

Integrals are most often used to find the area underneath the graph of a function.

*Common Functions*: Recognize the integral for constant, variable, reciprocal, square, and exponential functions.*Rules*: Use the PCAT Quantitative Ability Test Flash Cards to commit these rules to memory: multiplication by constant, power rule, sum rule, difference rule, integration by parts, and substitution rule.

Pharmacology is an exact science, depending on the structures and formulas of mathematics to be able to create and replicate a vast array of medicines. The expertise of the pharmacist lies in the ability to understand and manipulate these mathematical principles and combine them with their scientific knowledge. Because of the time constraints, it is imperative for students to be completely comfortable with their math abilities and understanding of the various branches of mathematics addressed in the exam.

There are highly beneficial strategies used to approach and resolve quantitative problems in the PCAT Quantitative Ability Review. When each objective is mastered, it is recommended that examinees practice solving examples of equations and expressions representative of it. The PCAT Quantitative Ability Practice Test provides the opportunity to assess growth and areas of need before undertaking the actual exam. Through the streamlined study process, prospective students can obtain the highest benefit with the least amount of wasted time. Going into the exam feeling well prepared is invaluable.

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Last updated: 03/13/2018

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