The PCAT Quantitative Reasoning section is designed to test the math skills that will be required in pharmacy school. The section contains 48 multiple-choice questions, though only 40 will count toward your score. The remaining 8 questions are experimental and do not affect your score. You will not be able to distinguish between scored and experimental questions, so you should treat every question as if it will be counted.
Approximately 50% of PCAT Quantitative Reasoning section will be word problems. You will have 50 minutes to complete the section (a little more than 1 minute per question), and a simple on-screen calculator will be provided.
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The PCAT Quantitative Reasoning section tests the following math concepts:
- Basic Math: 25%
- Algebra: 25%
- Probability and Statistics: 18%
- Precalculus: 18%
- Calculus: 14%
PCAT QUANTITATIVE REASONING: BASIC MATH
Though the test makers categorize a quarter of the PCAT Quantitative Reasoning section as testing “Basic Math,” it doesn’t mean the math is all easy to calculate, especially under time constraints. Even if you once had a strong, working knowledge of number properties and how to manipulate fractions, decimals, ratios, logarithms, and means, you may find that your knowledge has deteriorated through disuse, especially if you haven’t taken a math class in several years.
Here are some important concepts to know that are commonly tested on Basic Math:
- Real number: All numbers on the number line.
- Integers: All numbers with no fractional or decimal parts, including negative whole numbers and zero; multiples of 1.
- Reciprocal: The result of switching the numerator and denominator of a fraction. The reciprocal of 3/5, for example, is 5/3. The reciprocal of 2 is 1/2 because 2 can be considered to be the fraction 2/1. Multiplying any number by its reciprocal will result in 1.
- Order of Operations: Whenever you have a string of operations, be careful to perform them in the proper order: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (PEMDAS). Multiplication and division should be performed together in order from left to right, and then addition and subtraction should be performed together in order from left to right.
- Fractions: You should know how to perform basic operations with fractions, including multiplying, dividing, adding, and subtracting.
Other concepts tested include ratios, decimals, scientific notation, percents, averages, and logarithms.
PCAT QUANTITATIVE REASONING: ALGEBRA AND WORD PROBLEMS
50% of PCAT Quantitative Reasoning questions will be in the form of word problems, and many of these word problems will require you to convert words into math via algebra. Break down the information into small pieces and take things one step at a time. Word problems can often be translated from left to right, but this is not always the case.
Say you see the sentence: “The number of stamps in George’s stamp collection is twice the number that is 5 less than the number of stamps in Bill’s stamp collection.” Instead of trying to translate it into math all in one step, approach it piece by piece.
Whenever possible, choose letters for the variables that make sense in the context of the problem. For example, start by calling the number of stamps in George’s stamp collection G and the number of stamps in Bill’s stamp collection B. Now, think about the relationship between the two amounts: G is not compared to B but to 5 less than B, or (B – 5). So G is twice as large as (B - 5). To set them equal to each other, multiply (B – 5) by two. The equation is G = 2(B – 5).
The hardest part of word problems is the process of taking English sentences and extracting the math from them. The actual math in word problems tends to be the easiest part. The following translation table will help you start dealing with English-to-math translation:
|equals is, was, will be, has, costs, adds up to, the same as, as much as||=|
|times, of, multiplied by, product of, twice, double, by||x|
|divided by, per, out of, each, ratio||÷|
|plus, added to, and, sum, combined||+|
|minus, subtracted from, smaller than, less than, fewer, decreased by, difference between||—|
|a number, how much, how many, what||x, n, etc.|
PCAT QUANTITATIVE REASONING: PROBABILITY AND STATISTICS
Questions involving probability and statistics tend to be some of the most dreaded by test takers. The equations can appear to be confusing, and the questions can be time-consuming. Nevertheless, these question types can be broken down into predictable formulations that appear time and again.
The PCAT Quantitative Reasoning section tests you on the following probability and statistics concepts:
- Determining the probability of a given outcome, including multiple-event probability
- Mean, mode, range, and standard deviation
- Combinations and permutations
PCAT QUANTITATIVE REASONING: PRECALCULUS AND CALCULUS
Calculus and precalculus together constitute approximately one-third of the Quantitative Reasoning section on the PCAT, so be sure to spend sufficient time studying and practicing the material to feel confident on Test Day. Although you may remember completing lengthy calculations using obscure rules as part of your undergraduate coursework, the test makers do not require extensive knowledge of how to integrate the most difficult functions but rather only expect you to know the basics.
For precalculus, you will be expected to know:
- How to graph equations
- Complex numbers, including graphing
Calculus topics tested include:
- Limits & Continuity
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