Content Areas Study Guide for the MAT

Mathematics

Being prepared for math-related analogies will require you to have a thorough understanding of numbers, knowledge about mathematical operations including exponents and square roots, and familiarity with the skills and concepts taught in such high school math classes as geometry, algebra, and statistics & probability.

Algebra

A sampling of the types of algebraic concepts that might appear on the MAT® includes: coordinate, typically a position within a 2D plane defined by the intersection of one point on a vertical y-axis and a second point on a horizontal x-axis; equation, a mathematical statement that conveys the equality of two expressions; and parabola, a symmetrical plane curve that is more or less U-shaped. Other possibilities follow.

Examples

COMPLEX : IMAGINARY :: \(a + bi\) : (a. \(\;x = a + h,\;\) b. \(\;x^2 = -1,\;\) c. \(\;y = mx + b,\;\) d. \(\;A = \frac{1}{2}(b x h)\) )

The identifiable relationship within the above analogy is found between the first and third given parts: A COMPLEX number can be written in the form a + bi. So, the missing part must be how an IMAGINARY number (which is the square root of negative one) can be expressed. The correct answer is therefore \(x^2 = -1\).

(a. coefficient , b. axiom , c. vinculum , d. abscissa ) : ORDINATE :: HORIZONTAL : VERTICAL

The identifiable relationship among the given terms in this analogy is found between the first one and the last: The ORDINATE is the distance along the VERTICAL axis on a coordinate graph. So, the missing term must name the distance along the HORIZONTAL axis on a coordinate graph. This means the correct answer is “abscissa.”

Arithmetic

For arithmetic, you will need to be familiar with numerical, quantitative, and computational skills and concepts. The overall math level on the MAT® is not exceptionally high, so most concepts can be learned to the appropriate depth using introductory resources. Be forewarned, however, that the test has a habit of sometimes including rather obscure units of measure, such as butts, hogsheads, and troy pounds.

Examples

212 : (a. 273 , b. 100 , c. 373 , d. 50 ) :: FAHRENHEIT : KELVIN

Among the three given parts of the analogy, you can identify a relationship between the first and the second: The boiling point of water is 212 degrees on the FAHRENHEIT scale. It therefore follows that the missing part is the boiling point of water on the KELVIN scale. So, the answer is “373.”

(a. multiplicand , b. difference , c. quotient , d. dividend ) : PRODUCT :: DIVISION : MULTIPLICATION

Among the last three parts of the analogy, you can identify a relationship between the first term and the last: A PRODUCT is the answer to a MULTIPLICATION problem. So, the missing term at the beginning of the analogy must name the answer to a DIVISION problem. The answer is therefore “quotient.”.

Finance

Finance has to do with the management of large amounts of money, especially by governments or large companies. It typically encompasses such concepts as investing, budgeting, and other activities related to markets and economics.

Examples

(a. artificial intelligence , b. seasonal , c. sectoral , d. technical ) : CHART PATTERNS :: FUNDAMENTAL : STATE OF THE ECONOMY

Among the three given words, you can identify a relationship between the last two: FUNDAMENTAL refers to a type of market analysis that identifies trade opportunities based on THE STATE OF THE ECONOMY. So, the missing term must refer to a type of market analysis that identifies trade opportunities based on CHART PATTERNS (i.e., past market data). This means “technical” is the correct answer.

S&P 500 : RUSSELL 2000 :: LARGE-CAP : (a. penny , b. small-cap , c. mid-cap , d. large-cap )

Given the above analogy, you can find a relationship between the first and third parts: The S&P 500 is a stock market index composed of LARGE-CAP companies. So, the last part of the analogy must indicate the type of companies that comprise the RUSSELL 2000. The answer is therefore “small-cap.”

Geometry

Topics covered in high school geometry that might show up on the MAT® are too numerous to list in a concise manner. Perhaps the most succinct way to summarize a comprehensive study plan is to recommend reviewing all basic ideas related to the various types of two- and three-dimensional shapes, the different assortment of lines that exist (such as parallel, perpendicular, and arc), and the range of concepts related to measurement (such as pi, congruent, and perimeter).

Examples

PRISM : RECTANGLE :: 3 : (a. 1 , b. 2 , c. 3 , d. 4 )

A relationship is found among the first and third parts of the above analogy: A PRISM has 3 dimensions. So, the last part must indicate the number of dimensions belonging to a RECTANGLE. The answer is “2.”

CIRCLE : (a. sphere , b. cone , c. dodecahedron , d. cube ) :: TRIANGLE : TETRAHEDRON

Among the three given parts of the analogy, you can identify a relationship between the last two terms: A TRIANGLE forms the base of a TETRAHEDRON. So, the missing part must be a solid figure that has a circle as its base. The answer is “cone.”

Numbers

The mastery of numbers entails a fluidity and flexibility with respect to related terminology and principles, the ability to perform mental and written calculations, and a deep sense of what numbers mean. Bear in mind that one of the MAT®’s most reliable practices is the inclusion of Roman numerals, so be sure to review accordingly.

Examples

III : L :: XV : (a. CL , b. DC , c. CCL , d. XC )

Among the three given numbers, you can identify a relationship between the first and third: XV has five times the value of III. So, the missing number must have five times the value of L, meaning the answer is “CCL.”

PRIME : 3 :: COMPOSITE : (a. 5 , b. 7 , c. 9 , d. 11 )

Among the first three parts of the above analogy, you can identify a relationship between the first part and the second: Three (3) is a prime number because its only factors are 1 and itself. So, the missing part at the end must be a composite number. Since 9 is the only option that has more factors than 1 and itself, the correct answer is “9.”

Probability

Probability measures the likelihood of an event taking place.

Examples

PROBABILITY : PERCENT :: (a. 0.075 , b. 0.75 , c. 7.5 , d. 75 ) : 75

Among the three given parts of the analogy, you can infer that the relationship is between the second and last terms due to the fact that a PERCENT is generally expressed as a number between 0 and 100. On the other hand, a PROBABILITY is generally expressed as a number between 0 and 1. So, the missing part of the analogy must be a number between 0 and 1 that is analogous to 75 PERCENT, or “0.75.”

SIMPLE EVENT : ONE :: COMPOUND EVENT : (a. zero , b. one , c. more than one , d. two)

Among the first three parts of above the analogy, you can identify a relationship between the first and second terms: The probability of a SIMPLE EVENT involves finding the likelihood of one event occurring. So, the missing term must be the probability of a COMPOUND EVENT, which involves the likelihood of more than one event happening together. This means the answer is “more than one.”

Statistics

Statistics involves collecting and analyzing numerical data in large quantities, especially for the purpose of inferring proportions as a whole from those in a representative sample. The study of statistics includes such topics as variability, sampling, distribution, bivariate data, and more.

Examples

DEPENDENT : (a. research , b. interventions , c. analysis , d. outputs ) :: INDEPENDENT : INPUTS

Among the three given words, you can identify a relationship between the last two. The term INDEPENDENT refers to variables that are controlled INPUTS. So, the missing term must be the type of variables to which the term DEPENDENT refers, which are the outcomes resulting from altering the input. The answer is therefore “outputs.”

STANDARD DEVIATION : DISPERSION :: CHI-SQUARE : (a. difference , b. range , c. distribution , d. error )

Among the first three terms in the above analogy, you can identify a relationship between the first and the second: STANDARD DEVIATION measures how much DISPERSION or variation exists in a set of values. So, the last term must be what the CHI-SQUARE measures, which is how much difference exists between expected and observed counts. Thus, the answer is “difference.”